Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
NCTM or The Math Forum.



Re: at the background of logic
Posted:
Jun 13, 2013 7:20 AM


On Jun 12, 10:51 pm, Peter Percival <peterxperci...@hotmail.com> wrote: > 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"? > >
Yes it is read as A infers C, but it is taken to mean:
Given A we infer C
Also you can say "Given A; C is inferred"
Zuhair > > > > > > > > > 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. Mil



