fom
Posts:
1,031
Registered:
12/4/12
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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
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On 2/9/2013 6:19 PM, Charlie-Boo 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 0-place. A set is 1-place. 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 Aristotle--do 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
real-world situations.
Either physics is a collection of mathematical
hallucinations or there is a better explanation
of set theory.
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