Quine

For this session of PhiMath, we read Bob Hale’s paper “Properties and the Interpretation of Second-Order Logic”. He defends a deflationary conception of properties, which are the things we quantify over in second order logic. According to Hale, something is a property iff there could be a predicate that stands for it.

He looks into Quine’s claim that second-order logic is “set theory in sheep’s clothing”, which he understands as a broader charge motivated by the idea that second-order quantification carries heavy existential commitments. According to him, his deflationary interpretation of second-order logic can resist Quine’s critique. During the meeting, we consider Hale’s proposal and its implications for second-order logic.

For this session, we will answer the title’s question with the short and sweet: John P. Burgess’s Why I Am Not a Nominalist, a broad overview against various forms of nominalism.

Burgess responds to nominalist attempts to dispense with abstract objects in mathematical and scientific discourse, challenging both instrumentalist and reconstructionist forms of nominalism, among others. Burgess purports to shift the burden of proof onto the nominalist rather than the realist, by arguing that nominalistic reconstructions need (and in his view fail) to account for the role of mathematics in science. His critique addresses Goodman, Quine, and Field, among others.

Tibo will give a short presentation supporting the (in)famous Quine thesis that SOL is in reality ST, followed by a debate. The rules will be uploaded in due time.

Slides used during the presentation are available here (link now unfortunately broken).

Suggested Bibliography (They are freely accessible from your UvA student account)

• Quine W.V.O., Philosophy of Logic (2nd Edition), Chapter 5: ‘The Scope of Logic’, Harvard University Press, 1986. [PDF accessible from the UvA Library]