Re: Universal grammar

Hi Herman,

Herman Rubin wrote:
In article <1161318846.624985.11180@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Rob Freeman <groups@xxxxxxxxxxxxxxxxxxx> wrote:

So you want to factor some "human" factor X out of mathematical proofs?

I find the idea that there is an indefinable "human" element in
mathematical proofs quite radical. This is something quite new, and
unique to your own work, isn't it?

It is unclear whether there is a human element in the proof
itself. However, finding proofs is a very definitely human
process, even in situations in which we know that a machine
can find it in a systematic manner. Even with our "high
speed" machines, that is much too slow.

Also, it has been shown that, for any k, there are theorems
for which the shortest mathematical proof is at least k times
as long as a metamathematical proof.

I agree. There are strong parallels between maths and general
cognition. I only question the need to introduce a separate element to
explain that.

In particular, now that we see some aspects of maths are illogical, do
we need to fight that? Might not the illogical aspects of maths
displayed by incompressible strings be a better model for both?

Still, it is not inconsistent with Goedel's own interpretation, which
was that absolute "truth" existed, but that it must be outside of maths
itself.

Some aspects of truth exist, but not all which people want.

:-)

-Rob

.

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