The article examines how Salomon Maimon’s concept of number as ratio can be used to demonstrate that arithmetical judgments are analytical. Based on his critique of Kant’s synthetic a priori judgments, I show how this notion of number fulfills Maimon’s requirements for apodictic knowledge. Moreover, I suggest that Maimon was influenced by mathematicians who previously defined number as a ratio, such as Wallis and Newton. Following an analysis of the real definition of this concept, I conclude that within the framework (...) of Maimon’s philosophy, arithmetical judgments cannot be analytical, nor is arithmetic an objectively necessary science, but rather only subjectively necessary. We should also cast doubt on his claim that we can create real objects from pure concepts of the understanding. (shrink)

There is little doubt that Salomon Maimon was both highly respected by, and highly influential upon, his contemporaries; indeed, Kant himself referred to Maimon as the best of his critics. The appraisal and reformulation of the Kantian project detailed in Maimon’s Essay on Transcendental Philosophy played a significant role in determining the criteria of success for post-Kantian philosophy, and was thus crucial to the early development of German Idealism. Key aspects of Maimon’s transcendental philosophy remain, however, relatively obscure. In particular, (...) it remains unclear to what degree Maimon’s skepticism is internal to the Kantian framework, and how this skepticism is related to Maimon’s so-called dogmatic rationalism. The central aim of this project is to present Maimon’s as a distinct form of post-Kantian skepticism: one which poses significant problems for Kant’s theoretical project and which motivates a reformulation of the critical framework. In Kant’s eyes, pre-Kantian forms of skepticism are insufficiently critical insofar as they involve a commitment to transcendental realism. By contrast, I argue that Maimon’s skepticism does not involve a commitment to transcendental realism and that it strikes at the heart of Kant’s critical project insofar as it constitutes what I term ‘critical’ as opposed to merely ‘empirical’ skepticism. I further argue that Maimon’s rationalism provides the materials for a response to this form of skepticism. This thesis contributes to contemporary debates in the history of philosophy concerning the nature of Maimon’s coalition system and its relation to German Idealism, but also provides an alternative perspective on contemporary problems in the philosophy of perception concerning, in particular, the possibility of non-conceptual intentional content. (shrink)