Klarinet Archive - Posting 000257.txt from 2009/02

From: Michael Nichols <mrn.clarinet@-----.com>
Subj: Re: [kl] Fair Use
Date: Wed, 11 Feb 2009 22:49:03 -0500

On Wed, Feb 11, 2009 at 8:56 PM, Jonathan Cohler <cohler@-----.org> wrote:

> Last post on this subject. It is fruitless having a logical argument with
> people who refuse to use logic. :-(

Oh, I'm game for this one. You're trying to assert the propositional
logic statement

A -> B (A implies B)

where A = "X has never been adjudicated a copyright violation" and B =
"it is very likely X is not a violation"

I say to you that this statement cannot be proven false, but it's
useless, anyway.

The first problem is that there is no way to prove A. You can prove
"not A" by finding a case, but just because you haven't found a case
doesn't mean there isn't one. But if you do find a case (so "not A"
is true), then who cares whether A implies B, because it's premise
about a universe that doesn't exist.

The problem is that, assuming that you could prove A, your statement A
-> B is valid if and only if B is also true. That's because

A -> B

is equivalent to

(not A) or B [you can look this up in any introductory book on
symbolic logic if you don't believe me]

If we assume A, then the truth value of A -> B is equivalent to that
of B by itself. You can prove this symbolically as follows (using T
and F for true and false):

(not T) or B <=> F or B <=> B

That means that A -> B is useless to you as a premise for arguing that
B is true, because if A is true, you have to prove B is true just to
establish that A -> B is even valid as a premise. (And, as I said, if
A is false, then A -> B is also a useless premise because then it
tells you nothing about a universe in which A is false.)

Thus it is proved.

Incidentally, just because you can't prove something is false, that
doesn't make it true. Truth and provability are not one and the same.
Ever heard of Goedel's Incompleteness Theorem?

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