ONT Re: Excuses, Exergues
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John Collier wrote (JC):
Jon Awbrey wrote (JA):
JA, reinforcing the conative connotations of DH:
| It is a great HONOR
| and at the same time a NECESSITY
| for me to round out and DEVELOP MY THOUGHTS ON
| the foundations of mathematics, which I expounded here one day
| five years ago and which since then have constantly kept me MOST ACTIVELY OCCUPIED.
| With this new way of providing a foundation for mathematics, which we
| may appropriately call a proof theory, I PURSUE A SIGNIFICANT GOAL,
| for I should like to eliminate once and for all the QUESTIONS
| regarding the foundations of mathematics, in the FORM
| in which they are now posed, by turning every
| mathematical proposition into a FORMULA
| that can be concretely exhibited and
| strictly derived, thus RECASTING
| mathematical definitions and
| inferences in such a WAY
| that they are unshakable and
| yet provide an ADEQUATE PICTURE
| of the whole science. I BELIEVE
| that I CAN ATTAIN THIS GOAL COMPLETELY
| my proof theory, even if a great deal of WORK
| must still be done before it is FULLY DEVELOPED.
|
| DH, TFOM, page 464.
JC: And, Hilbert was proven wrong.
He did not give this as a definition
of mathematics, but as a hypothesis.
Yes, but what was he wrong about?
And was he wrong about something
that anyone might be right about?
What I am really after here is best seen in another light.
I am framing the question not to tabulate the contents of
some com-putative canons of universal mathematical theory,
but to examine the self-understanding of those engaged in
the hot pursuits and the cool contemplations of a life of
inquiry, moré mathematico. The standard of investigation
here is more like Habermas, 'Knowledge & Human Interests'.
On those grounds only do I judge finitism to misrepresent
the spirit of living and breathing mathematical strivings.
There are two kinds of finitism that need to be separated:
one is the existential recognition of our human finitudes,
the other is the desire to catch the cosmos in our bounds.
Sensible people know what rings true and what rings false.
Jon Awbrey
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