Slides here.

This will be a response to Chanwoo Lee at the 9th meeting of the Society for the Metaphysics of Science. TLDR version: How different is modelling in science from mathematics?

Handout.

You can read a fuller description of the project outline here.

Abstract: Set-theoretic potentialism is the view that whatever sets there are, there could always be more. Standard formulations of set-theoretic potentialism are given a modal two-valued treatment. We use some variety of modal logic — be it standard, positive-free, or negative-free — with an underlying two-valued classical logic. In this sense, the approach is local in that at the core of the semantics we look at what is made true by individual worlds. Mirroring theorems can then be used to recover much of standard set theory from a more global perspective, but unrestricted quantifiers are understood as implicitly modal (with the universal and existential prefixed by a necessity and possibility operator respectively).

The situation is complicated by a recent division between strict and liberal potentialism. Roughly speaking, liberal potentialists think that the modal facts about how the universe unfolds are fixed from the off. Strict potentialists, by contrast, hold that new facts can be “made true” as new sets come into being.

An further complication is that when working with collections, it is important to distinguish between two kinds. For extensional entities it is sufficient for two such collections to be identical that they have exactly the same members. Intensional entities on the other hand can change members across different possible worlds, and just because two classes have the same members over a domain does not make them the same class.

This project aims to (1.) establish a framework for dealing with intensions, and (2.) examine the strength of theories that one gets out. In particular, by using features of the possible world structure, we will provide an algebraic semantics to assess these questions. On this basis, there are at least preliminary indications that:

(1.) Though we might ascribe a many-valued logic to liberal potentialist, they should still hold on to classical logic globally.

(2.) The strict potentialist should accept intuitionistic logic. However, the strength of the logic motivated is contingent upon both the expressive resources allowed and the variety of potentialism in question.

Slides here. Paused slides here.

Abstract: A tension seems to lie at the heart of Gödel’s work on the epistemology and metaphysics of mathematics. On the one hand he seems to advocate a kind of platonism on which we have a quasi-perceptual grasp of the mathematical realm and certain axioms force themselves upon us as being true. On the other hand he is famous for (allegedly) saying that kinds of platonism cannot satisfyany critical mind. In this paper, I will argue that Gödel’s notebooks are informative for understanding and dissolving this tension. By drawing on his remarks, I’ll tentatively propose that there’s a viable interpretation of Gödel on which he holds a form of representationalism about mathematics. On this view we are able to form coherent, quasi-perceptual representations of mathematical reality, but they may be better or worse. Using this, I’ll argue that the use of Gödel as a kind of non-naturalistic piñata in the philosophy of mathematics is wholly unjustified, and that his work can be used as an inspiration for developing naturalist epistemologies of mathematics.

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This is an online conference, comprising both YouTube videos and an online panel session. The panel session will be Wednesday 20th March 2024, 0900-1000 UTC + 0, 1700-1800 SGT. A Zoom link will be distributed prior to the panel session via email (please sign up via the link above to receive it). YouTube videos of the talks (which can be watched prior to the panel session) are below.

Panelists:
Shannon Hayes. Project Coordinator, Children on the Move, International Organization for Migration IOM.
Dr. Prithvi Hirani. Program Officer, IOM, Displacement Tracking Matrix (DTM).
Dr. Nando Lewis. Project Officer, IOM, DTM Global Support Team.
Esther Mulwa. Data Consultant, DTM and PhD Candidate, City University, London

The panel session will be based on the following videos.

Videos: 
Neil Barton: (2 min)
Nando Lewis: (21 min)
Shannon Hayes: (12 min)
Prithvi Hirani and Esther Mulwa: (25 min)

Description. Data and computational reasoning play a critical role in humanitarian action. We need fast data-driven solutions to important and pressing problems. But what are some of the challenges faced by experts in this sector? And how might academia learn from and contribute to this area of research? This online conference, combining a mixture of YouTube videos and an online panel session, aims bring together academics and experts working on displacement.