From: Lee Corbin (lcorbin@tsoft.com)
Date: Thu May 30 2002 - 17:44:41 MDT
Hal writes
> In this case we can look at the peculiar, self-referential
> form of G and deduce directly that G cannot be true.
I think you meant to say that we can deduce that G
cannot be *demonstrable* within the system. G is actually
true, and Godel's Proof *is* the proof that G is true.
John writes
>> ALL self referencing sentences are invalid.
> Sounds like Russell's old Theory Of Types... Russell claims that "This
> sentences is written in English" is meaningless, and yet I somehow manage to
> extract meaning from it. An even greater sin according to Russell would be
> "In this post I express my agreement with the Theory Of Types" because both
> "this" and "I" are forbidden. Thus even if you agree with the theory you are
> not allowed to say so. Talk about censorship.
Thanks for the great examples! Some confusion earlier could
have been avoided if I had been able to think of such clear ones.
Rafal also wrote
> [Lee:]
>
>> All young stars are made of many gaseous molecules.
>> All things made of many gaseous molecules obey the
>> laws of statistical dynamics".
> somehow *does* limit the ontological possibilities! Quite
> amazing, when you stop to think about it.
### It is limiting only if you have a way of mapping the (assumed
### to be absolutely true) statements of logic onto the sensory
### reality.
(Yes, this is almost exactly what is called an *interpretation*.)
### If you had an absolutely true and full description of a part
### of reality, you might be able to put some constraints on it
### by an application of logic.
I don't see why it must be absolutely true and full. But anyway,
you go on
### Yet, both of the statements you use in your example are rife
### with little imperfections (How many is many? Are they really
### gaseous? What does it mean to "obey" here?). These imperfections
### leave enough wiggle room for the truth about reality to escape
### the merciless embrace of logic.
Well, I should have tried harder with a good example. Let me
utilize again my own invention for these purposes, which I
call "The Great Hawaiian Truth":
Some people have been to Hawaii. (GHT)
I submit this as an indisputably true statement. In the phrasing
of St. Anselm, only a fool would question the meaning of those
terms. (just joking) So how about "Hawaii is in the tropics",
as an additional premiss, even though it's not quite as ironclad
as the GHT (although "tropics" means exactly between X degrees
south and X degrees north, and can be measured to high precision
via astronomical techniques). But "the merciless embrace of
logic", as you so nicely put it, makes it therefore indisputable that
Some people have been in the tropics.
It is this degree of precision that Harvey Newstrom and many others
ideally strive for when they want to logically prove or disprove
something.
Lee
P.S. It will be interesting to examine Mark Walker's URLs, who wrote
>> The most interesting point (for me) has now moved on to
>> whether or how much logic, almost frighteningly, can
>> reach out of its metaphysical platonic universe to
>> affect, control, and constrain our material world.
> I have written on this idea in a couple of places, see
> http://www.markalanwalker.com/logic.html "Is logic About the World?"
> http://www.markalanwalker.com/kant.html "Beyond Kant's Tychonian Revolution:
> An Argument for Absolute Idealism"
but I haven't had time yet.
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