On Sep 19, 2008, at 3:10 PM, John F. Sowa wrote: (01)
> Ed, Pat, and Chris,
> That is a fair statement of what I have always assumed:
> 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
>> (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.
> But Pat complained, and Chris was somewhere in the middle.
> 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.
> CM>> Seems to me pretty clear that it does not mean that!
> 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.
> 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). (02)
Nonsense. Check out what kind of tuple we are talking about here: a
universe and a pair of interpretation mappings. We aren't talking
about finite-element analysis. (03)
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