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.

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