Infinite and number in Spinoza's philosophy

• Autor(a) principal: Ferreira, Giorgio Gonçalves
• Data de Publicação: 2021
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Kriterion (Online)
• Texto Completo: https://periodicos.ufmg.br/index.php/kriterion/article/view/35092
• topic: Espinosa; Infinito; Indefinido; Número; Contínuo; Spinoza; Infinity; Indefinite; Number; Continuous

The purpose of this paper is to analyze the relationships between infinite and number in Spinoza's philosophy. Thus, the analysis will begin by looking at Letter 12 and distinguishing the notions of actual infinite, indefinite, unlimited, and non-enumerable. At this point, the article will attempt to show in what sense the notions mentioned above differ and why they cannot be confused. In dealing with the notion of number and non-enumerable quantities, the analysis will focus on the example of non-concentric circles, offered by Spinoza, and will show that, besides the continuum, what is at stake in the example cited is what posteriorly would come to be known as irrational numbers. After that, the article will deal with the notion of beings of reason, and will show how the time, measure, and number differ as beings of reason. Lastly, the article concludes by pointing out that (i) it is the number that depends on infinite to be conceived, not the reverse; and that (ii) Spinoza's legacy opens the way for a new way of thinking about infinity, which will be explored by Cantor.