Slides here.

This will be a talk at the Set Theory Work in Progress Seminar on 10th January 2025.

Abstract: The Continuum Hypothesis featured top of Hilbert’s list of 23 problems in 1900. Today, we still consider the question, with various programmes pulling in different directions. This conceptual diversity raises a puzzle; in what sense are our thoughts about sets and the Continuum Hypothesis the same? In what sense do we disagree when we talk about it? A standard assumption takes it that one must either accept the full determinacy or radical indeterminacy of set-theoretic claims; that there is either no disagreement or complete disagreement about a unique intended subject matter. In this paper, I argue for a possible middle-ground. Assuming a representationalist view of how content is determined, I argue that whilst the Continuum Hypothesis can mean different things to different agents, it can also be determinate within certain communities.