Re: Is logic world-dependent or not?

Jan Burse wrote:
John Jones schrieb:
That's by the way. Besides, there can be no errors in a pre-conceived formalism, Godel or no Godel.

This is left as an exercise, can there be errors
in a pre-conceived formalism or not?

Maybe you do not understand me. To be clear:

- There can be errors in the pre-conceived
formalism itself. The human brain is not
perfect. So the self set goals of a formalism
might be violated by the self set formalism.

- There can be errors in the application
of the pre-conceived formalism. Again
the human brain is not perfect. So
the self, when applying his own formalism,
can make mistakes, in not following
the self set formalism.

Evidence of the above are plenty in the history
of mathematics and elsewhere. Here are some
examples:

- Frege's system had an error, pointed out by Russel.
(This is very very famous, goes under the
name Russel's Paradox)

Frege abused his worldly knowledge that an object cannot be a concept by making an object - number, stand as a concept for another number.

- When it is mondays to fridays, shops are open.
It is saturadays today. Therefore shops are closed
today. (Oops but no, there are many shops open
today)

Happens to me, A -> B, ~A |- ~B, (Denying
the antecedent) but is very common, and has
to do with some default reasoning (Completion,
we have A <-> B, insteaed of A -> B).

Maybe we need to follow more closely bio-linguistics
those days. Isn't trial and error a base for
evolution? (Damned should read Givon Talmy when
I have time)

The whole thing gets very interesting
in a socio-psychological setting (I didnt pick
it up in the above response, was assuming self
set formalisms).

Bye









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