In this contribution, we first discuss the aspects of the analytic method conceived by Kant in the Deutlichkeit that differentiate it from the Wolffian method and relate it to the Newtonian method. Compared to the philosophical tradition, the task of analysing concepts appears profoundly changed. Since Kant aims philosophy towards the world, he considers concepts as something given and intends to discern their characteristic marks by observing their usual applications. Although Kant abandons any attempt to define concepts nominally, he still (...) gives great relevance to words to the extent that concepts, according to him, acquire their meaning in the linguistic usage. We will also point out how for Kant the linguistic usage makes the analysis of concepts anything but easy and how a hermeneutic process is necessary for its completion. In distinguishing philosophical signs from mathematical signs, Kant provides the semiotic reasons that underlie his recourse to hermeneutics. (shrink)

This paper argues that in Christian Wolff’s theory of knowledge, logical regimentation does not take the place of experiential justification, but serves to facilitate the application of empirical information and clearly exhibit its warrant. My argument targets rationalistic interpretations such as R. Lanier Anderson’s. It is common ground in this dispute that making concepts “distinct” issues in the premises on which all deductive justification rests. Against the view that concepts are made distinct only by analysis, which is carried out by (...) the understanding independently of experience, I contend that for Wolff some distinct concepts are arrived at through experience. I emphasize that Wolff countenances empirical methods of obtaining distinct concepts even in mathematics. This striking feature of his view indicates how its empiricist elements can be reconciled with his injunction to follow “mathematical” method. (shrink)

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in this collection. I first examine the more general questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the (...) question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy of mathematics. (shrink)