FOM: Evolution and reason

[Neil Tennant]

I'm delighted that Bill Tait has invoked evolutionary theory as a possible
explanation (validation?) of our capacity for logical and mathematical
reasoning.

But if the individual's a priori is the species' a posteriori, this raises
the question of what it is *in the physical world* that is exerting the
selective force(s) in such a way as to produce brains that operate (at the
level of thought) in accordance with those so-called a priori's.

Bill, would you accept the following Uniformity Postulate for Logic?:
	
	There is a system S of logic such that:
	whatever the laws of physics, chemistry etc. might be in any
	possible world in which reasoning creatures could evolve, their
	reasoning would have to obey the laws of S.

Would you also accept the following analogue for mathematics?:

	There is a system T of theorizing about numbers such that:
	whatever the laws of physics, chemistry etc. might be in any
	possible world in which reasoning creatures could evolve, their
	theorizing would have to be consistent with T (i.e.
	extendible so as to include T, upon suitable translation).

I want now to pose a dilemma. If you accept these uniformity postulates,
then all that the evolutionary story delivers is an account of how we
attained to S and T, not why S and T are (necessarily) valid/true.
On the other hand, if you reject these uniformity postulates, then
the evolutionary story doesn't help to establish the necessary validity/truth
of the logic and number theory that we happen to have developed, because it
is given against the background of the concession that, had the evolutionary
process been governed by different physical laws, different logics or
number theories might have developed.

I prefer the first horn of the dilemma, and so am prepared to look elsewhere
than evolutionary theory for the explanation of the a priori status of logic
and arithmetic. I would argue that there are transcendental preconditions on
the very possibility of communication of structured thoughts about a shared
reality. These are expressed in the correct logic for the operators giving
rise to that structure. It follows as a corollary that, if we succeed in
*evolving* a system of such structured communication, then it will embody
as *norms* the laws in question; for they are the very precondition for the
possibility of such a system emerging in the first place.

Likewise for the concept of number. As soon as we have in place a conceptual/
linguistic system affording reference to things, characterization of their
properties and relations, and the resources to individuate and re-identify
things, the concept of number is available as a *necessarily possible*
extension of our system of referential/predicative/quantificational thought.
This is the kernel of truth in logicism.  The number of Fs is n if and only
if there are n Fs. With apologies to Kronecker:

	"God [i.e. transcendental constraints on the very possibility
	of (evolved) systems of structured communication] gave us the
	natural numbers AND logic; thereafter any rational thinker
	really could do all the rest."

Thus I tend to agree with both Randall Holmes and Joe Shipman in their responses
to Bill Tait.

Neil Tennant