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



Re: at the background of logic
Posted:
Jun 13, 2013 7:52 AM


Zuhair wrote: > 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:
Then, as a matter of English, it should be "A implies B". So far as the logic is concerned, it's interesting and I think you need to prove that expression1  expression2 has only one (informal) meaning. Perhaps you could start with a definition of wff.
> 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
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne



