Department of Philosophy
University of Victoria
P.O. Box 3045
Victoria, BC V8W 3P4
Email: ayap(at)uvic(dot)ca CV
I am currently an assistant professor in the Philosophy department at
the
University of Victoria, in British Columbia. My PhD work was done at
Stanford University, where I wrote a dissertation
entitled Mathematical Practice and
the
Philosophy of Mathematics under
the supervision of my co-advisors Michael Friedman
and Sol Feferman. Currently, I am working in several areas, including
the history and philosophy of mathematics and logic, continuing the
project I started in my dissertation, as well as in Dynamic Epistemic
Logic, studying the ways in which we can model changes in agents'
beliefs over time.
Work in Progress
A paper on Dedekind's conception of set, and its
relationship to his conception of a mapping, presented at CSHPM
2008. This is now turning into a paper connecting Dedekind with the
neo-Kantian Ernst Cassirer, which was presented at UC Riverside in 2010.
A paper discussing Noether and Dedekind, comparing the
sense in which each one can be considered to hold a mathematical
structuralist viewpoint, presented at HOPOS
2008.
Joint
work with Bryan Renne and Joshua Sack on Dynamic Epistemic Temporal
Logic. The shorter version of the manuscript can be found here.
The extended version is here.
Some Recent and Forthcoming Publications
"Gauss' Quadratic Reciprocity Theorem and
Mathematical Fruitfulness", forthcoming in Studies in History and Philosophy of
Science.
"Dynamic Epistemic Logic and Temporal Modality", in Dynamic Formal Epistemology,
Patrick Girard, Olivier Roy, and Mathieu Marion (eds), Dordrecht:
Springer, 2011.
"Logical Empiricism, Feminism, and Carnap's Principle of
Tolerance", Hypatia 25(2)
(2010): 437-454.
"Dynamic Epistemic Temporal Logic" with Bryan Renne and Joshua
Sack, in the proceedings of LORI 2009.
"Dynamic Epistemic Logic and Branching Temporal Structures" with
Tomohiro Hoshi, Synthese 169
(2009): 259-281.
"Predicativity and Structuralism in Dedekind’s Construction
of the Reals", Erkenntnis
71(2) (Sept 2009): 157-173.
"Revisiting Galison's "Aufbau/Bauhaus" in Light of
Neurath's Philosophical Projects" with Angela Potochnik, Studies in History and Philosophy of Science
37 (Sept. 2006): 469-488.
Mathematical
Practice and the Philosophy of Mathematics, PhD
Dissertation, Stanford University, July 2006.
Some Recent Talks
"Dedekind and Cassirer on the Construction of Mathematical
Concepts", UC Riverside Philosophy Colloquium, November 2010
"Epistemic Logic and Epistemology", UBC Spring Symposium, March
2010
"Dynamic Epistemic Temporal Logic", Workshop in Logic,
Rationality, and Interaction, October 2009 (with Bryan Renne and Joshua
Sack)
"Dynamic Epistemic Logic", UVic Economics Seminar, October 2009
"Mathematical Concepts and Fruitfulness", Philosophy of Science
Association, November 2008
"ETL, DEL, and Past Operators", Workshop on Logic and
Intelligent Interaction, European Summer School in Logic, Language, and
Information, August 2008 (with Tomohiro Hoshi)
"Noether and Dedekind on Structures and Ideals", International
Society for the History of Philosophy of Science, June 2008
"Language, Bias, and Logic", Canadian Philosophical Association,
June 2008.
"Dedekind's Conception of Set", Canadian Society for the History
and Philosophy of Mathematics, June 2008.
"What Can Logical Empiricism Do For Feminism?", BC
Philosophy Conference, Mar 2008.
"Product Update and Temporal Modality", Dynamic Logic
Montréal,
UQAM, June 2007.
"Predicativity and Determinateness in Dedekind's
Construction of the Reals", Society for Exact Philosophy, May 2007.
"Creation and Construction: Dedekind and Kronecker on the
Philosophy of Mathematics", UBC Philosophy Colloquium, Mar 2007.
"Dedekind's Structuralism in Historical Context", Logical
Methods in the Humanities Workshop, Stanford University, May 2006.
"Product Update and Looking Backward", Games in Logic,
Language and Computation 11, ILLC Amsterdam, September 2005
Dissertation
Title: Mathematical Practice and
the
Philosophy of Mathematics Abstract: Most views in the philosophy of mathematics can
be seen as addressing
the following questions: what are mathematical objects, and how do we
have knowledge of them? However, any account we give of how we have
knowledge of mathematical objects has to take into account what sorts
of things we claim they are; conversely, any account we give of the
nature of those objects must be accompanied by a corresponding account
of how it is that we acquire knowledge of them. In this dissertation, I
argue that attentiveness to mathematical practice suggests a more
fruitful approach to tackling these issues than the route typically
taken.
The history and practice of modern algebra yields an interesting notion
of abstract object, which is metaphysically "thin". A good illustration
of this is found in Dedekind's work on the theory of ideals, and the
way in which this work connects to his more general structuralist views
in the philosophy of mathematics. What this Dedekindian view gives us
is an alternative approach to explaining epistemic access to the
objects of algebra, which takes into account the methods of algebra.
For such objects, the explanation of how it is that we have knowledge
about them is simply given by the fact that all there is to them are
the structural properties by which they are defined in the first place.
