2000 HSS/PSA Program 1 - History of Science Society

PSA Abstracts
for the epistemic asymmetry and address what appears to be a foundational
problem, we introduce distinct introspective mechanisms that are tied to concept
formation systems on the basis of sensory/affective information entry.
Steven Awodey Carnegie Mellon University
Continuity and Logical Completeness: An Application of Topos Theory
The notion of a continuously variable quantity can be regarded as a generalization
of that of a particular (constant) quantity, and the properties of such quantities
are then akin to, and derived from, the properties of constants. For example, the
continuous, Real-valued functions on a topological space behave like the field
of real numbers in many ways, but instead form a ring. Topos theory permits
one to apply this same idea to logic, and to consider continuously variable sets
(sheaves). In this talk, such applications to logic are explained and made
accessible to the non-specialist. Some recent results in topos theory are then
discussed in this setting, and it is shown how some new and powerful logical
completeness theorems for systems of higher-order logic result.
Paul Bartha University of British Columbia
Richard Johns University of British Columbia
Probability and Symmetry
The Principle of Indifference, which dictates that we ought to assign two outcomes
equal probability in the absence of known reasons to do otherwise, is vulnerable
to well-known objections. Nevertheless, the appeal of the principle, and of
symmetry-based assignments of equal probability, persists. We show that, relative
to a given class of symmetries satisfying certain properties, we are justified in
calling certain outcomes equally probable, and more generally, in defining what
we call relative probabilities. Relative probabilities are useful in providing a
generalized approach to conditionalization. The technique is illustrated by
application to simple examples.
Joseph Berkovitz The London School of Economics and Political Science
206
Causal Loops in Quantum Phenomena?
A common view has it that there is a tension between quantum phenomena
and the special theory of relativity. Yet, an ongoing debate concerning the
prospects of relativistic quantum theories persists. In this paper, I consider
two recent arguments for the impossibility of certain relativistic quantum