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

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Peter Percival

Posts: 1,304
Registered: 10/25/10
Re: at the background of logic
Posted: Jun 12, 2013 3:51 PM
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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"?

> 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
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--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne



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