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Topic: at the background of logic
Replies: 5   Last Post: Jun 13, 2013 7:52 AM

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Zaljohar@gmail.com

Posts: 2,665
Registered: 6/29/07
Re: at the background of logic
Posted: Jun 13, 2013 7:20 AM
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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 semi-formal 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




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