From: Lee Corbin (lcorbin@tsoft.com)
Date: Thu May 30 2002 - 01:10:06 MDT
Louis writes
> 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.
If my "please check out some book on..." did offend, then I'm sorry.
I really thought that you hadn't seen self-referential sentences
in math papers before.
Second, the point of Godel's Theorem is *not* to prove that
there are *invalid operations*. Where did you get that
phrase? As you know, the point of Godel's Theorem is to
demonstrate that every axiom system contains statements
that are true but unprovable. The Godelian sentence G
to which I referred is true, but cannot be proved within
the system. Do you have any references for what Godel's
Theorem says about invalidity? I didn't think it said
anything at all about invalidity, which as you know, is
a technical term in mathematical logic.
> 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 referring to itself, it states
> it's own value.
I would say that one really can't get away with assigning any
truth value to "this sentence is true" in The Sentence. For
to do so would fall into the trap posed by The Sentence, namely
that it has a truth value of either true or false.
> 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.
>
> That's where you are getting hung up. Quit looking at semantics.
Quit telling me what to do ;-) [self reference joke]
> 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.
Yes, that's right. A syllogism in order to be valid must
be true regardless of its values. (By the way, would you
use "its" instead of "it's" for the possessive? Thanks.)
Lee
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