Category Theory in Philosophy of Science
This meeting will provide a final opportunity for members of the network, and all those interested in the application of category-theoretic methods in philosophy of science, to come together and discuss some of the themes that have emerged in the events held over the last three years.
Due to the ongoing Covid-19 pandemic, this meeting will take place online (via Zoom). For details of the Zoom meeting, please register using this form.
Speakers
The network members speaking at this meeing will be Thomas Barrett and Neil Dewar. We will also have a keynote lecture from Elaine Landry.
Watch selected lectures @youtube.
Program
Day 1 (Monday, 02 August 2021)
| Time | Event |
|---|---|
| 17:45 - 18:00 | Welcome and introductions |
| 18:00 - 19:30 |
Elaine Landry: As-Ifism: Mathematics and Method without Metaphysics Download Slides (105 kb) Download Handout (80,9 kb) |
Day 2 (Tuesday, 03 August 2021)
| Time | Event |
|---|---|
| 16:30 - 16:45 | Welcome |
| 16:45 - 17:45 | Neil Dewar: Internal Structure and Representation |
| 17:45 - 18:00 | Coffee break |
| 18:00 - 19:00 | Thomas Barrett: Property, Structure, and Stuff |
Abstracts
Thomas Barrett (UC Santa Barbara): Property, Structure, and Stuff
Philosophers of science have recently used a collection of tools from category theory to compare theories. The aim of this paper is to present and then substantiate, by appealing to a collection of simple results from model theory, one of these tools: the ‘property, structure, stuff’ classification scheme. Our discussion yields a few payoffs for the recent debate about equivalence of theories.
Neil Dewar (MCMP/LMU): On Internal Structure, Categorical Structure, and Representation
In recent philosophy of science, there has been much interest in the question of whether categorical equivalence is a good criterion for theoretical equivalence. One corollary of claiming that it is a good criterion would be that if some class of mathematical structures is represented as a category, then any other class of structures categorically equivalent to it will have, in some appropriate sense, the same representational capacities. Hudetz (2019) has presented an apparent counterexample to this claim: the category of finite vector spaces with linear mappings is equivalent to the category of natural numbers with matrices as mappings, yet (he claims) vector spaces have representationally relevant internal structure that natural numbers do not. In this talk, I discuss how the internal structure of a vector space is recoverable from the categorical data, and argue that (for this reason) the counterexample fails.top
Elaine Landry (UC Davis): As-Ifism: Mathematics and Method without Metaphysics
I will carve out an as-if interpretation of mathematical structuralism by disentangling methodological considerations from metaphysical ones. I begin first with Plato and draw important lessons from his account of mathematics. More specifically, my aim will be to show that much philosophical milk has been spilt owing to our confusing the method of mathematics with the method of philosophy, and that, as a result, mathematical considerations are conflated with metaphysical ones. I further use my reading of Plato to develop what I call as-if-ism, the view that, in mathematics, we treat our hypotheses as if they were first principles and we do this with the aim of solving mathematical problems. I then extend this view to modern mathematics wherein the method of mathematics becomes the axiomatic method, noting that this engenders a shift from as-if hypotheses to as-if axioms. This perspective is then set within a Plato-inspired methodological context to argue for an as-if interpretation of mathematical structuralism. Again, I pause to note that confusion of the method of mathematics with the method of philosophy, witnessed well by the Frege-Hilbert debate, has led to the continued conflation of mathematics with metaphysics. Finally, I combine Plato’s as-if account of applicability with Maddy’s more recent enhanced if-thenist approach to show how such conflations can and should be avoided in the current structural realist debates. My overall lesson then is this: when we shift our focus from philosophical problems to mathematical ones, we see that an as-if methodological interpretation of mathematical structuralism can be used to provide an account of both the practice and the applicability of mathematics whilst avoiding the conflation of mathematical and metaphysical considerations.top
Registration
To register, please fill out the registration form. Registered participants will be sent the information for the Zoom meeting prior to the workshop start.
Venue
Online.