From: Lee Corbin (lcorbin@tsoft.com)
Date: Wed May 29 2002 - 10:07:53 MDT
Louis writes
> > On the other hand, expressions that are logical
> > fallacies take the value "false".
>
> This is incorrect. If an argument breaks the rules of logic, then it can
> NOT be assigned ANY truth value. Breaking the rules of logic means that it
> is inconsistent, and NO value will give valid results.
We are speaking of different things. The logical fallacies that
I was referring to are those that arise in formal logic, which
should have been clear from context. But the term "logical
fallacies" is used in other ways than the strict one, and so
some of the confusion is my fault.
> The sentence ["if this sentence is true, then God exists"]
> is INVALID. Even if you switched God to something provable
> (like kangaroos), the sentence is still INVALID. Truth or
> falseness of the parts is irrelevant.
I agree. That sentence is not true or false.
> > Statements like "Many people have been to
> > Hawaii" have semantic, not logical content.
>
> This is a common dodge, but it infuriates mathematicians. (And I'll even say
> "us mathematicians" since I am one.) People claim math (or in this case
> logic) is simply a "different set of content" so doesn't apply. The fact
> that something is "semantic" does not make it immune to logic.
Yes of course statements like the above are not IMMUNE to logic!
As an example, "If all dogs have four legs and Rover is a dog,
then Rover has four legs." Now *that* has logical content.
Not the statement above. It contains constants and so its
validity depends on the interpretation (a technical term in
formal logic).
> Self-referencing sentences are "circular logic". That's what
> "circular logic" means. ALL self referencing sentences are
> invalid. (As per the above discussion, parts of these
> sentences may be observed to be true or false, but the
> logical train of thought is invalid, nevertheless.)
Since you are a mathematician, why don't you check out
non-well-founded set theory, which deals with circular
sets. It is simply wrong to say that all self-referencing
sentences, or structures, are invalid.
> > I alluded to the Godelian sentence G which refers to itself and is
>
> Funny, how you invoke the name of Go"del, but don't seem to understand the
> point of his work. Go"del proved that any mathematical system (which logic
> is) must either be incomplete or inconsistent.
Of course. But before you criticize what I said above,
please check out some book on Godel's proof, like the
Newman and Nagel one, or Godel, Escher, Bach. Indeed
there are such things as Godelian sentences that refer
to themselves, and can't simply say "they're invalid".
Godel's proof wouldn't work without them.
> > Whereas earlier philosophers might have said that
> > it's therefore meaningless, I still say that it cannot be
> > refuted just within the world of classical logic.
>
> What is "it" that you say cannot be refuted? You quoted someone else (whom
> you call "earlier philosophers") and then say "I still say it cannot be
> refuted". I don't think ANYone is refuting the earlier "philosophers" (whom
> I will call mathematicians). So what are you saying cannot be refuted?
The sentence "if this sentence is true, then God exists". I am
saying that its invalidity cannot be established by logic alone,
but our rejection of its use (say to prove something exists)
must be based on its semantic content, which is almost nil.
Lee
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