Reading meetings are the most common event hosted by our group. We read together/present a text, and freely discuss together.
In this session we will deal with a critique to some main ideas of Predicativists. They believe that, in some respects, arithmetic has some advantages that analysis and set-theory do not. Koellner puts this idea to the test.
Main Readings:
After talking about the infinite and Frege Arithmetic, it is time to turn to potentialism about set-theory. In this session we will turn to potentiality about the height of the cumulative hierarchy.
Main Readings:
Our second meeting of the year continues along the lines of potentialism. Now we turn to Frege Arithmetic and a genuinely potentialist account of it.
Welcome to PhiMath 2024! In our first meeting for this academic year, we will discuss a paper by Linnebo and Shapiro on the notion of Potential Infinity.
For our final meeting on structuralism, we cover the modal set-theoretic structuralism from Parsons and Linnebø. This rounds out the book we have been following and also our time with structuralism (for now).
For our next meeting on structuralism, we will be covering the two views championed by the authors of the textboock: Shapiro’s ante rem, or Sui Generis, structuralism and Hellman’s Modal Structuralism.
Main Readings
Chapter 5 and 6 in Hellman, G., & Shapiro, S. (2018). Mathematical Structuralism (Elements in the Philosophy of Mathematics). Cambridge: Cambridge University Press. doi:10.1017/9781108582933
For our second meeting on Structuralism in mathematics, we will be focusing on the category-theoretical side of the discussion. Stemming from work in algebraic topology, category theory has since the 1950’s become an indisposable tool for mainstream mathematics and is seen by some to encode the structuralist philosophy into mathematics itself. We will be reading and discussing some thoughts around the plausibility of using category-theoretic foundations for mathematics and whether this really follows the structuralist philosophy.
We are now covering the theory of structuralism in mathematics. This first meeting will be an overview of the general position and its various parts together with specific focus on set-theoretic structuralism. Over the course of the coming meetings, we will spend some time on various conceptions of structuralism and their proponents.
We are continuing our discussion about Higher-Order Logic (HOL), this time focusing specifically on arguments against adopting Higher-Order logics for various purposes. These arguments range from (HOL) being set theory in disguise, the (lack of) applicability of (HOL) for its intended purposes, and the serious metalogical issues the logic faces.
The reading group in the philosophy of mathematics is back and we hold the first meeting on the 12th of October. The topic will be Higher-Order Logic. We will base the discussion around Stewart Shapiro’s chapter “Higher-order logic” in The Oxford Handbook of Philosophy of Mathematics and Logic.