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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

 Messages: [ Previous | Next ]
 Charlie-Boo Posts: 1,635 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 1:38 PM

On Feb 10, 6:39 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 11, 7:24 am, fom <fomJ...@nyms.net> wrote:
>
>
>
>
>
>
>
>
>

> > On 2/10/2013 2:38 AM, Graham Cooper wrote:
>
> > > On Feb 10, 5:47 pm, 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,
> > >> 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.

>
> > > Right!  the physical world cannot contravene the platonic, so a set of
> > > truths may exist and a set of lies not...

>
> > > ** in Plato land where (angle1+angle2+angle3=pi) **
>
> > > it's the 1 metaphysics principle I subscribe to!
>
> > > I think LOGIC is just applying MODUS PONENS.
>
> > > backwards to axioms
>
> > > a1
> > >   \
> > >    theorem ?
> > >   /
> > > a2

>
> > > forwards to contradictions
>
> > >                x
> > >               /
> > > ~theorem
> > >              \
> > >               ~x

>
> > > Naive set theory should be able to cope with a SUBSET of WFF that have
> > > been sieved through various checks.   if you can formulate what the
> > > real world contradiction is, it can be unstratified.

>
> > Herc,
>
> > What you say here is Kantian.
>
> > Kant called logic the negative criterion
> > of truth (forward to contradiction).

>
> > And he ascribed the discernment of natural
> > laws to presupposition analysis under the
> > presumption of causes (backwards to axioms).

>
> > For what this is worth, your arguments
> > against Cantor's diagonal have been based
> > on transversal designs.

>
> > The march to infinity is most likely taken
> > using finite projective planes described
> > by difference sets.

>
> > If you want to see why, do an internet
> > search on "perfect difference sets" and
> > "neighbor detection"

>
> > Identity requires infinity.  Distinguishability
> > in the finitary context of automata is finite.
> > With respect to this, equivalence is defined
> > negatively.  Hence, it presupposes infinity.

>
> > Now, identity and diversity are intertwined
> > by negation.  Leibniz' principle of identity
> > of indiscernibles relates an object to all
> > of the objects of the system which are not
> > the given object.  This is like a geometry
> > where every pair of points define a line.

>
> > Naming is quantization process that requires
> > fewer resources.  It is Leibniz' principle
> > of indiscernibles restricted to "landmarks".

>
> > In network analysis they are using perfect
> > difference sets for this purpose.

>
> > Anyway, it may give you a different
> > perspective on some of your thoughts.

>
> > Glad you liked the remark.
>
> I think NAMING-object and EXISTS(object) and SKOLEM FUNCTIONS are all
> part of the same method.
>
> writing a function definition in programming language you just
>
> LET  x = 7
>
> all that's required!   PUT IT IN WRITING = THEN IT EXISTS(..)
>
> biggerthan(X , Y)  <-   X = s(Y)
> biggerthan(X , 0 ).
>
> Certain Proofs are viable since an Algorithm Exists to find the
> required solution.

Well, again, there are a few possibilities:

1. Prove (all x)(exists y)P(x,y)
2. Prove (all x) f(x) is defined and P(x,f(x)) for some function f.
3. (2) but also f is recursive.

Axiom of Choice:

x e y => f(y) e y

Is there such an f?

A much better question: Is there an f such that f({x,y}) = x v
f({x,y}) = y for all x,y ? You can't even do that! HA!!

CBL answer: Yes, there is such an f but we can't express it. :(

So all you PHP programmers must know that there is no way to find a
single value in \$p[\$x] without foreach - but Logic has no foreach. It
deals with non-r.e. sets! (Generalize non-r.e. to any non listable
sets.)

C-B

> Extrapoliate that down to all EXIST(X)  commands even for a
> straightforward object X.
>
> A(Y)  E(X)  X>Y
>   /\
>   | |
>   \/
> A(Y)  bigger(Y)>Y
> TRUE
>
> X EXISTS because an ALGORITHM is written.
>
> bigger() is the Skolem Function for EXISTS(X)
>
> you just DEFINE in writing what exists!
>
> Then
>
> ----------------------------------
>
> AXIOM OF SPECIFICATION gives a NAME to the set IFF it can exist.
>
> EXIST(Y)  xeY  <->   p(x)
>
> X is just a re-usable programming term like i,k,...
> Y is a unique name of the new set, again just by writing it!
>
> ----------
>
> I'm currently pondering using NOT(...) my PROLOG theorem type
>
> not( gt (0 , X ))
>
> as I can write that now in PROLOG
>
> <=>   ALL(X)   ~0>X
>
> and it gives me an ALL(X)  Quantifier without breadth first
> examination of all records although I think it has to examine inside
> the predicate gt(..) coding to return true.
>
> i.e.   NOT(  NEGATION-AS-FAILURE(  gt(0,X)  )
>
> would never terminate considering   0, s(0), s(s(0)), ... would all
> have to fail a search branch.
>
> However if it was stated   not( gt(0,X) )
> which atleast MEANS  ALL(X)   not( gt(0,X) )
>
> then the quantifier syntax could be atomic without any quantifer
> without working at the ALL RECORDS level...   perhaps most PROLOG
> recursive programs, usually 2 lines can have a proof by induction
> method applied automatically.
>
> Herc
> --www.BLoCKPROLOG.com

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