Paul [OPE-L:1365] says in response to Jerry that
"[a mathematical form of inquiry is more suitable for
investigation in political economy] on the precedent of
Pythagoras - the universe is number - the polemic of Hume and
the experience of the sciences."
Pythagoras's held that 'number is the essence of all things'
(Heath p47).
Entry to the Pythagorean school was conditional on worship of the
holy number four. Hippasus was allegedly expelled from it for
making known the discovery of incommensurable lengths(!)
Pythagoras was the first to proclaim the earth spherical, but his
reasons leave something to be desired: it was because it was 'the
most beautiful of all solid figures' (Heath 87).
This same reasoning produced the approach to astronomy which
lasted until Kepler, namely to deduce the actual movements of the
planetary bodies from the requirement of mathematical perfection;
hence the 'harmony of the spheres'. This tradition led Galileo to
be arraigned, made Copernicus's views a heresy, and held back the
(re)discovery of the actual movement of the heavens for one-and-a-
half millenia. Greek mathematics' reaction to Aristarchus'
proposition that the earth went round the sun was to have him
tried for impiety.
The Pythagorean number-worship tradition that the 'real' is the
mathematical, superior to the thing itself, culminated in Plato,
of whom Heath (p137) says the following:
"Plato conceives the subject-matter of astronomy to be a
mathematical heaven of which the visible heaven is a blurred and
imperfect expression in time and space; and the science is a
kind of ideal kinematics, a study in which the visible movements
of the heavenly bodies are only useful as illustrations"
I don't think we could find a more perfect description of modern
mathematical economics. The passage is so illuminating I will
reproduced it in full in a separate post.
General equilibrium systems of all types indeed consider the
subject-matter of economics to be a 'mathematical heaven' of which
the visible economy is a 'blurred and imperfect expression'.
Comparative statics is indeed an 'ideal kinematics, a study in
which the visible movements of the economy are useful only as
illustrations'.
As Anwar has insistently pointed out, the Sraffian concept of
determination is that of *mathematical deduction*. It replaces
objective causality with algebraic calculation. In the Sraffian
system the equation *is* the real. Thus values determine prices
according to the Sraffians if we can *calculate* prices from
values, an idea that has nothing whatsoever to do with either a
scientific or a Marxist concept of determination.
Their 'essence' of the economy is an equilibrium model of which
awkward reality is nothing more than an 'imperfect expression'.
The standard Marxist approach is deeply impregnated with this
attitude.
In my view mathematics as now used in economics is Idealism in
modern dress, pure and simple; unreconstructed Platonism. I am
dead against it. I think it one of the chief things from which
political economy has to be rescued.
And I think Jerry is dead right; formal mathematical logic is
decisively not dialectical. This is central. I would suggest we
might look at it this way: the world of mathematics is a world of
perfected and completed forms, but reality is not never perfected
and never completed.
Each particular mathematisation at one and the same time sums up
the development of thought so far, and sets the boundary on its
own further development. This can only be transcended by breaking
free of the frozen and finished perfection of the mathematical
form, which by virtue of the very fact that it is completed,
cannot evolve further and becomes a brake on thought from the
moment it is set on paper. It is the very perfection of the
mathematics which walls it off from further evolution.
The irony is that *real* mathematics understands this and has
spent the last fifty years formalising it. Mathematics understands
its *own* limitations better than its users do. It has learned a
great deal more humility than its uninvited prophets.
Of course we should *use* mathematics; what we have to avoid like
the plague is declaring it an independent source of truth.
The current practice of mathematical economics strikes me as
little more than modern number-worship based on the oldest and
most discredited of notions, that perfection of form is a proof of
truth.
The starting point is to distinguish sharply and categorically
between using mathematics to *formalise*, *test* and *criticically
organise* what is already present in our thoughts, derived from
the analysis of reality; and the idealist practice of which
Pythagoras was the pioneer, of endowing mathematical models with
truth superior to and additional to the reality of which *they*
are an inferior reflection.
Math is governed by the same rules as all algorithms:
+===========================+
! !
! GARBAGE IN, GARBAGE OUT !
! !
+===========================+
Alan
Ref: Heath, Thomas (1966).'Aristarchus of Samos: the
ancient Compernicus' (OUP)