Formal concepts seminar program
All sessions 2.15 - 4pm in GM 652 (unless otherwise announced)
Spring semester 2018
Monday 15th January
Main reading: Menzel, C. (1993). The proper treatment of predication in fine-grained intensional logic. Philosophical Perspectives, 7, 61-87.
THURSDAY 1st February 2.15-4pm in GM 652
Main reading: Hale, Bob (2015). Second-order logic: properties, semantics, and existential commitments. Synthese:1-27.
Secondary reading: Shapiro, Stewart (ms). Properties and predicate, objects and names: impredicativity and the axiom of choice.
Monday 12th February
Talk: Sam Roberts “Pluralities and sets in the multiverse”
Monday 19th February
Main readings: Horsten, L. and Linnebo, O. (2016). Term models for abstraction principles. Journal of philosophical logic: 45, pp.1-23
Optional: Maddy, P. (2000). A theory of sets and classes. In Between Logic and Intuition. pp. 300-316
Monday 12th March: Mini workshop on predicativity led by Stewart Shapiro and Sam Roberts 1pm-4pm
In the first half, Stewart Shapiro will present some background material on the notion of predicativity before looking at how it interacts with potentialist views of mathematics. In the second half, I will introduce a distinction between two kinds of predicativity: ontological and ideological. I’ll then argue that each kind leads to different general responses to paradox, culminating in the iterative conceptions of set and property respectively.
Thursday 22nd March 12.15pm - 2pm
Talk: Jose Ferreiros (Universidad de Sevilla) “Objects by Objectivity”
Monday 9th April
Main reading: On predicativity or Fine-Linnebo property theories
Monday 16th April
Main reading: Continuing on Fine-Linnebo property theories
Monday 7 April: Dan Marshall (Lingnan University)
Autumn semester 2017
Monday 16 Oct: Classes and sets
Maddy, P. (1983). Proper classes. Journal of Symbolic
Logic, 48, 113-139; Sect. I and (especially) II.
Parsons, C. (1983b). Sets and classes. In Mathematics in philosophy (p. 209-
220). Cornell University Press, https://www.jstor.org/stable/2214641
Monday 30th Oct: Classes in category theory
Feferman, S (2013). Foundations of unlimited category theory: what remains to be done. https://philpapers.org/rec/FEFFOU-2
Monday 27th Nov: Properties 1
Bealer, G. (1982). Quality and concept. Oxford: Clarendon Press.
Introduction: sections 1–3
Chapter 1: sections 6–10
Chapter 2: sections 12, 13, 15–17
Chapter 5: whole chapter
Sections 15–17 contain some formal results which depend on material from section 14; these can just be skipped. But it may be of interest to at least skim chapter 4.
The book is available on Oxford Scholarship Online:
Monday 11th Dec: Properties 2
Chierchia, G., & Turner, R. (1988). Semantics and property theory.
Linguistics and Philosophy, 11, 261-302.