FOM: Definition of mathematics

[Cristian Cocos]

I have always thought that the correct answer to this question has been around
at least since Hume and Kant. In Hume's terminology, mathematics deals with
"relations of ideas" as opposed to "matters of fact"; in Kant's words,
mathematics is the science of the Forms of Sensibility.

I find it useful rephrase this view in contemporary IT jargon: mathematics is
nothing but the (syntax of the) assembly language of the (generic) human brain
(...regarded as a computer, as most philosophers do in line with Fodor's LOT
hypothesis...). In other words, mathematics is the reflection of the inner
workings of the CPU of the Generic Epistemic Subject. Mathematics is for the
Neurophysiology of the brain what macroscopical Thermodynamics is for
Statistical Physics, and coming up with adequate mathematical axioms means
accurately representing the functioning of the brain.

Of course, this linguisitc "flavor" has been around at least since Carnap and
his "syntax of language." However I think that this amendament (language *of
thought*) is essential; it also helps to avoid the unbearable pluralism allowed
by his Principle of Tolerance.

(It should be obvious from the above comment that, unlike Kant, I make no
distinction between the sciences of Mathematics and Logic. I think that one
should resist the temptation to operate such a distinction, despite its
apparent success. Among other things, I find it hard to think of Mathematics as
a theory/science like any other, on a par with, say, Newtonian Mechanics or
Maxwell's Electromagnetism whereas Logic is supposed to act as a comon
background for the whole of human knowledge.)

Cristian Cocos
UWO