[OPE-L:1365] Re: Math, methodology and political economy

Paul Cockshott (wpc@clyder.gn.apc.org)
Fri, 8 Mar 1996 00:14:06 -0800

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Jerry asks if I am by implication condemning some list members
as ignorant by my statement that I dont accept that there is
anything that is unsuited to mathematical modeling, and
that if something is declared 'unsuited' that just indicates the
depth of our ingnorance and confusion in the field
in question.

Well of course I am saying that members of this list are
ignorant and confused, we all are. That is natural state of
all scientific investigation. As we become less ignorant
and confused we are able to pin down what we think more
precisely, make predictions and see if they turn out to
be true.

* On what basis do you claim that a mathematical form of inquiry is more
suitable for investigation in political economy than a systematic
dialectical [and primarily non-mathematical] method of inquiry?

On the precedent of Pythagoras - the universe is number - the polemic
of Hume and the experience of the sciences.

* Mathematics *by definition* is an expression of formal logic.

So Hoped Hilbert, so to at first did Russell and Frege, Goedel
and Turing showed that this is not entirely the case.
Mathematics are formal systems, but what we know from Turing,
is that formal systems have material supports. Thus a formal
process is also a material process, and, like all material processes
has implicit constraints. Though whether this is really germane
to your point is not clear.

Are there
instances in which dialectical logic can not be expressed in
mathematical terms?

What is dialectical logic?
Either you can define it clearly, formalise it, and then, subject
to the Goedelian constraints, we can use this to determine if a
dialectical argument is valid. Or, alternatively, it can not
be clearly defined, it means whatever the individual dialectician
wants it to mean, and becomes a license for any kind of arbitrary

If so, does that mean we formalize and linearize what we
are studying in order to produce mathematical "results" or do we accept
that some topics are more suited than others for expression in
mathematical terms?

Formalising and linearising are distinct. Many processes that are
susceptible to formal analysis are non-linear - for instance the
equationsfor the time derivative of the rate of profit taking into
moral depreciation are almost certainly non-linear. My hesitancy
about accepting Alan's hypothesis about inter-temporal conservation
of value are related to this. Such conservation seems highly unlikely
in a non-linear system.