Talk: Idit Chikurel (MCMP)

Title:

Grounds and Consequences in Bolzano’s and Maimon’s Mathematical Ampliative Analytic Propositions

Abstract:

My project suggests that ampliative analytic propositions serve as grounds and have consequences, based on examples from Salomon Maimon's theory of thinking (1753-1800) and Bernard Bolzano's (1781-1848) theory of science. Bolzano, who was familiar with Maimon’s logical work, is considered as one of the fathers of theories of grounding and of consequences. In my talk, I discuss what it means for a proposition to be ampliative analytic, i.e., informative and true, namely through mathematical examples. I focus on some of the requirements of grounding and consequences: I inquire after Bolzano’s notion of grounding as conceptual in light of his examples taken from Euclidean geometry, consider whether asymmetry is indeed a necessary condition for grounding, explore Maimon’s cases wherein grounding is actual but the consequences are logical (in Schnieder’s (2021) broader sense of the term), and examine whether contemporary thought on grounding is sufficient for explaining geometrical propositions of the Euclidean kind.