Ed, Pat, and Chris, (01)
That is a fair statement of what I have always assumed: (02)
EB> So my tenets:
> (1) the world itself is whatever it is.
> (2) our understanding of the world, or any aspect of it, is a 'model'.
> (3) our communication of our understanding is an inferior 'model'.
> I'm not sure whether any of those matches John's philosophy.
> I think I may be close to the positions of Pat and Chris. (03)
But Pat complained, and Chris was somewhere in the middle. (04)
PH>>> But let me ask: why, then, is it implausible to claim that the
>>> real world is an n-tuple? After all, what does this mean? It
>>> means only that the real world exhibits a structure which can
>>> be mathematically described in terms of n-tuples. (05)
CM>> Seems to me pretty clear that it does not mean that! (06)
PH> But that is exactly what it means. What else COULD it mean?
> Just apply model-theoretic thinking to the mathematical language
> itself. Or otherwise, seems to me, you must be assuming that
> some other semantics is being used when it comes to mathematical
> language. I don't buy this: but even if I did, I'd want you to
> tell me what kind of semantics you had in mind. (07)
Analytic geometry and partial differential equations are much
better than discrete tuples for describing the physical world.
And any "model-theoretic thinking" that the world consisted of
n-tuples would make it impossible to apply the limit methods
of calculus (unless you assumed that the world consisted of
uncountable infinities of n-tuples). (08)
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