To: | Avril Styrman <Avril.Styrman@xxxxxxxxxxx> |
---|---|
Cc: | ontolog-forum@xxxxxxxxxxxxxxxx |
From: | Pat Hayes <phayes@xxxxxxx> |
Date: | Fri, 1 Feb 2008 09:26:25 -0600 |
Message-id: | <p06230905c3c8e543ccd3@[192.168.1.2]> |
At 4:10 PM +0200 2/1/08, Avril Styrman wrote:
Quoting Pat Hayes <phayes@xxxxxxx>: I see the self-reference here: ...
There is no point in continuing this conversation. You really
should find something out about the topic you are talking about before
giving us your views about it. At the very least, it will give you
some guidance as to how to phrase your thoughts so that they can be
understood by others.
Pat
PS. To illustrate, allow me to analyze one paragraph:
1+1=2 is the same as understanding the difference between X and XX. No, its not. Is 1*1=1 the same as understanding that difference?
After all, this has two '1's in it, just like your XX. The addition
equation uses three signs - '+', '=' and '2' - which are not in the
X/XX example, and its comprehension depends upon knowing what they
mean, which is a lot more than being able to recognize the difference
between one thing and two (many insects can do the latter, but none of
them know much about numerals). You are right in claiming that the
ability to recognize the difference between one thing and two things
is very basic in psychology, and indeed appears to be genetic - it can
be found in infants only a few months old. But that ability is
not the antecedent of a proof.
Because it is so fundamental, it cannot be proved. That does not follow. It all depends on what one takes to be so
fundamental that all else will be derived from it. This is to some
extent arbitrary, of course, but the accepted 'gold standard' is one
of the formal set theories, typically ZFC.
If one starts to prove it somehow, it is clear the the one uses the It is clear, perhaps, that in order to understand any
proof one uses this ability. One also uses other abilities,
such as being able to perceive symbolic representations in text or
speech. But that is a psychological observation, and has no bearing on
the structure or properties of the proof itself, or on what 'provable'
means, or on what can or cannot be proved. Computers have no
psychology, but can both generate and check proofs.
And this It does not prove anything; and even as an informal
argument, it does not lead one to that conclusion. The conclusion is
false, anyway, as I have said: this simple fact can be proved in any
formal arithmetic, and without using the fact that X differs from XX
as any kind of antecedent.
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