‘What Is the Point of This Symbolism?’ Lessons from Louis Couturat for the Historiography of Logic

Historians of logic often distinguish between two traditions in symbolic logic at the turn of the twentieth century: the ‘algebra of logic’ or ‘algebraic logic’, on the one hand, and ‘mathematical logic’ or ‘logistic’, on the other hand. Moreover, many scholars have claimed that logistic instigated a ‘Fregean revolution’ in logic that has rendered the algebra of logic obsolete. In this paper, I problematize this common conception of a Fregean revolution by focusing on the work of Louis Couturat (1868–1914). First, I draw on the work of Couturat to illustrate that the question of what logical system one regards as most fruitful, crucially depends on one’s underlying conception of the aims of logical symbolism as such. Second, I use Couturat as a counterexample to the common conception of a Fregean revolution. I argue that Couturat’s logistic synthesized Russell’s logic and algebraic logic. The motivation behind this synthesis was the realization that both Russell’s logic and algebraic logic were fundamentally flawed as they only partially fulfilled the aims of logic as understood by Couturat. I conclude by raising further questions on the proclaimed independency of logistic from the algebra of logic.