C. S. Peirce and Aristotle on Time

Abstract

The question concerning the nature of time is intimately related to the traditional antithesis between the static a-temporal Parmenidean universe and the dynamic model of becoming. This is wonderfully illustrated in Peirce’s theory of the flux of time. In his rejection of the atomistic worldpicture, Peirce treated time in close relation to the physical processes. He thus propounded an extremely interesting theory which bears a kinship to contemporary theories of the arrow of time. However, what makes his approach extremely interesting is not only its air of modernity, but also its striking similarities with Aristotle (Physics, book IV, esp. chs. 10-14). My purpose, therefore, in this paper is to reconstruct Peirce’s theory of time in the light of Aristotle’s philosophy. My starting point will be Peirce’s analysis of continuity in relation to infinitesimals (6.109), through the use  of which he could treat time as a “continuum par excellence, (6.86, 1898) which is not a static collection of discrete instants, (see MS 137, p. 4-5, 1904), but a collection of real possibilia (see NE, 360), thus making possible the understanding of the flow of time (6.11). I will then proceed to the examination of Peirce’s connection of time, as a real continuum, with the idea of the infinite. In this respect, I will focus on his rejection of actual infinity – in the Zenonean-atomistic-Cantorian sense – and his adoption of the Aristotelian idea of potential infinite (Physics, book III, chs. iv-viii). I will, thus, argue that what led Peirce to pass from a logico-mathematical analysis of continuity to an ontological theory was his appeal to potentiality in his treatment of continuity-infinity-time. This, I believe, was the result of the influence he had received from Aristotle, who was also deeply concerned with giving to change, motion and becoming their proper place
in nature. Thus, both Peirce and Aristotle were able to built a dynamic theory of time, intimately related to the idea of potential infinity, which expresses a physical process progressively being actualized, so that it can never exist as a realized whole.