# reading group:

# mathematics for philosophy

**:: context**

Students at the Institute of Philosophy (and many philosophy departments across the world) are required to take an introductory course on logic, but after that single course, relatively little attention is paid to the use of formal/mathematical methods in philosophy. This seems to be at odds with how actual research in contemporary (analytic) philosophy proceeds: one can hardly open a book or a journal without encountering some mathematical symbols, terms and techniques. This holds true especially for subareas of philosophy such as philosophical logic and philosophy of mathematics, but also for, say, epistemology, philosophy of mind and philosophy of language, and even for subareas such as ethics and metaphysics.

The problem is that many of these mathematical ideas might be a bit daunting for the average philosophy student (with just that single introductory logic under her belt), who is thereby left missing out on many philosophically interesting ideas. The solution to this problem should of course not be that every philosophy student has to acquire a full-blown mathematics education! It is exactly this gap that the informal reading group on 'Mathematics for Philosophy' is meant to fill.

The goal of the reading group is to allow interested students (and staff members) to explore exactly those bits and pieces of mathematics that are most interesting/useful for understanding contemporary philosophy. We aim for breadth of coverage rather than narrow specialization: all topics will be discussed at an understandable level, and if a participant wants to exploring a particular topic that is relevant for her philosophical interests in more detail, she will have acquired enough basic knowledge to do this in a relatively independent fashion...

**:: text**

Eric Steinhart, 2009, *More Precisely. The Math you Need to do Philosophy*. The book's website is here.

(pdf files of the book's chapters will be made available to all participants)

**:: schedule**

Time: all sessions are from 12:00 to 14:00.

Location: the sessions of March 10 and April 28 take place in room C (00.16) of the Institute of Philosophy. All other sessions take place in the Salons of the Institute.

- March 10, 2015: Chapter 1:
*Sets* - March 17, 2015: Chapter 2:
*Relations* - March 24, 2015: Chapter 3:
*Machines* - March 31, 2015: Chapter 4:
*Semantics* - April 7, 2015: Easter break: no meeting!
- April 14, 2015: Easter break: no meeting!
- April 21, 2015: Chapter 5:
*Probability* - April 28, 2015: Chapter 6:
*Utilitarianism*(note:**room C**!!) - May 5, 2015: Chapter 7:
*From the Finite to the Infinite* - May 12, 2015: Chapter 8:
*Bigger Infinities*

**:: additional notes and links**

Related to session 1:

- Timothy Williamson's paper 'Must do Better' is available online here (the quote we read during the first session is on p. 14 and p. 17)
- Hannes Leitgeb's paper 'Scientific Philosophy, Mathematical Philosophy, and All That' is available online here
- Make sure to pay a visit to the website of the Munich Center for Mathematical Philosophy and have a look at their research page!
- Inspired by our discussion during the first session, I wrote some brief notes about Benacerraf's problem.

Related to session 2:

- Stefaan Cuypers's paper 'The Memory Theory of Personal Identity' is available here (it originally appeared as an appendix to his book
*Self-Identity and Personal Autonomy: An Analytical Anthropology*, - An interesting blog post by Peter Smith about the (non-)difference between unary and binary functions can be found here.
- And here is a useful video explaining some basic properties of equivalence classes.
- Have a brief look at the website for the book
*Revenge of the Liar*; the section 'About this book' contains a nice description of what a revenge problem is.

Related to session 3:

- You can experiment with Conway's Game of Life here.
- This video shows another nice example of a phase transition; there's some additional explanation in the video description.

Related to session 5:

- The axioms for Popper functions (similar to the Kolmogorov axioms for absolute probability functions) can be found here.
- This video explains Dutch book arguments (note: the video discusses both synchronic and diachronic Dutch books; during the reading group we only had the chance to talk about the synchronic kind!).

Related to session 6:

Related to session 7:

- This video provides a nice explanation of Hilbert's hotel.

Related to the Singapore birthday problem:

- Newspaper articles about the problem and the solution (in Dutch).
- Newspaper article about the problem (in English).
- I just discovered this video of Barteld Kooi's explanation of the solution. Note: this is essentially the same explanation as the one I gave during the reading group (session 7), which should not be too surprising, given that we are both making use of the very nice and powerful framework of 'dynamic epistemic logic' (actually, Barteld and I have written several papers together on this framework, as you can see here).

**:: participants (past and present)**

- Michaël Bauwens
- Stefaan Cuypers
- Lorenz Demey
- Stef Frijters
- Kevin Holmes
- Zhuran Li
- Hans Smessaert
- Wouter Termont
- Pieter Thyssen
- Wouter Vancoillie
- Karen Van den Bosch
- Dajo Vande Putte
- Louise Vandevelde
- Arne Verkerk
- Leander Vignero