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 associate professor in the Philosophy
University of Victoria, in British Columbia. My PhD work was done at
Stanford University, where I wrote a dissertation
entitled Mathematical Practice and
Philosophy of Mathematics under
the supervision of my co-advisors Michael Friedman
and Sol Feferman. My primary research areas are the history and philosophy of mathematics and logic, as well as feminist epistemology.
I am currently on the ASL Committee for Logic Education and am a board member of the Philosophy of Mathematics Association.
Practice and the Philosophy of Mathematics, PhD
Dissertation, Stanford University, July 2006.
"Emmy Noether and the History of Structuralism: Invariants and Ideals", Carnegie Mellon University Colloquium, February 2016
"(Hip) throwing like a girl: combat sports and norms of female body comportment", CSWIP 2015, October 2015
"Structural Influences on Carnap", Virtual Seminar at Victoria University Wellington NZ, May 2015.
"Structural Influences on Carnap", Group Session for the
Society for the History of Analytic Philosophy at the Pacific APA,
"Argumentation, Adversariality, and Social Norms" Keynote address
at the Western Canadian Undergraduate Philosophy Conference, Victoria,
"Women in tech culture: What’s the big deal about diversity, anyway?" IdeaFest 2015, UVic, March 2015. (Public Lecture)
"The History of Algebra’s Impact on Philosophy of Mathematics", Innovations Workshop at McMaster, January 2015.
"Noether’s Mathematical Structuralism", PSA 2014, November 2014.
"Testimonial Injustice and Victim Blaming", WCPA 2014, October 2014.
"Feminist Radical Empiricism as Ideal Theory", UBC Spring Colloquium, March 2014.
"The History of Algebra’s Impact on Philosophy of Mathematics",
SFU History and Philosophy of Mathematics Colloquium, November 2013.
"Ad Hominem Fallacies and Epistemic Credibility", IVR 2013, July
"Teaching Logic, Fighting Stereotypes", ASL Panel on Logic
Education, February 2013
"Treatments of Time in Epistemic Logic", Logic and Interactive
Rationality Seminar, University of Amsterdam, January 2013
"Idealization, Epistemic Logic, and Epistemology," SFU Philosophy
Colloquium, September 2012
"Perfect Recall and Forgetting," Stanford Modal Logic Seminar,
"Dedekind and Cassirer on the Construction of Mathematical
Concepts," UC Riverside Philosophy Colloquium, November 2010
"Epistemic Logic and Epistemology," UBC Spring Symposium, March
"Dynamic Epistemic Temporal Logic," Workshop in Logic,
Rationality, and Interaction, October 2009 (with Bryan Renne and Joshua
"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,
"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
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
Title: Mathematical Practice and
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
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.