Abstract: This paper proposes a discrete-continuous model of cognition to resolve enduring philosophical difficulties surrounding time, motion, and infinity. The argument begins by establishing the transcendental necessity of discreteness: any cognitive act must already contain a distinction between consciousness and its object, making noncontinuous recognition a structural condition of cognition itself. Within this framework, a critical distinction is drawn between two types of discrete operation. Signifierdiscretization is a legitimate operation within the sign system that establishes differential relations among terms in coexisting continuity (space). Signifieddiscretization, conversely, is an illegitimate transgression that covertly attributes a discrete structure to the substrate itself. The paper demonstrates that this transgression occurs through a two-stage process: first, “retention” (Husserl) converts the nonjuxtaposable flow of successive continuity (time) into a juxtaposed surrogate in consciousness; second, the legitimate operation of signifier-discretization is applied to this surrogate, thereby concealing the original structural conversion. This model is then applied to critically re-examine several philosophical problems. Zeno’s paradoxes are diagnosed as an illicit conversion of successive motion into static, coexisting positions. Bergson’s intuitionism is shown to be self-destructive, as its proposed method of “intuition” inevitably presupposes the very discreteness it seeks to overcome. Russell’s logical atomism is criticized for its foundational commitment to signified-discretization, which is revealed as the source of its insoluble difficulties with relations, change, and self-reference. Finally, the paper extends this analysis to the foundations of mathematics. The Cantorian actual infinite (ἐνεργείᾳ ἄπειρον) is critiqued as an illegitimate product of converting the potential infinite’s (δυνάμει ἄπειρον) endless process in successive continuity into a completed object in coexisting continuity. Consequently, the Axiom of Infinity and the Axiom of Foundation in Zermelo-Fraenkel set theory are revealed to be non-logical, and in the latter case counter-logical, stipulations introduced to stabilize this structural distortion. The paper concludes that discreteness, while the necessary mode of cognitive operation, can never exhaust the continuous substrate, leaving a remainder that perpetually escapes its grasp. Keywords: discreteness, continuity, infinity, transcendental philosophy, retention, Zeno's paradoxes, Bergson, logical atomism, Russell, Zermelo-Fraenkel set theory
Tianle Han (Thu,) studied this question.