Letter to the Editor

The language of arithmetical theories considered here is L = +, ×, ≤, 0, 1 in which the symbols are interpreted as usual in elementary mathematics. Robinson's arithmetic is denoted by Q; it is a finitely axiomatized basic theory of the function and predicate symbols in L. Peano's arithmetic PA is the first-order theory that extends Q by the induction schema for any L-formula ϕ(x): ϕ(0) & ∀x(ϕ(x...

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a recursively defined function: one is for its recursive calls and the other is for its calls outside its definition. Bimorphic recursion in this paper can be neste...

Sider argues that, of maximalism and quantifier variance, the latter promises to let us make better sense of neo-Fregeanism. I argue that neo-Fregeans should, and seemingly do, reject quantifier variance. If they must choose between these two options, they should choose maximalism. 1: Introduction Benacerraf’s problem lies at the heart of philosophy of mathematics: the truth of mathematical sta...