fom
Posts:
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Registered:
12/4/12


Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 10, 2013 2:47 AM


On 2/9/2013 6:19 PM, CharlieBoo wrote: > On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote: >> >> How do you see Logic and Set Theory as being the same? > > Both are concerned with mappings to {true,false}. A propositional > calculus proposition is 0place. A set is 1place. A relation is any > number of places. (A relation is a set  of tuples.) > > So you have the same rules of inference: Double Negative, DeMorgan > etc. apply to propositions and sets. > > To prove incompleteness, Godel had to generalize wffs as expressing > propositions to expressing sets when the wff has a free variable.
Hmm...
This is naive set theory (which you have stated as being fine with your views).
I view set theory as being about the existence of mathematical objects. Naive set theory failed, in part, because of something in Aristotledo not negate "substance". Do not get me wrong. I am not planning to run out and buy a number 2 while I pick up my next Turing machine....
The problem, however, is that the connection of mathematics to any metaphysical truth (if such a statement can be sensible) requires that the objects represented in physics books (material objects) correspond with some sort of mathematical notion. So, while mathematics is abstract, there must be some sort of interpretation that accounts for its apparent ability to model realworld situations.
Either physics is a collection of mathematical hallucinations or there is a better explanation of set theory.

