From: Lee Corbin (lcorbin@tsoft.com)
Date: Mon May 27 2002 - 22:12:12 MDT
I had written, as an example of why logic, not grounded in reality
must be used with care
>> Theorem: God Exists.
>>
>> Proof: If this sentence is true, then God exists. Therefore,
>> God exists because that sentence is indeed true. How do we
>> know that it's true? Simple. A sentence is true when the claim
>> that it makes is correct (or true). Well, what claim does that
>> sentence make? It claims that if it itself were true, then God
>> would exist. But that's so! If indeed the sentence were true,
>> then God would exist. Since what the sentence claims is so, then
>> the sentence is true, and so God exists. Q.E.D.
Harvey pointed out that this seemed to be a clear case of circular
reasoning, which I guess is on his list of logical errors. I do
not view it as circular reasoning, despite its similarities, for
the following reasons.
The simplest example of circular reasoning that I know of occurs
when someone claims that A is true because B is true, and B is
true because A is true. We are right back to where we started,
still wondering why A is true. Even if only one sentence, or
claim is being considered, to say that A is true because A is
true would indeed be circular reasoning. It happens that
((A -> B) && (B ->A)) -> A (where -> means implies)
and
((A -> A) -> A)
are both logically invalid, although (A -> A) is valid.
He wrote
> This is an extremely clear example of the classical logical
> fallacy known as "circular logic." The first sentence refers
> to itself.
But that's not *necessarily* wrong, only dangerous. Several
branches of mathematics revel in self-reference, including set
theory (modern branches of it). Also, sentences that refer to
themselves are the key part of Godel's Proof.
> The resolution is provides is a restatement of its conditional
> proposition. The "if" statement cannot be resolved without recursively
> invoking another "if". No determination is possible without the same
> question being raised again at the next iteration.
I don't understand. If we begin to analyze "If this sentence is true,
then God exists", and examine the part before the comma, no particular
claim is being made. The semantical analysis and logical analyses can
stop there, (at least on the first pass). In the form "If X is true, ..."
analysis does not need to proceed at this point as to whether X is true.
But this notorious sentence is more than an exercise in logic: the
semantics becomes as unavoidable as if one were to examine the Great
Hawaiian Truth to see if it's valid (or true). ("Some people have
been to Hawaii.") The meaning of the terms in the GHT have to be
pondered; only by dereferencing the meanings of the terms in many
sentences, like the GHT, can their truth (or meaninglessness) be
determined.
Samantha wrote
> There is an obvious flaw. Point 1 merely restates the theorem
> supposedly but in fact says something different. It says "if it
> is true then it is true" effectively. This is worthless.
Quite so. It's worthless because A -> A is a tautology, and
because when considered from the point of view of what the
sentence could possible mean,... you're right, it's worthless.
> Point 2 assumes what is to be proved is already known
> to be true by a more convoluted reiteration of the
> totally empty Point 1. It ends up saying the theorem
> says what it does not. It says "God exists". It does
> not say, "If this theorem is true then God exists."
I'm sorry. I don't understand.
> The latter, if it did say that is perfectly valid when
> F -> F just as well as when T -> T. And no, the flaw
> is not a matter of semantics.
Nor that.
Because the wording of the "proof" jumps up and down levels,
making multiple references, it doesn't have a truth value
IMO. 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.
Hmm, would you agree that if the sentence *were* true (it's
not), then God would exist? ;-)
Lee
This archive was generated by hypermail 2.1.5 : Sat Nov 02 2002 - 09:14:25 MST