Re: Cerberus and Quine

From: Paul Holbach (paulholbachSPAMBAN_at_freenet.de)
Date: 02/23/05 

Date: 22 Feb 2005 15:05:44 -0800

> examachine@gmail.com wrote:

> While Paul is obviously very right in saying
> that truth does not have
> to conform to common sense, I think especially
> in caring about ordinary
> language, you have to do ordinary philosophy of
> language, and respect
> common sense, because in a strong sense,
> that is definitely what you
> want to explain.

I carefully chose my words when I said that common sense was *not
always* the key to wisdom.
I didnīt say "never"!

> The true philosophy of mathematics
> has to explain why and how axioms
> are selected, regardless of this
> confusing metaphysical talk.

Apart from the methodology of mathematics and the philosophy of
mathematics not being one and the same, the "true" philosophy of
mathematics has to provide substantial and elaborate answers to the
following crucial questions:

"The job of the philosopher is to give an account of mathematics and
its place in our intellectual lives.

- What is the subject-matter of mathematics (ontology)?

- What is the relationship between the subject-matter of mathematics
and the subject-matter of science, which allows such extensive
application and cross-fertilization?

- How do we manage to do and know mathematics (epistemology)?

- How can mathematics be taught?

- How is mathematical language to be understood (semantics)?

In short, the philosopher must say something about mathematics,
something about the application of mathematics, something about
mathematical language, and something about ourselves.
A daunting task, even without the job of eliciting first principles."
;-)

 [Shapiro, Stewart (2000). /Thinking about mathematics: The philosophy
of mathematics/. Oxford: Oxford University Press. (p. 15f)]

Regards
PH

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