
Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 11, 2013 1:53 PM


On Feb 10, 2:47 am, fom <fomJ...@nyms.net> wrote: > 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,
Failed meaning? There is nothing wrong with naïve set theory.
A. A wff maps SETS to SETS. E.g. if P(x,y) is a set then (exists M)P(M,x) is a set. B. x ~e x is not a set. C. x = y is a set. D. For any set M, x e M is a set.
How much of ZF can you prove from this? LOTS!
There are 3 kinds of formal systems:
SIMPLE: Correct and welldesigned e.g. Propositional Calculus, Combinatory Logic and CBL.
COMPLEX: Correct but can be smaller (Occam's Razor is not being satisfied) e.g. Peano Arithmetic is just any logic in which TRUE, ADD, MUL and their complements are representable.
HAIRY: False because all the primitives used in the hairy part are not axiomatized nor are their properties even known. A correct formalization is to axiomatize each primitive and all the primitives are in fact primitives  small e.g. ZF axioms are sometimes very hairy and guilty of this. There are no axioms for functions and other concepts contained with the harriest ZF axioms.
CB
> 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.

