Analysis and Necessity in Arithmetic in Light of Maimon's Concept of Number as Ratio

Idit Chikurel*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)33-67
Number of pages35
Issue number1
StatePublished - 31 Mar 2023
Externally publishedYes


  • Analytical Judgments
  • Arithmetic
  • Ratio
  • Salomon Maimon


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