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Re: at the background of logic
Posted:
Jun 12, 2013 3:51 PM


Zuhair wrote: > I think that all logical connectives, quantifiers and identity are > derivable from a simple semiformal inference rule denoted by "" to > represent "infers" and this is not to be confused with the Sheffer > stroke nor any known logical connective. > > A C can be taken to mean the "negation of A"
How does one read "A C"? Surely not as "A infers C"?
> A,B A can be taken to mean the "conjunction of A and B" > > x phi(x) can be taken to mean: for all x. phi(x) > > x, phi(y) phi(x) can be taken to mean: x=y > > The idea is that with the first case we an arbitrary proposition C is > inferred from A, this can only be always true if A was False, > otherwise we cannot infer an "arbitrary" proposition from it. > > Similarly with the second case A to be inferred from A,B then both of > those must be true. > > Also with the third condition to infer that for some constant > predicate phi it is true that given x we infer phi(x) only happens if > phi(x) is true for All x. > > With the fourth case for an 'arbitrary' predicate phi if phi(y) is > true and given x we infer that phi(x) is true, then x must be > identical to y. > > Anyhow the above kind of inference is somewhat vague really, it needs > to be further scrutinized. > > Zuhair > > > > > > > > >
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne



