Abstract

The paper investigates the notions of number, extensive quantity, algebraic quantity, similarity, and probability as introduced in Wolff’s mathematical writings, and evaluates the coherence of these definitions with Wolff’s presentation of the mathematical method. Wolff’s original epistemology is based on the belief that the discussion on the foundation of mathematics and on the history of mathematical ideas is essential not only to pure mathematics but also to its application and teaching. Mathematics is integrated into a larger body of knowledge and subordinated to philosophy, which explains the impurity of definitions and proofs and why certain notions, such as that of similarity and probability, cannot be understood without reference to ontology and logic. Wolff’s investigation of probable propositions allowed for a unique demonstrative methodology applied to philosophical, mathematical, and historical knowledge, because he described probable reasoning as an insufficient knowledge of the requisites for the truth of the premises. This explains the importance assigned to the right order of concepts and the inferential role of definitions. The paper shows the internal coherence between Wolff’s choice of mathematical definitions and his overall epistemology, and underlines the heritage of Descartes, of Barrow’s edition of Euclid’s Elements and of Aristotle’s notion of contiguity rather than the influence exerted by Leibniz’s mathematics or by Newton’s fluxional conception of geometrical quantities.