INDETERMINACY AND THE
PHILOSOPHY OF MATHEMATICS
SPEAKERS
ABOUT
According to the classical conception in the foundation of mathematics every statement has a determinate truth value, i.e. is either true or false. Until the discovery of independence phenomena, this was the prevalent conception of mathematics and it remains the standard view even today. In fact, Kurt Gödel demonstrated that in every sufficiently strong consistent system there are statements that are independent, i.e., statements that can neither be proven nor disproven within that system. This gave rise to new perspectives in the foundations of mathematics, casting serious doubt on the determinacy of all mathematical statements. The workshop aims at exploring and assessing these new ways of framing foundations beyond the classical conception.
TOPICS
Whereas indeterminacy is understudied in mathematics, it is a well-studied phenomenon in philosophy. This opens up a vast field of significant philosophical questions about the conceptions of indeterminacy in the foundations of mathematics. These include:
- How should we understand determinacy and indeterminacy in mathematics?
- Should determinacy in mathematics be best understood as conceptual, semantic, or metaphysical indeterminacy?
- Can tools developed to handle certain forms of indeterminacy, such as vagueness, in philosophy and logic be fruitfully applied to cases of apparent indeterminacy in mathematics?
- What are the relations between different conceptions of indeterminacy?
- How do categoricity results bear upon the question of determinacy and indeterminacy in mathematics?
SCHEDULE
09.00 – 09.30: Coffee and Welcome
09.30 – 11.00: Toby Meadows (University of California Irvine), Structure ‘n Junk
Abstract
In some corners of the academy, one hears that ZFC and its kin fail to provide a sufficiently structural approach to the foundations of mathematics. Despite delivering a pretty good foundation, ZFC also carries junk in its luggage. So the story goes. My goal in this talk is to make a few preliminary (and quite clumsy) moves to better understand and assess this claim. In particular, I’ll aim to sketch answers to the following three questions.
1) What is junk?
2) How might junk affect foundations?
3) What would a foundation free of junk look like?
11.00 – 11.30: Break
11.30 – 13.00: Xinhe Wu (London School of Economics), Vague Identity: A Uniform Approach
Abstract
There are many apparent examples of vague identity, i.e. examples where two objects appear to be neither determinately identical nor determinately different. Philosophers disagree on whether the nature of vagueness in identity is semantic or ontic/metaphysical. In this talk, I construct a novel many-valued semantic framework for vague identity. I show that this semantic framework is uniform: it works well with both a semantic and ontic conception of vague identity. I also argue that it has many other benefits and compare it with the alternatives. Finally I discuss Gareth Evans’ famous objection to vague identity in this new framework
13.00 – 14.00: Lunch
14.00 – 15.00: Chris Scambler (University of Oxford – All Souls College) & Cesare Straffelini (University of Barcelona), Indeterminacy or Relativity?
Abstract
In previous work, one of us has articulated an ‘indeterminate universe’ understanding of set theory; this talk will explain how that starting point naturally leads to a different, relativistic conception of the subject matter, and will then present some results about the relation between absolute and relative truth in the relevant sense.
15.30 – 16.00: Break
16.00 – 17.30: Tim Button (University College London), What should quasi-categoricity be, and why is quasi-categoricity significant?
Abstract
We all know that second-order ZF is quasi-categorical. But it is rare to discuss any other examples of quasi-categorical theories. This forces us to ask what quasi-categoricity is: that is, which features of Zermelo’s result are essential to the notion, and which are artefacts of considering ZF. In the first half of this talk, I will address this by presenting a taxonomy of quasi-categoricity-notions (with fun examples). In the second half, I will defend the significance of quasi-categoricity results against some recent criticisms.
19.30: Dinner at Tekehtopa
ATTENDANCE
Attendance is free, but in person only.
To register please fill the form below.
Deadline for registration: 30 April 2026.
VENUE
The conference takes place at the University of Oslo, Department of Philosophy, Classics, History of Art and Ideas, situated in Blindern Campus, building: Geor Morgenstiernes hus.
The conference room is GMH 652. This is the conference room situated at the 6th floor of the department, at the end of the corridor.
How to get to Blindern (Link 1/Link 2)
- Tram: line 17 and 18 towards Rikshospitalet, Stop at Universitetet Blindern (or John Colletts Plass in case of road works).
- Metro (T Bane): line 4 (Vestli via Storo), 5 (Ringen via Storo) 5 (Sognsvann), Stop at Blindern.
ORGANIZERS: Øystein Linnebo, Gioia Susanna, Davide Sutto, Sofie Vaas
FOR MORE INFORMATION, CONTACT