 Some Peirce scholars have also claimed that Peirce’s invention of quantifiers is a product of Peirce’s own philosophy of logic, which is different from Frege’s (Brady 1997; Burch 1997; Iliff 1997; Merrill 1997). Hintikka’s proposal (1997) to explain the main difference between Frege’s and Peirce’s contributions to modern logic is quite intriguing. Tracing back to Frege’s own distinction between calculus ratiocinator versus a lingua characterica, van Heijenoort adds a new dimension to these two opposing views of logic beyond what Frege alluded to (van Heijenoort 1967: footnote 1, p.  329).[21]  While Frege emphasized a difference between propositional and quantification logic, van Heijenoort located a difference in what is taken as a totality. Boole’s tradition does not make any ontological commitment about a totality, but it “can be changed at will” (1967: 325). On the other hand, Frege’s language is about the universe. Borrowing van Heijenoort’s distinction between Boole’s logic as a calculus and Frege’s universality of logic, Hintikka locates Peirce in Boole’s camp, calling it the model-theoretic tradition. Unlike Frege’s view of the universe, the model-theoretic tradition allows us to reinterpret a language and thus assign different universes to quantifiers. According to Hintikka, Peirce’s development of modal logic is a good piece of evidence to show how fruitful Peirce’s way of understanding quantifiers could be (Hintikka 1997). In the next section where Peirce’s graphical systems are introduced, we will revisit this issue.