From: Louis Newstrom (louisnews@comcast.net)
Date: Wed May 29 2002 - 20:44:13 MDT
from Louis:
> 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.)
from Lee:
> 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 am aware of self-referencing sets. They have the same problems as
self-referencing sentences. Their use of the word "valid" means that it can
exist. (More specifically, SOME self-referencing sets can exist.) This has
no bearing on the fact that self-referencing sentences are "invalid" in
logic, because it's a different meaning of the word "valid".
Lee:
> 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.
You obviously don't understand Godel's Theorem. It's whole point is to
prove that in any mathematical system there will be some operations that are
"invalid".
Yes they exist. Yes they are invalid. That's what the proof says.
Lee:
> > 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.
Louis:
> What is "it" that you say cannot be refuted?
Lee:
> The sentence "if this sentence is true, then God exists". I am
> saying that its invalidity cannot be established by logic alone,
Sure it can. A syllogism is "valid" if you can assign all of it's variables
any value and the syllogism still works. With your example, you have two
variables ("this sentence is true") and ("God exists"). You can't assign
("this sentence is true") a false value. By refering to itself, it states
it's own value.
You are quite simply using a non-assertion in an operation that requires an
assertion. It's like using 3 as a variable. It doesn't work.
> but our rejection of its use (say to prove something exists)
> must be based on its semantic content, which is almost nil.
That's where you are getting hung up. Quit looking at semantics. A
syllogism is either valid or invalid based on it's structure. The actual
values of the variables (true or false) has NO BEARING on whether it is
valid.
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