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 4:25 AM


On Wed, 12 Jun 2013, 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" > > A,B A can be taken to mean the "conjunction of A and B"
Requires both that and A,B B.
> x phi(x) can be taken to mean: for all x. phi(x)
Confusion of propositions and objects.
> x, phi(y) phi(x) can be taken to mean: x=y
It can?
> 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.
What's a constant predicate? > 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.
Confusion unto Jabberwocky gibberish.
> Anyhow the above kind of inference is somewhat vague really, it needs > to be further scrutinized.
The confusion of predicates and objects is a know failure.



