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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: 1,218
Registered: 10/25/10
Re: at the background of logic
Posted: Jun 13, 2013 7:52 AM
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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 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:


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



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