fom
Posts:
1,969
Registered:
12/4/12


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 4:24 PM


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.

