 It is striking that Peirce, already in 1885, had clearly differentiated between propositional logic, first-order logic, and second-order logic. He was aware that propositional logic is significantly weaker than quantificational logic, and, in particular, is inadequate to an analysis of the foundations of arithmetic. He could then have gone on to observe that second-order logic is in certain respects philosophically problematic, and that, in general, our grasp on quantification over objects is firmer than our grasp on quantification over properties. The problem arises even if the universe of discourse is finite. We have, for example, a reasonable grasp on what it means to speak (in first-order terms) of all the planets, or to say that there exists a planet with a particular property. But what does it mean to talk (in second-order terms) of all properties of the planets? What is the criterion of individuation for such properties? Is the property of being the outermost planet the same as the property of being the smallest planet? What are we to say about negative properties? Is it a property of the planet Saturn that it is not equal to the integer 17? In that case, although there are only a finite number of planets, our second-order quantifiers must range over infinitely many properties. And so on. The Quinean objections are familiar. 