Science And Math Was: Python's Lisp heritage

[Lulu of the Lotus-Eaters]

|> Mathematics as a special branch of Psychology.  Mathematics describes
|> the laws of thought, but at a level of abstraction that applies to any
|> thinking being.

Tim Daneliuk <tundra at tundraware.com> wrote previously:
|no compelling evidence to support the idea that "...thought patterns
|will be constrained by the rules of Mathematics."
|If you take this position, you are arguing that
|*all* human intellectual activitiy like creative action, analysis,
|emotion, need, and so on can, at least in priciple, be described
|mathematically.

This goes further than I need to or intended my remarks to.  I would
certainly not claim that *ALL* human intellectual activity is
mathematical.  There are many other facets of human thought that have
nothing to do with mathematics (e.g. those examples I listed in passing:
Oedipal complex; short/middle/long-term memory; prototyping... lots of
others).

The quantifier sort of goes in the other direction.  Any *BEING* that
thinks about mathematics must think about it in certain ways (the
martians, etc).  It might be that something (or someone, say with
certain brain injuries; some of the cases Oliver Sacks describes are
interesting here) can think in many ways, but does not think about
mathematics.  OK, good enough.  But anything that *does* conceive the
concepts "two", "sum" and "four" *must* think that 2+2=4 (or at least
not conclude its contrary).

I don't think of 2+2=4 as a fact about apples that might be counted,
exchanged, stored, etc.  Of course there is a practical application of
addition to these concrete matters; and quite likely piles of apples are
useful for teaching a child basic arithmetic.  But fundamentally 2+2=4
is a (Kantian) fact about the nature of cognition.  And so is Godel's
incompleteness proof, even if most thinkers never happen to think about
it--if they *were* to think about it, they nature of thought compells
the conclusions of the proof.

Yours, Lulu...

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