[FOM] Preprint: "The unification of Mathematics via Topos Theory"

Brian Hart hart.bri at gmail.com
Thu Jul 8 19:49:28 EDT 2010

I agree that in this time of increasing fragmentation in the
foundations of mathematics that an approach emphasizing unity is very
welcome but is your approach open-ended and therefore powerful enough
to encompass any future foundational fragmentation?  Since mathematics
is an open-ended discipline (as Gödel's incompleteness result reveals)
who knows where the future of foundational studies will take us and so
any overarching plan for final and complete unification seems to
likely be only temporary and thus illusory.  Set theory could be
considered one of these foundational approaches as a generalization of
the concept of number but in time it was shown to be inadequate to
found the entire and vast mathematical edifice.  Now category theory
largely supplants it as a more versatile foundational theory which is
compatible both with classical _and_ intuitionistic logics.  Category
theory is a very capable and flexible tool, no doubt, but can it
really exhaust the inexhaustible?

On Thu, Jul 8, 2010 at 8:05 AM, Olivia Caramello <oc233 at hermes.cam.ac.uk> wrote:
> The following paper, recently presented at the International Category Theory
> Conference 2010, might be of interest to subscribers to this list:
> O. Caramello, "The unification of Mathematics via Topos Theory"
> Abstract:
> We present a set of principles and methodologies which may serve as
> foundations of a unifying theory of Mathematics. These principles are based
> on a new view of Grothendieck toposes as unifying spaces being able to act
> as 'bridges' for transferring information, ideas and results between
> distinct mathematical theories.
> The paper is available from the Mathematics ArXiv at the address
> http://front.math.ucdavis.edu/1006.3930.
> Comments are welcome.
> Olivia Caramello
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