[OPE] Mistaking Mathematical Beauty for Economic Truth

Well, from the arguments I have provided in the past on OPE-L, it should be
clear that I don't think there is any such thing as a "dialectical logic" (a
system of logical rules) independent of a particular subjectmatter, though
the subjectmatter may contain dialectical characteristics which can be
discovered upon inquiry.

So I don't really think there is such a thing as a "dialectical logic" in
general - dialectical analysis does not lead to only one logically
compelling conclusion, and the validity of the dialectical inference depends
on the meaning of the subjectmatter - at best you can say that there is such
a thing as "dialectical reasoning" or "dialectical reason" which aims to
define the specific meaning of the subjectmatter by systematically
investigating both what it is, and what it is not, where understanding both,
and the relationship between them, is essential. As an extreme, Sartre for
example devises a dialectical ontology out of the categories of "Being" and
"Nothingness".

I think the main thing to understand is, that to describe explain fully what
is involved in human reasoning, deductive and inductive inference are
insufficient, since human reasoning involves many non-arbitrary judgements
which cannot be formally reduced to deduction or induction only, since they
involve "meta-choices" of meaning concerning which deductions and inductions
are actually applicable. If we aim to show that these "meta-choices" are
rational, we require a meta-level of analysis, which contains those
deductions and inductions, but goes beyond them.

That is to say, that rational judgments often involve operating at different
logical levels simultaneously - the choice of an inference or premiss at one
level of analysis is guided by the choice of an inference or premiss at
another "meta-level" of analysis, which - this is the point - is not
entailed or contained at the first level, i.e. is not reducible to it. The
"meta-level" may at the most abstract level obviously consist of certain
assumed metaphysical categories, for which there can be no proof, other than
that they validate themselves by the results they achieve.

If e.g. I hammer a nail into a piece of wood, this involves me practically
in making judgements on the basis of interrelated abstractions and
specifications which cannot be fully specified in formal logic, e.g. as a
computer programme, but which are nevertheless non-arbitrary. I suppose I
could formalize the task into a finite set of operational instructions, but
even if I did that, there is no guarantee that the hammerer will
automatically succeed at first try.

Normally we would say, that "through practical experience" (through
successive behavioural adjustments) the student learns to hammer the nail
into the wood successfully. But this involves a reflexive subject-object
relationship between the student, the hammer, the nail and the wood. I
suppose I can also create a machine which hammers nails into wood, but I can
only do so, by systematically eliminating all kinds of possible moves which
the student can make, but which the machine cannot make, reducing the
possible number moves to only a few.

If for example I say that free will and determinism are compatible, this
seems logically contradictory in the first instance, insofar as by
definition something is not free, if it is determined. Yet I can restate the
meaning of free will and determinism in such as way that they are opposites
which presuppose each other - on the one side, free will cannot exist in an
indeterminate, random chaos since the total chaos provides no basis for
asserting free will (the very meaning of a free choice in that situation is
unclear), while on the other side, a pattern of determinism cannot even be
recognised or assumed, without a certain freedom to cognize (actively
identify, distinguish and generalise) reflectively about, the determinism.

Developing this idea, I can show that it is possible to choose freely
between a limited range of options, but that I cannot just choose
"anything", and thus I can prove that certain actions were due to mainly to
(internally) freely made choices, and others due to (externally) determined
influences. Point is that if I lacked the ability for dialectical (meta-)
relativisations, I might falsely exaggerate the realm of free choice or the
realm of determinism, or mistake the one for the other, leading to all kinds
of reifications (subject-object confusions).

But if I can choose between a limited range of determined options, then this
itself implies that there is more than one logical response possible to a
determined situation, which means that no deduction to exclusively one
logically compelling conclusion can apply. Whereas I can logically formalize
that predicament, I cannot logically formalize the choice made themselves,
except by introducing another level of logical analysis, according to which
the choice made can be viewed as (logically) determinate, but as soon as I
study the simultaneous interaction of the two different levels, I am likely
to encounter dialectical relationships which depend on the efficacy of
meanings ruled out by the principles of Aristotelian-type logic.

Jurriaan

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Received on Mon Sep 14 07:19:48 2009