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

Horsten, L. F. M., & Hannes, L. (2009). How abstraction works. In A. Hieke, & H. Leitgeb (Eds.), Reduction, abstraction, analysis (pp. 217 - 226). ontos verlag.

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:

http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780198244288.001.0001/acprof-9780198244288

Also, here: http://campuspress.yale.edu/gb275/quality-and-concept/

Monday 11th Dec: Properties 2

Chierchia, G., & Turner, R. (1988). Semantics and property theory.

Linguistics and Philosophy, 11, 261-302.