Talk: Engineering Set-Theoretic Concepts

This will be a talk on 28th April at the National University of Singapore. Slides here.

Abstract: In this talk I’ll argue that we’re now at a conceptual crossroads regarding the iterative conception of set. To do this I’ll appeal to work on conceptual engineering. I’ll argue that conceptual engineering has formed a part of set-theoretic activity since its inception as a mainstream area of mathematical research, and that the development of the iterative (and other) conceptions of set was in part responding to inconsistency in the naive set-concept. I’ll then argue that whilst the iterative conception can be taken to be a consistent concept in its own right, it is deficient in various ways (in particular, it fails to tell us enough about the nature of infinite sets). Contemporary set theory, I’ll argue, has now moved to a maximal iterative conception of set, and this conception is inconsistent. Many contemporary accounts of the ontology underlying set-theoretic practice should be conceived of as attempts to engineer consistent conceptions of the maximal iterative concept of set. I’ll explain two such conceptions, and tentatively conclude that discussion should focus less on the vexed and seemingly intractable issue of ontology, and instead concern itself more with the (nonetheless difficult) question of the relative theoretical virtues of alternative conceptions.

Talk: Computation: How hard can it be?

This will be a talk on 28th April at the National University of Singapore. Slides here.

Abstract: This talk will explain the notion of a computation and the importance of the idea that some computations are more difficult than others. I’ll begin by explaining the rough idea of computers and algorithms, and how a single computer is able to implement many different programs. We’ll then look at some examples and see that there are different algorithms for solving the same problem. I’ll then present the idea that there’s a fundamental limit to what can be done with computers. I’ll close with possible questions regarding the link between computational difficulty and the ethics of computation.

Talk: Engineering Set-Theoretic Concepts

Slides here. This will be a talk at the UCI LPS Colloquium.

Abstract: In this talk I’ll argue that we’re now at a conceptual crossroads regarding the iterative conception of set. To do this I’ll appeal to work on conceptual engineering. I’ll argue that conceptual engineering has formed a part of set-theoretic activity since its inception as a mainstream area of mathematical research, and that the development of the iterative (and other) conceptions of set was in part responding to inconsistency in the naive set-concept. I’ll then argue that whilst the iterative conception can be taken to be a consistent concept in its own right, it is deficient in various ways (in particular, it fails to tell us enough about the nature of infinite sets). Contemporary set theory, I’ll argue, has now moved to a maximal iterative conception of set, and this conception is inconsistent. Many contemporary accounts of the ontology underlying set-theoretic practice should be conceived of as attempts to engineer consistent conceptions of the maximal iterative concept of set. I’ll explain two such conceptions, and tentatively conclude that discussion should focus less on the vexed and seemingly intractable issue of ontology, and instead concern itself more with the (nonetheless difficult) question of the relative theoretical virtues of alternative conceptions.