Re: Category theory and Rosen

[David Sumpter]

glen e. p. ropella wrote (selective quoting):
>It seems to be an implication of Goedel's
>Incompleteness Theorem is that there necessarily exist undecidable
>sentences in any formal system.... in other words, a formal system
>requires external influence. 
>
>Rosen knows he can't
>devise a formal system that incorporates final cause, so he's going
>to define a *ratio* of "unentailed elements" to "entailed elements"
>and then he's going to force that ratio *towards* zero.
>In so doing, he achieves a kind of approximation to reality that is
>remarkably akin to the what Cantor, Liebniz, and Newton did.

I think formal systems must have an external influence since they were made by 
`us' with our limited view of the world (i.e. I'm not a Platoist - I'm not sure 
why if God were to give us one idea it would be mathematics!). However, this 
doesn't mean that Godel's therorems find the inacurracies in what we made up. 
It 
simply points out another feature of the thing we created. As must have been 
said through a hail of controversy over and over again - Godels theorem is 
simply a liar's paradox.

We created formal systems in an attempt to describe the world. They wern't made 
for answering the question of `what does it all mean?'. Glen seems to be 
suggesting Rosen is trying to use them to answer that question, all be it by 
reducing doubt to zero. I've always thought this is impossible for a horribly 
naive philosophical reason: I can never be sure that Glen exists or anything 
exists AND it is also impossible to attach a probability his existance. Meeting 
didn't make him any more likely to exist as neither do his long emails [grin]. 
But I have to get on with my life looking at the cause and effect of Glen's 
life 
and I may want to use a formal system to analyse this. None of this removes the 
fact that there is always something I may never know AND I will never be able 
to 
assess the probability of my being wrong.

I'm sorry if I brought what was meant to be a scientific discussion down to an 
`up in the skys' thing but it seemed to be going that way.

I'm probably (though without an assessed degree) wrong,

David.

---------------------------------------------------------------
David J.T. Sumpter
Mathematics Department, UMIST, P.O. Box 88, Manchester, M60 1QD

http:\\www.ma.umist.ac.uk\dsumpter\index.html
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