3 - Frege’s conception of logic

Summary

Frege is of course an important progenitor of modern logic. The technical advances he made were comprehensive. He clearly depicted polyadic predication, negation, the conditional and the quantifier as the bases of logic; and he gave an analysis of and a notation for the quantifier that enabled him to deal fully and perspicuously with multiple generality. Moreover, he argued that mathematical demonstrations, to be fully rigorous, must be carried out using only explicitly formulated rules, that is, syntactically specified axioms and rules of inference.

Less clear, however, is the philosophical and interpretive question of how Frege understands his formalism and its purposes. Upon examination, it appears that Frege had a rather different view of the subject he was creating than we do nowadays. In lectures and seminars as far back as the early 1960s, Burton Dreben called attention to differences between how Frege viewed the subject matter of logic and how we do. The point has been taken up by several commentators, beginning with Jean van Heijenoort. The technical development historically required to get from a Fregean conception to our own was discussed in my ‘Logic in the twenties: The nature of the quantifier’. Yet there is currently little appreciation of the philosophical import of these differences, that is, the role in Frege’s philosophy that his conception of logic, as opposed to ours, plays. Indeed, some downplay the differences and assign them no influence on or role in the philosophy. Thus Dummett says only that Frege was ‘impeded’ from having the modern view by a particular way of looking at the formulas of his Begriffsschrift. I want to urge on the contrary that Frege’s conception of logic is integral to his philosophical system; it cannot be replaced with a more modern conception without serious disruptions in that system. The reasons for this will, I hope, be instructive about the roots of Frege’s philosophizing.