rapaport@cs.buffalo.EDU (William J. Rapaport) (11/20/87)
STATE UNIVERSITY OF NEW YORK AT BUFFALO
BUFFALO LOGIC COLLOQUIUM
COLIN McLARTY
Department of Philosophy
Case Western Reserve University
NOTES TOWARD A NEW PHILOSOPHY OF LOGIC
Today, logic is generally conceived as, more or less, describing pure
laws of thought. But categorial logic has given an extensive, rigorous,
formalized version of the claim that logic is simply the most abstracted
aspect of concrete knowledge. In particular, different subject matters
may have different logics.
Categorial logic also urges a kind of structuralism: A subject matter
(represented by a category) is seen as being determined by the relations
to be considered among objects rather than by any specification of the
individual constitutions of the objects.
These points are illustrated by two examples. Differential geometry is
one abstract representation of the world, one subject matter, with its
own non-classical logic. Set theory is another, later, subject, with
classical logic. I discuss the way set theory was derived from geometry
in the 19th Century.
Other philosophic applications of topos theory are based on the idea of
a topos as a world in which truth varies over a range of viewpoints,
which might be the situations of situation semantics or times in tense
logic. All these considerations together argue that there is no one
logic or one fundamental structure to the world.
Wednesday, December 2, 1987
4:00 P.M.
Diefendorf 8, Main Street Campus
For further information, contact John Corcoran, (716) 636-2438.