The Role of Structure in Leibniz’s Mathematical Thought
Abstract
This paper examines the role of the notion of structure in Leibniz’s mathematical thought. I show (i) how Leibniz’s structuralist understanding of truth and reason conditions his methodological formalism; (ii) how Leibniz’s prioritization of arithmetic over geometry is founded on his relational and structural conception of number; (iii) how his mathematics of infinity, i. e. his calculus, relies on the structural traits of infinity; and lastly, (iv) how the concept of structure is the indispensable partner of the concept of expression that Leibniz considers universal and metaphysically fundamental. I conclude that the power and innovative character of his mathematical thought stems from a mathematical structuralism that is supported by a structural conception of truth and reason, and an even more fundamental metaphysical structuralism.
Keywords
number | quantity | structure | formalism | expression | calculus | nombre | quantité | structure | formalisme | expression | calcul | Zahl | Menge | Struktur | Formalismus | Ausdruck | Inifinitesimalkalkül