Abstract

This paper consists of two parts and has two aims. The first is to elaborate on the historical-philosophical background of Cantor’s notions of infinity in the context of Spinoza’s influence on him. To achieve this aim, in the first part I compare Spinoza’s and Cantor’s conceptions of actual infinity along with their mathematical implications. Explaining the metaphysical, conceptual, and methodological aspects of Cantor’s expansion of the orthodox finitist conception of number of his time, I discuss how he adopts Spinoza’s motifs to overcome the challenges on his way to proposing his transfinite infinites. To achieve the second aim, i.e., to investigate the philosophical foundations of Cantor’s transfinite infinites, I follow a three-step outline analyzing Cantor’s three principles along with their metaphysical and epistemological-linguistic aspects. I analyze the strengths and weak sides of Lakoff and Núñez’s Basic Metaphor of Infinity and Pantsar’s Process → Object Metaphor, then compare their interpretations with mine. I conclude that the metaphors can be improved when their source domains are limited to the target domains they apply to and when supported by a thorough analysis of the historical-philosophical background of their target domains.