Frege’s Puzzle, Ordinary Proper Names, and Individual Constants

Abstract

My aim in the following observations is simply to remind Frege’s motivations for introducing the Sinn, and some important facts about his use of ‘=’. I think they are relevant at the time of scrutinizing what has been called “Frege’s puzzle”. First, Frege does not use the identity sign ‘=’ exactly as we do; second, his notion of object is not a substantive one (physical or mereological), but a schematic one; and third, Frege’s notion of proper name is quite different from ours or that of common sense. At the end, I tackle Glezakos’ problem about the individuation of names. I conclude, like Glezakos, that Frege’s puzzle is not that puzzling, but for slightly different reasons. Frege’s theory of intentionality and the rules that govern the use we make of schematic sentences in the process of formalization are keys to understand why Frege posed the problem the way he did. However, I do not believe that Frege’s solution holds for ordinary proper names. I think that Frege’s solution works much better when the substituends for ‘a’ and ‘b’ are complex expressions like definite descriptions or full declarative sentences, because these expressions express articulated modes of presentation, while the incomplex expressions, like ordinary proper names, do not express their mode of presentation in virtue of a definite convention, and then arbitrariety is unavoidable.