Date: Sun, 24 Jan 1999 19:09:51 +0100
Subject: Re: Brouwer and Bhaskar


Dear Jim (and all),

          . . . one of those many loose ends . . . ;-|

a couple of months ago you asked:
>But does Bhaskar accept Brouwer's Constructivism?

Yes, i think so . . . but

This really is an interesting question, one worth discussing
in depth and with the major texts at hand, but the speeds
and unexpected bifurcations of mailing-lists always makes
me weary and unwilling to procede or even to try; anyway
allow me to offer some thoughts by way of small exerpts in
the form of paraphrases and demi-quotes, w'll see what
comes of it ...


(1) On Brouwer's Intuitionism
Brouwer was a strange guy. When asked, he always replied that
he became a mathematician because it offered him a "quiet life
and a good salary" and, that his sole interest in mathematics was
his hope (conviction) that it could bear some insights on the "great
questions of life". [But he also once revealed that "the difference
(sic) in intimite nature between a woman and a lioness, is far less,
than that between two brothers-in-friendship (two males)".]

At the beginning of this century there was a fears debate among
mathematicians concerning the characteristics of infinite sets,
and within this debate Brouwer advocated (1907) the view that
a consequent deployment of Aristotelean logic would inevitably
lead to illicit ontological claims (in math.). He therefor rejected
the arch of Aristotelean logic viz. 'the principle of the excluded
middle' (and the rest).


* some ontological considerations:

- according to Brouwer there is no (metaphysical or other)
warrant to presuppose the existence of any mathematical
(or logical) object (or truth) prior to its construction;

- mathematical objects are constructions of the human mind;
before their construction they are neither real nor true, but once
constructed they exist independent of and are irreducible to our
use/knowledge of them; futhermore is it possible -and even
necessary to assume- that some constructions will never come
to a finished end, thus never will be finally constructed at all;
(cf. e.g. states-in-process, products-in-progress)

- mathematical objects do not exist predependent from or a
priori to their construction, they both come into being through a
mo(ve)ment imo best described by way of the buddhist concepts
of 'dependent co-arising' and 'united co-emergence' (Brouwer
imo seems influenced by Buddhism), and so only after a
successful construction a certain 'necessity a posteriori' is granted;
("scientific truths are nothing more than a chimera of human
desire")

- although mathematical objects are constructions of the human
mind this doesn't mean that they are created 'out of the grey',
(new) constructions are produced by means of antecedent or
previous constructions and this process of (re-)production
ineluctably takes place in a socio-geohistorical context.


* some epistemological considerations:

- according to Brouwer to know the meaning of a mathematical
object is to know how to perform the practices that lead to its
constuction (and i.a. the ability of re-construction); [it is said
that this Brouwerian argument awoke Wittgenstein -in 1928-
from his philosophical slumbers]

- "there exist no apriori axioms or deductions, there is only
evidence"; what counts, in the last instance, is performing and
showing your constructions; (math.) problems are not solved
by discovering or applying (logical plausible) deductions, but
only through the "invention of the 'right' constructions".

- for mathematics to obtain knowledge of its objects of investigation,
language and logic are unreliable tools; the only permitted 'instrument',
Brouwer argued, is our *time-intuition*: our ability to count, the
experience of *one-twoness*, the perception of the pulse in time.

     Time-intuition is the production basis for simple constructions
     (repetitions) called "choice-rows" like: -AT- -AT- -AT- -AT- -AT- , i i i i i ,
     () () () () () , 1 2 3 4 5 , do re mi fa sol , * % ± $ =A7 , or whatever.
     [one of the first successful constructions in math. was:(1)->(2)]
     [[ "choice-rows" could be conceived as "research programmes"]]

     [btw. this time-intuition is futher grounded in and originating
     from activities like breathing, walking, singing, dancing etc..
     and probably in even evolutionary deeper activities like
     birdsong, animal mating- and hunting/gathering-behaviour.]

- his simple conception of pure time-intuition made Brouwer
famous and notorious, but because of its apparent simplicity it
was easily misunderstood; it is very important to stress that
Brouwer conceived time-intuition more as a *sense* and less
as a cognitive programme or mental structure.

- qua time-perception humans are both passive sensors of the
flow of time and active constructors of discrete moments in
time. This time-sensation is (perception) without any perceptual
content, which ought to be ranked as our *primal sense*, is more
premordial and operating on a more fundamental level than our
other 5 senses.

     (it's interesting to notice here that Brouwer renounces Kant's
     a priori of space, but only to hold on even more strongly
     to his a priori of time.)

To appriciate the rigour of Brouwer's time-intuition here one
must understand that knowledge, obtained solely through the
traditional 5 senses, is highly illusionary, obstructional and
contentious and as such inexorably vitiates thought and being
alike.
=46or Brouwer "the only aprioristic element (in science) is *time*"
and our time-intuition is as basic and universal a scheme of
action and reference as one can get, and hereby both the only
acceptable base for and limiting condition of any scientific and
math. endeavor.


* some sociological considerations

- Brouwer was a mathematician and not a sociologist, so it's a
bit odd to consider 'his sociology' here, but nevertheless
Brouwer held some very strong views and beliefs on society,
which he (albeit modestly) defended and practiced throughout
his whole life.

- the society Brouwer envisaged was one of material sobriety and
ascesis; people sould live in small communities (or even better in
solitude), inwhich they ought to cultivate a close relationship with
nature and the "Self".

- closely connected with this life is the activity of meditation (or in
Brouwer's word "zelf-inkeering"[inwardness]) and it is regared
as the sole key to a true free life of artistic and mystical depth.

- futhermore Brouwer held a deep disdain toward mass-economy
and its mass-technological products which in his opinion were a
disastrous encroachment of one's private life and society in general.

[Isn't it ironical that he was killed -run over- by a car in front of
his house (1966)?].

                                            ~

(2) On Bhaskar's Realism
Roy Bhaskar, who imo is one of the most brilliant philosophers
of this moment, has developed his own brand in the philosophical
tradition called Realism. This development can be sketched along
the following lines:

- in 1975 he wrote RTS in which he advocated (contra Hume's
Empiricism and Kant's Transcendental Idealism) a new realist
theory of science, a new philosophical ontology dubbed as
"Transcendental Realism";

- in 1979 he writes PON which sets out to evaluate critically
the (im-)possibilities of Naturalism (guised in positivist and
hermeneutical traditions alike), thus leading to a subsequent
philosophical repositioning he (and others) then rebaptize as
"Critical Realism";

- in 1993 DPF is published and -via a radically new and
original theory of dialectics (challenging the whole of western
philosophy)- a futher deepening and elaboration of the critical
realist programme takes place. Within this programme Bhaskar
clearly states his own position as "Dialectical Critical Realism".

     [btw. i think DPF is a must for everyone interested in the
     confutation of the socio-political crotchets of most post-
     metaphysical, -humanist, -structuralist and -modernist thinking]

- (at the moment us bhaskarites are awaiting his next phil. turn,
allegedly a turn to the East :-)


* Bhaskar's ontology
The core principles on which Bhaskar's realist ontology pivots
are: Intransitivity, Transfactuality and Stratification.

< Intransitivity >
- according to Bhaskar "western philosophical tradition has
mistakenly and antropocentrically reduced the question of
what is to the question of what we can know. This is the
_epistemic fallacy_ viz. the failure to distinguish between
the intransitive and the transitive dimensions of reality."
(or "the reduction of being to our knowledge of being, and
by so collapsing ontology into epistemology")

- intransitivity here refers to the reality of entities (things,
structures, tendencies) which exist and act quite independently
of our identification and description of them. (here intransitive
entities are conceived as "non-observable generative
mechanisms possessing causal powers" featuring also
"(relative) endurance and relationality")

- transitivity refers to the reality of knowledge (science, theory,
meaning) which is a socially produced, transient and geo-
historically contingent account of intransitive entities (e.g.
in so called 'laws of nature').

- from this it is recognized that "being contains, but is
irreducible to, knowledge, experience or any other human
attribute or product. The domain of the real is distinct from
and greater than the domain of the human-empirical."

< Transfactuality >
- transfactuality refers to the 'trans-f/actual' operation of
intransitive entities independently of the states (opened or
closed) of the system in which they occur, and thus " the
domain of the real is distinct from and greater than the domain
of the actual (and hence the empirical too). Failure to appreciate
this results in the _fallacy of actualism_, collapsing and
homogenizing reality. ...laws of nature must be analysed as
ransfactual, as universal (within ther range) but neither actual
nor empirical."

< Stratification >
- stratification refers to the notion ontological depth (contra the
monolithic and/or monovalent ontologies of various monisms)
claiming that reality contains multiple and different ontological
strata which Bhaskar primary identifies as the domains of the
Real, the Actual and the Empirical, whereby the causal conatus
of real entities can be possessed unexercised, exercised
unactualized, and actualized undetected or unperceived.

- in addition to the above mentioned vertical stratification (R-A-E)
Bhaskar also distinguises horizontal stratifications reflected by
the (geo-histrorical) differentiations in nature and man, in societies
and cultures, sciences and arts.

- the possible configurations of interplay between the strata of
this ontological grid are manyfold, and on Bhaskar's terms any
adequate description of them should in base use concepts like:
non-identity, dialecticisation, bipolarity, absenting absence,
emergence, mediation, reciprocity, rhythmicality, becoming,
learning, reflexivity, concrete univerality, (sub)totality, hiatus,
autonomy-within-duality, systemic openness, emancipation ....


* Bhaskar's epistemology
The key concepts here are: (i) epistemical relativism, arguing
all knowledge (meaning, theory, science) being socially (geo-
historically) produced and transient, in principle fallible, and
belonging to the transitive domain of reality;

- (ii) judgemental rationalism, entailing that the only 'good
grounds' for preferring one theory over another are 'rational'
ones; thus "if one theory can explain (and hypothesize) more
significant phenomena in terms of its descriptions than the
other can in terms of its, then there is a rational criterion for
theory choice, and a fortiori a positive sense to the idea of
scientific development over time (cf. RTS)"

- (iii) explanatory and emancipatory critique, asserting the
claim that all theories have practical, moral and political
implications (so being non-neurtal); thus to critize (or contradict)
a theory is at the same time [a] to critize the society in which
it holds sway, and [b] to offer explanations remeding its
ignorance and liberating it from false beliefs.

     The fusion of "is and ought", the bridge between "fact and
     value" which Bhaskar tries to advocate here is ".... that the
     moral good, more specifically a vision of a freely flourishing
     society, is implicit in every expressively veracious action or
     remark."

- on the whole one might say that Bhaskar is trying to fuse
both analytical reasoning, confined to an ontology of stasis,
and dialectical reasoning, attuned to an ontology of dynamis;

     In fact this is a fusion between theory and pratice, acknowlegded
by the idea that we not only know things, but we also act amongst
them. "If we were not accurately connecting with the world in the
world's terms, not ours, a fair percentage of the time, we would
not be around to argue about truth."


* Bhaskar's sociology

- probably the most significant notion of Bhaskar's sociology
(social ontology) is his "Transformational Model of Social
Activity". On this model "society is" conceived as both "[a]
a pre-existing and (transcendentally and causally) necessary
(pre-structured) condition for intentional agency but equally
[b] as existing and persisting only in virtue of it."
The thesis is here that, social "objects and relations, of which
knowledge is obtained in the social activity of science, both
exist and act independently of human beings (and sense-
experience)."

- an other couple is "structure" (society) and "agency" (human
being) both having irreducible causal powers whereby society
is viewed as both the 'condition' and 'outcome' of human activity
and human activity as both reproducing and transforming society,
thus meaning that humans are always living in a world of
structural constraints and possibilities that they did not produce
nor choose, but, by having to act upon them, are also always in
a position to change them.

- it is important to stress that Bhaskar sharply distinguishes
between (i) the genesis of human action, lying in the reasons,
intentions and plans of human beings and (ii) the structures,
paradigms and meanings governing the reproduction and
transformation of social activities.

- the upshot of Bhaskar's sociology is i.a. an ethics containing the
vision of an eudemonistic society as "assertorically imperatival
sensitised solidarity", one wherein human beings, cosmologically
dependent, are persistently seeking freedom and flourishing and
-by absenting absences, removing ills, constraints and blockages-
to avoid harm, for each and all of us.

Concluding one could say that according to Bhaskar (social)
irrealism (of any kind) is ontologically incomplete and as such
de-totalizing reality and "symptomatic of an alienation of human
being from the cosmos and a lack of autonomy that only a
eudemonistic society oriented to universal human emancipation
can rectify." Irrealism, thus, ought to be condemned as anti-
democratic and anti-emancipatoric.

=46or me the most convincing reason for adopting a realist position
is the acquisition of a framework for the rational discussion of
(socio-) ontological questions, one which in the mean time is
focussed upon furnishing programmatic (pre-)conditions for
development toward an eudemonistic society.

                                            ~

(3) "But does Bhaskar accept Brouwer's Constructivism?"
Above i tried to sketch roughly the imo most salient ideas of
Brouwer and Bhaskar, now let's return to Jim's initial question.

As far as i know Bhaskar never mentions Brouwer,
so what follows is my personal take on the matter.

- on the ontological level i see no problems.
According to Bhaskar "Ideas (including category mistakes,
logical contradictions etc.) are a part of everything, and
everything is real", so such ideas as Brouwer's "time-intuition",
"choice rows" and "mentally constructed mathematical objects"
are real and existent entities for both Brouwer and Bhaskar.

The intransitive and transfactual aspect of math. objects is
satisfied imo by Brouwer's claim that math. constructions are
mental inventions of our experience of/in the flow of time,
socially expressed and concretisized in (geo-)historical
contingent "choice rows".(and stratification is a matter to
discover by the science of math. itself, e.g. topology)

- on the epistemological level i see no problems either.
=46uthermore i see a straight line from Brouwer's rejection of
Aristotelean logic to Bhaskar's deployment of the Epistemic
=46allacy, both warning us not to make illicit ontological claims
on pure epistemo-logical grounds. Also Brouwer's low fiducity
in language is paralleled by Bhaskar's concept of the Linguistic
=46allacy (viz. the reduction of being to -what can be expressed
in- language).

     Brouwer's view, that mathematical objects and mental
     constructions are ontologically distinct but epistemologically
     inseparable, would only be challenged by Bhaskar if
     Brouwer was advocating a solipsistic postition here,
     but he doesn't, because Brouwer demands concrete
     empirical evidence of every found construction; (thus the
     personal construction of "choice rows" might be called an
     entirely private enterprise, but finished "choice rows" are
     really there, ready to be examined and evalueted by us.


- on the sociological level i''ll be brief because i think there
is enough room in Bhaskar's eudemonistic society to hold
some esoteric sects of intuitionist topologs and -farmers.

always yours,
Jan (call me a eudaemonistic topological farmer)
====




     --- from list heidegger-AT-lists.village.virginia.edu ---