From: Louis Newstrom (louisnews@comcast.net)
Date: Wed May 29 2002 - 06:53:57 MDT
----- Original Message -----
> Many people would suppose "If this sentence is true, then
> God exists" to have a truth value, namely false.
...
> 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 inconsistant, and NO value will give valid results.
As an example, consider why division by zero is not allowed:
1 * 0 = 2 * 0
divide both sides by zero
1 = 2
That's why the term is INVALID is used. It is not TRUE, it is not FALSE, it
is a contradiction, and no truth value can be assigned. The above sentence
about God is INVALID. Even if you switched God to something provable (like
kangaroos), the sentence is still INVALID. Truth or false-ness of the parts
is irrelavent. An invalid syllogism simply cannot be used.
> Statements like "Many people have been
> to Hawaii" have semantic, not logical content.
This is a common dodge, but it infuriates mathmaticians. (And I'll even say
"us mathmeticians" 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.
> You make it sound as though you don't agree with any of
> the points of my previous post. Is that true? In it I
> explained why self-reference is not always circular or
> illogical.
I am not the person you addressed this to, but I'll put in my two cents and
say that you are wrong. 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.)
> 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 p
oint of his work. Go"del proved that any mathematical system (which logic
is) must either be incomplete or inconsistent. Mathematicians have chosen
to call certain operations (like division by zero, or use of circular logic)
as invalid. In other words, they chose to have a consistent set of rules
that was always consistent, and always gave the same answer.
> > > 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?
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