Computers as embodied
mathematics and logic:
Implications for
computer applications, HCI and AI
by Kristo Ivanov, prof.em., Umeå University
Dec 2015, Research review
(version 261013-2115)
<http://www8.informatik.umu.se/~kivanov/BrouwerComputMathLog.htm>
< https://archive.org/details/BrouwerComputMathLog_201801 >
CONTENTS
Link
to a General Disclaimer
Introduction and literature
Intuitionism and formalism
Rejected parts of Brouwer's
dissertation
A feminist parenthesis on quantum
mechanics
Recognizing the problems in the
"Rejected parts"
Life, art, and mysticism
Commentary on "Life, art, and mysticism"
Symptoms: ontology of logic
Symptoms: syntax, semantics,
pragmatics
Buddhist models of the mind
Analytical psychological approach
The analytical
psychologist Jung's approach
A diffuse conclusion
A concluding exercise
-----
In the search for an understanding of the "essence" of
computation in order to better grasp the intellectual impact of information
technology I decided to look into controversies about the foundations of
mathematics and logic as bases of formalisms that are embodied in computers,
such as Boolean algebra and binary arithmetic for digital electronics,
algorithm theory and numerical analysis, analytic geometry for graphics, and
symbolic logic for software development. In an age of computer graphics,
acoustics, and haptic technology it is easy to get a perception that knowledge
of meaning of computation and of computers, not to mention its ethical
implications if any, is less relevant for design of new equipment or use of
what is already available. The meaning of "use" itself is obfuscated
by the seeing computers as tools instead of theory-laden instruments, as well
as by the availability of techniques of human-computer interaction - HCI - and
of so-called artificial intelligence - AI, mediated through HCI. The matter is
further complicated by the submersion of computation into continuously arising
neologisms and terms such as virtual reality or digital materiality without a
clarification, for instance, of whether reality is material and digitality is
mathematical.
Resuming: the main message of this article is
that only if we understand what we are doing with the basic formalisms of
mathematics and related logic, geometry and such, we will understand what we
are doing with computers. And this is
valid even as the computing is used to generate sensory stimuli like visual,
auditory or haptic which introduce artistic and emotional dimensions that are
focused in another
essay of mine on the philosopher Kant's third critique. My
writing is also motivated by my purpose of facilitating the further
investigation of systemically related issues by potential readers. In order to
save space and simplify the editing of this work, this is done by means of rich
bibliographical references indicated in the links associated to the underlines
of key words, available only for those who need them while reading the text on
a computer that is connected to the Internet. For further details about the
style of the style of my writing this text I wish to refer at once to the last
paragraph of the conclusion of the whole essay.
Before going further: as a preliminary didactic advice on how to read
the text that follows it is to read my research-disclaimer, and to note
that the text is not written in a narrow linear logical sequence with the
purpose of supporting one single thesis, motivating extremely logical readers
to stop reading this text exclaiming: "The text is too long - what do you
want to say?" Logic itself together with mathematics is here called into
question. Nobody would dare to ask the same question of, say, a criticism of
quantum physics unless the critic criticizes a detail in a logical-mathematical
edifice that for the rest is hoped to be left intact supporting the old
established mainstream thesis.
On several occasions I witnessed the "mystical" fascination
experienced in interaction with computers: it appears in "religious"
wars about which is the best computer brand or programming language, but most
clearly in computer
addiction including mobile phones and in games, and
unfortunately less clearly in misjudging benefits if not even costs of
computers such as in business, government and private life. The latter is
partly portrayed in the "productivity
paradox", not to mention the recurring myth of AI, i.e.
"artificial intelligence" taking over humanity and the whole world,
notwithstanding opportunely ignored or misunderstood research like the reported
in The Design of Inquiring
Systems (more about it below.) The only courageous direct hint of
critique I met in my searches had been Clifford
Truesdell's in his An
Idiot's Fugitive Essays on Science (1984), especially its essays on
The
scholar, a species threatened by the professions and the
apparently controversial The
computer: ruin of science and threat to mankind. I had also
read about a famous controversy on the foundations of mathematics and its
relation to logic. It attracted my attention since mathematics and logic as
embodied in computers have been often if not always considered as the most
reliable fields of scientific method, human knowledge and their philosophical
guides. I also was puzzled by the fact that such foundational controversies
were mostly ignored in today's computing and information science, as if the
controversies had been solved. It turns out that probably they were eventually
ignored because of "more important" military and
industrial-commercial perceptions of a trivial and opportune "good enough".
My earlier, naively ambitious attempts in this vague
research direction recall the "remember
not the sins of my youth" but can
have some general interest for their references. They may be surveyed in old
papers like Presuppositions of formal methods for development of computer systems (pdf, 1983), Logic
and psycho-logic: A Logical-psychological perspective of computer support (pdf, 1990), and more generally in a draft of a research program on Logic
and psycho-logic: A logical-psychological perspective of computer support (pdf, 1990). They are also mentioned marginally but significatively in
related context such as in my essay Belief and
Reason (1993).
In my latest efforts I did study the recurrent
name of a key-mathematician involved in the controversies mentioned above: L.E.
Jan Brouwer. For this purpose I concentrated upon his
"ideological manifesto" in
Jan Brouwer, Intuitionism and Formalism (pdf-format) in the Bulletin of the American Mathematical Society (Vol. 37, No.1, 1999, pp. 55-64 reprinted from Vol 20, No. 2, 1913, pp. 81-96.)
The second and third texts consist of an
introduction to Brouwer original book in Dutch and the book itself:
Walter P. Van Stigt, Introduction to Life, Art and Mysticism (1996, pdf)
That is, the book got a for our present
secular epoch disconcerting, unfortunate if not outright repelling title that
in its English translation appears as
Jan Brouwer, Life, Art and Mysticism (1905, pdf)
Both the last mentioned
works were published as articles in the Notre
Dame Journal of Formal Logic, (vol. 37, No. 3, Summer 1996.) Because of my
need for a better understanding of van Stigt's
English translation from the Dutch I checked my readings of this Brouwer's book
against its Italian translation, that is,
Jan Brouwer, Vita, Arte e Mistica, (2015), the first published book in a language other than Dutch, with an introduction by Lorenzo Perilli and a very pertinent commenting essay by numerical analyst Paolo Zellini.
The last two main papers in by Brouwer
himself, translated into English that I will consider are presented in
Jan Brouwer: "Mathematics, science, and language", (original lecture in German, year 1928) in Paolo Mancosu From Brouwer to Hilbert: The debate on the Foundations of Mathematics in the 1920s. Oxford University Press, (1998), pp. 45-53. Also, more complete, in William Bragg Ewald, ed. From Kant to Hilbert: A source book in the foundations of mathematics. Vol. 2. (1996). Oxford Univ. Press (pp. 1170-1185). Commentaries by Vladimir Tasic in Mathematics and the roots of postmodern thought, pp. 44ff. and notes p. 163 as well as by Mark van Atten in the Stanford Encyclopedia of Philosophy.
and
Walter P. van Stigt's translation of The rejected parts of Brouwer's dissertation on the foundations of mathematics, in Historia Mathematica, Vol 6, No. 4 (1979).
This historically and theoretically meaningful
rejection of parts of what became a famous mathematical dissertation bears
meaningful resemblances with the case of another doctoral dissertation of Erik
Persson on realistic computing (cf. virtual reality) that I was appointed to be faculty opponent for at
Lund university in 2003.
The issue is extremely complex and the more so
for a non-mathematician like me who studied mainly engineering maths such as required for electronic engineering. Such a
complexity is obvious the simple context of the misuse of mathematics such as in Ralph Abraham's contribution to Mathknow: Mathematics, Applied Science and Real
Life (2009), but much more in writings that deal with the
controversy in which Brouwer was involved. See especially in the kind of
summary offered (in Italian) by Giovanni
Sambin, Per una
dinamica nei fondamenti (pdf) i.e. "For a dynamics in foundations", 2005 or the list of
research subjects in the list of research publications by Richard Tieszen, or in earlier historical times, in Imre Lakatos (ed.) Problems in the Philosophy
of Mathematics: Studies in Logic and the Foundations of Mathematics (1967). In the last mentioned work one can see,
for example, contributions by Y. Bar-Hillel who was an acknowledged
inspiration for defining the concept of data and information in the original
school of Swedish Theoretical Analysis of
Information Systems by the grand old man of Swedish computer information
systems, prof. Börje Langefors. The latter's conception of what data, information and systems are or
how they should be defined was later questioned by me in The Systems Approach to
Design and Inquiring Information Systems, presaging my need of the present ongoing study.
The complexity of the involved issues that,
however, also hides some main questions, is also evidenced by whoever seeks
orientation in further comments or explanations in the following complementary
sources
Luitzen Egbertus Jan Brouwer in Stanford Encyclopedia of Philosophy
Dirk van Dalen, Mystic, Geometer, and Intuitionist: The Life of L.E.J.Brouwer, (volumes 1 and 2, 2013), or volume 1 (1999) and volume , (2015) as in secondary sources such as in the review by Bonnie Shulman of the volume 1, by Richard Tieszen of its chapter 2 "Mathematics and Mysticism" (pdf) in Philosophia Mathematica (3, Vol. 8, 2000, pp. 217-224, and by I. Grattan-Guinness in Bulletin of The American Mathematical Society (Vol. 36, No. 4, 1999, pp. 529-532). Refs. to more reviews here.
Paolo Zellini, La Ribellione del numero [The rebellion of the number]. Adelphi (1985), esp. pp. 20-30 and 133ff. Summary of Spanish translation here.
Other parallel cross-checking literature that
has been consulted is
L.E.J. Brouwer, in Wikipedia
Raymond L. Wilder, "Relativity of standards of mathematical rigor", in Dictionary of the history of ideas, vol. III, pp. 170-177 (on Brouwer esp. p. 176f.), the author having also written the relevant book Mathematics as a cultural system (1981).
Stephen Orr, Brouwer's Mysticism – The Hegelian in all of us
L.E.J. Brouwer, a Mathematician on Self, Hermitary
Henk Barendregt, Buddhist models of the mind and the common core thesis on mysticism (pdf), an article that is relevant for our studies of the relation of Brouwer's thought to later psychology
Mark van Atten & Robert Tragesser, Mysticism and Mathematics: Brouwer, Gdel and the common core thesis (pdf, orig. published in W.Deppert and M. Rahnfeld Klarheit in Religionsdingen, Leipziger Universittsverlag, 2003, pp. 145-160)
Brouwer's Philosophy of Mathematics (pdf). A review article of L. J. Brouwer, Collected Works, North-Holland/American Elsevier. Vol.1 and Vol. 2, 1975-1976) in Erkenntnis 15 (1980), pp. 105-126
J.J. O'Connor & E.F. Robertson, Luitzen Egbertus Jan Brouwer (biography)
Philosophy of Mathematics: Intuitionism. In mathematics-in-europe.eu
Ernst Snapper, The Three Crises in Mathematics: Logicism, Intuitionism and Formalism. (pdf)
L.E.J. Brouwer, Consciousness, philosophy, and mathematics. In Paul Benacerraf & Hilary Putnam (eds.) Philosophy of Mathematics: Selected Readings. New York: Cambridge University Press, 1983 pp 90-96 (Excerpted from 10th International Congress of Philosophy, Amsterdam, 1948. Proceedings I, Fascicule II (Amsterdam: North Holland, 1949), pp. 1243-1249.
L.E.J. Brouwer, Lectures on Intuitionism. Historical Introduction and Fundamental Notions. Source: Brouwer's Cambridge Lectures on Intuitionism (1951). Publ. Cambridge Univ. Press, 1981. (Most of first lecture plus appendix of fragments.)
Miriam Franchella, Brouwer and Nietzsche: Views about Life, Views about Logic. History and Philosophy of Logic, 36:4, 367-391. <http://dx.doi.org/10.1080/01445340.2015.1048968>
Robert J. Leonard, Ethics and the Excluded Middle: Karl Menger and Social Science in Interwar Vienna. Isis 89, No. 1 (March 1998), 1-26. (Published by the University of Chicago Press on behalf of the History of Science Society.) The introductory abstract sets the stage: "This account of Menger shows how, on the eve of Hitler's arrival in Vienna, social scientific, mathematical, and political debates there were deeply intertwined."
There are indeed many secondary sources as the
above, which attempt to survey and resume both Brouwer's heritage and the
controversy at the turn of the past century as represented mainly by two
protagonists, Brouwer himself and the famous mathematician David Hilbert. In mentioning these sources I refrain from considering others which to different
degrees are more "technical" in the sense of specialized and of
difficult understanding by the educated general reader including myself. Some
examples are
Edward Nelson, Understanding Intuitionism (pdf), at Princeton University
Alan Weir, Formalism in the Philosophy of Mathematics, in the Stanford Encyclopedia of Philosophy
Mark van Atten, The Development of Intuitionistic Logic in the Stanford Encyclopedia of Philosophy
Wikipedia's Intuitionism
Rosalie Iemhoff, Intuitionism in the Philosophy of Mathematics in the Stanford Encyclopedia of Philosophy
W.W. Tait, Gödel's interpretation of intuitionism (pdf)
I only checked such secondary sources to the
extent that I could ascertain that nothing in them seemed to contradict my
reflections in the present article. It will be essentially grounded in the text
found in Brouwer's own aforementioned late (1999) article "Intuitionism
and Formalism" and in his aforementioned early (1905) book Life, Art, and Mysticism including its
introductions written by Van Stigt and Perilli, plus van Stigt's
editing of The rejected parts of Brouwer's
dissertation on the foundations of mathematics (1979.)
Brouwer starts his article Intuitionism and Formalism with a concise
definition of science as consisting of the isolation of causal sequences
supplemented by human activity in view of bringing about desired phenomena, and
leading to natural laws that often treat only the mutual relations between the
results of counting and measuring with certain degrees of mathematical
approximation in experimental situations. The latter qualification of
"approximation" was not supposed to hold for the so-called exact
sciences mathematics and geometry, they were "exact". By the
beginning of the 20th century two different schools could be distinguished:
intuitionism (largely French) claimed that mathematical exactness exists in the
human intellect, while formalism
(largely German) claimed that such exactness exist on paper.
In this present essay I intend later to deepen
the question of what is meant and what is to be meant by the terms exactness beyond what is to be inferred
from my PhD dissertation on the concept of accuracy of information, and further by the terms in intellect vs. on paper. All this considering that ultimately
we need to understand what happens today, and why we apparently seek ultimate
salvation in the exactness of computers and related communication technology.
To understand the clash between these two
currents of intuitionism and formalism we leave for the moment aside the third
current of logicism as suggested in the mentioned article by Ernst Snapper, The Three Crises in
Mathematics: Logicism, Intuitionism and Formalism. Brouwer starts dwelling in what he calls an old form of Kantian
intuitionism that had already been completely abandoned, in which time and
space were taken as forms of conception inherent in human reason. The axioms of
arithmetic and geometry were "synthetic a priori" judgments, i.e.
independent of experience and not capable of analytic demonstration,
maintaining their exactness in the world of experience as in the abstract,
because of their proof or disproof was simply unthinkable.
Brouwer goes on illustrating the opposed view
of formalism that negates the human mind's capacity of containing inherent
judgments or exact images of geometric or number axioms. From simply assumed
axioms we can deduce other relations between mathematical entities by means of
logical reasoning, they having no
significance except for the possible efficacy of their projection into nature.
Modern philosophers of science often addressed this latter question by studying
Galileo Galilei, as Alexandre Koyr does e.g. in Études d'histoire
de la pensée philosophique (1961/1971, pp. 348ff.) and in his Études d'histoire
de la pensée scientifique (1966/1973, pp.
186ff.). Brouwer recalls that the common attitude to that question is
exemplified by what appears to me as irresponsible:
"To the philosopher or to the anthropologist but not to the mathematician, belongs the task of investigating why we believe in certain systems of symbolic logic and not in others, in particular why we are averse to the so-called contradictory systems in which the negative as well the positive of certain propositions are valid"
which is an intuitionistic tenet of the
rejection of the excluded middle. The article continues
explaining why the latest developments of mathematics at the turn of the
century as well as the discovery of non-Euclidean geometry seemed to contradict the
Kantian conception of the "a priori" on
which relied intuitionism, and was an apparent confirmation of formalism. The
a-priori question is didactically explained also in certain system philosophies
as expounded in West Churchman's The Design of Inquiring
Systems (chap. 6). Brouwer,
however, does not yet intuit the systems problem that, as we will see below, he
touched upon in the context of his pioneer attack on the
environmental-ecological problem at the beginning of his earlier book Life, Art and Mysticism. Brouwer concentrates instead upon what is most important for us here:
the basis for mathematical and logical thinking that is embodied in computers.
The contradiction of the early Kantian
a-priori fundaments of intuitionism, did not convince Brouwer about the
rightness of formalism but rather about the need of revising intuitionism by
abandoning Kant's apriority of space while concentrating on the apriority of
time in the human intellect. And this is the intuitionistic heart of the matter
that involves the conception of the human
intellect in its relation to mathematics and logic. Later on shall we dwell on the question of the structure of human
intellect in the light of Carl Jung's psychological conception
of intellect, mind or psyche. Here I will refer Brouwer's
"neo-intuitionistic" – as he calls it - elaboration of the workings
of an intellect that is taken as given:
"This neo-intuitionism
considers the falling apart of moments of life into qualitatively different
parts, to be reunited only while remaining separated by time as the fundamental phenomenon of the human
intellect, passing by abstracting from its emotional content into the
fundamental phenomenon of mathematical thinking, the intuition of the bare
two-oneness." [My italics.]
Brouwer continues with calling this two-oneness (cf. bi-unicity) as an
individual's primordial or basal
intuition of mathematics in which the connected and the separate, the
continuous and the discrete are united. In this present paper of mine I wish to
expose how, in the context of analytical psychology, this very same basal intuition of mathematics can be connected to basal
conceptions of the human mind: Marie-Louise von Franz dedicates the chapter 5 of
her book Number and Time (Northwestern Univ. Press, 1970/1974) to the "The Number Two",
including several explicit references to Brouwer (pp. 70n, 71. 87, 96n). It
represents psychological research that borrows some additional scientific
respectability from the involvement of the renowned physicist Wolfgang Pauli. It indicates the potentiality for future research (later reported here) to establish a bridge to
both computers and psychic processes beyond "small unimportant parts of
the brain" or of the "head" (cf. later, below), along the lines
of the present paper of mine. And this with due regards to the historical roots
of false equation Psyche=Mind=Head=Ego, alternatively Skull=Brain=Mind=Psyche,
as recalled by James Hillman in his The
Myth of Analysis (Northwester Univ. Press, 1972, pp. 153-154, 245.)
These considerations may ultimately explain the reasons for the ultimate
failure of Brouwer's attempts to keep mathematics ethical and
"clean".
The article considered here, on intuitionism and formalism, goes observing that
the so called primordial or basal intuition mentioned above is not only of
mathematics but also of geometry because since Descartes we can reduce all
geometries to arithmetic by means of the calculus of coordinates. Brouwer
continues noting that all mathematical sets can be developed out of the basal
intuition, and that in the construction of these sets neither the ordinary
language nor any symbolic language can have any other role than that of serving
as a non-mathematical auxiliary, to assist the mathematical memory or to enable
different individuals to build up the same set.
Formalism is instead compelled to presuppose
the existence of a world of mathematical objects, and independent of the
thinking individual, obeying the laws of classical logic and whose objects may
possess with respect to each other the "relation of a set to its
elements".
By applying technically
the above to the concepts of finite and infinite sets, Brouwer sees that the
intuitionist can never feel assured of the exactness of a mathematical theory
by such guarantees as the proof of its being non-contradictory, the possibility
of defining its concepts by a finite number of words, or the practical
certainty that it will never lead to a misunderstanding in human relations.
For our purposes in this present paper,
however, it is enough to note that there is the use of the term intellect, intuition, abstraction from emotional content, unification of the continuous and the discrete, individual, independence of thinking, understanding, and human relations. In doing so Brouwer calls into question problems
that also belong to philosophy, psychology and sociology. In particular, the
remarkable need of abstraction
from emotional content is also mentioned in the context of the history of mathematical notations, as represented e.g. in the classical work by Florian Cajori. At
Brouwer's time (1913) such areas were not so sharply distinguished and there
was no depth psychology that I relate to the analytical psychology of Carl
Jung, or of systems thinking that I relate in particular to aforementioned work
of West Churchman. They would have stood in contrast to the formalist idea
still alive today of mathematical systems and computer systems as sets and
relations between elements or components of sets. In particular, Carl Jung
started at the time immediately after the turn of the century to elaborate his
own psychology that to a great extent incorporated the above-mentioned terms
used by Brouwer, something that obviously is necessary for evaluating the need
and the consequences of trying to "abstract from emotions". Brouwer
had implicitly already questioned formalism in science and techno-systems by
his early perception of systemic ecological problems, implicitly suggesting the
need for a systems theory . In view of the poverty of
his contemporaneous psychology he had based his more
psychological stands in Life, Art, and
Mysticism (published 1905 but with positions maintained until the end of
his life) upon Christian, Buddhist and Hindu thought as perceived at that time
in the German cultural sphere.
As an important curiosity regarding to abstract from emotional content, as
well regarding the difference between intelligence as smartness or wisdom, we
may recall what Plato famously writes in his Republic
VI (§491e):
"[...] shall we not similarly affirm that the best endowed souls become worse that the others under a bad education? Or do you suppose that great crimes and unmixed wickedness spring from a slight nature and not from a vigorous one corrupted by its nurture, while a weak nature will never be the cause of anything great, either for good or evil?".
The continuation of the present paper will
then consist in considering details of the above as they can be found or
deduced in Brouwer's Life, Art and Mysticism. This will show that he was a precursor of the elaboration of the
concept of systems, and it will allow us to revert from his references to
Eastern conceptions of mind or intellect to their Christian and Jungian
correspondents. This will also explain the paradox of the success of
intuitionistic ideas in algorithm theory, and the fateful hegemony of formalism
(David Hilbert, John von Neumann, Alan Turing), allowing for the intrusion of
military, commercial and industrial interests in the development of, and
applications to computation.
That is, many issues that today are masked by
a-philosophical and a-ethical talks and neologisms as virtual reality without understanding reality, digital materiality without understanding neither materia nor digits nor number, nor compositional design without realizing (and therefore ignoring)
that it deals with systems thinking, and such. Among other things, as a
"bonus" or byproduct, it should also become clear that Brouwer's
apparently misogynistic, problematic, and paradoxical attitude to womanhood in
the above mentioned work has serious historical antecedents in the Christian
tradition (cf. "habet mulier animam"), and at the sources of modern psychology as exemplified by Juan Luis Vives and their further treatment by Carl Jung. It can also be the result of a misunderstanding based on a sort of
Jungian introverted thinking-intuition
attitude, and an identification of his psyche with elements of the
unconscious in the form of the concept of anima
(anima obsession, or possession, popularly and roughly illustrated on the Internet).
Earlier examples of applications of Jung's psychology in my work can be found
in my texts The illusion of
communicative information, Political Correctness, and Ethics in Technology.
In particular it will be necessary to deal
with the meaning of the intuitionistic hypothesis of "the fundamental phenomenon of the human intellect, passing by
abstracting from its emotional content into the fundamental phenomenon of
mathematical thinking, the intuition of the bare two-oneness" (my
italics.) It could mean that despite its apparent "acrobatic"
complexity, mathematical and logical
thinking is a sort of minimal thinking. It engages the most
simple, primitive a-priori level of the so-called intellect, sparing
psychic energies for acrobatic performance and consequently aggressive,
attractive "success" in all fields and for all simpler purposes that
do not require other higher functions of the so called
intellect. Obviously, however, this does not prevent that attitudes and
functions of the psyche in contact with the unconscious, such as introversion,
extraversion, thinking, feeling, sensation, and intuition will later interact
with the psychologically, intellectually flawed results of applying computer operations
or communications. This will in turn influence, for instance, the dynamics of
language, the apprehension of graphic images, and aesthetic or ethic
dimensions. These issues are observed, for instance, by Richard Stivers in Technology and Magic: The
Triumph of the Irrational (e.g. pp. 26 and 63) and
accords with the philosophy of technology that was addressed in my essay on Trends in philosophy of
technology.
Ultimately the application of
"Jungian" analytical psychology may uncover also the reasons for the
failure of Brouwer's intentions with intuitionism, non only
in replacing formalism but mainly in guaranteeing the connection between
mathematics and ethics. On the contrary, the aforementioned work by Zellini suggests how some ideas of intuitionism could be
kidnapped for the development and consequent misuse of later algorithm theory.
REJECTED PARTS OF BROUWER'S
DISSERTATION
The meaningful resemblances with the case of
another doctoral dissertation on "realistic computing" (cf. virtual reality) that I mentioned above have to do with what
is mentioned in The rejected parts of
Brouwer's dissertation on the foundations of mathematics. They are about Brouwer pleading passionately with his doctoral (thesis)
advisor prof. Korteweg about the latter's suggestion
that he remove the "philosophical" first part of his draft.
The Rejected
Parts published year 1907 have a very tight connection with the
controversial book Life, Art and
Mysticism, published a couple of years earlier, in 1905. Its
controversiality is evidenced by the comments that are bestowed by van Stigt and partly borrowed from others, as follows: a
generally solipsistic philosophy (as I understand it, nearly epistemological solipsism) and a rather pessimistic and misanthropic outlook on and attitude to
life, an extreme view on life science and his fellowmen, a passionate
involvement in a romantic revolt against intellectualism and industrialization,
Brouwer fulminates against all things human and singles out the human intellect
as the cause of all evil, pessimistic views, appreciation of mysticism and
Eastern philosophies, and low regard for women, pessimism and a mystical
attitude to life, bizarre flavour, etc.
I purport to show in the course of this
article that most of this pessimism is motivated as a contrast to the extreme
optimism in the viewing of science in general and formal sciences in particular
by the turn of the century. Most if not all the other judgments above can be
clarified by enframing Brouwer's psyche in Carl
Jung's typology (his Collected Works, vol. 6) as an "introverted
thinking-intuitive type whose attitude to women is indeed an attitude to, or
influence from unconscious femininity as represented by the Jungian image of anima, which, by the way, may have been
the positive source of his uncommon insights. Brouwer had not recourse to what
today is depth psychology since Jung, following Freud, was starting working at
it at about the same time. Furthermore, the perceived bizarre mysticism or
mystical attitude to life would be explained and incorporated in Jung's
psychology and its integration with Eastern philosophies. Most objections to
Brouwer's "mysticism" are, for instance, based on Western
misunderstandings of mysticism that are unraveled in Harold Coward's chapter on
the issue in his book Jung and
Eastern Thought (1985, chap. vii, reprinted from Philosophy East and West, vol.
29, 1979.) All this complication was necessary for Brouwer in order for him to
affirm, on the basis of his time's philosophical and psychological knowledge,
the relevance of a moral value judgment for the practice (rather than
"application") of mathematics and what we nowadays might call the use
of computers.
The apparently successful projection of
mathematical structures into the natural world since Galilei, depending upon
what it to be meant by success (cf. earlier reference to Koyré)
may be the result of forcing nature into preconceived ways of exploitative use
of natural resources, and of prior knowledge. The "success" in form
of forced consistency of various areas of modern physics may portray the
commonality of interests in its applications. Its maintained consistency by
means of a plethora of esoteric "mathematical tools" and
"thought experiments" (cf. the mind-blowing context of so called EPR-paradox) may be analog to the forced consistency obtained in the past in
Ptolemaic astronomy by means of gradual patchwork-adjustments of computation of
orbits of celestian bodies, until the serendipitous
advent and posterior rationalization of the Copernican revolution.
In presenting The rejected parts of Brouwer's dissertation, Van Stigt refers to
Brouwer's interpretation of causality as essentially mathematical: the ability
to link events in the mind, to see sequences and repetition of sequences in
time, to link sensations as the immediate source of awareness of time and discreteness.
It is the source of man's power to predict the future and interfere in the
course of events. This "intellectual or mathematical" way of looking
at the world is not only a one-sided concentration and interpretation of
reality: by ignoring and will fully
removing aspects which deviate from the expected course of events, man
supplements and creates more regularity than exists in nature, he makes the
world linear or "one-sided". The regularity observed in nature is
due to the nature of the measuring instruments and physical science has value
only as weapon, not concerning life. It is clearly inferior and has nothing to do with religion or wisdom. More
in detail, in Brouwer's own words:
"Man has the faculty, accompanying all his interactions with nature, of objectifying the world, of seeing in the world causal systems in time. The primordial phenomenon is simply the intuition of time in which repetition of "thing in time and again thing" is possible, but in which (and this is a phenomenon outside mathematics) a sensation can fall apart in component qualities, so that a single moment can be lived through a sequence of qualitatively different things. One can, however, restrict oneself to the mere sensation of theses sequences as such, independent of the various degrees to which objects are perceived in the world outside are to be feared or desired. (The attention is reduced to an intellectual observation.) The human tactics of "acting purposively" then consists in replacing the end by the means (a later occurrence in the intellectually observed sequence by an earlier occurrence) when the human instinct feels that chance favours the means."
This description by Brouwer recalls the famous
problem of technological "creep" or unforeseen applications or
consequences, good and bad, of particular technologies. It characterizes most
advances of technology and also falsely legitimizes the eventual benefits
(possibly rewarded by Nobel prizes) of basic research that is seen as motivated
(but not financed!) by "curiosity". Its "unforeseen" also
recalls modern decision and systems theory in that it suggests how "probability"
that he calls chance, in practice, is misunderstood and misused in the minimal
thinking with the most primitive a-priori level of the so
called intellect (e.g. in evaluations of risks involved by nuclear power
plants). This in contrast to the recommendations and deeper problems framed by
modern systems theory (Churchman's Design
of Inquiring Systems, chap. 3 on "the anatomy of goal seeking",
and chap. 10 on "basic models of inquiring systems".)
From all this follows Brouwer's disapproval of
applied mathematics that today we see
in computers: it promotes man's rule (i.e. not God's rule) and lack of wisdom
that will spoil environment making it intolerable. And this was written at a
time when there was no relevant environment consciousness except for the
intuitions of a beginning consciousness of environmental systemic aspects of
"nature" in the work of Alexander von Humboldt, George Perkins Marsh, and John Muir that Swedish readers can
appreciate in the summary by Tomas Öberg in Svenska
Dagbladet (18 October 2016.) Van
Stigt continues mentioning a glimmer of hope and optimism in that Brouwer
believes that pure "mathematics practiced for its own sake can achieve all
the harmony as found in architecture and music. ..."
It is my experience that this recourse to
architecture and consequently "design" as a main modern expression of
the hope of being able to integrate art with science has appeared in an
unfortunate destructive way in Western society in general and university
research in particular, because of intuitions much less sophisticated than
Brouwer's. It appeared through the bizarre sudden shift of emphasis from the
sixties' logical positivism (in Sweden B. Langefors
inspired by Y. Bar-Hillel) and the following Marxist systems development, over
to the concept of design while
forgetting the eighties- and nineties's pragmatist
dialectical systems. This motivated me to write down several reflections, some
of them in "telegraphic-powerpoint" style,
such as Ethics and Politics in
Design and Systems Cultures, and in a more readable
structured way in my The Systems Approach to
Design and Inquiring Information Systems. At the time I
could get some inspiration from Christopher Norris' What's
Wrong with Postmodernism (1990) but I could not yet avail myself of the
insights of works relating more clearly socialism to postmodernism, such as
Stephen Hicks' Explaining
Postmodernism: Skepticism and Socialism from Rousseau to Foucault (2004, expanded
edition 2011).
It is symptomatic that the USA domination of
Western university research ignores such thoughts that are egregiously common
in e.g. the French cultural sphere. One example is Alain Gras' writings (in French) that
include references to Galilei and others, such as about Abatement as spiritual fact (in Entropia, No. 11,
Autumn 2011, pp. 30-44.) Heidegger's bombastic "standing-reserve" in his The
Question Concerning Technology echoes Brouwer's early clear and
simple insights. This may also be gradually obvious in the field of HCI (human-computer interaction) when considering that ongoing progressive computerization of society
and of social interaction violently forces
humans to (attempt to) adapt their more or less unconscious mental models and behavior to preconceived computerized structures. Such phenomena can
be exemplified and perceived as problems in the use of computers, particularly
in problems of human-computer interactions. Swedish readers can appreciate one best description of how computer
technology "rapes" the minds of citizens in Anna-Lena Laurén's
article "App, app, app - det börjar
likna Bolsjevism!"
[App, app, app - it begins to resemble
Bolshevism!" (Dagens
Nyheter 14 October 2018) and the follow-up by Ylva Hasselberg "Hejda
digitalbolsjevismen" [Stop the digital Bolshevism]
(Dagens Nyheter 23
December 2018). See also the description of
bugs such as in the ticket system of Stockholm's public transportation, (En bugg
i SL:s biljettsystem, i.e. A bug in the
ticket system of Stockholm's Transportation, in Swedish language, Metro-Stockholm, 22 Dec. 2015.) It
becomes more a question of forcing
human thought, trust and behavior, relinquishing self-reliance, into anonymous
structures that are required for the functioning of computer software and
hardware as much as supposedly for humans' purposes. This is the
kernel for understanding why the issues of this essay are relevant for the
field of HCI and consequently also for AI (artificial intelligence).
In the long run such forcing of human thought, trust and behavior for
the functioning of computer software may gradually extend in the form of police
surveillance of the whole society seen as dependent upon integrated computer
networks. As such, the phenomenon will be analog to what happens with basic
infrastructure of electric and associated nuclear power plants. In a French
book Grandeur
et Dépendance: Sociologie
des macro-systèmes techniques (PUF, 1993, pp.
248ff.), the author Alain Gras, also a student
of man-machine
interaction, has indeed a section dedicated to generalized
surveillance seen as remedy to human danger in technical systems. Ultimately
all this stuff, in the absence of a valid religious "infrastructure",
overflows politically in bizarrely advanced anarchist analyses such as Tiqqun's The
Cybernetic Hypothesis.
Phenomenologically, in the sense of dealing
with the description and classification of phenomena, this kind of forced
thinking and behavior, at its extremes in industrial techno-science including
computer applications, may be related to the savant syndrome, i.e. a "success" obtained in narrowly defined tasks,
paradoxically enframed in complex computer systems,
adapted to very narrowly focused brain-psychic activity, and having to be
mitigated by an in-depth study of reports of broader mathematical minds such as
portrayed in the book Fascinating Mathematical
People. Or in the stories
involving Benoit Mandelbrot with his unconsciously “divine” interest for
“the uncontrolled element in life”, celebrated in the book on Life in Many Dimensions, associated to the unending speculation-games of the type Mandelbrot Set with Fibonacci, unconsciously related to recursiveness or functional recursion (Fibonacci again) and to the philosophical and theological Eternal Return. Or exemplified by physicists like Isaac Newton, Wolfgang Pauli whom I survey in another essay, and Werner Heisenberg. These are not matters of
small importance. They are often building blocks in theological matters, as
well Mandelbrot is adduced in discussions about evolution and “design”, as in
the case of Jason Lisle’s video on “Atheists cannot explain the secret code seen in creation” (see also here).
At the same time this might explain the
parallel aversion in certain quarters against systems thinking in general and
social-humanistic thinking such as in West Churchman's systems approach and
Carl Jung's psychology. Time-sequential thinking, and in particular logic
linear thought cannot by definition be envisaged to take in account events
outside the immediate time sequence that are then perceived as irrelevant (to
the linear logical chain.)
I will continue here excerpting and
occasionally commenting words taken from the text of The Rejected Parts (of
Brouwer's dissertation) emphasizing Van Stigt's observation that the final
version of Brouwer's dissertation on the Foundations
contains much of his negative appreciation of applied mathematics
and logic and remains of his moral disapproval. The Rejected Parts, van Stigt
writes "are important for the clear statement they give of Brouwer's
motivation for his fundamental theories, for the expressed positive valuation
of pure mathematics, and for providing a further context of what, in cryptic
form, still exists in his Foundations."
Now over to the text of the Rejected
Parts that I edit together with some of its notes (in parentheses),
and reproduced in italics while my own interspersed comments are written in
normal font.
All human life originated in a one-sided constriction of nature [literally: "making one-sided -- human concentration on one single aspect of nature and adapting nature accordingly] and has protracted its existence in an "externalization," man impregnating nature with the human self and repressing other one-sided developments. This externalization by man, making his environment subservient to the full development of his humanity, appears to us (if we knew the world intellectually, i.e. with a mathematical causal eye) as a process whereby nature itself becomes linear and regular and all other life repressed or adapted to mankind. (Since the adaptation of the environment leads human life further and further away from the natural state which originally supported man, this conquered and adapted environment will ultimately become intolerable to mankind.)
The above observation by Brouwer can be seen as a premonition of the
environmental crisis of our time, including pollution, global warming and the
rest.
We find linearity and regularity, for example in bees; there it does not result in any sort of special power. But man has the faculty, accompanying all his interactions with nature, of objectifying the world, of seeing in the world causal systems in time. (This "seeing", however, is a human act of externalization: there is not real e x i s t e n c e.. of objective natural phenomena as can be ascribed to nature itself: the seeing originates in man, is an expression of man's will alone, independent of nature which itself exists independent of man's will.)
The process that Brouwer calls objectifying and externalization recalls
what Carl Jung considers when discussing the process of extraversion in his
conceptualization of extraversion vs. introversion. This text shows how Brouwer
could be accused of solipsism when focusing on his claim that there is no real
existence (his own italics) of objective natural phenomena as can be ascribed
to nature itself, if one ignores his following qualification that nature itself
exists independent of man's will. Such an accusation seems to me to follow from
lack of understanding for what he calls an act of externalization, which turns
my attention to what much later Jung would come to name projection, pending the
question of whether it is willful or not which in turn requires an
understanding of the act of willing. The unravelling of this psychology under
the keywords extraversion and projection is scattered
around in Jung's Collected
Works, CW, volume 6, Psychological
Types. An analysis that recalls Brouwer's reasoning above is to be
found in CW vol. 8 The
Structure and Dynamics of the Psyche, (p. 451 ,
§ 864), as in West Churchman's The
Systems Approach and its Enemies, (the whole chap. 3 on
"Logic: General, and p. 147), but our and Brouwer's focus is now upon the
role of mathematics. Brouwer continues:
The primordial phenomenon is simply the intuition of time in which repetition of "thing in time and again thing" is possible, but in which (and this is a phenomenon outside mathematics) a sensation can fall apart in component qualities, so that a single moment can be lived through as a sequence of qualitatively different things. One can, however, restrict oneself to the mere sensation of these sequences as such, independent of the emotional content, i.e. independent of the various degrees to which objects perceived in the world outside are to be feared or desired. (The attention is reduced to an intellectual observation.)
This last observation required that the reader is attentive to Brouwer's
use of the adjective intellectual
as related to intellect, which in turn requires a recourse to
psychology where intellect would probably correspond to Jung's thinking on the basis of the
perception or rather sensation
raised by the object-thing.
The human tactics of "acting purposively" then consists in replacing the end by the means (a later occurrence in the intellectually observed sequence by an earlier occurrence) when the human instinct feels that chance favours the means. However, since the link between end and means is observed in the intellect without the control of more central instincts (a restriction which will make the process even more intensive and more generally applicable), the reliability of the human conviction that the parts of the sequence belong together in reality is far from absolute and can constantly be disproved; this is experienced by the intellect as a discovery "that the rule no longer applies".
Brouwer also observes that the "tactics" in general is the
source of human power, to discover regularity in a limited domain of phenomena
independently of other moments and other phenomena, which therefore can remain
completely concealed from the intellectual observation: to maintain the
certainty of observed regularity as much and as long as possible, one tries to
isolate systems, i.e. exclude observations which disturb this regularity. When
one fails or has the courage to not exclude these observations may appear the
so-called serendipity that characterizes breakthroughs. One example I suggest
with some reticence is the Nobel
prize in physiology or medicine awarded in year 2018 for the
"discovery of cancer therapy by inhibition of negative immune
regulation". The serendipity was expressed at the award ceremony as being
that instead of concentrating on the direct causal chain of destruction of
cancer cells, the wider immune system was taken into account. My point is that
a still wider approach may be required, without necessarily entering into the
controversies of so called integrative
medicine as it is understood today, as it relates to Asklepian medicine and cultural studies of the archetypal
image of physician's existence by Károly Kerényi.
Brouwer's observation above is consistent with the principles of modern
decision making where the mentioned "chance that favours
the means" corresponds to probability as conceptualized e.g. in West
Churchman et al. Thinking for
Decisions: Deductive Quantitative Methods (1975), where, furthermore, the
ends are supplemented with the individual worth or value of the ends. To
counter or compensate for the above mentioned attempts
to "isolate systems" was in turn what motivated the later development
of systems theory. But, we repeat that our focus here
is the role of mathematics as it is embodied in computers where such
mathematics is necessarily disembodied from its applications, raising the
question of the meaning of its success or "successful application":
The process of objectifying the world through the primordial intuition of "repetition in time" and "following in time" gains in generality by the construction of mathematics from the same primordial intuition, without reference to direct applicability. In this way man has a ready-made supply of unreal causal sequences at his disposal, just waiting for an opportunity to be projected into reality. One should bear in mind that in mathematical systems with no time coordinate, all relations in practical applications clearly become causal relations in time; e.g. Euclidean geometry when applied to reality shows a causal connection between the results of different measurements made by means of the group of rigid bodies. Needless to say, in the application of a mathematical system, in general, only a fraction of the elements and substructures finds their correspondence in reality; the remainder plays the role of and unreal "physical hypothesis." Similarly, even with a limited development of method, the observed sequences no longer consist exclusively of phenomena evoked by man himself (acts without any direct instinctive aim, but carried out solely to complete the causal system into a more manageable one). The simplest example is the sound image (or written symbol) of number as a result of counting, or the sound image (or written symbol) of number as a result of measuring (this example shows how infinitely many causal sequences can be brought together under the viewpoint of one single law of causality on the basis of a mapping the numbers through mathematical induction.) [My boldface.]
I hope to not exaggerate the importance of this section that for the
first time gives me the impression of understanding the comments about
Galilei's famous mathematization of science. My intuition is that this
contributes to an explanation of the "success" of the mathematization
of modern science that, to take only one example from the mathematized field of
quantum mechanics, is the explanation of its (mathematical) success as
suggested in the story of the famous physicist Paul
Dirac as related to the earlier mentioned Wolfgang Pauli. If his atheism did
not approach him to God then it approached him to perceiving that he became
gradually godlike by means of mathematics as described in Wikipedia's excerpt
from an article he wrote in the May 1963 edition of Scientific American:
"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe."
Then, Dirac claims that, instead of asking why, "we simply have to
accept it" and in the bargain that we have to accept that man (beginning
with Dirac himself) becomes more godlike the more he mathematizes his
conception of the universe. Dirac's colleague Wolfgang Pauli summarized all
this by his famous remark (also in Wikipedia, later applied by others to Richard
Dawkins in his evolutionism) that "Well, our friend
Dirac has got a religion and its guiding principle is 'There is no God and Paul
Dirac is His prophet.'" This is part of the great but limited discussion
of Eugene Wigner's article "The Unreasonable Effectiveness of Mathematics
in the Natural Sciences" in Communications
in Pure and Applied Mathematics, vol. 13, No. 1 (February 1960). It
is as inconclusive as Richard Feynman's quotes about
mathematics, or Roger Penrose's video on "Is
mathematics invented or discovered? Wigner's article is anyway summarized in
context by Krister Renard in an essay written in Swedish with the analog title
of "Matematikens osannolika användbarhet" (lecture
in English for sale here). A more superficial
summary with further references is found in Wikipedia.
Brouwer's approach suggests instead man's distancing himself from God
and it seems consistent with later detailed discussions of the matter such as
in the historical context of Galileo Galilei, in Alexandre Koyré's Études d'Histoire
de la Pensée Scientifique (1966, especially p. 189f., 211f., 258.)
Contrary to Koyré, however, Brouwer does not stop at
affirmations such as considering mathematics (and geometry) as a-priori bases
for modern experimental science. He goes further and questions the a-priori
base of mathematics itself (in the apriority of time, and its relation to the
so far undefined intellect). What is remarkable, however, is Brouwer's early
observation, (on the basis of what Koyré
inadvertently acknowledges in the ultimate necessity of "experience"),
of the environmental impact of mathematized industrial science at a time when
environmental issues had not yet made a societal impact. And it is now a so far
undefined "environment" that must include people who get affected by
the computerization of the world.
The strategy of objectifying the world forces man even more to eliminate the "deviating" influences and thereby to abnormalize his environment. The nature of the phenomena within a certain domain changes not only through the elimination of the influences which deviate in this domain itself, but also through the degeneration of the environment of these phenomena because of the removal of influences which deviate with respect to another quite different group of phenomena. [...] In this way science, in a process of increasing self-perfection, will strengthen its power to obtain results but debase the value of these results.
We observe in this context that "mathematical viewing" is only instinctive, i.e. justified insofar as it is directed to a world which is considered to be external; to try and direct it to inner perception is a serious error (moreover, there would never be any agreement between the results of mathematical viewing from different viewpoints). What Kant describes as "Transcendental analytic" can only be described as idle play.
Compare the above with what Jung writes in his foreword to the I Ching (CW 11, § 967) at a time when climate and
apocalyptic global warming was not yet a societal issue but Brouwer already had
noted the environmental problem:
What Kant's Critique
of Pure Reason failed to do is being accomplished by modern physics. The
axioms of causality are being shaken to their foundations: we know now that
what we term natural laws are merely statistical truths and that thus must
necessarily allow for exceptions. We have not sufficiently taken into account
as yet that we need the laboratory with its incisive restrictions in order to
demonstrate the invariable validity of natural law. If we leave things to
nature, we see a very different picture: every process is partially of totally
interfered with by chance, so much so that under natural circumstances a course
of events absolutely conforming to specific laws is almost an exception.
Jung's words may need to be qualified but the issue is bravely studied
and explained in West Churchman's The Systems Approach and its Enemies (starting in chap. iii, "Logic: General", p.
54). It is related to power (and politics
and even war) for enforcing "incisive restrictions". Brouwer
combines this process of degeneration and devaluation with a consequent
observation that the
passionless language (also reason for creation of mathematical
notations, cf. the earlier reference to Cajori) of
objectification of the work in mathematical systems allows the emotional content to be
completely different (and ignored) for different individuals. It this way the
resulting agreement between mathematical systems of reality in different
individuals allows the enforcement of a particular will over all others
"out of fear or desire associated with certain elements in the
system." Fear and desire are basic categories in Brouwer's analysis in
several other contexts.
A FEMINIST
PARENTHESIS ON QUANTUM MECHANICS
Quantum
mechanics or quantum physics will be repeatedly mentioned in
overlapping reflections in this paper. Hereafter in this section it will be
referred to as QM. It is a described
as a fundamental theory in physics that provides a description of the physical
properties of nature at the scale of atoms and subatomic "particles".
I mean "particles" in quotations marks because it is a theory that it
is formulated in various specially
developed mathematical formalisms. This relates in turn to symptomatically
muddled connotations and relation between mathematical
physics and physical
mathematics.
What is interesting in this context is then that QM
does not deal with particles as they
are understood in common language but with specially developed mathematical
formalisms. It is also interesting to note that QM has been
"kidnapped", and in my view misused in a way that happens to give
credibility to other areas of speculative research. One of them is represented
by Karen
Barad's feminist theory, which challenges "individualist
metaphysics" by building upon quantum physics in order to show the
"entanglement of matter and meaning" in phenomena which are "the
ontological inseparability of intra-acting agencies". More on this
language below.
I think that Karen Barad has a point in remarking the complexity of what
an object and a measurement is, but the impact of her message is due to her
adduction of the scientific prestige of QM or rather logic and mathematics. It
is beyond the grasp of common people and most academicians who, consequently
have no opportunity to follow her arguments. My own point is that her message
is a logic reconstruction of the problems that were already considered by
Brouwer in the above text. I will not fall into the trap of attempting to
build-up a network of arguments in order to convince the reader about all this.
It would be the same kind of trap as to try to use logic in order to criticize
abuses of logic as I claim that critics of Immanuel Kant's model followers are
tempted to do in questioning the actual trends towards of computerization of society. I will rather suggest to those
who are receptive to criticism, how the misunderstanding of logic and
mathematics outlined by Brouwer enable their misuses and undermine arguments.
The more so for those who, contrary to QM-physicists do not have special aptitude
for formal science as explained in my essay on The Meaning of Human-Computer Interaction. The conclusion will also be in harmony with my view
of feminism as advanced in my contribution to Reason and Gender.
In Quantum mechanics and the
paradox of mutual exclusivity (Social Studies of Science, vol. 41, No. 3, June 2011, pp.
431-441), Trevor Pinch offers a
critical but basically respectful review of his colleague (in the sociology of
science) Barad's book Meeting the universe halfway: Quantum physics and the
entanglement of matter and meaning. (Observe:
matter and meaning, not matter and
human psyche). In his text, however, one finds passages that properly interpreted
expose the problems announced by Brouwer in The
Rejected Parts above, continued in
the next section after this
parenthesis. My point below will be
that the apparent "mystique" of QM is the result of a defective
psychology with its origins in
philosophy and its later derailments, in its attempts to grapple
with the relation between mathematics and reason, which I develop further in
the above mentioned paper on computerization. I must
also contextualize the whole issue by emphasizing that the connection to
feminism appears to be due to its eagerness to focalize upon and to relativize
the human (cf. woman's!) body to the point of problematizing the
human by conceiving a post-human. And
this is done by simplifying the conception of the human psyche by reducing it
to a supposed materiality. In the
following I will reproduce in italics excerpts
from Trevor Pinch's review, followed by its page number in parenthesis, and by
my occasional comments:
Quantum
mechanics is a peculiar theory because it is used routinely by physicists, is
the basis for much psychology, and the consensus is that its predictions have,
up until now, always been verified - on all accounts it is a vastly successful
theory. Yet what the theory means, its foundations, are notoriously obscure.
What we might call the "big issues" of quantum mechanics - its
completeness and correspondence with reality, the nature of the fundamental
entities it describes and what they mean for our conceptions of space, time,
and matter, and the relationships between measuring instruments and system
being measured - used to be much
discussed by leading physicists when the theory was formulated in the 1930s.
The famous debate between Einstein and Bohr and Einstein's dislike of the
theory for its statistical basis are the stuff of legend. The "Copenhagen
Interpretation" of quantum mechanics, in homage to Bohr's influence,
became the accepted wisdom and physicists
were happy to stay in their labs and increasingly not worry about foundational
issues - after all they could still calculate, make predictions, make
technologies (including atomic bombs), and get funding for their work.
Increasingly, worrying about foundational issues passed to the terrain of
philosophy. Philosophy, as all physicists know, is good for you in small doses
but ultimately can be dispensed with. [p. 432, my boldface]
Yes: "happy and not worrying about foundational issues - after all
they could still calculate, make predictions, make technologies including
atomic bombs"?
Not even now, in the middle of the hyped apocalyptic
global warming of climate, people do seem to realize that this could be said of
each one of the hundreds or thousands of technologies which contribute to such
global warming. A global atomic third world war would already, if yet too late,
made us understand the problem of being so happy in not caring for foundational
problems, if they were indeed only "foundational". The hope seems to
be, to remediate with "more of the same", new "unfounded"
technologies that will offset the global warming, continuing with the not
caring for the ethics in
technology.
For the rest, Brouwer himself addresses the question of measuring instrument below. It is to be
compared with The Design of Inquiring
Systems where the issue of measurement is addressed in a special chapter on
"Singerian inquiring systems" and is preceded by a treatment of what
is ignored here, the question of what a system
is to begin with. Concerning the "statistical basis" it is correct to
note that statistics is far from implying theory, as correlation and
mathematical relation are far from implying causation. An appreciation of
statistics requires an in-depth understanding of the meaning of probability,
and in turn it requires the kind of discussion that precedes the discussion of
systems, as done in Churchman's books Theory of Experimental Inference, and Prediction and Optimal Decision. The feeling of powerlessness and hopelessness that
invades the reader in being directed to such references is the same that should
invade the enthusiasts of quantum mechanics prior to their becoming its
enthusiasts and upon their asking for its foundations. For the rest it is interesting to note that the progressive
disregard for foundational issue reminds that it is the same phenomenon has
occurred with the foundations of mathematics itself. It is that same
mathematics or mathematical physics that also stands at the core of quantum
mechanics and constitutes the object of our whole article.
She
[Karen Barad] advocates nothing less than a new metaphysics for the field.
Unfortunately…when outlining her agential realism approach her writing changes
from the crystal clarity of dealing with the physics to a series of dense
assertions about such matters as agency intra-actions, becoming, phenomena,
causality, dynamics, materiality, and the role of the post-human …[L]et me simply say that sections of this book contain some of
the densest prose I have recently read in the field.
[433]
In another essay
on computerization and elsewhere (here, and especially
here) I did already
address the phenomenon of "bombastic" language, the low level of philosophical
argumentation, the deliberate obscurantism of the prose, the wildly exaggerated
claims, and the constant striving to give the appearance of profundity by
making claims that seem paradoxical…also
observable among enthusiasts of AI (artificial intelligence) and in references
to quantum physics. Pinch's language is,
however, exemplary for the restrained and elegant style in its criticism of the
language that other would have described as bombastic and revealing problems of
rather obscure argumentation.
Also of great historical significance is the small
number of physicists who explicitly rejected the Copenhagen consensus and who thought that the business
of interpreting the quantum theory was too important to be left to
philosophers. David Bohm [was one such physicist. [434]
Regarding the Copenhagen consensus, see how the Stanford
Encyclopedia of Philosophy writes about it: "The Copenhagen interpretation was the first general attempt
to understand the world of atoms as this is represented by quantum mechanics.
The founding father was mainly the Danish physicist Niels Bohr, but also Werner
Heisenberg, Max Born and other physicists made important contributions to the
overall understanding of the atomic world that is associated with the name of
the capital of Denmark. -- In fact Bohr and Heisenberg
never totally agreed on how to understand the mathematical formalism of quantum
mechanics, and neither of them ever used the term “the Copenhagen
interpretation” as a joint name for their ideas."
It is remarkable that two founding
fathers did not understand what they had founded. Or did not agree on
"how to understand" the mathematical formalism that was supposed to
represent the relations in the empiricism of the experiments. My explanation is
that the human Spirit when it does not relate to theology and religion seeks
its expression in a religion renamed into a muddled metaphysics, or reduced to
aestheticism as I claim in discussing
computerization, or reduced to politics as I claim in another
theological context. And the two trends coalesce in one if one tries to
understand how Marxist thought relates to postmodernism as addressed by
Christopher Norris in What's Wrong with Postmodernism. It also addresses trends in my own discipline of
informatics as I comment the concept of design in the so-called Work-oriented design of computer artefacts in
the context of human-computer
interaction. Indeed:
Bohm found allegiance with physicists in the Soviet
Union who also had the temerity to question quantum mechanics at the time. The
story of these physicists and their struggles has
never been fully told... When I interviewed Bohm in 1975
he told me that he had written his 1951 textbook - regarded by many physicists
at the time as the best account available - in order to try to understand the
theory, and the more he delved into it
the more he realized he didn't understand it. He rejected Bohr's idealistic
metaphysics…[and] produced his rival materialistic
interpretation of quantum metaphysic. [435, my boldface]
Pinch notes Bohm's times in the U.S. as being related to Free Speech movement, and I perceive in turn it being
further related to New Age. At the time,
Bohm's work environment was characterized by speculations about extra-sensory
perception, telepathic powers, parapsychology and such, until the eighties when
as Pinch notes, physicists took on other, newer realities: the "quantum
entanglements became further entangled with military and corporate funding,
giving birth to quantum computing, quantum cryptography, and quantum
teleportation". Wikipedia remarks that the New Age is said to employ
terminology and concepts borrowed from science and the New
Physics, having a number of prominent influences from
professional scientists such as just David Bohm, and Ilya Prigogine. The name
of Carl
Jung was also "kidnapped" in diverse speculations. That happened
because it was sensed that his (misunderstood) work had references to perceived
"mysterious spiritual" phenomena that were the focus of Eastern
thought and could explain the unexplainable.
A core of the unexplainable considered by Barad in her musings about the
mysteries of QM is the so-called wave-particle duality, (cf.
"mutual exclusivity") which
is in turn summarized under the label of interpretations of quantum mechanics. In the latter reference appears a terse statement of
the present state of the art: "Despite nearly a century of debate and
experiment, no consensus has been reached among physicists and philosophers of
physics concerning which interpretation best represents reality"; whatever reality is, (more below), beyond
the mind-blowing theorizing about "virtual reality". I perceive that
there is something paradoxical and comical in wondering about reality in an
extremely mathematized context: for instance, as Wikipedia reports, in October
1993, a Scientific American's article with the title "The Death
of Proof" observed that the growing complexity of mathematics was
undermining traditional concepts of mathematical
proof.
It is seldom noted that the "core of the core" appears in the
idea of "representing" and "reality" or in what can be
denoted as representationism. Wikipedia relates this to the "philosophy of
perception and of mind and the debate about the nature of conscious
experience" and further to what is included in epistemology vs. reality
(non-mentioned ontology) and neuroscience. What
is opportunely not mentioned is the role of mathematics that happens to make
all this discussion abstruse for most educated readers, and the role of the unconscious mind, which is the reason for all my interest for Brouwer
and for Jung.
But Barad does not recur to Jung, to whom I myself arrived through a
series of serendipitous references in The
Design of Inquiring Systems (pp. 203-205, 244, 261, 272, 277, 280). She (and perhaps even her reviewer
Pinch) does not understand the relation between the practice of science and her
own discipline of science studies, as
well as her musings over Bohr's question of repeatability of experiments as
related to "extrapolation from agreement over outcomes of measurements to
some sort of knowing mind" (in the absence of God):
Bohr and indeed Einstein, were committed to a form of
humanism whereby they gave priority to humans and how humans agree over
measurements. According to Barad, this is a mistake and leads to a subjective
trap whereby it is easy to extrapolate from agreement over outcomes of
measurements to some sort of knowing
mind which recognizes the measurement as such. It is a short step to views,
such as suggested by Wigner and von
Neumann, that quantum phenomena only actualize when they encounter the
consciousness of a human. … Barad's extension of Bohr's position into what she
calls agential realism seems to rely on three major points. First, she argues
that Bohr's notion of language as
being about linguistic concepts shared between humans is too narrow, and that a
more sophisticated notion of language is needed. Here she draws upon a materialist reading of Foucault to
ground language in what she calls material discursive practices. Second, she
extends the rather limited notion of
apparatus that Bohr (and most scientists) share… Third, Barad argues, that
humans themselves are produced by nature. She focuses upon bodies, and drawing
upon Monica Casper's work on fetal parenthood and STS
[Science &
Technology Studies
at Cornell University?] on ultrasound technology, she offers a materialist
critique of Judith Butler's overly human-centered
performative approach to the body.
Barad's own performative approach of agential realism
is heavily indebted to Bohr in the key aspect that phenomena…are instantiated
by the material agencies found in pieces of [measurement] apparatus. Her notion
is that the world is a place of becoming. Intra-actions (interactions between
two entities, not only a human and ad non-human) occur everywhere and these
produce phenomena… Her major point is that we as humans are not outside observers, but we are part of
the world in its ongoing intra-activity…[A]t the same time she wants to claim
that agential realism should be the basis for doing science studies and also as
a new basis for ethics. [p. 437f, my boldface]
I allow for such a long quotation in order to open for the insight that
it is the breakdown of reason in the context of communication and their
consequent divorce from mind and spirit that leads to the questioning of what
is human consciousness and what is human
including language itself. Not to
mention logic that Brouwer conceives
as abstracted from it. All this while there is a startling oblivion of the possible if not probable problems with the
"language" of mathematics. Not to mention that repeatability
seems to be often conceived as precision instead
of accuracy, as I have been striving
to explain in my doctoral dissertation on Quality-control
of information. While
discussing the difference between doing science or writing about it as a scientist vs. as observer-student of scientists she does not seen
aware of the problems of Hegelian philosophy's central tenet that every
observer is observed. (We meet here also the insight of the earlier referred
work on The Design of Inquiring Systems). Being so, Barad does not build upon
the historical struggle about how agreement is reached and why conflict arises
in science (and politics, cf. Bohm and Soviet Union and Barad's materialism). It is significant that mentioned
physicist Eugene
Wigner with his work that is a cornerstone in the mathematical formulation of
QM, approached the core of the problem but failed in his famous and
inconclusive The Unreasonable Effectiveness of Mathematics in the
Natural Sciences. It is also
significant that Pinch and Barad do not generally acknowledge that the earlier
mentioned David
Bohm came even closer to the core of the QM-problem in that with his
interest for consciousness and thought he entered in extensive interaction with
the philosopher Jiddu
Krishnamurti. This appears to have been thoroughly studied by David Edmund
Moody whose research focused on
overcoming misconceptions in the sciences, and certainly would have opinions on
our issues. It is interesting and symptomatic that interest for Eastern thought
and religions also characterized another avowed atheist and "founding
father" of QM, Erwin Shrödinger.
I claim that we arrive here at a crossroad, since "consciousness
and thought" is more than consciousness and thought if it is to be
completed with the problem of the unconscious,
leading to Jung's psychology. It parallels Krishnamurti in that it related
Western philosophy, including philosophy of science, to Eastern thought. In
doing so, Jung also warns for the "autonomy of the unconscious". In
the foreword to Suzuki's Introduction to
Zen Buddhism, for instance, in the context of psychotherapy he warns:
"[A] direct transplantation of zen to our
Western conditions is neither commendable nor even possible" (Collected
Works, CW 11, §905). The only alternative I see
is the challenge of analytic psychology unless the scientist happens to strive
for something like the following, expressed towards the end of Barad's review:
Barad states that feminist science studies is about gender and science in the making,..
and although she does emphasize a new ethical framework that stems from her
post-humanist viewpoint, and claims that understanding how bodies are made
materially has important consequences for gender, I failed to see how this
understanding impacted the version of the entanglement experiments as she
presents them. Perhaps having science on
your side is the right political move, and she is also right that we need
to think about how we engage with the people we study and at the same time
study them. But I do not think the solution is to reproduce the paradox of
mutual exclusivity between science and science studies. [p.
440, my boldface]
Yes: "having science on your side is the right political
move", (as having phenomenology on your side can be a right philosophical
move when taking care of the body in philosophy
of technology). I perceived this when a feminist senior student at
my university department of informatics enthusiastically referred to Barad's
work. My intuition is that the problem met in QM is best understood as an
analog to the teachings about the history of alchemy. In an essay about The psychic nature of the alchemical work, Jung
writes
But, just because of
this intermingling of the physical and the psychic, it always remains an
obscure point whether the ultimate transformations in the alchemical process
are to be sought more in the material or more in the spiritual realm. Actually,
however, the question is wrongly put: there was no "either-or" for
that age, but there did exist and intermediate realm between mind and matter,
i.e., a psychic realm of "subtle bodies" whose characteristic it is
to manifest themselves in a mental as well as a material form. This is the only
view that makes sense of alchemical ways of thought, which must otherwise
appear nonsensical. Obviously, the existence of this intermediate realm comes
to a sudden stop the moment we try to investigate
matter in and for itself, apart from all projection; and it remains
non-existent so long we believe we know anything conclusive about matter or the
psyche. But the moment when physics touches on the "untrodden, untreadable regions," and when psychology has at the
same time to admit that there are other forms of psychic life besides the
acquisitions of personal consciousness - in other words, when psychology too
touches on an impenetrable darkness - then the intermediate realm of subtle
bodies comes to life again, and the physical
and the psychic are once more blended in an indissoluble unity. We have
come very near to this turning-point today. [CW 12, § 394, my boldface].
Yes, blended in the indissoluble language(s) of mathematics in QM and
computer science, if yet without the support of Christianism. Does this blend have the same meaning as in Barad
expression: "the entanglement of
matter and meaning"? And are there
any conclusions? Perhaps there are: conclusions about the blending of the
psychic and physical in spiritualized psychic or mathematized science in the
communities doing research on quantum physics and feminism:
[T]he unconscious,
being unknown, is bound to coincide with itself everywhere: lacking all
recognizable qualities, no unconscious content can be distinguished from any
other. This is not logical sophistry but a very real phenomenon of great
practical importance for it affects the problems and identification in social
life, which are based on the collective (and indiscriminable)
nature of unconscious contents. These, once they have taken possession of
certain individuals, irresistibly draw them together in mutual attraction and
knit them into smaller or larger groups which may easily swell into an
avalanche. [CW 12, § 431]
Carl Jung does not muster much more than the following, written in 1936:
The power of science
and technics in Europe is so enormous and indisputable that there is little
point in reckoning up all that can be done and all that has been invented.
Quite another question begins to loom up: Who
is applying this technical skill? In whose
hands does this power lie?... Western man has no need of more superiority
over nature, whether outside or inside. He has both in almost devilish
perfection. What he lacks is conscious recognition of his inferiority to the
nature around and within him. He must learn that he may not do exactly as
he wills. He does not know that his own soul is rebelling against him
in a suicidal way. -- Since Western
man can turn everything into a technique, it is true in principle that
everything that looks like a method is either dangerous or condemned to
futility. [CW 11, § 869-870, my italics and boldface]
That is: "He must learn that
he may not do exactly as he wills." If the question is "why and
how" to (not) do it, the answer may be: religion and God's will, which for
many is not more volatile than QM has revealed to be even for a founding
father. "God's will" can also be read into the Kurt Gödel's study on
incompleteness and undecidable propositions: a cursory
reviewer of a late biography of Gödel, Journey to the Edge of Reason, suggests to celebrate his proof as
"that even the most rigid numerical bureaucracy contains the tools by
which a higher truth will always be able to effect an escape". A
preparatory answer may come from reflection over how man has already been
splitting the atom with ensuing explosions, but also the living cell and the family,
with their potential analogous "explosions" or consequences for
mankind. And Schrödinger's book What is Life? is
claimed to have inspired others to research the gene, which
led to the discovery of the DNA double helix structure and how genetic
information might be stored in molecules. But please observe: all this was
paradoxically done without really knowing
what information is, to begin with, as shown in Churchman's The Design of Inquiring Systems.
Finally: in the first quotation of this section, above, QM looks indeed
like a "method" when "physicists
were happy to stay in their labs and increasingly not worry about foundational
issues - after all they could still calculate, make predictions, make
technologies [including atomic bombs], and get funding for their work". Or
see what professors of physics and colleagues are quoted to say below at the beginning of the concluding exercise of this whole
essay. And now, having in mind the problem of the "startling oblivion of
the language of mathematics"
expressed above, we may better understand the rest, below, about the rejected
parts of Brouwer's dissertation. Rhetorically: if esoteric mathematics is a language, the QM-folks do not know what they are talking about, and why they do it if it is not for getting
knowledge that is power to make it work, including for money and terror weapons
of mass destruction.
NOTE:
Early in the year 1996 I obtained a copy of an extremely relevant Swedish doctoral
dissertation at Uppsala university (Dept. of History of Science
and Ideas, ISBN 91-506-1140-2) by Suzanne Gieser involving the
physicist Wolfgang Pauli, Nobel-prize
winner in year 1945 (cf. lecture
1946, esp. the next to last paragraph), as pioneer of QM. I cannot discuss
here this forgotten dissertation but can recommend it for its depth and
coverage. It ends in mind-blowing complexity that, however, does not include
the problematics of abuse of esoteric mathematics and logic at the interface
between philosophy of science and theology. Such problematics, however, can be
read in the mentioning of psychic distress and life-crises of some of the
scientists. There are no comments (Gieser, pp. 21-36) on how Pauli left
the Roman Catholic Church and later may have tried Jung's psychology as a
substitute, instead of as a bridge back to it. The dissertation was edited and
translated into English as The Innermost Kernel. Depth Psychology and Quantum Physics: Wolfgang
Pauli's Dialogue with C.G. Jung. (2010, hard cover 2005). Springer Verlag.
Berlin and Heidelberg, (ISBN 978-3-642-05881-3). The issues in the present text
are discussed mainly in (in the Swedish edition's) part 1, chap. 3, and part 3
chap. 5. I have commented Gieser’s text in a separate essay
on quantum mechanics, computers and psychology.
For the rest, after writing my text with the final quotation, and making
a browser-search on technics, science and Jung, I happened to find the
following improbable reference: Carl Gustav Jung, Quantum Physics and the Spiritual
Mind: A Mystical Vision of the Twenty-First Century [found also here], in Behavioral
Science (Basel) 2013 Dec; 3(4): 601-618. I find it focused upon QM in its
relation to (again) mainly Eastern thought, but it cannot address the abuses of
mathematics and logic such as those related to QM. My text is focused upon the
mathematics and logic that else is taken for granted and abused, and upon
religion as Christianity whose doctrine also can be logically abused.
RECOGNIZING THE
PROBLEMS IN THE "REJECTED PARTS"
In my attempts to understand Brouwer's
reference above to the Transcendental
Analytic as "idle play" I also tried to understand something of
the intricate field of philosophy of mathematics, and in particular the philosophically "canonized" Immanuel Kant's philosophy of mathematics where, Philip Kitcher notes (in Kant and the Foundations of Mathematics), that pure mathematics includes geometry, arithmetic, algebra,
kinematics, "pure mechanics" and, he thinks, analysis. Encouraged by
the example of colleagues who had studied Kant's Critique of Pure Reason (F. Max Müller's
translation, Anchor Books, 1966) as a step for understanding information
systems I dwelled in its treatment of mathematics in its Transcendental analytic, such
as its mentioning of "counting" (p. 61, A76f., B102f.) or
"number" (p. 65, A:83f., B:112f.) in the section III of Book I, about
"Pure concepts of understanding, or of the categories." Not finding
anything that recalls Brouwer's problem (and this may be the reason for his
description of "idle play",) I went over to what is considered as the
explicit basis for his famous philosophy of mathematics, in the Critique's Transcendental Dialectic, "The
discipline of pure reason in its dogmatical use" (pp. 465-479, A710ff.,
B742ff.). I found there something that may be consistent with Brouwer's
message, namely the following (p. 471f., A725f, B:749f.):
"The great success which attends reason in its mathematical use produces naturally the expectation that it, or rather its method, would have the same success outside the field of quantities also by reducing all concepts to intuitions which may be given a priori, and by which the whole of nature might be conquered [...] Nor there seem to be any lack of confidence on the part of those who are masters in the art of mathematics, or of high expectations on the part of the public at large, as to their ability of achieving success, if they only would try it."
Further summarizing comments about all this can be found in the Stanford
Encyclopedia of Philosophy, and its intricacies become mind-blowing in a thesis
by Gary Martin Seay on Kant's Mathematical Synthesis, but for me it is still an open question whether
Kant's reasoning implies or is consistent with Brouwer's conceptions and his
condemnation of "idle play" and consequences for the application of
"mathematical machines" to human activities rather than to phenomena
of natural science.
Brouwer continues exposing the difference between the mentioned
"passionless language" and the language of mysticism which may convey
contemplative thoughts that are independent of superficial human collusion and
animal emotions of fear and desire, appearing as meaningless to those who seek
communication of mathematical systems. In this way he tries to foster the
understanding of the remarkable book he had written some years earlier, Life, Art and Mysticism, already
mentioned above.
Is it surprising that not only do we succeed in observing sequences which repeat themselves again and again, but that so many groups of phenomena affecting our naive senses in totally different ways can be brought together under a few general aspects which are covered by simple constructible mathematical systems? This really would be a miracle, were it not for the simple fact that the physicist concerns himself with the projection of the phenomena on his measuring instruments, all constructed by a similar process from rather similar s o l i d bodies. It is therefore not surprising that the phenomena are forced to record in this similar medium either similar laws or no laws. For example the laws of astronomy are no more than the laws of our measuring instruments when used to follow the course of heavenly bodies
This last sentence is indicated by van Stigt
as having been crossed out by Brouwer himself, and this may be an indication
that Brouwer had overstepped his own intentions in an improper expression that
would give the impression of sheer solipsism. On the other hand, however, it
may be question of interpretations of the meaning of "solipsism"
since for all practical purposes the important thing is the relation between
human observers and so-called reality, rather than philosophical reality per se that can be
cheerfully neglected as it already is in computer science in its dealings with
"virtual reality". But indeed, Brouwer may touch here one aspect of
the measuring instrument that seems
to have been ignored in the context of quantum mechanics (cf. the above section) when differentiating it from the observer. Namely, the instrument already incorporates in itself a theory that is chosen
and accepted by the observer himself. That is, if not also initially conceived and constructed by him. Observations of nature and environment
are important in that they point to the mysterious and seldom addressed
question of the strange, not to say mysterious capacity of mathematics to act
"humanly", i.e. to foster human understanding or rather prediction
and manipulation of nature as if it, mathematics, were the "language"
of nature. What both Brouwer and we ourselves are trying to do here is to
understand what happens to our conception not only of nature, but also of
anything partly falling outside nature such as humans when we apply that sort
of eyeglasses constituted by the mathematical machines, in the broad meaning of
mathematics. And this, besides the already mentioned Design of Inquiring Systems, may
be of utmost importance for understanding the import of late developments of so
called artificial intelligence (AI), exemplified by the reseach
laboratory OpenAI (see here and here), on "Deep learning" or
applications of the type "Xiaoice" or "AlphaGo", or the Generative Pre-trained Transformer GPT-3 used to create
prose, poetry and AI-journalism (Swedish review
here), not to mention
"Emotional AI" as well as some of the criticism directed against it,
such as "What
emotional AI fails to grasp about emotion".
A basic distinguishing faculty of humans with respect to nature is free will,
despite many people including scientists are trying today to
"deconstruct" it in terms of determinism and atheism. Our discussion
can be seen as touching the question of free will as related to nature, while
free will is coerced and cast into predetermined forms by imposed structures of
human-computer interaction, and thereby also mediated human-human interaction
such as so-called social media. I am not sure to which extent one has to deepen
a proper understanding of the conundrum of free will in order to
understand what is happening and its consequences, including computer addiction
as a result of playing havoc or gambling with the degrees of freedom of the
will. I see, however, that such an understanding is absent in dealings with so
called artificial intelligence - AI - that eschew teleology in favor of
mechanism, as in mathematical speculations on "infinity
and the mind" exemplified by Rudy Rucker. They have not yet
incorporated the lessons from e.g. West Churchman's The Design of Inquiring Systems. Humility in
face of this matter may in due time be fostered by an in-depth study of Kant's
discussion of free will in his Critique
of Pure Reason, second division: Transcendental Dialectic, Book II,
chap. II, section 9 on "Explanation of the cosmological idea of freedom in
connection with the general necessity of nature" (pp. 371ff., A:538ff.,
B:566ff.). Nevertheless such a discussion will
probably not take place because of the inaccessible complexity of this type of
literature and of Kant in particular. Many modern philosophically and
technically sophisticated researchers still dwell in the sixties' analytic
philosophy or cultural
Marxism, and many have swiftly moved over to phenomenology, post-structuralism, post-phenomenology, post-humanism and such. Some move to anthroposophical criticism, all
of them apparently avoiding evaluation of variants of pragmatism that otherwise
is praised in the Western USA-influenced culture.
Science, therefore, makes sense only when man in his struggle against nature and his fellow men, uses the calculations of counting and measuring; in other words, physical science has value only as a w e a p o n, it does not concern life - indeed it is a disturbing and distracting factor like e v e r y t h i n g in any way connected with struggle.
In this way Brouwer continues touching upon controversial issues which
require a deepening of the philosophy and theology of technology that I have
otherwise considered in my earlier mentioned Trends
in Philosophy of Technology. Theologically it
is a matter of the relation between man's and God's will that to my knowledge
is programmatically considered in Carl Mitcham and Jim Grote's (eds.) Theology
and Technology: Essays in Christian Analysis and Exegesis. Theological
discussions seem to be centered on the meaning of Genesis 3:19 "By the
sweat of your face You will eat bread" as related to human reason as a
gift of God in Genesis 1:27 "God
created man in His own image, in the image of God He created him",
supposing the legitimacy of using reason for at least partly redeeming himself.
Besides common knowledge that much if not most technology derives from military
needs Brouwer is also known to have been since early youth interested in
theology, which he took very seriously, as shown in his profession of faith
(see below).
But mathematics practised for its own sake can achieve all the harmony (i.e., an overwhelming multiplicity of different visible, simple structures whithin one and the same all-embracing edifice) such as can be found in architecture and music, and also yield all the illicit pleasures which ensue from the free and full development of one's faculties without external force.
Brouwer suggests here the source of all speculations associated in later
years to the treatment of computer applications in terms of aesthetics as in
architecture, which I tried to problematize in my The search for a
theory of hypermedia, and music,
whose "mystical" relation to mathematics is known since antiquity and
Brouwer implicitly suggests by his reference to the "primordial
intuition" of time that is common to both mathematics and music. In the
computer age all seems to have started with Douglas
Hofstadter's Gödel, Escher,
Bach: An Eternal Golden Braid, which does not
seem to eschew secular "mysticism" when properly described in Wikipedia as "not about the relationships of
mathematics, art, and music, but rather about how cognition emerges from hidden
neurological mechanisms. In that book Hofstadter presents an analogy about how
the individual neurons of the brain coordinate to create a unified sense of a
coherent mind by comparing it to the social organization displayed in a colony
of ants." Brouwer forestalled the misuse of the ant-analogy by
pointing out the "illicit pleasures" in the last quotation of his
above, something that would come to be the object of justified controversy
about Herbert Simon's ant-analogy in his book The Sciences of the Artificial (reviewed
by West Churchman in Contemporary
Psychology, vol. 15, 6 June 1970, pp. 385f.) In pursuing the
question of illegitimacy Brouwer continues referring to the mathematician Henri
Poincaré in his La Valeur de
la Science [The value of science]:
Poincaré [...] is inclined to reduce all aesthetic affections to such an affection of harmony. Perhaps his notion of aesthetic affection is simply an affection of harmony; but even according to him it is more: he says "outside science and aesthetic there is nothing but "le pur néant" [The pure nothingness]. He therefore seems to believe that it may be this aesthetic affection which is referred to as the highest good for mankind, preserved with such great difficulty. This shows the blinding effect which the immoral, free and full development of human faculties has also on him.
This is what I recalled in other computer-contexts, often associated
with the turn towards "Design", as being the well known but seldom recognized popular version of aestheticism, as paragraphs with this keyword are found e.g. in my
East
and West of Information Systems,
The
Systems Approach to Design,
Whither
Computers and Systems?,
Trends
in Philosophy of Technology, and
Ethics
and Politics in Design and System Cultures (seminar notes)
This represents a particular thread in European culture during at least
the last 200 years and whose immense potential for mind-blowing confusion is
illustrated in the discussion of moral aestheticism and of the
early mentioned books on postmodernism. Van Stigt's edited Rejected Parts of Brouwer's dissertation
continues with a discussion of the creation of mathematical systems
in the exterior world as a moment in the process of externalization, i.e.
"of holding out against the exterior world." It is followed by
considerations about Kant's Transcendental
Aesthetics, about objectivation, language in philosophy, causality
and free morality. The discussion, however, becomes gradually more intricate
also because rejected paragraphs require for their understanding to be related
to other paragraphs that were not rejected and do appear only in Brouwer's
dissertation. Such discussion falls therefore outside the limits of space and
purpose of my present text. It is enough to acknowledge that externalization is coupled
to processes considered in analytical psychology.
LIFE,
ART, AND MYSTICISM
A presentation and commented summary of Brouwer's book on Life, Art and Mysticism is not
necessary since, supplemented with a description of its historical-cultural
context, it is available on the net, in the previously mentioned Dirk van Dalen's Mystic, Geometer, and Intuitionist: The Life of L.E.J.Brouwer, (pp. 63-74.) An appreciation is
also found in Walter
P. Van Stigt, Introduction to Life, Art
and Mysticism. My purpose here in to highlight some particular
thoughts that may show to be relevant for the conception of computers as
embodiment of mathematics, and of logic as understood by Brouwer.
Anticipating many later and modern issues in philosophy of technology, Brouwer
starts noting problems of environmental destruction while apparently influenced
by the Rousseau-like "theory
of the natural human", meaning, as Wikipedia expresses it, that
Brouwer "looked to a hypothetical State of Nature as a normative
guide". This does obviously mean that there are important theological
presuppositions for the bases and the consequent understanding of the purposes
of his work. It does not require that Brouwer should have borrowed the rather
confusingly convolute theological
presuppositions of Rousseau. Dirk van Dalen in chapter 1, "Child and
student" of the first volume of his book Mystic, Geometer, and Intuitionist, concludes (p. 20), possibly on
the basis of Brouwer's early profession of faith in the early 1900 in the Dutch
Remonstrant
Church (summary here, theologically related to Arminianism), that in his philosophical views he "had adopted a rigorous,
Schopenhauer-like, view of the world, religion, and his fellow human
beings." He states that his profession of faith in a rather
"liberal" brand of Protestantism explains, his critical stance on
certain forms of established religion as expressed in chapter 3, "Man's
Downfall, Caused by the Intellect") such as his
statement that "Art and religion in this world are only grand morphine
industries" (p. 398.) I myself find that the theological analysis of
Brouwer's thought would certainly require a deeper and more correct
understanding of this issue, on the basis of Arminianism.
In the book's chapter 2 on Turning
into Oneself, Brouwer talks about the need of withdrawing from the
attitude that causes environmental destruction by "turning into
oneself". Van Dalen explains how this must be interpreted theologically
and psychologically in that Brouwer had very early focused his attention of the
essence of the ego as related to "given" perceptions, rather
independent upon the objective world out there, and therefore he appeared
rather "solipsistic". Here we have, again, a connection to Jung's
psychology in the sense of introverted ego-thinking supplemented by intuition,
i.e. (in Jung's conception) unconscious perception.
The reach of Brouwer's psychological ambitions would be reiterated so
late as in 1948 when he is reported (by van Dalen, pp.
832f.) to have reiterated his views about the inverse part of the
"turning into oneself", i.e. the original fatidic "exodus of
consciousness from its deepest home", which would consist of three phases:
the naive phase (creation of the world of sensation), the isolated causal phase
(where causal acts take place), and the social phase (in which cooperation with
the individuals finds its place.) In the causal phase I understand that also
mathematical projection takes place, regardless whether mathematical patterns
are developed in the social phase.
In this way Brouwer was also touching the problem of consciousness, which eludes
the most modern discussions of artificial intelligence. In order to understand
the immense problem that Brouwer was trying to address, starting in his youth
and at a time when most mathematicians (and psychologists) had neither the
interest nor the knowledge necessary to grapple with it, we can point out Erich
Neumann's The
Origins and History of Consciousness, (1954, German orig. 1949.) In
Neumann's terms Brouwer seems to be concerned with a spirituality that had lost
touch with reality and the instincts: "The form which this kind of
degeneration usually takes in the West is not spiritual inflation, but sclerosis
of consciousness where the ego identifies with consciousness as a form of
spirit. In most cases this means identifying spirit with intellect, and
consciousness with thinking" (p. 386.)
In the rest of chapter 2, in two pages (393f.), Brouwer repeatedly
mentions the term "self" at least 15 times, including the
"you" of "yourself" corresponding to the "ego",
without attempting to define it. As far as I can see this self may correspond,
in Jung's terms to both his own concept of self and, especially, to what is as
yet unconscious. This is so because the self as an empirical concept related to
the psyche designates the "whole range of psychic phenomena in man".
As expressed in Jung's Collected Works volume 6 or CW6 (Psychological Types, §
789 and 797), this is almost identical to the definition of the psyche as
"the totality of all psychic processes, conscious as well as
unconscious". The editors of CW6 add, however, that the inference from
this comparison would seem to be that every individual, by virtue of having a
psyche, is potentially the self. It is only a question of "realizing"
it. But the realization, if ever achieved, is the work of a lifetime, possibly
under the guidance of a spiritual adviser that once would have been a priest
or, in later times, a "therapist". That is, under the guidelines for
a sort of yoga master or, in our
Christian tradition, according Loyola's
spiritual exercises and Clorivière's guidelines
for prayer (also in Swedish
translation) or, in our modern times, a "gnostic"
analytic psycho-therapist. In this case Brouwer is only ignoring the lifelong
work that is necessary for the "return to the self" and seems to be
assuming the it can be done, albeit requiring an "effort" to
"overcome an inertia", as an act of free will for
"self-reflection" that "can withdraw from the world of
causality". This optimistic attitude of Brouwer may be attributed to his
feeling of identification with the experiences of the mystic Jakob Boehme, his main
inspiration in these thoughts: Brouwer must have needed to use the words of
Boehme for describing his own early experiences.
For our purposes in this essay it must be
finally mentioned that Brouwer offers in this essay an indirect clue about the
reason for the fascination exerted by computers. Among the difficulties met for
the "return to the self" he mentions the downfall caused by
"fear and an obsession with saving, born from the illusion of time",
and "the desire and lust for power, born from the illusion of space."
Considering that on several occasions he refers to the need to free oneself
from the shackles of worldly fear and desire, it follows that the computer,
especially in the form of mobile smartphones with their instant spatial
communications paradoxically offers an illusion of freedom from the illusions
of both time and space.
In chapter 3 about Man's Downfall, Caused by the
Intellect Brouwer can be seen as presenting a criticism of science.
He dwells upon the downfall caused by the intellect chained to fear and desire.
Man is chained to its "intellect", and he is incapable of lifting
itself in self-reflection. Unfortunately, in the whole
argument, Brouwer leaves "intellect" as undefined as the earlier
self, and one of our purposes here is to relate this intellect to what
especially later psychology would come to name as psyche, with due regard
to former Greek philosophy and Christian conceptions of spirit, soul and body, such
as e.g. described in a CBN (Christian Broadcasting Network) entry. Anyway, in
Brouwer's own words:
This highly valued intellect has enabled man and forced him to go on living in desire and fear, rather than from a salutary sense of bewilderment take refuge in self-reflection. Intellect has made him forfeit the amazing independence and directness of his rambling images by connecting them with each other rather than with the self. In this way the intellect made him persist with apparent security in the conviction of a "reality", which man in his arrogance has made himself and had tied to causality, but in which in the end must feel totally powerless.
In this life of lust and desire the intellect renders
man the devilish service of linking two images of the imagination as means and
end. Once in the grip of desire for one thing he is made to strive after
another as a means to that end [...]. Brouwer goes on explaining that the act aimed at the
means, however, always overshoots the mark to some extent - the means has a
direction of its own, diverted at an angle however small from that of the end.
It acts, therefore not only in the direction of the end, but also in other
dimensions that we could call unforeseen consequences while many perceive as an
end what was originally [and for others, we may add] only a means. Brouwer
notes that if this "deceptive jump" from end to means is repeated
several times, it may happen that a direction is pursued which not only
deviates but opposes and counteracts the original one. Brouwer applied this
insight to the development of industry and the consumption of natural resources
including the balance of nature, expanding his reasoning to the production of
industrial tools and therefore to the essence of technology. Unforeseen
consequences lead repeatedly to the uncovering of hidden assumptions and
consequent anxiety about the future, craving for the power to predict its
course: that is, requiring a science to support technology. Or:
Science, which in its original form was wholly subservient to industry, has made up all kinds of general assertions in and about the world of perception. These come true as long as it pleases God; but one day they will suddenly be contradicted by facts and then our scientists will claim, "O yes, of course, we always made this or that tacit assumption." In their incompetence they then set about complicating the issue even further and making so-called corrections and improvements.
[And, continuing:]
But science does not confine itself to serving industry: again the means becomes and end in itself, and science is practised for its own sake. Bodily awareness has strayed so far away that it is all concentrated in the human head, ignoring and excluding the rest of the body. At the same time man becomes convinced of his own existence as an individual and that of a separate and independent world of perception. At this stage there are radical changes in the direction of man's attention, and these constitute scientific thinking. For scientific thinking is nothing but a fixation of the direction of will within the confines of the head, and a scientific truth no more than an infatuation of desire living exclusively in the human head.(My emphasis.)
We can see here a possible source of modern phenomenological approaches
with emphasis upon the body, such as those that were considered in my essay Trends
in philosophy of technology with special focus on information
technology. The interest for the "body" as a
attempted contrast to the "head" can also appear in queer forms of
"feminist
techno-science", partly based on feminist interpretations of
(pdf) "quantum
theory". A problematic feature of the analysis above is that in face of
the lack of an appropriate psychology the ego of the psyche is equated with the
"head", paradoxically further contrasted to the "body" as
if the head including its implicitly considered and often emphasized
"brain" did not belong to the body. In some
late phenomenological approaches the body is further differentiated
from the "skin" in the context of "touching", as if it
were a sort of metaphysical differentiation between the ("its") body
and the environment or "the other", apart from or based on the
logical Aristotelian
considerations of sense of touch. In view of analytical psychology,
however, the basic problem that Brouwer encounters in his analysis is the
inability to analyze the situation of the ego itself with its consciousness and
will. This is the source of innumerable analytic difficulties including lately
such as in debates about the philosophy of free will among analytic
philosophers such as Harry Frankfurt and David
Widerker, which has wide implications for informational
decision theory. We find there a systematic and unreflective use of the
apparently unproblematic concept of (a unique) "agent" corresponding
to one "head", after it having been widely problematized in
Churchman's systems approach (The
Design of Inquiring Systems, chap. 3) by means of the split between
researcher, manager and client, not to mention the problem about their
"head" or "intellect", mentioned above. Back to Brouwer:
Every branch of science will therefore run into deeper trouble; when it climbs too high it is almost completely shrouded in even greater isolation, where the remembered results of that science take on an independent existence. The "foundations" of this branch of science are investigated, and that soon becomes a new branch of science. One then begins to search for the foundations of science in general and knocks up some "theory of knowledge". As they climb higher and higher confusion grows until they are all completely deranged. Some in the end quietly give up; having thought for a long time about the elusive link between the intuiting consciousness (which develops from the perceptional world) and the perceptional world itself (which in turn only exists through and in the forms of the intuiting consciousness) - a confusion which arose from their own sin of constructing a perceptional world - they then plug the hole with the concept of the e g o, which was self-created with and at the same time as their perceptional world; and they say, "Yes, of course, something must remain incomprehensible, and that something is the ego that comprehends."
The above has direct implications for the whole of computer science, especially the quagmire of AI, its
neologisms such as "neuro-morphism", and the phraseology associated
to its already mentioned "deep learning", machine
learning and data mining, which are built upon the concept of mathematical
computing machines and presupposes the view of (theory of) information as a
theory of knowledge. Brouwer explains further how this in turn is a temptation
for the assumption of an incomprehensible and therefore unchallenged monolithic
concept of ego. In doing so, however, Brouwer ignores both the need and the
possibility of an analysis (and synthesis) of the ego as related to
consciousness and to the unconscious as proposed in analytical psychology or
exemplified in the earlier reference to Erich Neumann. From these shortcomings
originate also affirmations that have raised the suspicion of solipsism in the
context of a construction of the perceptional world.
Brouwer continues describing and foreseeing results of this state of things as
reflected in environmental destruction, menaces to human physical and mental
health with consequent rise of the medical and entertainment industry (that
today culminates in computer-supported "edutainement").
They imply behaviors that, at Brouwer's time, can be seen as presaging the new
age hype, accompanied by the "myth of drugs" and followed by its
repeated disappointments. Sometimes it is perceived (e.g. by B. G. Rosenqvist
in Svenska Dagbladet, in
"The
drug that formed the ideal society", in Swedish) how the concept
of "drug" salvation appears in Aldous
Huxley's late utopic book The Island (1962). It
seems to be the result of his reflections upon Huxley's (related to George
Orwell) earlier famous dystopic book Brave
New World (1932), recalling the European cultural environment of
the early Brouwer who, however, had the insight of preferring Christian
salvation.
In a chapter 4 dedicated to "atonement" Brouwer, in a
preaching prophetic tone that characterizes the whole book, recommends a sort
of mystical attitude to life that borrows even words from Jacob Boehme and
resembles both Buddhism and Christianity in the spirit of Thomas à Kempis' Imitation of
Christ. It is easy to guess that such an attitude in the
ambit of Western science could only be possible in dedication to mathematics
for its own sake. The step from there to mysticism is natural and is portrayed
in the chapter that follows:
Chapter 5 is dedicated to "language" and I have already used some of
its argument in my earlier essay on Information
and Debate. In this chapter Brouwer criticizes logic for being
"life in the human brain" using here the term brain instead of the
earlier reference to "head" indicating the he uses them as synonyms.
Among other things he states that:
[R]idiculous is the use of language when one tries to express subtle nuances of will which are not part of the living reality of those concerned, when for example so-called philosophers or metaphysicians discuss among themselves morality, God, consciousness, immortality, or the free will. These people do not even love each other, let alone share the same subtle movements of the soul; sometimes they even do not know each other personally. They either talk at cross-purposes or each builds his own little logical system which lacks any connection with reality. For logic is life in the human brain; it may accompany life outside the brain but it can never guide it by virtue of its own power. Indeed, if there is a harmony of will, logic may well fall by the wayside ...
Ridiculous [...] is the use of language when there is an argument and people try to come to an agreement by means of reasoning. [...] In everyday life language only makes sense as a means of holding the already harmonious will of two people together on one path. [...] Language can accompany man's will to dominate the will of others or his will to keep the movement of wills together; for example, the war cry of Red Indians accompanies the will to break the will of others.
Yes, language as the source of logic can be used, in the absence of
mutual love or friendship, for "man's will to dominate the will of
others", the more so with a science embedded in abstruse
"mathematical tools" that disregard not only the meaning of
mathematics but also the difference between tools and theory-based instruments.
Such tools insulate the scientific communities from a shared democratic
understanding and criticism by the general public and other narrow scientific
specialties who do not share knowledge about the particular mathematical tools.
Let us also remind that this may be illustrated by what happens in the
Internet's social media's logically structured communications when clusters of
people, including children in schools, get to bully other clusters or,
especially, individuals, or start revolutionary gatherings, today always with
supposedly democratic aims. The question about language was part or the
polemics of that time regarding the relation between logic and mathematics
where Brouwer saw mathematics fundamental and originally individual, and
independent from logic seen as based upon the need for (necessarily imperfect)
language communication. The implications for computer communications beyond
logic and along language are then clear. For example, Facebook, Twitter,
group-blogs and so-called search motors have already been noted for
facilitating the pooling together of people in sub-cultures with similar
convictions and for achieving what Brouwer mentions as "language, which
presumes a harmony of will, may well be used to accompany strife and
combat." It is possible
to figure out the import of it all for the filtering implied in the process of
peer review and publication in established influential scientific journals.
This touches upon cultural aspects of "rhetoric" that I have
previously (1997-1998) considered in a paper on The East and
West of Information Systems. In the context
of a Swedish blog debate
about climate and global warming I have seen a member (pseudonym
"Nils G") of one dominant sub-culture irrupting into the community of
another deviant sub-culture and requesting that they turn more
"objective" and hoping to be allowed to start including further opposing
arguments. This attitude reveals a misunderstanding of the "Hegelian
inquiring systems", in West Churchman's conception of
The Design of Inquiring
Systems, since they presuppose a recognition of the fact that the
most important debates are indeed "objectively" driven by the
participant parties' passionate conviction that they are right in very
important matters. This implies a recognition that all people are in different
degrees legitimately influenced by feelings, intuitions, unknowns or
unconscious factors. One can claim either to be "objective" or to
require necessary additional arguments, but others can legitimately refuse to
agree about such a requirement, as it is indeed the case regarding the
legitimacy of e.g. the Holocaust, pedophilia or, earlier, atheism itself. In
the best case, a synthesis of opposing views is supposed to be obtained by a an
"external" observer of the opposition (having another related
parallel passion.) This may include the case of the creation of a special,
"theory-laden" communicative language such as in pastoral counseling
or psychoanalysis. Hegelian approaches to language not to mention logic,
however, were not within the horizon of Brouwer at the time, the less so for
mathematics based on a "primordial intuition", despite his
acquaintance with Hegelian philosophy through his early contact with Gerard
Bolland.
In the context of "ridiculous use of language" which in my
mind recalls the modern Western phenomenon of "political
correctness" Brouwer refers in two occasions in this chapter
5 to the "brain" in the context of language as
Only in the very narrowly restricted domains of the imagination such as in the exclusively intellectual sciences—which are completely separated from the world of perception and therefore touch the least upon the essentially human—only there can mutual understanding be maintained for some time. There is little scope for misunderstanding notions such as “equal” and “triangle,” but even then two different people will never feel them in exactly the same way. Even in the case of the most restricted sciences, logic and mathematics - a sharp distinction between these two is hardly possible - no two different people will have the same conception of the fundamental concepts on which these two sciences are constructed; and yet their wills are parallel, and in both there is a small, unimportant part of the brain which forces their attention in the same way.
[...]Once someone is imprisoned in the belief of a logically coherent (i.e. conceived without pain in a certain region of the brain) complex of externalities, which he calls "reality", it becomes rather difficult to follow him in his folly, and even more difficult to try to evoke in him a particular emotion or state of mind be means of words which he can only interpret in accordance with his reality. [My boldface]
These latest
considerations indicate that the diffidence of people towards mathematics needs
not be a result of their identification with the fox in what Aesop means in the
fable of the fox
and the sour grapes, as rarely gifted mathematicians and rationalist
sympathizers may be tempted to have it. It may be even the other way round,
regarding diffidence towards whatever recalls religion, mindfully cherished and
respected by a majority of world's population. Mathematics and logic can even be a preferred opportunity
for young gifted individuals to excel in them since it is natural that their
figuratively "small unimportant part of the brain" is the main part
of the brain that is available to them: other "parts of the brain"
and their interactions have not yet become active in "important"
adult matters such as work-life, love, suffering, death and religion.
This is something to think about when praising children and youngsters for
their "brainy" superiority to elders in intuitive proficiency
(Brouwer's "primal intuition in time sequences") in handling new
computer gadgets that are "fingered" in the spirit of Richard
Stiver's Technology
as Magic that is "it works but have no idea of why - what
happens" and do not know what "works" means. Similarly,
individuals gifted with a mathematical mind may be perceived as being polymaths
or universal geniuses in numerous intellectual fields thanks to their mental
reduction of the fields to mathematical or logical form, as they appear in the
perspective of mindless human-computer interaction (HCI). During a late
revision of this present paper, an economic-financial example that was highlighted
in the press in November 2022, is the case of 30-years old Sam
Bankman-Fried and FTX,
once the third-largest cryptocurrency-trading platform. The reports in The Economist and Wikipedia (should) say it all, reminding also cases of analog analytical logical-mathematical
giftedness such as of Adam Neumann
and the related business WeWork . and Sam Altman
as related to general
artificial intelligence (Open AI, ChatGPT, etc. as per April 2023)
and its financing, or sheer analytical financial genius of a Bernard Madoff. The
matter, however, is more serious than that, inasmuch examples such as of Ben Shapiro
and many others in the field of science (exemplified by
Albert Einstein and Wolfgang Pauli) suggest the effect
of inborn giftedness for mathematical-logical thinking as related to the famous
controversial question of superior Ashkenazi
Jewish intelligence (see also here
and here).
My
own annotations on
my copy of Carl Jung's book Memories,
Dreams, Reflections recorded
by his associate Aniela
Jaffé, indicate that I first bought and read it in April
1975 but happened to definitely relate it to this essay of mine in July 2023.
The book is interesting especially because it tells
about the author's psychological interpretation of his understanding and
feelings in meeting mathematics. Such feelings, when experienced by common
educated people can easily be dismissed for being caused by lack of giftedness
or sheer stupidity. The complexity of Jung's account requires literal
quotations (cf. pp. 43 ff., 340 ff):
[…] I felt a downright fear of the
mathematics class. The teacher pretended that algebra was a perfectly natural
affair, to be taken for granted, whereas I didn't even know what numbers really
were […] they were nothing that could be imagined, mere quantities that
resulted from counting. To my confusion these quantities were now represented
by letters, which signified sounds, so that it became possible to hear them, so
to speak. […] No one could tell me what numbers were, and I was unable even to
formulate the question. […] But the things that exasperated me most of all was
the proposition: If a=b and b=c, then a=c. even though by definition a meant something other than b, and,
being different, could therefore not be equated with b, let alone with c. Whenever it was a question of
equivalence, then it was said that a=a, b=b, and so on. This I could accept,
whereas a=b seemed to me a downright lie or a fraud. I was equally outraged
when the teacher stated in the teeth of his own definition of parallel lines
that they met at infinity. […] My intellectual morality fought against these
whimsical inconsistencies, which have forever debarred me from understanding
mathematics. Right into old age I have had the incorrigible feeling that it,
like my schoolmates, I could have accepted without struggle the proposition
that a=b, or that sun=moon, dog=cat, then
mathematics might have fooled me endlessly – just how much I only began to realize at the age of
eighty-four. All my life it remained a puzzle to me why it was that I never
managed to get my bearings in mathematics when there was no doubt that I could
calculate properly. Least of all did I understand my own moral doubts concerning mathematics.
In a later section of the book, in the
chapter "On life after death", Jung introduced some exceedingly
complex ideas about the relation of human death to the realm of consciousness
vs. the unconscious or "the intermediate stage between unconscious and
conscious cognition". It would take us too far in this our context but the
following extracted comment (p. 341) may give a taste of the relation to
mathematics:
Ideas of this sort are, of course,
inaccurate, and give a strong picture, like a body projected on a plane or,
conversely, like the construction of a four-dimensional model out of a
three-dimensional body. They use the terms of a three-dimensional world in
order to represent themselves to us. Mathematics goes to great pains to create
expressions for relationships which pass empirical comprehension. In much the
same way, it is all-important for a discipline to build up images of
intangibles by logical principles and on the basis of empirical data, that is,
on the evidence of dreams. The method employed is what I have called "the
method of the necessary statement". It represents the principle of amplification in the interpretation of dreams, but can
most easily be demonstrated by the statements implicit in simple whole numbers.
My point with these quotations is to
suggest that mathematics because of its very nature introduces unconscious
processes in the human mind while surreptitiously merging them with ordinary
conscious ones. It all recalls what has been considered in this essay about
both the aforementioned Brouwer and Zellini, as well
giving a hint of the ultimate mysteries of quantum physics (more on this above
and below) in the relation between psyche and matter. An alternative equivalent
conception presented
in my Information
and Theology is
the balance between the inner knowledge of human psyche vs. natural science and
knowledge of the outer world. This role of the unconscious and inner knowledge
of the human psyche related to (the aesthetics of) mathematics and logic also
explains the problems of addiction (not only of children, but also of
“childish” adults), including computer
addiction, the overhype of virtual
reality, and the success of mathematical-logical
minds in all sorts of modern endeavors including mathematized technoscience or white
collar crime. The latter is most brilliantly
exemplified by the genius of Bernard
Madoff and
by the fact that “Internet AI personalities” such as Tom Bilyeu at Impact Theory and Emad
Mostaque: see here a
logical conversation between them with the ambitiously alarming title How
Ai will disrupt the entire world in 3 years - Prepare now while others panic. The
latter have strong opinions about AI there is a penchant for bold
entrepreneurship and/or interest in “volatile” activities, financial and
others, as hedge
fronds. And
much entrepreneurship with empty talk about AI may be conscious or unconscious
attempt to commit “white collar crime”. Who is capable to discuss the degree of
consciousness vs. unconsciousness in order to determine culpability and whether
it will be considered as financial
crime?
The technical mind has been colorfully
exposed in studies of the philosophy of science in the tradition of Jacques
Ellul. Some of the deep approaches in the latter’s
“anarchist” tradition (examples here, here,
and here),
however, have sometimes missed the point when they lose the connection to broad
Christian theology, philosophy and its derivate (Carl Jung’s analytical)
psychology. This appears in the following de-contextualized excerpt
from one of the deep approaches (to Cybergnosticism, further
explained here), followed
sometimes by my notes in italics in square brackets in order to not leave
everything in the general “Comment” at the end:
[J]ust like alcoholics and drug addicts, game-addicted
children are now regularly treated by psychologists and psychiatrists in order
to get rid of their addictive behaviour, [Yes, but
how effective in this treatment on what grounds, and why, since it may by then
used for treating all “addicts”, and how should they be defined and identified,
since they may be even scientists?]
[M]any
videogames take advantage of techniques similar to those used by the military
to harden people emotionally. [Yes, but what kind of the treatment of these
hardened people would be allowed and recommended by the military leadership vs.
ex-post by e.g. the “Veteran benefits fof PTSD” or equivalent organizations?]
As the driving force of la Technique is,
according to Ellul, the crave for absolute efficiency in all human endeavours. [Ellul himself is quoted in Wikipedia from
his book “The Technological Society” as writing: “Not even the moral conversion of the
technicians could make a difference. At best, they would cease to be good
technicians. In the end, technique has only one principle, efficient ordering. What about the difficulty, to begin with, in defining “efficiency” vs. “effectiveness”, the more so when it is not even recognized that the difference lies in
the conceptualization of the systemic boundaries of (whose?) craves.]
It was Eric
Voegelin’s intriguing and much-debated thesis, that there is a deep-seated
disorder in our civilisation rooted in a ‘gnostic’
sentiment of alienation and discontent with reality perceived as evil, in the
con- sequential ‘gnostic’ turn away from this reality [Psychologically, or
how else, is a “sentiment” to be defined, compared with, say a thought,
intuition or perception?]
Arguably,
we cannot get at the real motives and ideas behind the computer phenomenon in
general, and the cyberspace and virtual reality sub-phenomena in particular,
nor arrive at a proper understanding of their roots and future direction of
growth, unless we take into
account these mighty metaphysical driving forces and motivations […] [How
about metaphysical forces and motivations, if not within the frame of a
religion’s theology?]
It is my
thesis that the roots of cyberspace and cybergaming must be investigated in a
much wider context than is done in these and other similar works so as to
clarify and make comprehensible the motive background and worldviews of the key
personages of the field. [What about the difference between (here) “roots”
vs. “forces and motivations” in the previous paragraphs].
They rest ultimately only upon the
criticism by Gnosticism and
overworked erudition and rationalism (paradoxically, an apparently own “gnosticism”) of the one “political philosopher” Eric
Voegelin. Wikpedia
summarizes, as
it follows some of his critics’ opinions, which match my own impression from my
readings and comment of Voegelin in another context of Information and Theology:
[C]ritics
have proposed that Voegelin's concept of Gnosis lacks theoretical precision.
Therefore, Voegelin's gnosis can, according to the criticis, hardly serve as a scientific basis for an
analysis of political movements. Rather, the term "Gnosticism" as
used by Voegelin is more of an invective just as "when on the lowest level
of propaganda, those who do not conform with one's own opinion are smeared as
communists.”
That is, “smeared as gnostics”,
as I heard one of his followers smeared Carl Jung, based on Voegelin’s readings
of second hand texts on him (as contrasted to e.g. Jordan
Peterson’s practice as first hand reader of
original texts). Until further notice I assume that the Jung's attitude
mentioned above is motivated by his psychic inclination to watch upon the unique (psyche)
instead of "playing God" or suffering an “Ego inflation” by imagining
oneself as understanding mathematics seen as God’s language, and searching
general "laws" of nature where the human being himself tends to be
“abstracted from” or is regarded as only an object of an undefined or
pantheistic "Nature". A concretization of these thoughts is suggested
by problems and the history of debates on the world’s first societal
introduction of personal
identification number - PIN in
Sweden (as a number = “John Smith”), followed
by national
identification numbers all
over the world as I
explain in my essay on The
Meaning of Man-Machine Interaction. It
is meaningful to remember the practice of tattooing a number on the skin of
prisoners in Nazi concentration camps, followed today by the increasing use of
PIN’s, not the least for (who’s?) control of the
population by means of face recognition systems and biometric
identifiers. All
facilitated by alleging a struggle against “terrorism”. And all this while
never reflecting upon the meaning of or relation between identification
and individuation, and
never reflecting upon the phenomenon, in certain corrupt political regimes, of
governmental production of false “identification” documents, including vehicle
registration plates.
When faith and allegiance is rested on an assumed Democracy and technology
instead of on God, then the unavoidable failures of democracy imply a
dependence upon anonymous human power whose policing of citizens offsets the
loss of judgment caused by the computerized technological logical bypass of the
network of multiple human judgments.
The extension of these problems reaches
the import of the whole issue of my text on the consequences of the
computerization of society which follows the conclusions of the present essay,
and that I rhetorically named Computerization
as Design of Logic Acrobatics but
somebody else could have called On
the Digitalization of Society.
It is the case of late science dominated by people who are especially
highly proficient in applying the "small part of their brain"
(really, their psyche) dedicated to mathematical-logical manipulations, and
consequently develop extreme self-confidence if not outright arrogance that
guides them to worldly managerial or professional success.
This phenomenon seems to be common particularly in the area of computer
science as exemplified by computer scientists such as Herbert Simon, or lately in
the case of luminaries in climate research and global warming, such as climate
research such as Hans
Joachim Schellnhuber. It is gift that also enhances the capability to win
debates cheaply by reducing complex systemic issues to oversimplified linear
logic sequences of computable apparent "arguments" (most often using
undefined concepts) as I illustrate in two other texts on "debates" and on "climate
change and global warming". Nevertheless, depending upon the particular
personality of the thinker, it can also enhance the capability to unravel
complex issues to the point of legitimately bedazzling the reader or the
listener. It may be the case with a remarkable essay by Olivier Rey on Que faire des différences? [What to make of the differences?]
where differences concern also those between citizen and foreigner, or man and
woman, a sore point in the issue of equality or of radical feminism.
After further considerations that include the drift from defective
language to a consequent philosophy based on a supposed meaning of language
Brouwer foresees a rude awakening in front of perceived deficiencies and
contradictions or a flight from the "world of intellectual perception with
its man-made laws" or to the highly acclaimed "science" [sic,
within quotation marks.] His diffidence concerning language is echoed by my own
considerations about the difficulty if not impossibility of debate in Information
as Debate, touching matters of major importance concerning
ethics and politics of science. This type of insights motivates Brouwer to move
further into the four last extensive chapters 6-9 of his book with the titles
of Immanent Truth,
Transcendent Truth,
The Freed Life,
and Economics. In
doing so he can be interpreted as entering gradually into the domains of
"mysticism" where the term, however, must not be understood as in the
popular daily secularized verbiage of modern Western languages.
Chapter 6 is dedicated to cultural criticism in those forms of human
enlightenment and communication beyond the aforementioned limitations of
language, as evidenced by worldly arts and literature, which are in my view
erroneously taken by "Nietzscheans" like Heidegger and Alain
de Botton as estheticist tools for a
"religion for atheists": art as religion. The subsequent chapters 7
to 9 take the necessary further step into the forms represented by religion or
mysticism, a mysticism understood critically as, for instance, in Harold
Coward's book Jung and Eastern
Thought (1985, chap. vii) and echoing some of the most serious
currents of Western philosophy such as in the treatment of "Quietism" and the
contrast between Leibniz and Schopenhauer as depicted in
Émilienne Naert's Leibniz et
la Querelle du Pur Amour [Leibniz
and the Dispute of Pure Love] (1959.) In the chapter on Le Quiétisme
vu par Leibniz et Schopenhauer [Quietism seen by Leibniz and
Schopenhauer], pp. 232ff., the descriptions in the text confirm the proximity
of Brouwer to Schopenhauer's thought. The relevance of the latter for the
philosophy of psychology is indicated by Carl Jung's references to the latter,
which take almost as much space in his Collected Works' General Index (volume
20) as the number of references to Plato. It must be
noted that the complexity of the background of the question requires, for a
proper interpretation, the kind of theological knowledge that is advanced, for
instance, in Fr. Raymond Gawronski, S.J. Word
and Silence (1995) as noted also
in my related article
on the hopelessness of communication in debates.
There is no need for me to go deep into the mentioned last chapters 7 to
9 that need no further explanations beyond the meaning of mysticism, and are
found in the original book in question with the text available on the net in
pdf-format at the link already
specified earlier, above. They are already summarized in the likewise mentioned
introduction to and overviews of Brouwer's book that are the best and most
detailed source for understanding his thought, such as Walter P. Van Stigt, Introduction to Life, Art
and Mysticism (1996, pdf).
The main necessary observation is a reference to a part of chapter 6 that deals
with the repeatedly criticized and misunderstood treatment of womanhood, or
Brouwer's supposed "misogyny". I think that the a
key paragraph for an in-depth understanding of what Brouwer is expressing is
the following:
There is a balance between man's burden of guilt and the burden of labor and toil imposed on him. A similar balance is found between woman's wantonness, her inborn capacity for karma burdening, and the measure of femininity which this world offers in temptation. In a world of humble acceptance of given karma there would be no women.
I sense that these thoughts are the author's probably unconscious
attempt to capture the theological meaning of the biblical "original sin", made by
a man with superior intelligence who was struggling, in terms which later would
be conceived by analytical
psychology, to defend himself from a dangerously close contact
with his anima. The latter,
being unconscious, was then projected into womanhood, i.e. "women
considered collectively". It is remarkable that Brouwer reached so far and
deep in his analysis at the turn of the century, without detailed theological
knowledge and at a time when analytical psychology was still being conceived.
This was probably made possible by his understanding and application of
Christian mysticism and Eastern thought. His shortcomings in this respect
probably caused the ultimate failure of Brouwer's program for a supposed
ethical pure mathematics. The failure of the program led among other things to
the purely instrumental (and commercial-industrial) mathematics of algorithm
theory for computers (cf. the reference to Paolo Zellini above). Nevertheless Brouwer's shortcomings appear to me as
incomparably milder than the misandry or present ongoing and tragic
misunderstandings of masculinity corresponding to the animus. This goes on in
branches of modern feminism, as I suggest in a
writing about the case study of a renewed glorification of
SCUM - "Society for Cutting Up Men", and it is a feminism that is
closely related to the spread in Western societies of a sort of feminization
that critics denominate as cultural
Marxism and political
correctness. An unraveling of the socio-psychological implication
of these problems will probably necessitate a study and development of the
insights of the previously mentioned book The
Myth of Analysis by James Hillman.
We should not forget, however, that for our purposes of connecting
Brouwer's criticism of science to the embodiment of mathematics and logic (in
computers) the most relevant aspect seems to be the phenomenon of projection in science,
mentioned above in the context of his supposed misogyny. While it can be said
that modern science consists in differentiating the observer's own projection
into nature (cf. astrology and alchemy) from what it is "actually
there", the reader will have observed in the present text up to here that
the term projection used by Brouwer appears in several forms such as projection
into nature of mathematical structures, as (synonymously) act of
externalization, projection into reality, projection of phenomena on measuring
instruments, or mathematical projection. This is also related to the question
of mathematical-logical
isomorphism with "reality", that in my view is the object
of complex misunderstandings as exemplified in a dissertation by Marius Cohen
on Reality
as a Mathematical Structure, in contrast to
ambitious attempts as by Krister Renard in his essay on Predicate Logic and on (in
Swedish) mathematics with a
corresponding video
of a lecture (in English). This will be the object of a future
section.
Continuing our concern with chapter 6, should be noted that it is
dedicated to a rather detailed analysis of various artful, often false, forms
of communication beyond science and ordinary language, as in literature of
epics, comedy and tragedy and music addressing the illusion of time, and visual
arts (that at the time, without multimedia) addressing the illusion of space,
in order to convey what the author calls immanent truth. It is often not
perceived that such an idea has already made its presence felt in the
ramifications of computer science. It has happened, e.g., in the fashionable
recourse to musical "improvisation", or
"architecture" and "design" as a source of inspiration in
the study of applications of late computer technology or multimedia, prompting my
own attention in papers dealing with the Kantian classification
of arts as well as his critique
of judgment.
Chapter 7 on "transcendent truth" follows the failures of the
search for immanent truth in chapter 6 and is said to represent the Kingdom of
God. It also represents Brouwer's courageous confession of the possibility of
moving from the daily world to his realm of faith and his distancing from the
world. This world today, one hundred years after his writing, is explicitly and
visibly dominated by the dogmas of religious secularization. It purports to
show the apparent impossibility to live a pious and genuine, intransigent
Christian life in a modern society where "God is dead" and all
transcendent truths such as in music, visual arts, literature and poetry are
submerged in contrafacts or fake products. The only solution would be a
commitment to sheer mysticism that relinquishes the hope of language
communication. As Brouwer writes, adding later quotations by the mystic Boehme
and the Bhagavad Gita (that,
together, with Hindu and Chinese philosophy, also is symptomatically referred
to by West Churchman in his
The Systems Approach and its Enemies) such a commitment offers the
link to our original question of computation and systems:
It treats the questions posed by metaphysics, such as immortality, freewill, the meaning of art and religion, and the foundations of morality, as riddles hatched by the intellect; in doing so it removes all mystery and yet shows the impossibility of solving such questions by reasoning.
Brouwer could have added questions posed by Chapter 8 on "the freed
life". It seems to depict the final result of above commitment to
mysticism: refraining from debate or the preaching the truth, in terms that
recall the commitment to quietism mentioned above, apparently implying also
care in contact with society's current political correctness:
For a man therefore life will move toward absolute solitude [...] he listens carefully and waits patiently for the revelation of inner contradictions of that intellect [...] begins to resent all his links with society; he is forced to exercise extreme care in human company [...] disturbing influences will only help his patient move away from human society...
Brouwer's style of writing shifts thereafter towards poetry or
description of a dream that is sheer mysticism and, for modern understanding,
requires the help of depth or analytical
psychology, especially in terms of the meaning of
"introversion" or, more specifically, thinking-introverted attitude
(as popularly
described on the net) as related to the process of individuation which required
a plunge into Carl Jung's Collected Works, mainly vol. 6 on Psychological
Types.
Ultimately, one could say that the coupling of the critique of language in
chapter 5 to the references to mysticism in the following chapters 6 to 8 may
resume the essence of the "Word" and its connection to philosophical
and theological "Logos", as famously outlined by Thomas
Aquinas in the first lectures of chapter 1 of the Commentary on the Prologue of the Gospel
of St. John (recently
translated into Swedish as Kommentar till Johannes-Prologen, (Svenska
Katolska Akademien, 2015.)
Chapter 9, the last one, on "Economics" refers to "one
more evil", describing the "free life" in detachment to a fallen
world, in terms that most readers will most probably label as pessimistic and
misanthropic. It can also be understood, however, as a extremely blunt interpretation of the Bible's
"fall
of man", as the biblical interpretation of Genesis chapter 3, combined
with a questioning and mocking of modern man's ambition to rescue this world by
means of economic (profitable) technology and own concepts of justice. The text
is hard to grasp against our background of modernity but, for instance, the
concept of a ridiculous justice pending towards the "socialism" of
Brouwer's time, has its counterpart in Blaise Pascal's Pensées (examples: pages of
the original manuscript 69, 165, 169, 453, or, in general, the section V in the
French edition, Nelson Éditeurs, 1955. English translation with introduction by
T.S.
Eliot, at project Gutenberg, here, see Index,
"justice" and "injustice".)
Special importance for the purposes of this present paper of mine about
computers is the example of Pascal's scientific interest as mathematician and
physicist who defended the scientific method and designed a mechanical
calculator as precursor of computers. As he explains in the
preface of the Pensées, however, he relinquished these interests in favour of the perceived premises for his scientific and
engineering work, acquiring the posthumous status of "Christian
philosopher". Throughout Étienne
Périers preface to the Pensées' French edition of year 1955, appear
considerations that recall Brouwer's extremely quietist thoughts, which
permeate this last chapter 9, also recalling the fundamental Christian message
of Thomas à Kempis' The
Imitation of Christ.
COMMENTARY
ON "LIFE, ART, AND MYSTICISM
The Italian translation of Brouwer's book surveyed above includes an erudite
commentary (not yet translated from the Italian) that borrows particular
interest from the fact that it is written by the previously mentioned numerical
analyst, and professor of mathematics Paolo Zellini. He is
widely known in Italian cultural world for books beyond the
narrow understanding of his discipline, relating to the history,
philosophy and essence of mathematics, some of them having been translated into
other languages including English and German.
Zellini starts surveying Brouwer's initial motivations for
the study of mathematics, as they were related to his religiosity and early
commitment to the Remonstrantse Kerk. He sees that
Brouwer perceives that faith requires the historically famous and controversial
sacrifice
of the intellect. Brouwer perceives that the so-called intellect (that
Jung would criticize for being equated to the rationality of the ego,
disregards the whole psyche) deserves suspicion because of its failure in this
human world, a failure that we today would relate to cultural impact of
technology and environmental issues such as climate change. This perceived
failure, apparently disregarding the "success" of science, is
exemplified by the corruption of instrumental science put at the service of
commerce and industry, and, in general, of petty human desires residing in the
"head" as site of this undefined intellect. Such insights would have
led Brouwer to a basic ascetic and solipsistic, misogynous vision of life that
was to be reflected in his lifelong way to conceptualize and do mathematics.
For my purposes here it is important to note once again the absence of a
discussion of what is to be meant by intellect and its seat in the head that
today would be most probably equated further to the brain, in the spirit of
what has been critically called for brain mythology. It is a term that was duly
considered by Jung himself on several occasions (especially in his Psychological Types, CW6,
§516) and it returns nowadays in other purely scientific contexts such as in
the journal Brain Structure
and Function. It reminds that neuropsychology presupposes
informatics in terms of understanding of what data and information is as well
as understanding of the relation between (space?) structure and (time?) function such as presented
in West Churchman's The Design
of Inquiring Systems (chap. 3, pp.43ff.), a work that indirectly introduces also the
relevance of Carl Jung. Occasionally some few of these
aspects appear in critical articles such as in Jorge Ibáñez, Is
the brain a computer?. All these
considerations seem to be ignored in "strategic neuro-research" or "computational
brain science", as suggested in modern or postmodern
mathematical and biological dreams and speculations recalling brain mythology,
while forgetting the historic lessons of the scandal of “scientific” lobotomy. It is a worldwide network also exemplified by key
names such as Florian Markowetz and it can be
seen as sort of trendy computerization of old basic ideas of mathematical
biology into "computational biology" that merges with the powerful
rhetoric of "artificial intelligence". The press reports that
computers will be developed with an "inbuilt
own will", while I have met engineers who with support of
certain philosophers deny that humans themselves have a free will. This is a
field originally expressed by Nicolas
Rashevsky, and developed later by his followers within a
mathematical-logical concept of systems diverging from Churchman's ideas and
represented by Robert
Rosen and Herbert Simon. Simon, in
particular, is an excellent example of how a mathematical mind can appear as a
polymath or type of renaissance genius by mathematizing basic knowledge in
several different fields of knowledge. It is one example of the dazzling effect
of mathematics (and logic) that today is experienced in its embodiment in
computer technology.
In Zellini's interpretation Brouwer's
perspective is cast in a sort or apocalyptic dress that makes it natural to
accept the basic impossibility of changing or improving the world. It opens
only the ascetic option of silencing desires and sensations that imprison man
in the logic of an alienated world. Zellini remarks
vividly how these thoughts of Brouwer embarrassed his entourage who tried to
silence them, starting from the publication of his dissertation and up to the
posthumous publication of his collected works. This reminds me of society's
attitude to analogous peculiarities such as Isaac
Newton's or Carl Jung's misunderstood
interests for alchemy and, in general, for what is nowadays seen as occult studies. In my own
experience I met the same attitude in my function as faculty opponent according to
the canons of a Swedish
doctoral dissertation. The event, concerning the relations between computer
science and gnosticism has been well
documented and available for the readers' understanding the dynamics of such
attitudes.
Brouwer's quotations from intellectual signposts such as Meister
Eckhart, Jacob Böhme and Bhagavad Gita were considered embarrassing, despite of
their portrayal of what Zellini denotes as the
climate of philosophical introspection that mathematics was going through at
the transition between the 19th and 20th centuries. It was a matter of
contrasting a specifically mathematical thought and the nature of the intellect
and human will, as it was being done for decades in Europe because of
uncertainties and obscurities raised by research on the logical foundations of
number and mathematical infinity. Brouwer's theses of Life, Art and Mysticism were
kept unchanged in his more mature and creative thought during the following
decades. They influenced Brouwer's choice of theoretical presuppositions and
helped to clarify the concept of
algorithm that supports all informatics and scientific calculus
since the design of the first big digital computers around the fifties. Zellini sees as equally important his so called Fixed
Point Theorem that today is a necessary presupposition of all
computational and applied sciences.
Significantly, Zellini concludes a subchapter
of his essay in the Italian book translating Life,
Art and Mysticism musing over that Brouwer would not have welcomed the
forthcoming applications of his achievements that paradoxically both
implemented and at the same time betrayed his deepest intentions. In Zellini's words: "But this surely was not the only
occasion in which the unforeseeable course of history ended in overthrowing the
meaning and purpose of a project." My own reflection upon that is that
this overthrowing or at least the illusion and delusion are a hint about the
defective psychology if not also theology and consequently politics underlying
Brouwer's thought. A symptom may also be the paradox implied by his obvious use
of his own intellect outside mysticism in order to discuss and counter an undefined or misunderstood intellect in the practice of
mathematics.
Zellini continues, however, showing how Brouwer can be
understood as working out his own intellect in order to free it from those
dimensions that chain it to the external world that is governed by the causal
links of necessity and evil. In this Zellini performs
a tour de force by adducing Plato (e.g. Phaedo, 83 a6-b1), Jakob Böhme, Meister
Eckhart, Simone Weil, H. de Balzac, Bhagavad Gita, Orphic tradition (on the
relation between Time and Necessity), Émile Boutroux,
Luther's thought, Augustin of Hippo, and coupling to Hebrew mysticism as well
as to Hegel's philosophy. In this respect Zellini
treats Brouwer's process of developing mathematics in a
analogous way to how Carl Jung treated the development of psychology, i.e.
taking into account the historical records of West, without explaining away
philosophy, apparent "occultism", and religion as background of the
obscure modern, supposedly scientific "intellect". That is: it is a
question of taking in account the concerns and efforts of past generations as
much as today's environmental thought about e.g. pollution and climate change
in supporting claims to take into account the lives of future generations.
Zellini recalls that it is the effort of interiorizing basic
human thought that motivates Brouwer to ground mathematics upon the intuition
of time, suggested
by Immanuel Kant in his Critique
of Pure Reason (p.91, B: 153-156) to be the main condition for the
intuition of ourselves, of our internal state. I suggest that those who want to
muse upon Kantian bases of Brouwer's mathematical thought direct themselves to
the mentioned Critique in the section on
the Method of Transcendentalism, chap. 1, section 1 on The discipline of pure reason in its
dogmatical use (p. 465ff., esp. 471, A:721-725; B:749-753). It is
the intuition of time that when leaves the interiorizing effort and relates to
the intuition of space in the observation of objects in the real world raises
sets of sensations related by an intuition of (chains of) causality. The
extension of the causal nexus into various sets of sensations supplies a
mathematical theoretical repertory of sequences of data that only need the opportunity of being projected into the
real world. It is this projection that justifies the apparent
success of applied mathematics, which, however, programmatically ignores (until
further notice of new problems) whatever is extraneous to the chains that
happen to have been observed and considered. This requires (my note) the
so-called control of the so called "environment" if it is going to
"work", and where such environment includes forced human behavior
including its operation of machines and computers where uncontrolled or uncontrollable
aspects (of behavior) are called "errors". They are then said to be
due to the "human factor" as seen and defined by the implicit
occasional observer who happens to have the interpretative prerogative. All
this includes also the phenomenon of elders having to buy and with the help of
children to learn to use "survival kits" in the form of mobile phones
in order to manage details in their daily lives.
Following the post-Kantian developments with new non-Euclidean
geometries (Bolyai, Gauss, Lobachevsky), Zellini
remarks that the human intellect is organized for the elaboration of various
geometries, independently from our daily empirical reality. Brouwer removed
from the empirical space all connotations of mathematical necessity.
Mathematics exists independently from any external experience and the latter is
completely independent of mathematics. Consequently
mathematics as well as geometry with its Cartesian reduction to arithmetic is
independent of externally perceived Euclidean reality. Mathematics is best
developed on the basis of a space-independent inner reality and on a willful action deployed
in time, displaying succession
as the form of the principle of reason in time. Numeration and calculus would
be brought back to successions (cf. algorithms, below) that could be maintained
free from externally raised necessity or fear, free from ambition and desire
and from the ballast of real object. Compare the symptomatic paradoxical
attraction exerted in computer
addiction and especially by computer gaming [my note]. In all this
sort of play and its mysterious oscillation between internal and external, Zellini emphasizes Brouwer's attribution of it to the role
of the whimsical free will, and its mysterious oscillation between the knowing
and acting Ego, internal and external, self-conscious or seduced by power. In
the context of will, Brouwer's conceptions seem to be influenced by the
philosophy of Schopenhauer and I find it interesting for my purposes here to
note that Carl Jung's psychology in its unraveling of the concept of will gives
due consideration to Schopenhauer: in Jung's collected works' General Index
(CW20) there are more than 80 entries for references to his work.
For illustrating the question between externa reality and mathematics it
is appropriate to intercalate in this review of Zellini’s
book a quotation from his La dittatura del calcolo, (2018)
[The dictatorship of calculus], pages 87-89. Milan: Adelphi. (My trans. based
on DeepL):
With algorithms we also witness that systematic
reversal of means into ends in which Simone Weil and the famous mathematician […]
Jan Brouwer had seen, from different perspectives, the truest cause of our
existential malaise. The algorithm is also a source of power, like gold,
weapons or machines. Not so much a neutral instrument subject to our will as an
autonomous bearer of a credibility that borders, at times, on divine-like
veracity. As the summum bonum of
capitalist ethics of which Max Weber spoke - "the gain of money and more
and more money, stripped of all eudemonistic or merely hedonistic ends and
thought of in such purity as an end in itself" - so too, the bearer of a
similar purity of purpose, is the algorithm, magnified by a scientific
importance that extends from theoretical foundations to the most unpredictable
material applications, from the simplest digital operations to the boundless
dimensions of large-scale computation.
The aura of prestige of the algorithm rests on the
objective reality of its applications as well as on the myth fueled by the
abstract and universal power of mathematics, in which Dedekind had placed the
most subtle and ambitious abilities of our thinking. One could repeat here
words already used by George Mosse in his analyses of the dictatorships of the
20th century: "Myth and reality operate together," and between myth
and the real world there is a "dialectic more materialistic than the
Hegelian dialectic," albeit irreducible to the confrontation between
forces or social classes, destined to strengthen both.
The myth might now be summed up in the formula aeì o ánthropos arithmetízei, which extends from the world to the human
being the famous sentence that has spanned centuries of philosophy in the West,
and which Dedekind did not fail to add in support of the thesis that the
mathematician is akin to a demiurge. That formula can now be transferred by
weight to the computer, of which as well it can be said, not incorrectly, that
it operates with numbers. And it is then the sharing of an arithmetic thought,
inherent in the computer as in the human being, that prompts us to delegate to
the machine not only our calculi, but also the innermost reasons for which they
were devised.
The basis of the algorithm is mathematical and purely
physical in nature, because it cannot disregard the calculator and an effective
computational process. However, computational efficiency is measured,
predominantly, in mathematical terms. Algorithms for recognizing humans or
vehicles, as for countless other images, are based on machine learning
processes: a neural network is trained to recognize certain figures, giving
answers that are compared each time with the exact ones. It refines the network
by degrees-this is what learning consists of-thereby progressively reducing the
error, that is, the gap between its wrong answer and the exact one. [...]
Yes, please note “the reversal of means into ends”,
“theoretical foundations…to the most unpredictable material applications”,
“objective reality …myth fueled by the abstract and universal power of
mathematics”, “myth a reality”, “thesis that mathematician is akin to a
demiurge”, “delegate the machine…the innermost reasons for which they were
devised”, “effective computational processes”, “answers…compared with the exact
ones”.
But what and why is that “myth” beyond Carl
Jung’s conception in analytical psychology? What is
“objective reality” related to myth (as problematized
in quantum physics)? What is (computational) “efficiency” compared with the “effectiveness”
(of the computational process)? What and
whose is the “exactness” of the answers (compared with
precision and accuracy, as in my doctoral dissertation?
Leavin now aside this intercalation, Zellini
in the earlier reviewed book repeatedly emphasizes Brouwer's distinction
between internal and external by means of the original intuition of
"bi-uniqueness". It consists in retaining a first sensation together
with a successive one in order to set up a first distinction between present
and past. Zellini also reminds that the repetition of
this mechanism stands at the basis of the concept of iteration and,
consequently of algorithm, adducing a relevant reference to a classical paper
by A.N. Komolgorov and V.A. Uspensky On the definition of an algorithm (American
Mathematical Society Transactions, 2nd series, XXIX, 1963.) For our purposes
here, and for an understanding of internal-external with respect to the
interiority of uncorrupted thought, it is also important to recall that the
iterative application of an algorithmic operator presupposes the operator as
well as the applicator, i.e. a stability or permanence that is a sort of
"selfhood". Or, as Zellini expresses it,
there is an affinity between Brouwer and idealistic
philosophy. It was evidenced through the mediation of Hermann Weyl (cf., inter
alia, his Philosophy of
Mathematics and Natural Science) and expressed by Novalis inasmuch
"Selfhood [Selbstheit] is the fundament of all
knowledge since it is the fundament of permanence in what is changing."
According to Zellini, Brouwer seems to have equated selfhood with the
constructional activity of the mathematical (mathematician's) mind while
proving the "existence" of mathematical entities, and thereby
invalidating the logical principle of the excluded
middle. In general Brouwer was proving that the
logical principles in current use cannot be the fundament of truth or of the
discovery of truth. We cannot apply logic in a world that is too complex to be
dominated by logical laws. In this way Brouwer's criticism of the intellect
became a circumstantial criticism of logic. In that context Zellini
also shows a criticism of the mathematical continuum (such as in set
theory or in topology) that becomes
more "digital" and ultimately betrays Brouwer's own intentions.
Ultimately it leads, under the pressure of the military and industrial
establishment, to the abandon the personal constructional element and allowing
itself to be automatized. I wish to complete one of Ludwig Wittgenstein's
sentences inspired by Brouwer and quoted by Zellini: "Mathematical logic
has completely perverted mathematicians' thought, letting go for structure of
facts what in reality is a superficial interpretation of the forms of our
everyday language." I wish to add that it is this fake "analysis of
the structure of facts" that we nowadays gradually embody into the
software of computers in our computerized society.
In following his own thought further, Zellini
(p. 176) adduces Weyl's interest for the subjectivism of G. Fichte's philosophy
that problematizes what is external vs. internal to the observer, recalling in
me as reader what in Jung becomes the relation between the Ego
and the Self. Fichte in his
The Vocation of Man exposes the principle that exteriority is only
the mode in which things get articulated in our conscience.
All these considerations and Zellini's further
discussion of the concepts of mathematical continuum and infinity indicate
their import in set theory and the attempts to order reality by means of
enumeration. I see this as a reminder of the concept of mathematical systems
and, further, the elaboration of difference between them and the concept of
system itself as exposed by Churchman in his book The Design of Inquiring Systems. It includes a
discussion between what is internal
and external. This
is done in terms of a problematization of the concept of input (p. 107) and,
ultimately, by means of references to Carl Jung (p. 244f., 261-263, 272, 277)
and his conceptualization of the psyche and the Ego vs. the Self. Some
clarification of the references to Jung can be found in Churchman's later work
on The Systems Approach and
its Enemies (p. 130ff.).
My conclusions from Zellini's valuable
commentary of Brouwer's work is that it indirectly
uncovers details of the reasons for its paradoxical failure with regard to his
deep personal commitment - and this despite its important intuitions about the
apparent success of mathematics in science in general, and computer science in
particular. This failure reveals that the flight from a misleading causality
cannot be resolved by a flight into misunderstood internality. According to
developments in psychology conceived after Brouwer's formative years, the so called internality can also suffer from irruptions of
"external" forces that pervert the quest
for the Self.
If we are to complain for the complexity of the issue, it must be
understood that it is complex
and the fault is ours, in our wishful thinking that it must and can be
philosophically simplified mirroring the military-industrial, social-engineering, techno-science, and technostructure frames of mind
that often unconsciously dominate our secularized big science culture. To give
a taste of what this all is about I will finally take the following excerpt
from one comment in Amazon's presentation of
Zellini's translated book A Brief History of Infinity, an infinity that
today is perceived as such in the computerized world-wide-web but is supposed
to be solved by means of an unknown algorithmic power.
"Paolo Zellini's sources are wide ranging, almost intimidatingly so. We readers encounter the philosophical thoughts of the Platonists, Aristotle, the Pythagoreans, Anaximander, the Chaldeans, Duns Scotus, St. Thomas Aquinas, Giordano Bruno, Nicholas of Cusa, Raymond Lull, Descartes, Leibniz, Goethe, Kant, Hegel, Russell, Simone Weil, Quine, Popper, Wittgenstein, and many others. Similarly, on the literary front we meet Cervantes, Kafka, Borges, Musil, and others. Mathematicians are prominent also. Zellini discusses the provocative ideas of Descartes, Newton, Leibniz, Dedekind, Poincare, Cauchy, Weierstrass, Bolzano, Frege, Du Bois-Raymond, Cantor, Russell, Whitehead, Gödel, Von Neumann, Zermelo, Skolem, Brouwer, and many others."
To appreciate Zellini’s valuable intellectual
ambitions I recommend to perceive the difference between his and other's range
of interests and corresponding possible insights, in the alternative approach
represented by Rudy Rucker in (on the net) Infinity
and the Mind: The Science and Philosophy of the Infinite (1982-2005),
and published by Princeton
Science Library (2004).
Several years after writing the above in the first version of this
present paper of mine I happened to read the Italian original (published 2016,
whose pages I refer to) of Zellini’s later book The Mathematics of the Gods and the Algorithms of Men:
A Cultural History (2020). It
convinced me that Zellini did not understand the most
important in the whole Brouwer, and in particular his earlier quoted:
They either talk at
cross-purposes or each builds his own little logical system which lacks any
connection with reality. For logic is life in the human brain; it may accompany
life outside the brain but it can never guide it by virtue of its own power. Indeed,
if there is a harmony of will, logic may well fall by the wayside ...
I think that this happens because Zellini, relating logic and mathematics,
reaches back more than 2000 years in selected parts of philosophy but never
enters into the conquests of psychology or what “brain” stands for, psyche,
intellect, reason, will, perception, feelings, love and whatever. In fact, he
mentions the most important philosophical and theological term of logos (pp. 26, 46, 58, 78, 81, 83), but
not a single time the often associated term of eros as in Neoplatonism and Analytical
psychology. And despite many references to “gods” never with
reference to meaning of the meaning of logos
in Christianity as I remark in my
essay on theology. Despite Zellini’s
reference to the “laws of thought” (p.156), and to Purusha (p.44) that are
extensively discussed in analytical psychology, Zellini
sees mathematics as only related to physical reality (never entering, however,
into the morass of quantum physics), but having a
reality of its own that extends to its use even in social science represented,
however, by (unmentioned: mathematized) economics well beyond econometrics (p. 169). This
limitation is never reflected upon, not even when touched upon as in the
reference to Henri Bergson (p.137). I see
the case of Zellini as an example of the tragic
limitations and failure of a brilliant mathematical mind in the passionate
search for ultimate truth, and at the same time as an example of the failure of
democracy in its impotence in evaluating the import of modern mathematized
science and technology in human affairs, such as in the “game theory” of the cold war or in the
mathematics of computer simulations of climate warming.
This section is based on Miriam Franchella's article "On
Brouwer and Nietzsche: Views about Life, Views about Logic". History and Philosophy of Logic, 36:4,
367-391 (2015). The article consists of a comparison between Brouwer and
Nietzsche regarding in their views in five respects: attitudes to life,
science, mathematics, and logic. It relies heavily on original works including
several other studies of Brouwer and Nietzsche. I will not dwell more deeply
into the matter except for stating my conviction that the whole complex issue
is related to the historical division of
logic between formal and material logic.
Nietzsche is seen by Franchella as well aware,
as Brouwer is, of the suffering in human life. Nevertheless
he declaimed a joyful positive conception of it "with an aim of enhancing
and defending the disruptive nature of life in its originality and creativity,
from those who wanted to downgrade it to mere survival, scheme, rule." He
would observe mathematics and science including physics within this
life-promoting and survival framework. Because of this, and differently from
Brouwer, Nietzsche sees it important to dominate the world. For him it is
important that the "intellect" sets a "subject" before
"objects" that are generated or named by its metaphors, connecting
them to one another with causal links. Metaphors mediate between physiological
perception and imagination, from image
to sound to word. Language maintains a useful yet fictitious
"reality" in daily life, (that for Brouwer consisted in maintaining
two or more wills cooperating in a single direction.) What we perceive is only
some part of the continuous flowing of reality. "Causality is appearance.
Our belief in causality is due to our faith in strength that we experience when
we do something, yet force moves nothing; the force we feel does not 'put our
muscles in action'. Causality is only created by thought, which introduces
constraint in the process of succession."
So, Nietzsche is seen as criticizing the alleged truth of science in a
way that has similarities but also differences with respect to Brouwer.: the
scientific world is made up of "fictitious entities interrelated in a
fictional way for the sake of survival",
while truth (the thing-in-itself) would be the absolute, the non-perspective,
the non-anthropocentric. For Nietzsche the content of science is an
epistemological lie regulated by society, and such knowledge or lie, like
mathematics and logic, is finalized, the result of perspectives. In its claim
to truth science is a faith, and as such, it can be likened to religion. From Franchella's relate it seems obvious that Nietzsche abhors
religion mediated by priests. I see that he rather adopts science itself as his
"religion" where survival
(until further notice?) is his sort of god. I am
tempted to regard postmodern or smartly denominated "non modern"
(with the purpose to escape critics of postmodernism) scientific
intellectualism as being influenced by these Nietzschean thoughts, as
represented, for instance in France, by studies in the tradition around Bruno Latour, about the
social construction of science. It would explain the puzzling de-emphasis on
the question of truth in science and on normativity, on why and how to do or
not to do science, in favour of a dazzling brilliance
in aestheticizing descriptivity, celebrating
creativity and survival in the form of career success. It is here we find the
basic difference between Nietzsche and Brouwer.
Nietzsche is seen as not devoting much attention to mathematics. What is
interesting is that for him it was based on the concept of the "Ego"
which is configured as a unity, and on the existence of identical objects. This
is so because Nietzsche as quoted from this Posthumous
Fragments notes that we have borrowed the concept of unity from our
"I" concept, our oldest article of faith which, as seen earlier in
this text, has been definitively questioned by later analytical psychology. And
in his Human, All too Human: "The invention of the laws
of numbers is made on the basis of the original error that there are several
similar things (but there is in fact nothing equal), at least that there are
things (but there is no 'thing'). The presumption of multiplicity always
presupposes that there is something which manifests itself in many instances,
but the error here is already being felt, already there are beings or units
which do not exist." Nietzsche is quote again stating the
our feelings of space and time are false for they lead to logical
contradictions, despite of the results getting perfect certainty in their
relationships: "One can build on them - until the last end, when erroneous
basic assumptions get in contradiction with the results, e.g. in the theory of
atoms." [My translations from the German quotations.]
Not having read Nietzsche's whole original text and not fully
understanding the reasoning behind all this, I happen to think about quantum
physics. Several physicists colleagues of mine have
confessed that it "works" but that they do not understand it and
believe that nobody really understands, whatever understanding really means. A
popular review that is appropriate for the general reader of this paper of mine
is found in "Relativity
and quantum mechanics: the battle for the universe" in The Guardian, 4 November
2015. An overview is also to be found in sections of Wikipedia's entry on
"Physical
paradox" where there are references about piecemeal
ad-hoc mathematical manipulations "conveniently sidestepping the
philosophical issue of what actually occurs". So, truth has been relegated
to philosophers or, rather, to conflicts between philosophical schools in the
name of the idea that "it works", possibly meaning that e.g. nuclear
bombs really explode, i.e. far from the scientific, pragmatist meaning of
"implementation" that
depends upon mutual understanding.
Franchella goes on noting that Nietzsche extends the earlier
mentioned insights to geometry that "is also based on an untruthful
leveling of sensory experiences: we introduce them into reality to make it
static, predictable and controllable so that it becomes reassuring" or, in
Nietzsche's own words (still in Human,
All Too Human): "The same is true of mathematics, which would
certainly not have arisen if one had known from the beginning that there is no
exact straight line, no real circle, no absolute quantity measure in
nature."
So the difference from Brouwer can be inferred by what
was shown above about his reliance on Kant's view of foundations of
mathematics, but like Brouwer Nietzsche is seen concerned about the morality of
mathematics as part of human knowledge. Nevertheless
it is not judged so negatively since, like science and logic, it requires
honesty and discipline in introspection in its practice, and is a useful lie which is
regulated by (a trusted!? - cf. Marxism) society, becoming acceptable to be
transmitted as truth. What I do not see discussed is the problem of the
endorsement of utilitarianism that is
implicit in the appeal to usefulness.
Regarding logic Nietzsche notes that since its Aristotelian conception
it assumes the identity of (self-identical) objects, that things dealt in
logical sentences are or remain equal in the course of reasoning and
application of its conclusions or, as I understand it, that they are stable
even if we perceive that they are in continuous change. This means that the
will to logical truth can only be carried out after a fundamental falsification
of all happenings. Nietzsche sees that from this follows that there is an
"instinct" which is capable of both means, first the forgery and then
the implementation of a point of view: logic does not come from the will to
truth.
I see the mention of "instinct" as an implicit reference to
concepts that would later be developed in analytical psychology, justifying
that references to Nietzsche occupy more than a whole page in the Index volume
(CW20) of Jung's collected works. This is emphasized further in Franchella's quoted German text: "The course of
logical thoughts and conclusions in our present brain corresponds to a process
and struggle of instincts, which in themselves are all very illogical and
unjust: we usually only experience the result of the struggle, so quickly and
so hiddenly is this ancient mechanism now playing within us." My
translation of Nietzsche's quoted German text goes on considering the origin of
the logical, suggesting that it had a survival value in the course of
evolution, in the sense (as I understand it) that for survival it is better to
shoot first and think later, i.e. to assume likeness and oversee details, or
practice trial and error rather than to hesitate in doubts and subtleties. Franchella quotes and expands on a sentence in German:
logic soothes and gives confidence. "It does not emerge from objective
data in our possession but it is a pattern that we sneak into the continuous
flow of perceptions in order to control it. It is, like science and
mathematics, a useful simplification to avoid drowning in uncertainty or
anxiety but it is not 'true' in the profound sense of the term." In the
course of academic debates about which I did write a particular debate-essay, I have sensed
this all in terms of an unwillingness of people with logical minds to question definitions of fundamental
terms they happen to use, which often amounts to an unwillingness to question
the basic assumptions of their logical trains of thought.
---
Perhaps this is the place for making a pause in order to see how
presuppositions of logic, like "instincts" or "struggle of
instincts", also appear in the now academically popular field of
phenomenology such as in the discussion of the "Origins of Geometry"
found in Edmund Husserl's famous The
Crisis of European Sciences (1970). Let us disregard for the moment that geometry
after Descartes belongs to mathematics rather than logic. Husserl writes (p.
377) about intersubjective meaning and "the same merely factual
presuppositions of understanding":
It is a general conviction that geometry, with all its truths, is valid with unconditioned generality for all men, all times, all peoples [...] The presuppositions of principle for this conviction have never been explored because they have never been seriously made a problem. But is has also become clear to us that every establishment of a historical fact which lays claim to unconditioned objectivity likewise presupposes this invariant or absolute a priori. Only [through the disclosure of this a priori] [interpolation by phenomenologist Walter Biemel] can there be an a priori science extending beyond all historical facticities, all historical surrounding worlds, peoples, times, civilizations; only in this way can a science as aeterna veritas appear. Only on this fundament is based the secured capacity of inquiring back from the temporarily depleted self-evidence of a science to the primal self-evidences. - Do we not stands here before the great and profound problem-horizon of reason [...] a root in the essential structure of what is generally human, through which a teleological reason running throughout all historicity announces itself [...] grounded upon the foundations of the universal historical a priori [...] leads further to the indicated highest question of a universal teleology of reason. [My emphasis.]
For purposes of honesty I must account for the fact that after the
appendix on origins of geometry it is Eugen Fink writes in
Husserl's book a critical appendix on the Problem
of the "Unconscious" that, however, I do not know whether
Husserl himself would have approved despite his original mathematical mind.
Fink himself considers initially an objection to his text that follows, that is
tries to interpret the "un-conscious" according to the methodical
means for understanding consciousness. But he inverts the objection observing
the ever growing tendency of "depth-psychology" (a term
used for gathering the theories and therapies associated with the names of
among others Sigmund Freud, William James and Carl Jung) to conceive of
consciousness as a mere stratum of the concrete man and to oppose to it other
dimensions of life not traceable to consciousness.
Fink does not comment the philosophy
of the unconscious but states that the above study of the unconscious is
philosophical naïveté
consisting of an omission, because
one thinks that one is already acquainted with what the "conscious"
or consciousness is and dismisses the task of first making into a prior subject
matter what consciousness is. This would show our illusion that consciousness
is something immediately given, while the "intentional analysis" of
phenomenology destroys this illusion and leads one into a science of a new sort
"where one gradually learns to see and grasp for the first time what
consciousness is". As an account of intentional analysis puts it:
"The researcher mentally examines the object or state-of-affairs by taking
different imagined perspectives and making modifications, like adding or
subtracting or changing different features, to determine what is essential to
the meaning and what is not." For a "naïve" layman this sounds
like a mixture of ideas in introspection and meditation or, for me,
this looks as a paradoxical naïve attempt at an individualization of the "Hegelian
inquiring systems" as expounded and finally published in the
earlier mentioned The Design
of Inquiring Systems. The main difference from Nietzsche's talk
about struggle of instincts is that the phenomenological approach is a search
for the universal historical a priori and a universal teleology of reason by
means of a so-called intentional analysis through the imagining of perspectives
and such. Further comments on phenomenology impersonated by Husserl's main
heir, Martin Heidegger, are to be found in an earlier essay of mine on Ethics
in Technology.
---
Returning to Franchella, another quotation
from Nietzsche's German text (translated by me) that illustrates his conception
of the essence of logic, which in turn has had such a large influence on modern
western thought, including views on religion:
"As far as the logicians are concerned, I will never tire of underlining a little brief fact which is disinclined to be accepted by these superstitious people, namely, that a thought comes when it will, and not when 'I' want. So that it is a falsification of the fact that the subject 'I' is the condition of the predicate 'think'. It thinks: that that this 'it' is precisely that old celebrated 'I' is, mildly speaking, only an assumption, a claim, above all no 'immediate certainty'".
I see this sentence as a clue to Nietzsche's cultural contribution to
the deconstruction of the Ego and its reconstruction" into the concept of
psyche or mind that is illustrated further along Franchella's
quotations. The purpose was to put the concept of Ego in its proper context, as
it is the purpose of so-called depth psychology and, in particular, in
analytical psychology. Unfortunately Nietzsche's
approach and limitations, including his treatment of religion as it appears in Franchella's chosen quotations of Nietzsche, opened the way
for its derailment in the direction of postmodernism and nihilism.
Franchella goes further in considering inadequate Nietzsche's
criticism of logic as presupposing the existence both of objects and subject as
in ordinary language, since "from Frege [considered
'father' of analytic philosophy] onwards, the way in which logic expresses the
sentences of ordinary language is in terms of function-argument, borrowed from
mathematics and certainly neutral from an ontological point of view." I
think that here Franchella, despite of her
familiarity with Brouwer's work, misses his main point in that mathematics also
distorts reality in its application to the same. Nietzsche himself thought of
solving in Greek terms the problem of the shortcomings of "rational Socratic-Apollonian-Sophoclean"
logic-mathematics as tools of survival, by balancing them with the help of the
pre-Socratic and pre-Euripides Dionysian kind of creative art-aesthetics (that
today is represented by the trend towards "design"): "Perhaps
there is a kingdom of wisdom from which the logician is exiled? Perhaps art is
even a necessary correlative and supplement to science?"
Here is not the place to expand on explanations of these references to
Nietzsche's thought that can be overviewed in e.g. Wikipedia or in the Stanford
Encyclopedia of Philosophy including its entry on Nietzsche's
Life and Works. As already stated, my choice is to refer to
analytical psychology and its process of individuation, which has
incorporated such thoughts and those of the aforementioned Schopenhauer's who
also had influenced Brouwer.
Franchella concludes the essay with a very informative final
overview and comparison between Nietzsche and Brouwer who partly agree about
science, including applied mathematics and logic, seeing it as a biased human
product with problematic "sinful" morality. This is so because for
both of them it consists in projecting a "useful" pattern of
causality onto the world or in fostering survival and human control of other
humans and environment. Nietzsche, however does not consider it sinful as Brouwer
does because of its luring us into the sinful world. And yet can be said that
also Nietzsche sees it as "sinful" in its one-sidedness, in its
wanting, for purposes of survival, to "keep everything under control"
at the cost of suffocating creativity as the booming of the vital, the
individual, the unique, the special. Brouwer solves the sinfulness by means of
abstention or retreat from the world and from any "useful"
application of mathematics. He sees doing mathematics as a sort of
"introverted" intuitive and in this sense artistic activity.
Nietzsche solves his own brand of sinfulness by advocating an
"extroverted" balancing of scientific with artistic activity, which
recalls a vague resemblance to the idea of "bicameralism", which I
prefer to see as a balancing of psychological functions in the process of
individuation.
SYMPTOMS: SYNTAX, SEMANTICS, PRAGMATICS
In texts
about language it is typically stated that the study of language is often
divided into syntax, semantics and pragmatics. A similar division except for
pragmatics appears in computer science where the construction and application
of computer programs are investigated. The distinction between syntax (sentence
form) and semantics (word and sentence meaning) is said to be fundamental to
the study of language. Syntax is seen as the collection of rules that govern
how words are assembled into meaningful sentences.
Despite of
the frequent "dogmatic" use of these terms it is seldom mentioned
what is the source of this classification and the symptomatically confusing
interrelations it implies are exposed in the Stanford
Encyclopedia of Philosophy under the ambitious label of "The Structure of Scientific Theories". An understanding of the source
is found in the study of semiotics and its history, relating the whole
matter to Charles Sanders Peirce as exponent of a branch of the philosophical pragmatism
that through William James and Edgar Singer Jr. influenced the formative years of the
previously mentioned system theorist West Churchman. It is interesting to note
how syntax, syntax, semantics and pragmatics are more systematically defined by
the "father" of semiotics, Charles Morris (1901-1979) as rendered
in Wikipedia:
(1)
Syntactics/Syntax: relations among or between signs in formal structures.
(2)
Semantics: relation between signs and the things to which they refer; their
signified denotata, or meaning.
(3) Pragmatics: relation between signs and sign-using agents or interpreters.
What I wish
to show here is how the vain search for truth in these contexts evidences what
Brouwer objects to regarding the merging of mathematics with logic in syntax, which is the most common concept mentioned in computer science,
and consequently the shortcomings of the "secondary" problematic talk
about semantics that is the subject treated below, while pragmatics is left
completely vague. Consequently the whole division and
construction of the tripartite
syntax-semantics-pragmatics can be suspected for anonymously doing away with or
relativize the concept of truth under the label of "semantic theory of truth".
The
Polish-American logician and mathematician Alfred Tarski who dedicated to
mathematical logic felt the necessity to try to clarify the concept of truth
that evades the typical syntax studies of the computer field. For this purpose he wrote a noteworthy and symptomatic paper that in
the English translation has the title The Semantic Conception of Truth: and
the Foundations of Semantics(in
Philosophy and
Phenomenological Research, Vol.4, No. 3, March 1944, pp. 341-376,
review in the J. of Symbolic Logic, vol.9, nr. 3, 1944). Tarski initially
defines semantics as a discipline which, "speaking loosely, deals with certain relations between
expressions of a language and the objects (or 'states of affairs') 'referred to' by those
expressions". Without defining language except for presupposing only
formal languages, he then goes on in the following 30 pages circumambulating
around the concept of truth in examples of series of logical sentences. This
includes the use of "recursive procedure" in the definition of
"satisfaction" for the definition of truth, but without some sort (of
Brouwerian?) reflection upon the concept of recursiveness. Before this the
author states that "the problem of definition of truth obtains a precise
meaning and can be solved in a rigorous way only for those languages whose
structure has been exactly specified. For other languages - thus, for all
"natural, "spoken" languages - the meaning of the problem is
more or less vague, and its solution can have only an approximate
character." The conceptual bewilderment of this formal approach to
semantics can be easily overviewed in what is usually considered as semantics in computer science, where pragmatics appears under the
name of "implementation" of the function of the programs - i.e. that
they "work". This prevents from seeing that not only programming languages but also
particular software products or programs should be considered as
(axiomatic) theories about what (activity) is being
computerized.
We recognize
in all this Brouwer's reservations against the
"truth" or validity of logic applied to this world, which should
include computers and computerization. It is therefore symptomatic that it is
difficult to see a conclusion in Tarski's essay, except for exercises of
logical interchanges between syntax and formal semantics. There are only some
final remarks: he declares having doubts in connection with the evaluation of
scientific achievements in terms of their applicability. He believes "that
it is inimical to the progress of science to measure the importance of any
research exclusively or chiefly in terms of its usefulness and
applicability." Furthermore: "It seems to me that there is a special
domain of very profound and strong human needs related to scientific research,
which are similar in many ways to aesthetic and perhaps religious needs. And it
seems to me that the satisfaction of these needs should be considered an
important task of research." Paradoxically, the author's final words after
these final remarks are a statement that (nevertheless) nothing of this is
relevant to the content of the article itself, showing that the honorific link
between science, aesthetics and religion is just only honorific or, rather,
only nominally ennobling the type of science he represents.
These early
developments that we find in Tarski show up in plenitude how seldom we come to
more elaborate discussions of the ontology
of logic. The problem already appears in what was mentioned above
in the beginning to this essay when we mentioned contributions by Y. Bar-Hillel who was an
acknowledged inspiration for defining the concept of data and information in
the original school of Swedish Theoretical
Analysis of Information Systems by the grand old man of computer
information systems, prof. Börje Langefors. This affected the latter's conception of what
data, information and systems are or how they should be defined, showing up in
the basic phenomena of how the use of computers is perceived as obliterating the concepts of time and space in terms of simultaneity and ubiquity. In fact, despite of mathematics and logic being able to manipulate, as in
physics, these concepts of time and space - they are absent in their theory. In
this respects they recall the psychic phenomenon of dreams, and suggest a
reason for the suspension of consciousness as well for the phenomenon of
dependency upon computer gaming as related to virtual
reality and augmented
reality. In fact, the analytic psychology of
Carl Jung was considering such related phenomena in an essay named "The dreamlike world of India" (Abstracts of the Collected Works of C.G. Jung, ed. C.L. Rothgeb et. al., orig. in CW10, Civilization in Transition).
From the professional point of view of computer and information science,
however, these matters are reflected in the Tarski/Bar-Hillel/Langefors attempts to work with concepts of information
other than those in mathematics and logic. This was attempted through the
introduction of syntax-semantics (and rather neglected pragmatics), and the
consequent introduction of so-to-say "molecules" of information
(informational elementary "messages") composed of "atomic"
units or terms of an elementary message of information were the object or
entity (identifier) and therefore space, the characteristicum
(property part composed of variable type and variable value), and the time of
measurement (or time during which the object is affirmed or predicted to hold
the characteristic). In the spirit of the Churchman-Singer teleological theory
of measurement (cf. The Design
of Inquiring Systems) I supplemented or complemented them (in my
doctoral thesis om Quality-Control of information) with the error term. (Details in my papers "A subsystem in the design of informatics", and "The systems approach to design", the latter in Information Systems Frontiers,
Vol. 3, No. 1, 2001).
Leaving this
aside but subsumed, a review of the ontology of logic will now be considered in
particular in the form of a review of Nietzsche's approach that we already
considered above in Franchella. This is the case of
an article by Steven D. Hales with the title "Nietzsche
on Logic", in Philosophy and Phenomenological
Research, Vol. 56, No. 4 (Dec. 1996), pp. 819-835.
Hales starts
with a valuable summary of Nietzsche's criticism of logic that is similar to
the summary at the end of Franchella's text surveyed
above. His particular contribution is that he purports to show the paucity of
secondary literature criticizing Nietzsche's criticism and to show that
Nietzsche's original criticism does not detract from the value and necessity of
logic. He does so starting from an unstated position
that seems to be well represented by Tarski, above. This means that in contrast
to Franchella he does not consider Brouwer and his
relation between logic and mathematics.
Hales notes
that Nietzsche's own knowledge of logic "seems a bit quirky" since he
was certainly aware of only traditional Aristotelian logic and had read Kant
and Hegel and their followers, criticizing them as "philosophical
laborers" for showing (in "Beyond Good and Evil) the data of the past
into rigid logical formulas. For me this is particularly revealing since it was
also my strong impression in reading Kant, especially his Critique of Pure Reason.
But then
Hales reveals indirectly his standpoint by noting that Nietzsche (who lived in
the second part of the nineteenth century) seems wholly ignorant of the
"stars of the nineteenth-century logic". All of them were at the time
his not yet famous contemporaries, but are today considered as fathers of
modern logic, Augustus de Morgan, George Boole, Gottlob Frege. Hales mentions
also John Venn and C.S. Peirce without noting, however, that Peirce's most
famous contribution as pragmatics (cf. above) and pragmatism is symptomatically
totally absent in what he calls modern logic.
Hales notes
that Nietzsche in Human, All
Too Human declares that logic rests on assumptions that do not
correspond to anything in the real world, and in The Twilight of the Idols finds
"...science of formulae, sign-systems: such as logic and applied logic,
mathematics. In these reality does not appear at all, not even as a problem;
just as little as does the question what value a system of conventional signs
such as constitutes logic can possibly possess." And in The Will to Power:
"Logic (like geometry and arithmetic) applies only to fictitious entities
that we have created. Logic is the attempt to comprehend the actual world by
means of a scheme of being posited by ourselves; more correctly, to make it
formulable and calculable for us." And "The world seems logical to us
because we have made it logical". Or, further, "Logic is merely
slavery within the fetters of language." This latter remark recalls
Brouwer's observation that logic is deduced from the structure of ordinary
language, as the previous ones recall his noting the mathematical reality of
the world is a projection of our own causal perceptions.
With a sense
of relief Hales observes that despite Nietzsche's obvious reservations about
logic he is aware of its strengths as well, e.g. for drawing correct
conclusions (and convincing others, the problem being their premises). Hales,
however, sees a contradiction between Nietzsche's view that logic opposes life
while at the same time affirming that logic is useful for life. Hales
apparently misses that the one "life" refers to creativity while the
second life refers to sheer biological survival. Hales also sees that Nietzsche
weakens his claim that logic ("and rationality") is necessary for
life when he otherwise claims that it is merely
necessary for thinking,
meaning that one can indeed live without logic and rationality. In
my view all this follows from Hales' lack of stringency in defining thinking as
well as life. He seems to sense this when he subsequently needs to refer to
Nietzsche writing (in On Truth
and Lies in a Non-moral Sense) that "everything which
distinguishes man from the animals depends upon his ability to volatilize
perceptual metaphors in a schema, and thus dissolve an image into a
concept." Hales then reformulates it in his own words that so, humans
engage in a process of abstraction from sensory impressions to form concepts
and demarcate objects, ultimately giving raise to the "great edifice of
concepts" which "exhales...logic". So, despite of trying to
define thinking, without relating it to sensory impressions and images (even
"primordial" ones, as done in analytical psychology), Hales does it
in such a manner to be able to conclude that Nietzsche admits that giving up
logic means ceasing to think. And this thinking is done in opposition to
"mythically inspired people" or "the man of intuition" who
live in a dream where "the web of concepts is torn by art" or
intuition shatters the existing conceptual edifice with new metaphors, myths,
and art. So, to refuse logic would be to refuse (to think under the constraints
of) language.
Hales
considers on one occasion that it is possible to see Nietzsche, as I do, as
attacking formal logic,
but endorsing clear argumentation, rationality and thinking unpolluted by
superstition. Unfortunately Hales does not pursue what clarity, argument,
rationality and superstition ultimately are. He rather goes on giving two
reasons against the formal-logic/rational-thought dichotomy. The first one is that Nietzsche
does not "clearly" separate the issues of formal logic and rational
thought. But, let alone "clearly", at his time there was no express
formal logic, and still today there is not consensus
about what rationality is. If formal logic had already been available to
Nietzsche in his lifetime he would probably have been
eager to raise objections against it and about the concept of "form".
What happens here is that Hales unperceived takes stand for formal logic. And
this becomes more evident in his giving the second
reason against the dichotomy: Nietzsche is said to consider the
constraint of [natural!] language to be essential for thinking and hence for rational thinking (my square
brackets and italics). He also is said to regard logic as the infrastructure of
language (while I interpret Brouwer as seeing language as the
"infrastructure" of logic in the sense that logic is extracted from
ordinary language). And here comes the remarkable conclusion of Hales:
"Thus logic as the formal
semantics of natural language and of thinking is inextricably tied
together for Nietzsche". (My italics.)
So, in trying
to pin down "what exactly is Nietzsche's complaint against logic,
then?" Hales goes on questioning whether it is true that logic presupposes
the existence of things that Nietzsche considers fictitious in their use in
logic. Hales recurs to a sort of rhetorical argument in observing that
Nietzsche with his "imprecise and rudimentary understanding of logic"
used an inappropriate methodology and he would have needed some of the tools
acquired in the past century of logical development. "Ignoring what has
been learned about logic since Nietzsche's time is simply a Luddite approach to
a technical
issue." (My italics, is it a technical issue?). Secondly Hales purports to
illuminate problems that Nietzsche "could indicate only dimly" by
using "the concepts and clarity of modern vocabulary". He claims that
Nietzsche in his claims that logic falsifies reality or makes no claims about
reality ignores that modern
logic is divided into syntax and semantics. Hales notes then that
it is the syntactical aspect of logic that is formally aloof from the world and
that it is not the business of syntax to worry about reality. Its business is
formally aloof from the world: "It provides the rules for the manipulation
of operators, connectives, quantifiers, predicate letters, variables, and
constants of the formal system, how symbols can be moved around, and how
theorems are to be proven from the axioms."
In doing so
he recalls in a reader like me some of the observations we made above about
Tarski, that are to be renewed in what follows.
Hales reminds
that in modern logic the "interpretation" or "meaning" of
the formulas of logic is the business of semantics, specifying "domains of
entities of universes of discourse, along with an interpretation function that
leads us from the symbols supplied by the syntax to the entities in the domain.
The function assigns a unique object in the domain to each constant, tells us
which things the variables can stand for, and provides an extension in the
domain for each predicate letter.
But: what are
these mentioned entities, things or objects if not Nietzsche's
criticized things? And here comes Hales explanation of how the problem can be
explained away in the theory of modern logic. Yes, thingness is a requirement
of logic, we need things but
the nature of these things is a further question, one that is strictly speaking
beyond the purview of logic and more properly the subject of metaphysics or
ontology. (My emphasis.)
In this way I
think that Hales indeed explains away the whole problem together with the third
aspect of language mentioned at the beginning of this chapter, namely the
pragmatics of language as the infrastructure of logic. This is so because
semantic functions assigned to work out syntactic symbols are assumed to be
relating to non-controversial authoritative and objective consensual observers,
reality being "out there" in a "Gods Eye"
"externalist". This is what Churchman's The Design of Inquiring Systems covers under
Lockean inquiring systems, or naive empiricism, raising also the need of
differentiating and relating concepts of
intuition to concepts of postulation
in the philosophy of F.S.C. Northrop (cf. his The Logic of the Sciences and the
Humanities, and its use in my PhD dissertation on Quality-Control of Information). And Hales
feels uncomfortable in discussing this, observing that "realism and
antirealism are the focus of much current debate, and are notoriously slippery
terms." The "current" debate refers to the advent of used and
abused postmodernism in academic America around the eighties-nineties as considered
in an essay adduced in Hale's article, on "Nietzsche's Prefiguration of
Postmodern American Philosophy".
Consequently Hales goes on into the need of "an
investigation into the semantics of natural language" observing, however,
the failure of Rudolf Carnap to consider Nietzsche's concerns. I direct those
interested in such investigation to acknowledge my attempts to comment the
problems of the influence of Rudolf Carnap and Yehoshua Bar-Hillel upon the
field of informatics in Sweden, as presented in my paper on A subsystem in the design of informatics (1995). It is symptomatic that in order
to make sense of the above talk on semantics and about the claimed difference
between meaninglessness and falsity relies on acrobatic differentiation between
so called grammatical syntax and logical syntax. And so on, after a series of
manipulations it seems that the ultimate purpose of the juggling with syntax
and semantics, and the ignoring of pragmatics is the attempt to make logic into
a tool for discovery or construction of truth, where the concept of truth itself is not
called into question but, rather, definitionally explained away.
I think that
something meaningful arises in these reasonings when (p. 829) Hales writes that
Nietzsche contention is that "we categorize our sensory phenomena in a way
that suits our ends and purposes." Or (cf. The Will to Power) "humans have simply
chosen those interpretations that allow them to live and promote their
interests. This is how we have made the world logical, and formulable and
calculable for us."
This is
particularly meaningful because it indicates the need to move and enrich the
domains of logic and mathematics with a knowledge of their relation to
teleology. This is what is done in the already mentioned work of Churchman in The Design of Inquiring Systems where
initially, partly in the tradition of C. S. Peirce also mentioned above, the
second chapter on Leibnizian inquiring systems does away with the primacy of
badly understood logic and is subsequently expanded into teleology, naive
empiricism, Kant, Hegel, and the rest. What Hales seems to be doing, however,
is to miss the point by quoting the expressions "our ends and
purposes", "their interests" and "calculable for us".
The core of the problem is instead the question of our, their, and us, that is,
who is we, they,
and us, who is the
(competent according to whom) observer using the logic (and mathematics) and
whose empirical findings for whose and what purposes. Despite of not following
Hegel, Nietzsche is said to have been well acquainted with this work and this
explains his particular sensitivity to the issue as expressed in the emphasis
on the perspectival question. And we have not yet
considered the hypothesis of the observer as one more "thing" among
other things. What about the unity and stability of the observer - considered,
for example, in analytical psychology? There was a time in which the
"atom" also was conceived as a indivisible
and stable unit, prior to its disintegration.
Hales,
however, we have seen seems to solve the problem by relegating it to
"metaphysics or ontology". Even if things are fictitious, then logic does indeed work with these
fictitious things, and (p. 830) " this does not the slightest damage to
logic". He finds that, as Nietzsche is quoted to say, logicians rely on
faith and are superstition (positing as realities all those hypotheses such as
substance, attribute, object, subject, action, etc.), this is a fact about logicians, and not
one about logic itself. It would be a curious experiment to compare
this declaration with another most frequent nowadays that the problems caused
by faith in technology are a fact about the technicians and scientists and not
about technology or science itself. It is interesting to realize that in the
latter case the escape is guaranteed by claiming that indeed the problems are
caused by "the users" of technology, such as politicians deflagrating
atomic bombs or buyers and abusers of computers, not by the technicians and
scientists. But this escape is obviously not available in the case of logic
because of: who are the users of logic?
This is,
again, a core idea in Hales' article. What he is indeed revolting against is
what I myself also refuse in the interpretation of Nietzsche's provocative
declaration quoted from Beyond
Good and Evil, that "it is no more than a moral prejudice that
truth is worth more than mere appearance". I mean that such an
interpretation must be done questioning the meaning of truth, and criticizing
Nietzsche himself including his denigration of theology, instead of only
criticizing his criticism of logic. Nietzsche's denigration of theology in
terms of his stand against Christianity and its relation to Buddhism is a complex matter to be detailed
here. But I think that it is especially symptomatic in giving an opportunity
for understanding a basic shortcoming of his philosophy, which in turn
influenced so many others including Heidegger and "postmodern existentialism". Hales devotes several lines to
expose Nietzsche's illustration of non-identity, or non-persistence of
individuals or objects, by means of an indirect reference to the Torah
commandment "Eye for an eye" (Exodus 21: 23-25), to be hereby differentiated from New
Testament's "Love your neighbour as
yourself" (Mark 12:31). As I understand it the message is
that every action is uniquely tied to one (changing, in flux) individual and
cannot, with "the instinct of the herd" which is related to the
"herd morality" (see also Nietzsche and Morality) or what today recalls political correctness, be
logically attributable to any one in the future, the
less so in taking for granted that an injury will be repaid with a injury. Franchella (p. 383) had
even illustrated this very same matter with a German quotation from Nietzsche's
Posthumous Fragments that
I painstakingly translated for myself but because of its complexity I reproduce
only in the original German for the benefit of readers who understand it:
Der Calcul ‘thue nichts, was dir selber nicht angethan werden soll’ verbietet Handlungen um ihrer schdlichen Folgen willen: der Hintergedanke ist, daß eine Handlung immer vergolten wird. [ . . . ] Dagegen ist der Spruch werthvoll, weil er einen Typus Mensch verrth: es ist der Instinkt der Heerde, der sich mit ihm formulirt—man ist gleich, man nimmt sich gleich: wie ich dir, so du mir—Hier wird wirklich an eine quivalenz der Handlungen geglaubt, die, in allen realen Verhltnissen, einfach nicht vorkommt. Es kann nicht jede Handlung zurckgegeben werden: zwischen wirklichen ‘Individuen’ giebt es keine gleiche Handlung, folglich auch keine ‘Vergeltung’ . . . Wenn ich etwas thue, so liegt mir der Gedanke vollkommen fern, daß berhaupt dergleichen irgend einem Menschen mglich sei: es gehrt mir . . . Man kann mir Nichts zurckzahlen, man wrde immer eine ‘andere’ Handlung gegen mich begehen. (NF=Nachgelassen Fragmente, Posthumous Fragments, 1888, 22[1])
The problem
seems to be that Nietzsche extends this mechanism to the Christian message of
love that, indeed, in order to be genuine love must not presuppose a
retribution with an identical action of love, and consequently it is not a herd
mentality. Hales picks up this question in its implications for the explanation
of Nietzsche's interest in prudential reasoning and claim that it does depend
upon trans-temporal persistence.
In her
article, Franchella mentions Nietzsche's considering in essay II of the Genealogy
of Morals the relation debtor/creditor as responsible for
"instilling memory" in humanity, since the former must remember the
debt and the latter that he is owed the repayment. The debtor must also
remember the he himself is a thing that persists through time or that he is the
same person as the one who acquired the debt. Wish to avoid punishment
encourages his belief in persistent identity and repayment. "Thus this kind of reasoning leads to a belief in a
continuing ego or self, a belief that gets displaced onto other objects and so
creates the concept 'thing'." It impresses me is
that in a personal debate with a friend of mine who does not believe in free
will, he still accepts the need of crime punishment because it encourages the
abstention from crime due to fear of punishment. This seems to imply a paradox
in that punishment is supposed to both encourage persistence of an ego and the
disbelief in the existence of a free will, at the same time as Nietzsche makes
an issue of (whose) Will to Power.
It also
impresses me in Nietzsche's reasoning his paradoxical use of "he" or
"his" belief, which is postulating the persistence of a not only a
"he" but especially an "ego or self". The latter are
important distinct concepts in analytical psychology, not being a question of
ego or self but,
rather ego and self.
I expect to emphasize towards the end of this essay their distinction as the
key to resolving the apparent paradoxes in the discussions up to now.
Disregarding
all this, Hales, however, goes on in a defense of his own position on formal
logic instead of deepening himself into Nietzsche's criticism. Hales goes so
far as to defend truth by means of reference to a need for "plenty of
wholesome multivalent logics" and by claiming that interest for the
psychology of logicians is pure ad
hominem, to be comparable with what would be dismissing Nietzsche's
later work on account of his insanity. And his criticism of identity would be
another manifestation of his "anti-realism" about "things".
After a divagation about the concept of thing and change, in particular about
the bundle theory of objects prefigured by Berkeley and
Hume, Hales concludes that Nietzsche's critique is really about the applicability of logic than
it is about logic per se. He sees it as a critique of semantics and about
Nietzsche's own misunderstanding of semantics as necessarily referring to
objects that Hales resumes under the concept of "realistic
metaphysics". Hales reiterates that ''a realist
semantics is not the only one possible, and the universes of
discourse can just as well be populated with Nietzschean fictions as they can
be with things-in-themselves [whatever they are]." (My italics and square
brackets.)
Consequently Hales concludes in the last paragraphs
of his article that "The charge that logic or language is misleading is
ultimately a criticism of those who are thereby misled and is not an objection
that undermines logic as a science of thought or as a formal representation of
natural language." Questions about logic are relegated by him to
metaphysics and "faith" of logicians, i.e. to their sort of
"religion". While metaphysic(s) is a word that today is used for
depicting something imaginary or fanciful to be kept out of science and serious
discourse, the Webster's Third
New International Dictionary also offers the definition as a system
of first principles or philosophy underlying a particular study or subject of
inquiry, and a division of philosophy that includes ontology and cosmology,
treating of the relations obtaining between the underlying reality and its
manifestations.
All the above
may look rather "theoretical-abstract" iit
were not for its consequences in late problematic trends in The Logic of Information (2019), a book with the subtitle A Theory of Philosophy as Conceptual
Design, authored by the widely promoted Luciano Floridi
(also visible on YouTube). In the preface he
introduces the book as being a (third) middle ground between the first two
books in a planned tetralogy labelled initially, as a pun among colleagues, Principia Philosophiae Informationis (in analogy to Principia Mathematica?) and up to now consisting of The Philosophy of Information and The Ethics of Information plus
a planned one on The Politics
of Information. In the preface the book is alternately presented as
(1) A book neither in the
epistemological tradition nor about ontology, rather a book on the logic of
design and hence of making, transforming, refining, and improving the objects
of our knowledge, (2) Asking
what is the conceptual logic of information modeling, i.e. generating a
description of some structural properties of a system, (3) A study in the conceptual logic of
semantic information, (4) A
constructionist study in the conceptual logic of semantic information both as a
model (mimesis) and as a blueprint (poiesis).
As Wikipedia puts it the goal to develop a constructionist philosophy, where
design, modelling and implementation replace analysis and dissection.
In my own
words in the present text I would say that Floridi
tries to leave his early background in analytic philosophy and logical empiricism
(in Wikipedia on Floridi: "analysis and dissection") towards a
teleological systems theory (in Wikipedia
on Floridi: "design, modelling and
implementation"), despite of grounding his philosophy of technology in the
logical positivist Herbert Simon and his pragmatism in C.S. Peirce instead of
William James. But by shuffling around with undefined terms such as concept and conceptual), system, structure and structural (without its
relation to function-functional),
design, as well as
epistemology with
related ontology
and semantics
which I touched above in this section, he creates an esoteric quagmire, or as
his writes "this third volume too is not a page-turner, to put it
mildly". Such esoteric quagmire prevents criticism by cultured lay
non-specialist readers, and prevents the understanding of constructivist design
as being related the ethically laden teleology with the consequent ignoring of
ethical-theological issues considered in Churchman's The Design of Inquiring Systems, as
I expound in my essay on Information and Theology. I think that the attraction exerted by Floridi's
work relies on his extreme formal skill in building logical networks out of
disparate esoteric terms, or what Churchman calls "Leibnizian inquiring
systems", which academically seem to legitimize the troubling chaos of the
computerized world. As Floridi himself acknowledges:
"I may be moving out of the shadows of my three philosophical heroes
[Plato, Descartes and Kant?]. Not a plan, but this is what happens when you
follow your reasoning wherever it leads you."
I add:
"apparently regardless of what is that leads and should lead the
reasoning". In terms of analytic psychology, for an extremely logically
thinking and empirical psyche, this means to be "artistically" and
unconsciously led by feelings and intuition. It is an interesting case of
"enantiodromia", which also may characterize the
mind of those who drive the process of computerization of society. The end was
paradoxically postmodernism, and soon post-
and transhumanism, trends that
are already being studied.
We have now seen various approaches to the relation between mathematics
and logic that are embodied in computer, and the meaning of their
"application" as it is represented by their relation with reality. I
suspect that this may be way of also getting at the "core" of the
issue of philosophy of technology for which I refer eventually interested
readers to another earlier essay of mine titled Trends
in Philosophy of Technology.
We must now pause on what ultimately was referred to above as the non-controversial authoritative and objective consensual
observer of the reality "out there" in a "Gods Eye"
"externalist" perspective. The reader may have noted that
Nietzsche, for all his insights, claims that all is flux or change, and there
is no truth but only appearances in perspective. But who and how has
paradoxically guaranteed that this claim of Nietzsche is true? And if things
are changing bundles of changing properties, who can observe change from a
changing platform of observation? And if logicians or the "users" of
logical-mathematical computers claim that their guaranteed consensual
competence assures that there is persistence of identity in their own
personality, their own judgment, and in the elements of their logical formulas
or computer-software, then how do they know that this is true?
It seems obvious to me that the first requirement is the identity and
stability of the observer, logician or not. In the course of this article we have several times already referred to analytical
psychology but there are readers or "observers" that this has already
been superseded by later modern neuropsychiatry or neuropsychology. Others feel
that psychology and psychiatry is subsumed under religion or dharma, including
Christianity, Hinduism and Buddhism.
Therefore I could have started by considering an article by
Henk Barendregt on [pdf] "Buddhist models
of the mind and the common core thesis on mysticism" (in One Hundred Years of Intuitionism
1907-2007: The Cerisy Conference. Eds.
Mark van Atten, Pascal Boldini, Michel Bourdeau, Gerhard Heinzmann. Springer,
2008). When compared with the apparently more detailed and deep-going Buddhist
Epistemology by S.R. Bhatt and A. Mehrotra, it has one great merit
of trying to reach quite far, until comparing Brouwer's and Kurt Gödel's attitudes to
mysticism, reminding of the "mystical" experience of people getting
involved with computers and, in particular, in computer games as mentioned at
the beginning of this article of mine. It is a mysticism that reveals the price
our culture pays in form of computer abuse and dependence, and meaningfully
contrasts with the wholesale disposal of "metaphysics-ontology"
together with real semantics and pragmatics in formal logic as we saw in Hales,
above.
The problem with Barendregt's article, however, is that in explaining
Brouwer experiencing of the essence of consciousness it refers to an extremely
complex body of Eastern knowledge that easily overpowers us. Western readers
who live in a barely understood and often negated Judeo-Christian culture
cannot really expect to understand and intellectually assimilate a foreign one
as represented by what Barendregt, in a rather eclectic exposition, calls
"AM". It is done without any particular reference to what the letters
AM stand for, introducing it as a "model of conscious cognition inspired
by the Abhidhamma
and [or] Abhidharma" (see also in The Stanford
Encyclopedia of Philosophy). The words themselves are said to mean
higher-teaching, and they are said (in Wikipedia) to have been
considered in the West alternatively as "Buddhist psychology",
"Buddhist phenomenology", "Process philosophy",
"Philosophy, psychology and ethics", "extending into ontology,
epistemology and metaphysics", or simply "among the major
achievements of the classical period of Indian philosophy." Among other
things it analyzes six
types of causes (compared with Aristotle's four), reminding Brouwer's
emphasis of causality we have seen earlier in this text. To give an idea,
Barendregt reminds that the work consists of seven volumes comprising more than
5000 pages, leading its students to study commentaries, or commentaries of
commentaries. So much for those who have perceived this present text as too
long, heavy or obscure. It is, then, very relevant to consider that Francisco
Varela who, phenomenologically and problematically in turn
influenced computer scientists, based his position on Eastern thought,
especially Buddhism, as revealed in his book Ethical
Know-how: Action, Wisdom, and Cognition (Stanford Univ.
Press, 1999.)
A book on Philosophical
Issues of Information Systems (1997) which, by the way, does not
cover the issue of this essay, describes (p. 76) Varela as having developed
together with Humberto
Maturana "radical theories from a biological perspective,
concerning the nature of living organisms, their nervous systems, cognitive
capacities [whatever is their definition] and language (my brackets). This is
not to mention "neurophilosophy" (that
could be accounted for, as mentioned earlier, as "brain mythology"),
listed in Wikipedia's article on Maturana. And their findings have been
explored in the field of computer science by researcher such as (mainly) Terry
Winograd.
To get a taste of in what cognitive world does this
"phenomenological Buddhism" operates I will shortly present a
presentation of the Chilean engineer, entrepreneur and politician Fernando
Flores who worked in close contact and dependence upon the computer world, and
appears to be consistent if not harmonious with Varela. In a presentation
of Flores in the issue 57 (2009) of Strategy + Business the journalist and
consultant Lawrence M. Fisher tries to summarize a work that dazzles academia
because its eclecticism and rhetoric does not allow intellectual analysis, and
writes (excerpts):
"More controversially, Flores argues that there is no objective reality: that the human nervous system cannot distinguish between reality and perceptions. In practical terms, to Flores, this means that individuals and organizations are never fully trapped in any situation, even one as drastic as imprisonment — if they remain willing to change the way they think and talk about it. 'We human beings are linguistic, social, emotional animals that co-invent a world through language," says Flores. That means that reality is not formed by objects. [...] One uncontested fact is that the years of imprisonment turned Flores toward philosophy. [...] With endless time, he read and reread, devouring the works of the German philosophers Martin Heidegger and Jürgen Habermas; of the pioneering Chilean neurobiologists Humberto Maturana and Francisco Varela; and, perhaps most significantly, of John Searle, a Berkeley professor and former student of J.L. Austin. Searle had refined Austin's concepts into a practical set of phrases, coining the term speech acts to describe them."
Let's observe
the words, that there is no objective reality, the appeal to neuropsychology
that is aloof from most readers as much as metaphysics and ontology are, that
reality is invented through language [which, remember, was downgraded by
Brouwer, and that is in turn mediated by computer communication such as in
computerized social media], Heidegger and Habermas, Varela, etc. Putting all
this against what else was considered in this text of mine up to now it is easy
to see that it is a patchwork that evidences how a barely understood
"Buddhist" infrastructure does not work, at least in the sense that
it is not understood or understandable, and therefore confusingly mind-blowing
in our Western Judeo-Christian world.
In view of the above difficulties and as a preparation for further
analysis of our main problem I would like to mention also an earlier related
paper of Mark van Atten and Robert Tragesser on "Mysticism
and mathematics: Brouwer, Gödel, and the common core thesis", in W.
Deppert and M. Rahnfeld (Eds.) Klarheit in Religionsdingen
[Clarity in religious questions].
Leipzig: Leipziger Universitätsverlag
(2003). See also on the net some unidentified author's (alias David Koning
<david_koning@yahoo.com>) commentaries (2006) of the
text. Also
published (with and interesting list of similar books and
articles) in In Robert Tragesser, Mark van Atten & Mark Atten (eds.), Essays on Gödel's Reception of Leibniz,
Husserl, and Brouwer. Springer Verlag (2015).
Atten-Tragesser initially recall that the famous mathematician David
Hilbert starts his book Axiomatic
Thought (English version included in William Ewald, From
Kant to Hilbert: Readings in the foundations of mathematics, Vol. 2, 1996) stating that
"the most important bearers of mathematical thought have always [...]
cultivated the relations to the domains of physics and the [philosophical]
theory of knowledge." And that both went beyond philosophy, cultivating
relations to mysticism. Further they add that the distinction between
Philosophy and Mysticism is a matter of degree. To me that means also a
critical instance to the meaning of logic since for most people the difference
between philosophy and mysticism consists in their content of logic (and
empiricism).
The authors continue describing how Brouwer and Gödel each relate
mysticism and mathematics, and make a comparison. They recall what is for me
the ethical dimension in that they see mysticism as a sudden illumination that
makes people to see reality in a different light, given that reality is good
and mystical practice aims to perceive this Reality as Good. In the details of
the article that I will not survey in detail, they claim that this Good,
however, is not objective or the same for all varieties of mysticism. This is
so despite "the somewhat analogous case in the philosophy of science where
scientific realists hold to a common core thesis with respect to scientific
theories through the ages" that show massive disagreements and still they
all try to express the same objective reality.
We will not follow the article's argument except for some remarks. It
reminds Brouwer's observation that the greatest merit of mysticism is its use
of language independent of human collusion and of animal emotions of fear and
desire. Contemplative thoughts may come through without obscurity since there
is no mathematical system that distorts them.
"The mystical writer will even be careful to
avoid anything that smacks of mathematic or logic: weak minds might otherwise be easily made to believe and
act mathematically outside the domain where this is required either by the
community or their own struggles for life and end up in all kinds of follies."
[My italics.]
Gödel, on the other hand, is referred (on the basis of a book by
computer scientist Rudy Rucker's Infinity
and the mind, recalling Zellini's interest
for infinity) as perceiving abstracts objects or pure abstract possibilities by
having "to close off the other senses" and "to seek
actively". "Doing mathematics is one way to get into contact with
that Absolute [...] There is, then, no break between mathematics and mystical
practice." And referring to Husserl Gödel would have said that "At
some point [...] everything suddenly became clear to Husserl, and he did arrive
at some absolute knowledge. But one cannot transfer absolute knowledge to
somebody else; therefore one cannot publish it. [...]
One fundamental idea is this: true philosophy is [arrived at by] something like
a religious conversion." Atten-Tragesser, then, observe that it is likely
that Gödel tried to experience such an illumination or conversion and mention
that Gödel's personal library contained among others books on Christianity,
Islam, Buddhism and mystical-spiritual movements, concluding that in contrast
to Brouwer he believed (as Thomas Aquinas did?) that the
"intellect" (and psyche, which we shall survey below) has a positive
role to play in spiritual life.
In comparing Brouwer and Gödel the authors conclude that both were
looking for mystical experiences in which "openness of the mind to the
Absolute is operative", and that something is disclosed and imparted to
the person. They could have mentioned religion and God or Truth instead of the
Good and the Absolute" but obviously they find it inconvenient. They
state, however, that the imparting is preceded by a preparation or transformation of the person. The SELF must be brought into a
condition to receive, support, and appreciate what is to be disclosed. "This
preparation we see mentioned by both Brouwer (the abandonment of mathematics)
and Gödel (closing off the senses, etc.). Atten-Tragesser conclude the whole
article with the sentence: "Both were disgruntled with the materialistic
and formalistic philosophies prevalent at their time; both thought that these
philosophies could not do justice to the Good."
In the perspective of this present paper of mine, against the background
of such conclusions, the computer being an embodiment of mathematics and logic
in a materialistic and formalistic frame of mind cannot "do justice to the
Good". Its formalism programmatically excludes teleology of "the
good", and its mysticism expresses itself in the infatuation that lies at
the basis of computer addiction and feeling of awe for its sort of spiritual
power, recalling the Biblical saying that not all spirits are the Holy Spirit. Awe is indeed the
feeling of reverential respect mixed with fear or wonder that we all have felt
in the interaction with a computer until we eventually become insensibilized, albeit often addicted.
Finally, let's return to the above mentioned
statement that imparting of higher knowledge is preceded
by a preparation or transformation of the person and that the SELF must be
brought into a condition to receive, support, and appreciate what is to be
disclosed. This vocabulary with emphasis on the Self can be seen as
aptly representing a call to prayer and religion. At the scientific level where
the concept of science itself in is question, it can be seen as closely related
to analytical psychology of the perception of reality, which has been already
mentioned on several relevant occasions in this essay.
ANALYTICAL PSYCHOLOGICAL APPROACH
What is left is a better understanding of some key concepts that have
been used throughout our text up to now. As in logic, the conclusions depend
upon both the definitions
and consequently the stability - as we have seen - of the truth of the basic
assumptions. These have been mentioned above in terms of such words, among
others, as intellect,
(exodus of) consciousness
(from its) deepest home,
and (or) ultimately self
contrasted to the ego.
To illustrate and motivate the recourse to analytical psychology
let's consider some dictionary definitions of these terms and show their
complexity. In what follows I will only lightly edit and select the
alternatives that are most relevant for our problem, when several definitions
are given. My own comments are enclosed in square brackets, and those words
that are in turn most relevant within the relevant selections are underlined;
readers who already understand and are in agreement with the spirit of this
essay of mine up to now may be able to draw right away some correct conclusions
of it all without waiting for my further explanations below in the rest of my
text concerning the relevance of analytical psychology as alternative to the
related psychoanalysis.
One may start the inquiry trying to be simple starting with "intellect", one of
words mentioned most often in our discussion up to now, and that today is often
bypassed by the similarly used and misused "cognition",
Wikipedia claiming dimly to encompass a a hodgepodge
of "knowledge, attention, memory and working memory, judgment and
evaluation, reasoning and "computation", problem solving and decision
making, comprehension and production of language". A smart engineer
colleague of mine who appreciates simplicity as much as logic challenged me to
be logical in discussions of ethics while he downplayed a supposedly pedantic
need of definitions claiming that one must be able to rely on the intuitive
common sense of daily popular discourse. The next step in complicating the
issue would be consulting the so called Google
dictionary, or rather the definition appearing at the top of the
Google search. The source is reported as per
June 2017 to be the Oxford American College Dictionary. I start
using this Google only for the keyword
intellect and the search gives as the most complex result
INTELLECT (Google - Oxford American College Dictionary)
"the faculty of reasoning and understanding objectively, especially with regard to abstract matters" with closest synonyms being "mind, brain, brains, head, intelligence, reason, understanding, comprehension, thought, brainpower, sense, judgement, wisdom, wits." And, going over to the etymological question:
INTELLECT (The Online Etymology Dictionary)
The online etymology dictionary states about intellect that it is a latin-based translation of the Greek nous or "mind, thought, intellect, intellect" in Aristotle. A key word that also appears in the etymology dictionary is "discernment" (along with "a perception" and "understanding"). Discernment appears more clearly in the etymology of intelligence and intelligere i.e. from assimilated form of inter "between" (see inter-) + legere "choose, pick out, read," from the Proto-Indo-European root *leg- (1) "to collect, gather", all this suggesting that it is a question of an "art" of choosing or gathering [i.e. for a purpose in a systemic context.] [My square brackets, as they will stand for in what follows. Let us note that there is no mention of logic or mathematics, and that perception stands together with understanding, as well as mind together with head, brain, judgement and wisdom.]
If we choose a more ambitious source such as Webster's Third New International Dictionary (1971) we find, starting with intellect (from intelligere to perceive, understand):
INTELLECT (Webster's Third New International Dictionary)
1a: the power or faculty of knowing as distinguished from the power to feel and to will [this is the typical main source for separation between supposed cognitive knowing functions from feelings and willing.]
1b Aristotelianism (1): passive reason (2): active reason
1d Thomism (1): the receptive faculty of cognition that makes apprehensible the phantasms of intelligible forms -- called also passive intellect, possible intellect, potential intellect (2): the aspect of the soul that is immortal and constitutes the active power of thought operating upon the phantasms of intelligible forms -- called also active intellect, agent intellect.
2a: a person given to reflective thought or reasoning: a person of notable intellect.
Since there is above a reference to the less common word phantasm, let's consider its definition:
PHANTASM (Webster's Third New International Dictionary)
2: a sensuous idea or impression -- compare SPECIES
2b <all of the sensible qualities are but phantasms of the observer, not properties of the object -- Douglas Bush>. [Can relate to archetype in analytical psychology. So over to the mentioned SPECIES:]
SPECIES (Webster's Third New International Dictionary)
2b (1): a mental image, phantasm, or sensuous presentation (2): an idea or object of thought that is the similitude of an object in nature whether in the guise of a modification of sense or of a purely intellectual correlative of the natural object; broadly: FORM, ASPECT, APPEARANCE
EGO (Webster's Third New International Dictionary)
1: the self especially as inside one as contrasted with something outside (as another self of the world): as a metaphysical philosophy (1) in Descartes: the soul or an underlying mental or spiritual substance (2) in Kant: a transcendentally postulated unity either of apperception or of the morally free person -- also called pure ego (3) in Fichte: pure self-determining activity positing itself -- called also pure ego b empirical philosophy (1) in Hume: a complex of ideas or a system of successive mental states (2) in Kant: the conscious subject of experience (3): the consciousness of an individual's being in distinction from other selves c: SELF
2b: WILL
3 [translation of German ich] psychoanalysis: the largely conscious part of the personality that is derived from the id through contacts with reality and that mediates the demands of the id, of the superego, and of external everyday reality in the interest of preserving the organism.
I (Webster's Third New International Dictionary)
1: someone possessing and aware of possessing a distinct and personal individuality : SELF, EGO. [And since awareness has been mentioned several times, and its closest meaningful synonym in our context is consciousness:]
CONSCIOUSNESS (Webster's Third New International Dictionary)
1a awareness or perception of an inward psychological or spiritual fact : intuitively perceived knowledge of something in one's inner self b: inward awareness of an external object, state, or fact c: concerned awareness : INTEREST, CONCERN
2: the state of activity that is characterized by sensation, emotion, volition, or thought : mind in the broadest possible sense : something in nature that is distinguished from the physical
3: the totality in psychology of sensations, perceptions, ideas, attitudes, and feelings of which an individual or a group is aware at any given time or within a particular time span -- compare with STREAM OF CONSCIOUSNESS [...]
5: the part of mental life or psychic content is psychoanalysis that is immediately available to the ego -- compare PRECONSCIOUS, UNCONSCIOUS 2
It is should be easy to notice the degree of complication of the issue
when one compares the common sense "engineering" approach to
intellect etc., which roughly equates it to logic-mathematics and empiricism
(cf. logical
empiricism, also called logical
positivism, and hidden in Rudy Rucker's computer-oriented
mathematics), with what is implied by the above definitions. In
my experience, however, I have noticed that typical engineering minds of people
who are gifted engineers or logicians-mathematicians have difficulty to notice
this degree of complication, a phenomenon that I will regard as mainly
ethical-psychological beyond the materialism of
psychoanalysis. In fruitless discussions they persist in reducing
the issue to its simplest form, having induced me to write a whole essay
on debate and fruitlessness of debates and discussions on
complex matters, already denounced by Brouwer, when there is no bond of genuine
unconditional friendship.
In order to unravel psychologically the relation between
mathematics-logic, empiricism, and the psyche in its totality I will apply the
structuration offered by analytical psychology in general, partly summarized in
Jung's Collected Works, volume 7 - CW7, and of
psychological types in particular, in CW6. A quite
correct overview is offered in Wikipedia's article on
analytical psychology as per end of August 2017. In doing so I will not
enter into a debate about analytical psychology itself, a field that could
expand an almost limitless analysis in secondary and tertiary literature that I
also have consulted in the latest thirty years.
A preliminary taste of what is all about can be obtained in secondary
literature or original quotations on the net, such as in Wikiquotes on Psychological Type. On the basis
of the references given here above I will use analytical psychology's concepts
in order to draft a hypothesis on the problems considered in this essay,
including the shortcomings of Brouwer's approach and the criticisms for and
against it.
We can start, however, with a curious and mind-blowing philosophically
logical analysis of the first definition of intellect
above where both reason
and understanding side
by side, often recurrent in the whole of our text together with misunderstanding, are given
as synonyms. Reason and understanding, however are terribly complex and to be
differentiated in the most advanced and "canonized" texts of our
modern Western culture. The
Blackwell Dictionary of Western Philosophy (Blackwell Reference
Online) start summarizing the matter "Reason
and Understanding" as follows:
"Epistemology, metaphysics [German vernunft , reason; verstand , understanding, associated with to stand]. The distinction between reason and understanding was first discussed in Kant 's philosophy. Kant claimed that understanding applies its own categories to experience and generates scientific knowledge, while reason moves from judgment to judgment and seeks to go beyond the limits of experience. Reason tries to apprehend the unconditional, but ends with antinomies, in which reason falls into conflict with itself. Hegel offered a different account of the distinction. He considered understanding to be a fixed or mechanical way of thinking, which produces clear analysis and is in general the first stage of logic and science. But understanding isolates things from one another and is partial, finite, and without fluidity. Reason stands in contrast to the absolute fixation of the understanding. It is associated with inference and argument and tries to discover connections among truths. Reason has two forms. Negative reason uncovers and collapses the contradictions implicit in the abstractions of understanding. Positive reason draws positive conclusions from the work of negative reason. The final purpose of reason is to resolve all conflicts and to grasp totality. For Hegel, reason and understanding are immanent in the absolute idea..."
Having tried to understand (with my reason?!) Kant's all three Critiques, I am sure that the matter is complex indeed and
it convinced me that if one succeeds in understanding what is claimed then one
is stuck in Kant's own framework. The way out for me has been to try to read
some of Kant's historical critics such as the psychologist Carl Jung that
appears to be conscious and respectful of his Kant-heritage. My attitude (cf.
positive reason?) has also been formed by Kant's criticism inbuilt in my
doctoral counselor, often mentioned West Churchman, as represented by his two
main works The Design of
Inquiring Systems and The
Systems Approach and its Enemies. They also aim at incorporating
Hegel's criticism of Kant as implied in his own view of the very same concepts,
as illustrated by Nectarios G. Limnatis' book Reason
and Understanding in Hegelian Philosophy. But it does
not prevent "analyzers" to apply understanding
to everything: to the free will, logic, mysticism, Nietzschean philosophy,
(mis)understanding of semantics, etc. So much, then, for intellect seen as
reason and understanding, not to mention seen as only logic and empiricism.
And so on, if we were to return to my text in the present essay, from
the beginning. For example in the discussion about the
view of formalism vs. intuitionism on whether mathematical exactness is to be
found in the intellect
or on paper we
will find that elsewhere the question is expressed as whether it is to be found
in the abstract or
in the world of experience.
And what about the role of understanding in understanding: the intuitional attitude, the
abstracting of emotional content, unity and stability of the observer, mental
image - phantasm and sensuous presentation, the process of objectifying or
externalization, turning into oneself, the exodus of consciousness from its
deepest home, the essence of the ego as related to given perceptions, the self
vs. you and yourself, and the self that must be brought into a condition to
receive. (All this extracted from the text up now.)
I wished to go on now "explaining" the framework of analytical
psychology but it would take excessive space and effort in this context, while
explanations and summaries are easily found in the literature already
referenced in links above, for those who have a serious motivation to do so. I
prefer to approach the question by positing hypotheses about the psychology or
"psychological type" of Brouwer compared to those who use mathematics
and logic, including computers, in the alternative "modern" way
criticized by him. In doing so I eschew the dangers of being criticized for Ad hominem by adducing
without further analysis two reservations accounted for in Wikipedia's summary
about this issue: "Non-fallacious reasoning" and "Criticism
as fallacy". As also suggested by several items in
Wikipedia's article on ad hominem in the section "See also" (e.g. The
Art of Being Right) such further analysis leads recursively to the type of
problems that I already considered in my earlier essay on Information as
debate.
As mentioned earlier in this essay it is suggested that Brouwer was a introvert-thinking
type, now to be seen as supplemented with intuition as auxiliary function.
Going for once back to original literature, albeit in translation from the
German, we find the following in Carl Jung's Collected
Works, volume 6 or CW6. Because of my use of my annotated first
Princeton/Bollingen paperback printing with corrections of year 1976, and in
order to allow consultation of German or other originals, the references are
given to paragraph numbers instead of page numbers: § 578 ff. and 628ff.
Jung writes that
"I am fully aware that our age and its most eminent representatives know and acknowledge only the extraverted type of thinking...I will disregard all those sensations and feelings which become noticeable as a more or less disturbing accompaniment to my train of thought, and will merely point out that this very thinking process which starts from the object and returns to the object also stands in a constant relation to the subject...Now, when the main accent lies on the subjective process, that other kind of thinking arises which is opposed to extraverted thinking, namely that purely subjective orientation which I call introverted...The world exists not merely in itself, but also as it appears to me...If we were to ignore the subjective factor, it would be a complete denial of the great doubt as to the possibility of absolute cognition. And this would mean a relapse in the stale and hollow positivism that marred the turn of the century -- an attitude of intellectual arrogance accompanied by crudeness of feeling, a violation of life as stupid as it is presumptuous. But what is the subject?"
The subject is man himself, but later Jung goes into the relation
between ego and self:
"The really fundamental subject, the self, is far more comprehensive than the ego since the former includes the unconscious whereas the latter is essentially the focal point of consciousness...But it is a characteristic peculiarity of the introvert, which is as much in keeping with his own inclination as with the general bias, to confuse his ego with the self, and to exalt it as the subject of the psychic process, thus bringing about the aforementioned subjectivation of consciousness which alienates him from the object."
I understand from this that Brouwer through his study of Christian (and
Eastern) mystics was well aware, and shows it in his writings, of the
difference between his ego and self but most probably had been struggling
through most of his life in order to keep them separate. Then appear some
thoughts that recall the essence of "pure mathematical" thinking:
"But no more than extraverted thinking can wrest a sound empirical concept from concrete facts or create new ones can introverted thinking translate the initial image into an idea adequately adapted to the facts. For, as in the former case the purely empirical accumulation of facts paralyzes thought and smothers their meaning, so in the latter case introverted thinking shows a dangerous tendency to force facts into the shape of its image, or to ignore them altogether in order to give fantasy free play...
This kind of thinking easily gets lost in the immense truth of the subjective factor. It creates theories for their own sake, apparently with an eye to real or at least possible facts, but always with a distinct tendency to slip over from the world of ideas into mere imagery. Accordingly, visions of numerous possibilities appear on the scene, but none of them ever becomes a reality, until finally images are produced which no longer express anything externally real, being mere symbols of the ineffable and unknowable. It is now merely a mystical thinking and quite unfruitful as thinking that remains bound to objective data..." (§629 f.)
I see this as a possible description of the mathematical mind, indeed as
purely mathematical "free play of fantasy" that allows for the
"rich" production of mathematical products that later are used and
misused by "extraverted thinker" (§ 584-594) in projections upon
external objects in a process that was not intended by the introverted thinker,
such as Brouwer. And this would refer to the unforeseen application of his
algorithmic thinking to automatize numeric computations and software. And the
"mysticism" that is mentioned is not religious mysticism as
identified by the special case of Brouwer, but rather the mysticism of
secularized mathematicians who claim to approach divinity, becoming semi-gods
or their priests, since their god is supposed to have written cosmos in
mathematical language. Alternatively, it is the "mysticism"
experienced in the use and interaction with computers in general, and in
computer gaming in particular. All this happens while some Christian
self-righteous amateur theologians paradoxically criticize and condemn in
brainy analyses Jungian thought, often as they find it in critical secondary
sources, for being "gnostic", despite Jung's express declaration and
explanation of keeping distinct psychology from religion. Paradoxically these
brainy critics can ignore if not their own, at least the gnosticism of modern
science and technology in general, and of computers in particular, neverthelelss gladly using them daily or, ultimately,
becoming addicted to them.
The more detailed description of the Introverted
Thinking Type (§ 632-637, see below) contains further
considerations of the social behavior of those who are, always roughly,
characterized by it. They remind some
of Brouwer's traits as rendered and as I have understood them in his
biographical accounts. Some hints follow about extreme traits of the type understood as rather
an ideal
type, that in no way should be seen as personal. An ideal
type may happen to be better understood if put into the context of the
tradition of the German cultural sphere connected to other concepts such as Verstehen and Nomothetic
vs. Idiographic. This is not a wholesale endorsement of the
"correctness" of these concepts but mainly to show that their
creation points to an underlying necessity and to the existence of a problem.
And now over to some of the traits of the introverted thinking type who shares
with his counterpart, the extraverted thinking type, the remarkable need or
injunction of "abstraction from emotional content":
"If in his eyes his product appears correct and true, then it must be so in practice, and others have got to bow to its truth. Hardly ever will he go out of his way to win anyone's appreciation of it, especially anyone of influence...He usually has had bad experiences with rivals in his own field because he never understands how to curry their favour...In the pursuit of his ideas he is generally stubborn, headstrong, and quite unamenable to influence...[F]or him the relation to people and things is secondary and the objective evaluation of his product is something he remains unconscious of...In his own special field of work he provokes the most violent opposition, which he has no notion how to deal with, unless he happens to be seduced by his primitive affects into acrimonious and fruitless polemics...The various protective devices and psychological minefields which such people surround themselves with...serve as a defence against "magical" influences -- and among them is a vague fear of the feminine sex."
I repeat that this is a question of ideal
type, but it has some value for imagining the psychic structure and
environment of Brouwer, the motives for his relative isolation and for his
attitude to woman as surveyed above in our earlier text. In order to counteract
the wrong impression that introverted
thinking is basically negative, it should be compared with the
description of the extraverted
thinking type (§ 584-594) that typically exploited Brouwer's
findings ignoring its motivations, and on which I shall not dwell here. And
Carl Jung, returning to "the intellect", terminates his work on
Psychological Types stating in the Epilogue (§ 856):
"Whatever we strive to fathom with our intellect will end in paradox and relativity, if it be honest work and not a petitio principii in the interest of convenience. That an intellectual understanding of the psychic process must end in paradox and relativity is simply unavoidable, if only for the reason that the intellect is but one of many psychic functions which is intended by nature to serve man in constructing his images of the objective world. We should not pretend to understand the world only by the intellect; we apprehend it just as much by feeling. Therefore the judgment of the intellect is, at best, only a half-truth, and must, if it is honest, also to admit its inadequacy."
Having dedicated this analysis to illustrate how Brouwer's supposed
introverted thinking explains his insensitivity to how the outer world would
appropriate his results, I wish now to complete with illustrating how there may
exist a flaw in his assumptions about the reason for the ""exodus of consciousness from its deepest home", as
well as his assumptions about the undefined "intellect" as in seeing the human intellect as the cause of evil.
In Jung's conception an undefined intellect is substituted by the whole psyche
as constituted by ego-consciousness and different strata of unconscious with
its roots in the suggestions of Carl Gustav
Carus and systematized by Eduard
von Hartmann. Some basic concepts are presented in Carl Jung's CW7
Two Essays on Analytical
Psychology, exemplified by the all-important, crucial self so much mentioned by
Brouwer (§ 274 f.) In this context I repeat that in this paper, I do not enter
into the possible controversies about different psychological theories vs.
philosophy of science, the least so into those controversies caused by possible
misuses of depth psychology in the New Age movements. Likewise I do not discuss the misuses of (references to)
quantum physics in feminist theorizing as mentioned later, here below. For the
rest there is a sizeable secondary and tertiary literature on Jung and even
critical of Jung that I have consulted besides all his Collected Words, and is
available to all interested. Some examples are V.W. Odajnyk
Jung and politics: The
political and social ideas of C.G.Jung, E.D.
Cohen C.G. Jung and the
scientific attitude, P. Homans Jung
in context: Modernity and the making of psychology, A. Samuels Jung and the post-Jungians,
R. Noll The Jung cult, etc.,
the latter reminding that Jung himself did not want to build a
"school" and still less to leave a cult of personality, he himself
declaring "Thank
God, I'm Jung, and not a Jungian" (found in Barbara Hannah's
biography Jung: His Life and Work, 1976,
p. 78). In this he resembled West Churchman who personally to me repeated to be
happy for not being a "Churchmaniac". As it
has been remarked regarding Jung, however, there is no fault but,
rather, a merit in accepting a legitimate modest leadership.
The most ambitious among many overviews of Jungian psychology I know is
not easily available since it is contained in a an
older book by J.F. Rychlak Introduction
to personality and psychotherapy (Atlanta: Houghton Miffin, 1st ed.
1973, pp. 132-199, refs. 529-538). At risk of making some mistakes, missing
some terminological and professional nuances, I will use my own words upon what
I remember of my study of Jung's original collected works, starting about 40
years ago. The focus is to explain that the real psychic subject is the Self, a
psychic component that is supra-ordinate to and includes the Ego that in turn
interacts with the personal and the collective
unconscious. The subject's or initially the Self-realizing Ego's
interface with the collective unconscious in the external world is represented
outwards by the psychic entity of the persona, as the aspect of
someone's psyche that is externally presented to, perceived, expected or
required by others or society, analog to a role or character adopted and
presented behind a mask as facade, by an author or an actor. The interface with
the collective unconscious of the personal unconscious or shadow, with the
internal world of inborn or inherited common human characteristics is
represented by the "contra-sexual" entities of the anima-animus in biological
men respectively in biological women. They represent respectively the feminine
archetypal image in men and masculine in women, that I see as an unexplored
basis for explaining homosexuality and the ongoing LGBT phenomena,
especially in the Western world. An unconscious identification of the ego with
extraverted persona incurs into the danger of an identification of the ego with
the anima and ultimately of a projection of unconscious
contents upon others and upon nature or work environment. Such a process may
also explain some phenomena of computer
addiction and gaming where the primal intuition in time sequences
typical of mathematical thinking and music is overtaken by unconscious contents
and their automatisms, with the paradox that interaction with a mathematical
tool representing abstraction from emotional contents is overpowered by
addictive passion. Deeper understanding of such interactions between
"musical mathematics" and emotions or feelings may be obtained from
an analytical psychological study of what has been learned about the role of
music in the historical Doctrine
of the Affections, pioneered by Johann Mattheson and originally
suggested by Plato.
Other works seen to concentrate upon only mathematical aspects, such as in Ruth
Tatlow's Bach's
Numbers: Compositional Proportion and Significance, disregarding the
psychological aspects of numbers suggested e.g. in Jung's Psychological Approach to the Dogma of
Trinity (CW 11, p.107-200, §169 ff.) and in
A Self-realization incorporating the God-archetype from the collective
unconscious, or individuation in a mature
psyche is the result of harmonious sort of "negotiations" (cf. prayer
and worse synonyms - meditation, mindfulness) of the Ego with the two aspects
of the collective unconscious through its interfaces, by means of one of the
particular attitudes (introversion
or extraversion) and psychic
functions (rational thinking or feeling, and irrational
sensation or intuition), which are most consciously available to the
individual's (whole psyche's) closest ideal type mentioned
earlier. Immaturity as absence or failure of individuation, and reliance upon
an isolated thinking function corresponds to Brouwer's warning for that "scientific thinking is nothing but a
fixation of the direction of will within the confines of the head, and a
scientific truth no more than an infatuation of desire living exclusively in
the human head", where the will submitted to desire
corresponds to an unconscious underdeveloped feeling-function.
At this point it is necessary to note that the
aforementioned psychic components or entities are not imagined out or thin air
as it may appear to people who have never studied all aspects of psychology, as
the discipline has historically emerged out of philosophy. They and their
interactions, in analogy with the entities found in, say, particle or quantum physics, are
conceptions that had to be postulated in order to explain and make consistent
sense of a wealth of empirical observations of actual human behavior or
expression of convictions, historically such as alchemical speculations by
e.g. Newton, the personal
development of Blaise Pascal, and clinical
observations such as in neurosis or schizophrenia.
THE
ANALYTICAL PSYCHOLOGIST JUNG'S APPROACH
My own annotations on my copy of Carl Jung's book Memories, Dreams, Reflections recorded by his associate Aniela Jaffé, indicate that
I first bought and read it in April 1975 but happened to definitely relate it
to this essay of mine in July 2023. The book is interesting especially because
it tells about the author's psychological
interpretation of his understanding and feelings in meeting mathematics. Such
feelings, when experienced by common educated people can easily be dismissed
for being caused by lack of giftedness or sheer stupidity. The complexity of
Jung's account requires literal quotations (cf. pp. 43 ff., 340 ff):
[…] I felt a downright fear of the mathematics class.
The teacher pretended that algebra was a perfectly natural affair, to be taken
for granted, whereas I didn't even know what numbers really were […] they were
nothing that could be imagined, mere quantities that resulted from counting. To
my confusion these quantities were now represented by letters, which signified
sounds, so that it became possible to hear them, so to speak. […] No one could
tell me what numbers were, and I was unable even to formulate the question. […]
But the things that exasperated me most of all was the proposition: If a=b and b=c, then a=c. even
though by definition a meant
something other than b, and, being
different, could therefore not be equated with b, let alone with c.
Whenever it was a question of equivalence, then it was said that a=a, b=b, and
so on. This I could accept, whereas a=b seemed to me a downright lie or a
fraud. I was equally outraged when the teacher stated in the teeth of his own
definition of parallel lines that they met at infinity. […] My intellectual
morality fought against these whimsical inconsistencies, which have forever
debarred me from understanding mathematics. Right into old age I have had the
incorrigible feeling that it, like my schoolmates, I could have accepted
without struggle the proposition that a=b,
or that sun=moon, dog=cat, then mathematics might have fooled me endlessly
– just how much I only began to
realize at the age of eighty-four. All my life it remained a puzzle to me why
it was that I never managed to get my bearings in mathematics when there was no
doubt that I could calculate properly. Leas of all did I understand my own moral doubts concerning mathematics.
In a later section of the book, in the chapter "On life after
death", Jung introduced some exceedingly complex ideas about the relation
of human death to the realm of consciousness vs. the unconscious or "the
intermediate stage between unconscious and conscious cognition". It would
take us too far in this our context but the following extracted comment (p.
341) may give a taste of the relation to mathematics:
Ideas of this sort are, of course, inaccurate, and
give a strong picture, like a body projected on a plane or, conversely, like
the construction of a four-dimensional model out of a three-dimensional body.
They use the terms of a three-dimensional world in order to represent
themselves to us. Mathematics goes to great pains to create expressions for
relationships which pass empirical comprehension. In much the same way, it is
all-important for a discipline to build up images of intangibles by logical principles
and on the basis of empirical data, that is, on the evidence of dreams. The
method employed is what I have called "the method of the necessary
statement". It represents the principle of amplification in the interpretation of dreams, but can most easily
be demonstrated by the statements implicit in simple whole numbers.
My point with these quotations is to suggest that
mathematics because of its very nature introduces unconscious processes in the
human mind while surreptitiously merging them with ordinary conscious ones. It
all recalls what has been considered in this essay about both the
aforementioned Brouwer and Zellini, as well giving a
hint of the ultimate mysteries of quantum physics (more on this above and
below) in the relation between psyche and matter. An alternative equivalent
conception presented
in my Information and Theology is the balance between the inner knowledge of human
psyche vs. natural science and knowledge of the outer world.
Until further notice I assume that Jung's attitude is
motivated by his psychic inclination to watch upon the unique (psyche) instead of "playing God" by searching
general "laws" of nature where the human being is regarded as only an
object of an undefined or pantheistic "Nature". A concretization of
these thoughts is suggested by problems and the history of debates on the
societal introduction of personal identification numbers in Sweden followed by national
identification numbers all over the world
as I explain in my essay on The Meaning of Man-Machine Interaction.
The extension of these problems reaches the import of
the whole issue of my text on the consequences of the computerization of society
which follows the conclusions of the present essay, and that I rhetorically
named Computerization as Design of Logic Acrobatics. A concrete manifestation of the latest problems of
computerization, which at the same time illustrates the psychic derangements of
mathematical thought as suggested in Jung's account is the open letter Pause Giant AI Experiments: We call on all AI labs to
immediately pause for at least 6 months the training of AI systems more
powerful than GPT-4. By August 2nd,
2023 when I accessed it, it had gathered more that 33000 signatures, upon what
I consider as a legitimate fear that is paradoxically based on wrong premises,
reminding an analog "moratorium" that I recall in my essay on Trends in the Philosophy of Technology. They are wrong "Leibnizian" premises as
explain in my paper on
Artificial General Intelligence and ChatGPT.
Several partial conclusions have been distributed above in the form of
comments along the various chapters. Not all of them will be summarized below
where I will rather focus on formulating some completions besides the basic
resuming tenet mentioned at the beginning: the
main message of this article is that only if we understand what we are doing
with the basic formalisms of mathematics and related logic, geometry and such,
we will understand what we are doing with computers. And now I can
add my conviction that ultimately it all is a theological and religious
question - the meaning and survival of our Judeo-Christian culture in face of
techno-science.
I wish also to emphasize that the literature surveyed in this text of
mine will always be insufficient in view of the complexity of the issues that
were covered. I will illustrate this with only one example, an excerpt from the
context of "A blog about religion, science, philosophy" that
introduces many other interesting ideas not considered here, and is taken from
an article I recommend, with the title Zen
and the Art of Science: A Tribute to Robert Pirsig. In an argument
that leads to reflection about the never resolved crisis in the foundations of
mathematics and basic rules of logic, the author (writing under pseudonym the
apparent pseudonym "m. servetus") who else
writes interesting stuff about Knowledge
without Reason tells about Robert
Pirsig noting that
[...] the number of hypotheses could easily grow faster than experiments could test them. One could not just come up with hypotheses – one had to make good hypotheses, ones that could eliminate the need for endless and unnecessary observations and testing. Good hypotheses required mental inspiration and intuition, components that were mysterious and unpredictable. The greatest scientists were precisely like the greatest artists, capable of making immense creative leaps before the process of testing even began. Without those creative leaps, science would remain on a never-ending treadmill of hypothesis development – this was the “infinity of hypotheses” problem. And yet, the notion that science depended on intuition and artistic leaps ran counter to the established view that the scientific method required nothing more than reason and the observation and recording of an objective reality.
Consider Einstein. One of history’s greatest scientists, Einstein hardly ever conducted actual experiments. Rather, he frequently engaged in “thought experiments,” imagining what it would be like to chase a beam of light, what it would feel like to be in a falling elevator, and what a clock would look like if the streetcar he was riding raced away from the clock at the speed of light.
[...T]he nature of mathematical discovery is so mysterious that mathematicians themselves have compared their insights to mysticism. The great French mathematician Henri Poincare believed that the human mind worked subliminally on problems, and his work habit was to spend no more than two hours at a time working on mathematics. Poincare believed that his subconscious would continue working on problems while he conducted other activities, and indeed, many of his great discoveries occurred precisely when he was away from his desk. John von Neumann, one of the best mathematicians of the twentieth century, also believed in the subliminal mind. [...]The Indian mathematical genius Srinivasa Ramanujan was a Hindu mystic who believed that solutions were revealed to him in dreams by the goddess Namagiri.
Intuition and inspiration were human solutions to the infinity-of-hypotheses problem. But [...] there was a related problem that had to be solved — the infinity of facts. Science depended on observation, but the issue of which facts to observe was neither obvious nor purely objective. Scientists had to make value judgments as to which facts were worth close observation and which facts could be safely overlooked, at least for the moment. This process often depended heavily on an imprecise sense or feeling [...]
It is a pity that the text does not dwell upon a quotation from Pirsig
which got imprinted in my mind since I read his famous Zen and the Art of Motorcycle Maintenance in
1977 (p. 110, my italics):
The cause of our current social crises [...] is a genetic defect within the nature of reason itself. [...] It begins to be seen for what it really is - emotionality hollow, esthetically meaningless and spiritually empty.
To return now to Brouwer I mean that his basic error besides his
"introverted" neglect of probable misuse by others of his method and
results, is the assumption that the damage caused by an undefined
"intellect" (paradoxically used by him in his own work) would come
exclusively from diverted attention from a likewise undefined self to the
external physical world. All this while there can be as many intrusions,
including archetypal images besides the basic intuition of time, coming from
the inner world of the collective unconscious. He himself seems to have been
struggling with his anima as most clearly exemplified in his apparently bizarre
attitude to "women considered collectively" in his early book on Life, Art and Mysticism.
On the other hand it is evident from the
material overviewed here and biographical details that Brouwer worked very hard
to achieve a spiritual readiness akin to an "individuation" by means
of a kind of continuous meditation and a familiarization with Christian and
Eastern mystical traditions that imply prayer. This may be more
than the atomic bomb's "genius" Robert
Oppenheimer with his late awakened conscience after the terror
crimes in Hiroshima and Nagasaki is said to have done. Despite his rather
introverted attitude Brouwer evidently also struggled to practice some
extraverted activity such as participation in the scientific community, its
conferences, publications and debates. Nevertheless we
also saw indications that he ultimately got somewhat socially isolated even if
his results came into the domain of use by other mathematicians, and ultimately
in extraverted industrial and military activities. His intuitive sensing of the
self was probably not sufficient to allow an integration of his ego with his
unconscious, let alone his negative shadow and anima.
In any case he succeeded in identifying, especially in the environmental
issues of his time, the danger of extraverted thinking combined with the
auxiliary function of sensation that leads to projection of fantasies of power
over nature and human communications. The success he envisaged, however, would
not come from the limitations of his mathematics but rather from his and
especially others' psychological maturity and capacity to understand and
integrate in their own work Brouwer's insights. This would have implied
consequent research by others along his line of thought and their renouncement
to improper applications of
a tempting mathematics with its supported technology and its supporting formal
logic.
Personally I feel intrigued by the necessity of a better
understanding of what may be Brouwer's main insight for our purposes. It is the
essence of isomorphism in its relation
to formalism,
since it lies at a ground to the phenomenon of mental projection and fitness of
mathematical, and consequently logical forms into nature and the whole external
world including humans and their activities that today are the object of
intense computerization. Thereby we might understand why humans find
consistency in their understanding of selected and causally structured pieces
of formalized world whose common characteristic may be to be object of their
often unconscious will to power, "infantile" dreams of omnipotence,
which consequently are projected into the environment including nature,
constituting the psychological essence of scientific technology. Since it is a
question of supremacy of "morphism" or form over content, whatever it is or should be,
it is also a question of understanding its essence. It is supremacy of
fragmented forms over content that leads the trend of computerization, and this
may also clarify the title of this article being the computer as
"embodiment", the form of form, or meta-form. It leads many computer
and information researchers today to abstract from the essence of computation
and communication mentioned at the beginning of this essay, luring them into
playing down the systems approach and dealing instead with the fashionable
trend of "design" with computer graphics, acoustics, haptic
technology and talk about numerous neologisms such as digital materiality being
a new materiality, or virtual reality being a new reality.
One hypothesis could be that such a supremacy of form over content may
be related to aestheticism in its relation
to ethics, already implicit in the role of art in Nietzsche's philosophy or, as
defined in The
American Heritage Dictionary: "An artistic and intellectual movement
originating in Britain in the late 19th century and characterized by the
doctrine that beauty is the basic principle from which all other principles,
especially moral ones, are derived." [My italics]. On an earlier occasion
I had already the opportunity to advise the author Gunnela Ivanov of a doctoral
dissertation on "design" (in Swedish, pp. 303-305) that
Friedrich Schiller had exceedingly interesting thoughts about the matter in his
Textes Esthétiques (Paris, 1998):
"Sur les limites nécessaires
dans l'usage des belles formes"
[On the limits necessary in the use of beautiful forms], pp. 82-83 and 86-87,
(corresponding to vol. XXI in Schillers
Werke - Nationalausgabe, edited by
Helmut Koopmann and Benno von Wiese, pp. 17-18 and 23). If I may guess, a
superficial and easy but probably defective way to convey the complex idea as I
understand it, would be that since Platonic beauty is the form of the good that
in Western Christian culture is symbolized by God, people more or less
unconsciously tend to feel themselves exhilarated, good or "godly",
when they are in contact with beautiful forms, in our case mathematical ones,
the more so if this is combined with an additional feeling of
"divine" power thanks to a divinely intelligent mind that approaches
god's own designer-mind. This corresponds to the fake feeling of the sublime that I treat in
another text
on computerization. For atheists, all the same: "I am best".
The same phenomenon may be active in the overpowering feeling experienced by
different psychic constitutions in composing, performing or listening to
different kinds of music. My criticism of the Wagner-cult, not to mention
modern times' satanic metal music fatidically related to phenomena like Charles Manson's cult, exposes
paradigmatic examples, whose understanding would be enhanced by an
understanding of Plato's references to music (e.g. Republic III 398 ff., IV
423d ff., Timaeus 47c ff., Laws II 653 d).
The "renouncement" or moratorium mentioned above is a
cultural, moral and theological social matter that is portrayed in the
difficulties experienced in philosophy of technology with its paradoxical appeals
for a "moratorium" in the development of technology. There are studies
(see here, and here, recalling
Joseph Needham's most famous and pioneering Science
and Civilization in China) of, for instance, why and how high civilizations
such as in China's history did not develop the Western kind of science.
Ultimately it would mean a renouncement to search for certain kinds of
"knowledge" to the advantage of others, to renounce working for the
development of certain kinds of (mathematically) advanced technology, in our
case computer technology, and or a renouncement to the extent of its use. At
the theological level some of these aspects can be subsumed under the criticism
of Brouwer's implicit quietism we already
mentioned, as it may be seen permeating even Kempis'
Imitation of Christ. The
problematic attitudes and life choices involved in these questions, analog to
Brouwer's, are illustrated in the modern world literature, and exemplified in
Thomas Merton's famous partial auto-biography The
Seven Storey Mountain (1948, 1998 ed.
especially pp. 304, 310f., 319, 323, 344-347, 361.)
Ultimately it is not an indictment of mathematics or its usefulness,
proudly advocated by those few who feel elect to "understand" it. It
is, rather, an appeal to keep to an ethical usefulness as implied in genuine
pragmatism as I understand it in the tradition of William James and West
Churchman where "use" implies an ethically justified goal and justified "tools"
or, rather, instruments, far from the supposed neutrality of techno-science.
That means also a mathematics, geometry or logic that are not confined to the
thinking sphere as defined in analytical psychology but are kept related to the
feeling and intuitive functions as also suggested in, albeit
criticized, anthroposophy. In fact Rudolf Steiner explains this
attitude as I read it in the Italian translation Nascita e Sviluppo Storico della Scienza [Birth and
Historical Development of Science] (Milano, 1982) of the original Der Enstehungsmoment
der Naturwissenschaft in der Weltgesichte
und ihre seitherige Entwickelung, (Opera Omnia n. 326, 1977, referring especially
the third and fourth of the nine conferences held in Dornach
between 24 December 1922 and 6 January 1923).
Naïve as it may appear or even be in the eyes of present day's
established mainstream mathematicians and scientists (just because they are
established), particularly mathematical physicists that were already challenged
by the previously mentioned Clifford Truesdell, we should be warned by the fact
that there are enormous vested interest and a whole
military-scientific-academic "industry" that thrives on the
paradigmatic status quo. It includes the cheap rejection of complex
psychological and social theories on the basis of the requirement that they
should allow their "falsification", while espousing defective
thinking about the meaning
of falsification. The effects of the creation of e.g. metamathematics or metalogic, although
unperceived by the general public, will be analogously mind-blowing as those of
meta-ethics as seen by
those who subscribe to Christian ethics. The creation
and application of the tripartite "syntax-semantics-pragmatics" will
focus on formalistic syntax, "magically" explain away pragmatics with
valued goals of humans, and tie semantics to extravertedly
sensed objects in the spirit of logical
positivism and analytic
philosophy. They also stand at the basis of scientific physical
reductionism that spoils conclusions from the work of quantum physicists such
as Carlo Rovelli (see below). The extent of strange mind-blowing (mis)uses of
such creations is and will be analog to the ongoing general computerization of
life under controlled (cf. police-controlled terror-safe) laboratory-like forms
of user
interface and human-computer
interaction, and to queerly innovative feminist uses of the
abstractly mathematized quantum physics, for instance, in Karen Barad's Meeting
the Universe Halfway: Quantum Physics and the Entanglement of Matter and
Meaning, (Duke University Press, 2007). The contrast between
such approaches and studies of relations of quantum physics to psychology can
be appreciated in Suzanne Gieser's ambitious The Innermost
Kernel. Depth Psychology and Quantum Physics: Wolfgang Pauli's Dialogue with
C.G. Jung (Springer-Verlag, 2005, based on her PhD
dissertation, in Swedish, at Uppsala University, 1995, ISBN 91-506-1140-2).
In this context of quantum physics and its (mis)understandings I must
mention more recent publications by the theoretical physicist Carlo Rovelli who has become
known for his work on and popularization of relational
quantum mechanics. In the book Seven
Brief Lessons on Physics, and later in The
Order of Time (e.g. in chap. 3 and 6) he popularly relativizes the
concepts of object, time and space, and thereby those of presence and existence. These
complexities undermine in a fruitful way the common lay (and some theological)
objections or considerations about the existence of God. At the same time,
however, they also tend to undermine all certainties, giving a taste of postmodernity that also
encourages the misuses of references to quantum physics mentioned in the
previous paragraph. I have concluded that one if not the main shortcoming in
Rovelli's approach is that he does not problematize the concept of the
observation as being psycho-logical,
i.e. necessarily mediated by the psyche
(not to mention Spirit).
He understandably does not dwell into this, reducing psyche to the
"functioning of the brain", decorated by indiscriminate
"emotions" that are said to include passions and "love".
They are seen as aesthetically giving colour to human
life, as he himself does in his text by means of a rich (but inconsequential)
display of erudite, moving poetic references to philosophy and the arts.
Paradoxically Rovelli even displays, with reference (chap. 12) to Augustine
of Hippo, similar insights to Brouwer's about the nature of
music without, however, relating them to mathematics. Rovelli treats the
observer and psyche of a human being in the light of physical reductionism (disregarding
its controversies), paradoxically
related to his deconstructed observer-"object" that he sees as
constituted by his (its) interactions with the environment. This, without considering
that this observer sees from both the "outside" and the
"inside", as body and a psyche that consists of more entities that an
Ego. Furthermore, the popularizing language he uses in the book hides that the
observations (theoretical physics)
are mediated by an extremely mathematical
reasoning that ignores Brouwer's message. It is a similar shortcoming
undermines the otherwise deep-going work of Arnold Gehlen's Die Seele im technischen Zeitalter
(chap. II, 1-2, Italian
trans.). Consequently Rovelli does not reflect upon
his own account of the misuse of mathematics in commenting the (apparently?)
"long series of successful experiments"
supporting physics Standard Model (in Seven Brief Lesson on Physics, p.
32):
It's a theory which looks, at least at first sight, piecemeal and patched together. It's made up of various pieces and equations assembled without any clear order. A certain number of fields (but why these, exactly?) interacting between themselves with certain forces (but why these forces?) each determined by certain constants (but why precisely these values?) showing certain symmetries (but again, why these?). We're far from the simplicity of the equations of general relativity, and of quantum mechanics.
As if "aesthetical" simplicity and elegance would have solved
the question. Ignoring Brouwer's message and the essential meaning of a
mathematics leads Rovelli into a psychological and theological nihilism, in the
spirit of ignored sociopsychological interactionism. It is extreme
mathematical reasoning that isolates from social cultural criticism and enables
mathematical minds to be popularly perceived as polymaths. It enables
Rovelli to create a new synthesis in his relational quantum mechanics, creating
a logically well structured and therefore
treacherously convincing story with a mixture of hypotheses and empiricism,
with (atheistic) references to both buddhism and hinduism, and with e.g. the trivial rediscovery (The Order of Time, chap. 12)
of the concept of "system" that, undefined, is used indiscriminately
as much as "world" or "nature", as much as system is used (in Seven Brief Lessons..., pp.
18, 60, 74), or "objects" are found "only in abstract
mathematical space" (idem, p. 16) but they "work well" (pp. 18
,38) as Brouwer also notes with regard to misuse of causality. All this while
the human "observer" no longer observes (p. 33) or no longer speaks
but a word's meaning depends on "where it is spoken" (or heard? p.
57), and "the information that one physical system has about another has
nothing mental or subjective about it" (p. 68).
In consideration of Rovelli's obvious proficiency
it is motivated to adduce Socrates in Plato's observation (Republic
VI, 491d-e, here trans. by Paul Shorey) that it is "natural
that the best nature should fare worse than the inferior under conditions of
nurture unsuited to it". The stronger impact of misled gifted scientists
can cause more damage, and in this case I do know of
only one other knowledgeable scientist, Kelley L. Ross, who could review and
challenge Rovelli's "Seven Lessons" on his own
professional terms.
If all this is not enough let's recall the announced advent of
additional "mathematical tools" such as quantum
computers. Unfortunately it will not
require a better understanding of mathematical "tools" inasmuch they
will be welcomed, to begin with, for military applications, recalling Brouwer's
warning about scientific methods' basic motivations and their consequent
essence. The message of this article is nevertheless that it is better to ask
ourselves how this squares with the idea of good
mathematics without reverting to the old irresponsible tenet that it is neutral
and its goodness depends politically upon its or "our" supposedly
good applications, guaranteed by our own goodness or explicit commitment to
doctrinal righteousness. The problem is analog to the repeated announcement of
advantages of artificial
intelligence, while neglecting the lessons of what it implicates,
as expounded in the already mentioned The
Design of Inquiring Systems. I guess the lessons are that if one cannot create computers that
"think" as well or better than humans, it is possible to teach or
force humans who do not already do so in culturally deprived work environments,
to think and act like rudimentary computers.
Thereafter it will be only logical and natural to claim that it is
better to replace them by genuine modern computers, which can handle more
complex logic and mathematics with faster processing and larger memory. Much
debate about AI is idle play around this sort of tautology while ethics and
morals are reduced to "moral rules" seen as the "core of our
human values", psyche and mind are reduced to "brain", causal
chains are reduced to "goals and means", machine learning is reduced
to induction-deduction, and computers are reduced to "algorithms".
With such a background it is not a question of whether humans will be replaced
by "super-intelligent" machines leading to the absurdities of technological
singularity, since they already are being and will be progressively replaced. The question is
rather which countermeasures can be taken today to offset or meet the cultural
and pragmatic consequences it will bring, reviving the core idea of the Frankenstein novel. The
whole hype of "superintelligence"
and its apparent criticism, hangs on a
basic misunderstanding of the roles of mathematics and logic, and its
consequences in the abuse of techno-science, in particular of computer-oriented
techno-science. Such abuse gets even coarser in the industrial-commercial
fields, an example being in the search of manpower by a Swedish multinational home
appliance manufacturer. The advertising supplement The Scholar distributed with the main morning newspaper Svenska Dagbladet (in February, 2022), announces (p. 18) that “Data
science and AI” open up exciting future prospects in the company”. It specifies
further that the company is looking for new competent colleagues for the
application of data science and IoT
[Internet of Things] in its manufacturing. It is looking for Data Engineer, Data Modeller,
Lead [meaning Leader?] of Data
Assets, Senior Azure, Developer,
Senior Data Scientist, and Senior Solution Architect. Most of the
terms being barely known neologisms that suggest a prestigious occasional
“future” for technicians who have learnt or trained certain momentarily hyped
computer-anything.
What about the status of these questions in contemporary literature
about technology, ethics and responsibility? To my knowledge among the most
ambitious approaches there is the already mentioned Carl Mitcham with his late
contribution (2015) Rationality
in Technology and in Ethics. In: Gonzalez
W. (eds.) New Perspectives on
Technology, Values, and Ethics. (Boston Studies in the Philosophy
and History of Science, vol. 315. Springer, Cham.) The connection to my present
text is, however, better sensed in his comprehensive article integrally
available on the net Technology
and the Burden of Responsibility, where he refers for once to
mathematics and rationality:
"Modern engineering and technology ... introduce into the making activity an engagement with phenomena via mathematically analyzable forces in a sensorium extended through instrumentation into chemical composition at the level of atoms and molecules…In the techno-lifeworld so constructed by the rational taking in account of more than directly experienced phenomena, it is not surprising that moral behavior likewise must move beyond the primacy of anything approaching natural intuitions. Moral conduct too has to become more conscious, more rational, and take more into account."
It is to be noted, then, that what I have been discussing throughout
this present text is the ultimate problem of "via mathematically
analyzable forces" in a "sensorium extended through
instrumentation". All this, as we saw, is related to the meaning of
"more conscious, more rational, and take more into account". In an earlier paragraph Mitcham quotes from William Akin's Technocracy and the American Dream (1977):
"One influential effort at formulating engineering responsibility led to the technocracy movement and the failed idea that engineers more than politicians should wield political power. Henry Goslee Prout, a former military engineer who became general manager of the Union Switch and Signal Company, speaking to the Cornell Association of Civil Engineers in 1906, described the profession in just such leadership terms: The engineers more than all other men, will guide humanity forward [...] On the engineers [...] rests a responsibility such as men have never before been called upon to face."
What appears in the discussions of this present text is also that the
task reaches beyond engineering and information science that rely on so-called
empirical evidence, mathematics and logic. What is never (dares to be)
mentioned is that "consciousness and rationality" in engineered
computer systems may be framed, as suggested by Brouwer, through psychology and philosophy into basic religious
(in our highly technological Western cultural heritage - Christian) and
theological tenets. They are supposed to regulate humans' values, the
interactions among themselves and, consequently, with nature. Provocatively:
ethics and responsibility may be "follow the Ten Commandments" (or most
or at least some of them?) and the rest, the correctly understood
"conscious rationality", may follow.
Having come this far I must remind the reader of the reasons for my
apparently weird sort of academic writing in this article written as a
summarizing "swan song" in a relative hurry at an advanced age (80)
with a perceived lack of time left for work. If it were not so, I know how it
should have written: e.g. as Jean Guitton recommends in
his Le
travail intellectuel ["A
student's guide to intellectual work"]. I write with an excess of
details, without sufficient revisions for improved clarity of expression, in a
language that is not my mother tongue, with a profusion of references given in
the links associated to the used words, links that are intended for only those
who need them, and are only available to be read for those who read this text
on the computer. I wish to leave a "heritage" to those few readers
who are genuinely interested in pursuing this kind of research, to confirm or
revise it on the basis of further detail. The general idea of "why I write
as I do write" is to be found elsewhere
in my homepage, (and at the concluding end of other pages), a version
being also found in my blog. I make frequent use of Wikipedia-references because of
their often "good enough" comprehensiveness and easy overview in
terms of standardized layout. This is done, however, with full knowledge and
evaluation of their possible shortcomings that are partly declared in
Wikipedia's own auto-criticism. I have also already accounted elsewhere for my critical attitude to Wikipedia. For the rest I am grateful for any comments I may get as I am grateful
for all contributions that formed me during during
several decades of work. I intend to read and acknowledge all comments, but I
apologize if I will not be able to comment the comments, still less to be
available for discussions or debates about the text because of reasons that I
partly expose in another essay especially devoted to the frequent sterility of debates, including peer
review and publication.
Long after writing the above text a colleague told me about news in
quantum physics as presented in the link (June 17, 2021) "Physicists
bring human-scale object to a standstill, reaching a quantum state". It
refers to details in a scientific paper in Science, 18 June 2021, Vol. 372, No.
6548, pp. 1333-1336. I have only knowledge of mathematics and basic quantum
mechanics from courses in electronic engineering (William Houston, Principles of Quantum Mechanics, New
York: Dover, 1959) I asked for orientation from a couple of colleagues who are
knowledgeable about the state-of-the-art. One of them, professor of plasma
physics summarized his view:
"Quantum
mechanics [QM] is very useful, and as you know, can be used to calculate many
new verifiable results. - But no one really understands why it is so good, so I
recommend my students to just count, instead of asking undefined questions.
"
The other colleague commented the above answer of the first one. I
choose only a few lines of his comments, beyond the rest that mostly lies above
my competence:
"[The]
professor of plasma physics is exactly on the same line as I am. Einstein also
had about that same attitude. Now, however, it seems that some experiments in
recent years support Bohr's interpretation and do not support Einstein's view
of QM. But regardless of this, one can successfully use QM without
understanding it philosophically. Your plasma physics professor's view is
pragmatic and I do not think you can blame him. Since we do not have a certain
meaningful answer, we must be content with the fact that it works in an
incredibly fantastic way."
What are we to make out of this? I think that it illustrates how far we
travel from the Brouwer's trail, while the "pragmatic" attitude
(verifiable result, successful use, it works) does not fit what appears to me
to be the most thoughtful vein of pragmatism, the philosophical
pragmatism, of William James. It is easy to
forget that in this meaning of pragmatism, pragmatic truth "works",
but is must work also for enabling of achievement of what is good, not only of
what is profitable, pleasant or exciting without need of "understand
philosophically". Such understanding is seen as a merely decorative
feature of understanding, as, paradoxically, in the analytical
philosophy's facile separation between facts and values
(engineers/administrators and politicians/priests).
As a concluding exercise I propose is to relate the above to the
following thoughts. First, consider the analogy of seeing the Isaac Newton,
pioneer of modern physics, but also interested in prophetic interpretation & escathology, as well in alchemy
that especially today are downplayed and silenced. This recalls the fuzz
about the rejected parts
of Brouwer's dissertation and issues that would have to wait until the
twentieth century, as Carl Jung's psychology and his cultural criticism, as in Civilization in Transition (1970).
I ask the reader to consider the exercise of evaluating the possibility
of an analogy with a hunter (the pioneer scientist) that with sacrifices and
risk for his own life traps in a cage or kills a dangerous wild beast, and then
others (pragmatic smart technical-mathematical scientists) follow like hyenas
throwing themselves over the cage or the carcass, doing research on how
pragmatically use it or profit on it. Or then consider the case of the
"unsinkable" Titanic, an archetype of the technical hubris of "many
new verifiable results" in advanced naval architecture and ship
construction. Or, finally, consider the ending of quantum physics and all the
rest of the world if the Cuban missile crisis had had an
unfortunate ending "working in an incredibly fantastic way" as in the
past atomic bombings of Hiroshima and
Nagasaki, or as in the possible future following the
escalation and spread of nuclear weapons. All this while disregarding the issue
of climate warming, or environmentalism that already worried Brouwer. The
difference between the relevance of these three analogies for our purposes is
the degree to which they illustrate the development, meaning and application of
advanced mathematics intertwined with logic. The bulk of educated humanity does
not understand the meaning of advanced mathematics, as mathematical pragmatists
do not understand Newton's and Brouwer's understanding. Such reciprocal
misunderstanding neutralizes the role of devout democracy in controlling this
issue.
And, regarding the meaning of advanced mathematics, and mathematical
logic, or mathematical statistics, or mathematical science: when I wrote most
of the text above I did not expect that about 10 years
later I would read in The Economist (October 12, 2026) an article with the
titles The
end of mathematics? AI’s mathematics blitz pushes science into strange new
territory. Other disciplines should take heed. See also here.
All of it to be included, if I make it even if my readers don’t (!), in my
other papers on Computerization
as abuse of formal science, and Artificial General Intelligende and ChatGPT.