
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 1:38 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, 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. > > > > 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 NAMINGobject 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 nonr.e. sets! (Generalize nonr.e. to any non listable sets.)
CB
> 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 reusable 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( NEGATIONASFAILURE( 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 > predicates added, and humans seem to reason about ALL quantifiers > 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

