Re: Current Issues in the Philosophy of Practice of Mathematics & Informatics

[Robert Dawson <rdawson@cs.smu.ca>]

On 7/26/2015 12:33 PM, Patrik Eklund wrote:
> Philosophy of mathematics is still philosophy and has nothing to do with
> mathematics, since philosophy does not adhere to any mathematical
> principles.
>
> Philosophy of logic is the same, since philosophy does not adhere to any
> logical principles.
>

By an argument such as this, it would appear that you could say that
bacteriology has nothing to do with bacteria, because you cannot grow
bacteriology on a Petri dish or sequence its DNA -and obviously this
would be absurd.

I think the source of the confusion here is that mathematics is
reflexive in a way that bacteriology isn't:  mathematics/logic _does_
feed back into itself and become a tool for doing more
mathematics/logic.  It's thus tempting to think that anything outside
this loop is not part of mathematics/logic.

However, the loop is not closed, and cannot be.  There are questions
which are legitimate parts of mathematics/logic that cannot be answered
internally.  I'm not talking about Goedel incompleteness here (though
one might), but about why we do what we do.  If we want to say what
constitutes mathematics worth doing - to say why Fermat's Last Theorem
or the Riemann Hypothesis are more important that the (3n+1) problem or
finding palindromic sequences in the decimal expansion of pi - we cannot
do this by calculation and proof.  This is an example of a place where
philosophy of mathematics can have a genuine connection.

-Robert Dawson




[For admin and other information see: http://www.mta.ca/~cat-dist/ ]