Re: Is Validity Just a Hypothetical or Conditional Characteristic?



Jan Burse wrote:

If you have a proof of the validity of
a sentence, you can look at the proof,
and will learn a lot of about the contribution
of the parts of the sentence to the validity
of the whole sentence.


If you have a valid sentence P -> Q then there is a
sentence P' = P of the form

P1 & P2 & P3 ... & Pn (0 < n)

and there is a sentence Q' = Q of the form

P1 & P2 & P3 ... & Pm (0 < m <= n).

That is, each conjunct of Q' is a conjunct of P'.

In a valid argument P -> Q the conclusion asserts,
in part or in whole, what is asserted by the premises,
and no more.

This is what makes a valid argument is valid.

The behavior of truth and falsehood in valid and
invalid arguments follows naturally from the above
fact.

This is demonstrable in the propositional calculus
(0th order logic). Regrettably, I have not yet
found a demonstration in the predicate calculus
(first-order logic).

--
hz

P.S. -- I posted this once earlier this evening, but
it seems to have disappeared into the aether. I have
followed up to sci.logic only -- someone can repost
it to the other newsgroups if they like. Sorry if
duplications appear.

.