Idit Chikurel

This article examines the sceptical dimension of Salomon Maimon’s theory of invention. It suggests the following: (i) Most of Maimon’s methods are intended to increase the degree of certainty that we can attribute to propositions, but not to achieve apodictic certainty. (ii) Maimon’s various forms of scepticism, for example, doubt and the antinomies, should be considered as belonging to a scale of doubt wherein degrees of certainty and probability can increase and decrease. (iii) His methods of invention offer various means for increasing the degree of certainty, such as finding more connections to other propositions and analyzing whether a condition expressed in a proposition is true or whether it is only a pseudo-condition. (iv) The method of transforming problematic propositions into true propositions indicates that Maimon’s sceptical stance sometimes made way for rational dogmatic thought, since this transformation is in the opposite direction of what is usually advocated by sceptics.

In this article, I address an uncharted topic in the scholarship on Salomon Maimon – the great influence that Bacon's philosophy had on Maimon. I suggest that by considering Maimon as a Baconian, we achieve a better understanding of Maimon's work, especially in three respects: (i) his use of natural histories to achieve philosophical insights, (ii) the employment of induction to find new propositions and establish known ones as certain but not as objectively necessary and (iii) a probabilistic view of science, wherein we acknowledge that we can achieve higher degrees of certainty attributed to propositions but are unable to show that empirical propositions are objectively necessary. It is in this context that I propose to use the term ‘ladder of certainty’ and discuss how it is connected to Maimon's skeptical stance.

How can we invent new certain knowledge in a methodical manner? This question stands at the heart of Salomon Maimon's theory of invention. Chikurel argues that Maimon's contribution to the ars inveniendi tradition lies in the methods of invention which he prescribes for mathematics. Influenced by Proclus' commentary on Elements, these methods are applied on examples taken from Euclid's Elements and Data. Centering around methodical invention and scientific genius, Maimon's philosophy is unique in an era glorifying the artistic genius, known as Geniezeit. Invention, primarily defined as constructing syllogisms, has implications on the notion of being given in intuition as well as in symbolic cognition. Chikurel introduces Maimon's notion of analysis in the broader sense, grounded not only on the principle of contradiction but on intuition as well. In philosophy, ampliative analysis is based on Maimon's logical term of analysis of the object, a term that has yet to be discussed in Maimonian scholarship. Following its introduction, a new version of the question quid juris? arises. In mathematics, Chikurel demonstrates how this conception of analysis originates from practices of Greek geometrical analysis.

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.