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Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

Replies: 53   Last Post: Feb 13, 2013 3:53 PM

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 Charlie-Boo Posts: 1,633 Registered: 2/27/06
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

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, 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,

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 well-designed 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.

C-B

> 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.

Date Subject Author
2/1/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 camgirls@hush.com
2/4/13 Charlie-Boo
2/4/13 billh04
2/4/13 Charlie-Boo
2/4/13 William Hale
2/4/13 Lord Androcles, Zeroth Earl of Medway
2/9/13 Graham Cooper
2/5/13 Charlie-Boo
2/4/13 Graham Cooper
2/5/13 Charlie-Boo
2/5/13 Graham Cooper
2/5/13 Brian Q. Hutchings
2/6/13 Graham Cooper
2/6/13 Charlie-Boo
2/4/13 fom
2/4/13 Charlie-Boo
2/4/13 fom
2/5/13 Charlie-Boo
2/7/13 fom
2/9/13 Charlie-Boo
2/9/13 Graham Cooper
2/11/13 Charlie-Boo
2/10/13 fom
2/10/13 Graham Cooper
2/10/13 fom
2/10/13 Graham Cooper
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Graham Cooper
2/13/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 fom
2/5/13 Charlie-Boo
2/5/13 fom
2/6/13 fom
2/11/13 Charlie-Boo
2/11/13 fom
2/13/13 Charlie-Boo
2/13/13 fom
2/4/13 Graham Cooper
2/4/13 Charlie-Boo
2/5/13 Charlie-Boo