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From: esk@wucs.UUCP (Paul V. Torek)
Newsgroups: net.philosophy
Subject: Rosen on logic and proof
Message-ID: <844@wucs.UUCP>
Date: Wed, 20-Mar-85 16:41:13 EST
Article-I.D.: wucs.844
Posted: Wed Mar 20 16:41:13 1985
Date-Received: Thu, 21-Mar-85 04:17:35 EST
Reply-To: pvt1047@wucec1.UUCP (Paul V. Torek)
Organization: Washington U. in St. Louis, CS Dept.
Lines: 48

>From me (>>) and Rich Rosen (>)	{ihnp4 | harpo}!pyuxd!rlr
>> "Rational" has a narrower meaning than that.  It may be a vague
>> word, but you can't stretch it that far -- talk about Humpty-Dumpty-ism.

>Hardly.  If by rational, you imply something about decision-making processes,
>well, don't rivers and rocks make "decisions" about which way they will flow
>and fall?  Quite rational, they way they make those "decisions"...  

No it isn't rational, that's the whole point.  Only a Humpty-Dumpty would
describe the processes in rivers and rocks as "rational".

> Can you prove that [logic] is truth-preserving?  Especially when the 
> definition of truth and falsehood, concordance and contradiction, are 
> fundamental to the notions of logic.

Yes, you can prove that logic is truth-preserving, though of course you 
have to use logic to do it because you have to use it to prove *anything*.
And of course a proof is not likely to win any *new* adherents to logic.

> Oh?  The notion of proof involves making no assumptions either way about the
> validity/falsehood of a notion, and showing that, based on other assumed or
> proven givens, it MUST be so.  Try doing that for logic...

The notion of proof involves making no assumptions about the *truth*/falsehood
of a statement.  Logical laws are rules of inference however, not statements,
and neither true nor false.  So using them does not assume truth/falsehood of
anything, yet it allows us to evaluate certain things which *are* statements
*about* logic, such as that it's truth-preserving.  No doubt you are asking how
rules of inference are supposed to be evaluated; the answer is that they
can be checked against each other or against the meanings of certain logical
connective words (it is part of the meaning of "if ... then ..." that it
can be used in a Modus Ponens argument).  Beyond that, validation is neither
possible nor necessary.

>> Read again what I said (edited [now twice], but meaning unchanged):
>>	Carroll ... shows ... that reason is not a premise but rather the 
>> way of getting from premises to conclusions. 

> THIS, what you've just said, is a premise!  Prove it!  (That's the whole 
> point here.)  

That reason is not a premise?  That follows from the fact that it's a rule
of inference, which is different.  That it's rules of inference?  That's
what Carroll proved, that reason's function is not performed by treating
it as a premise.
				--The aspiring iconoclast,
				Paul V. Torek, ihnp4!wucs!wucec1!pvt1047
Don't hit that 'r' key!  Send any mail to this address, not the sender's.