Second-Order Logic: If not Set Theory in Sheep’s Clothing, What is it Then?
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.