This will be a talk on Juliette Kennedy’s book Gödel, Tarski and the Lure of Natural Language, to be held at the Pacific APA. Handout here. I’ll raise some questions concerning the relationship between the notion of formalism freeness and that of mathematical structure.
Talk: Limitations of Logic
This will be a very short talk to the intro logic students at the University of Oslo. Slides here.
Talk: Work in progress on the iterative conceptions of set
This will be a talk in the Oslo Logic Seminar. Handout here.
Abstract:
In this talk, I will present some early-stage work in progress on the iterative conceptions of set. In a recent booklet (itself entitled Iterative Conceptions of Set) I’ve argued that we can think more generally about the iterative conception as a way of generating sets, without committing to the Powerset operation. The booklet is rather “programmatic”, however, and leaves a lot of mathematical questions open. In this talk I’ll try to accomplish the following things:
(1.) I’ll present the rough idea I gave in the booklet.
(2.) I’ll outline one application I’m working on (a version of Steel’s multiverse programme), and the challenges I’m facing there.
(3.) I’ll present some thoughts about how one might try to extract a general notion of an “iterative conception of set”, at least model-theoretically.
Talk: Make It So: Imperatival Foundations for Mathematics
This will be a talk at the workshop Generative Metaphysics and the Philosophy of Mathematics. Slides here.
Abstract: This article articulates and assesses an imperatival approach to the foundations of mathematics. After Fine, we call the program `procedural postulationism’. The core idea for the program is that mathematical domains of interest can fruitfully be viewed as the outputs of construction procedures. Fine argues that this viewpoint has various potential epistemic and ontological benefits in philosophy of mathematics; and in any case we think the guiding idea is interesting enough to warrant close inspection. We offer a logic for `creative’ imperatives—imperatives that command the introduction of new objects into the domain—and show how to treat the concept of indefinite iteration in that logic. We then give consistency proofs for arithmetic and set theory starting from the formalized hypothesis that certain commands statable in the resulting logic are executable. Using this framework, we will assess whether the view can claim to have epistemic and ontological benefits over standard `declarative’ approaches.
