The tightrope of real genesis: on philosophy's generative thirdness and the creative self-grounding of thought

The paper poses a philosophical problem: how can thought overcome entrenched antinomies (e.g., rational/empirical, transcendental/historical, continuous/discrete, global/local) without collapsing into either dogmatic absolutism or naturalized relativism? The author argues that the locus of this overcoming is a generative “thirdness” or genetic hinge at which novelty, invention, and real genesis occur. This third site is neither pole but the disjunctive articulation that produces and presupposes them, and it is where Ideas (in a broadly Platonic sense) are actualized through dialectical suspension of polarity. The purpose is to configure the conceptual landscape around this genetic tension and to develop a dialectical method capable of grasping real genesis as the price of the very division into opposed terms. The importance of the study lies in reclaiming a systematic, non-mystical commitment to truth in genesis—an approach that aims to reanimate philosophical, mathematical, and scientific thinking by focusing on the conditions and processes through which new forms and concepts emerge.

The paper synthesizes a set of thinkers to articulate the notion of generative thirdness: (1) Jean Cavaillès and Albert Lautman on an “ideal dialectic” and the generative necessity of mathematics within historical development, aiming to render contingency necessary via dialectical unfolding; (2) Gilles Châtelet (and Badiou’s reading of him) on articulation, polarization, and the rhythm of learning, emphasizing dialectical generation over axiomatics and the separation-disjunction of discrete/continuous and intensive/extensive; (3) Charles S. Peirce on abduction as the initial, hypothesis-forming logical operation prompted by surprise, with later interpretations by Caterina and Gangle highlighting abduction as deformation of epistemic frameworks within concrete contexts of knowledge and ignorance; (4) Michael H. G. Hoffmann on diagrammatic reasoning as a vehicle for abductive learning and resolving the apriorism/inductivism dichotomy (e.g., the Meno’s diagonal); (5) Cécile Malaspina on an epistemology of noise, situating the information/noise distinction within entropy and emphasizing metastability (via Simondon) as enabling the genesis of form between absolute uncertainty and complete redundancy; (6) Further touchstones include Derrida on the historical incarnation of the transcendental, Zalamea on the trans-operativity of contemporary mathematics and relative universals, Longo (Anna) on Lautman’s dialectics of discovery, Longo (Giuseppe) on the theory-relativity of randomness, Thom on the need for geometric intelligibility, and Catren on stereoscopic co-deployment within the absolute. Together these lines of thought converge on a genetic realism grounded in a third, abductive-dialectical site that mediates and produces classical oppositions.

This is a conceptual, systematic-philosophical inquiry employing: (1) Dialectical analysis of polarities (e.g., transcendental/historical, rational/empirical) to identify a generative third site that both presupposes and produces opposed terms; (2) Abductive reasoning as a methodological hinge, treating surprise and contextual ignorance as engines of hypothesis-formation that deform and renew conceptual frameworks; (3) Formal-exemplary analysis via diagrammatic reasoning (Hoffmann/Peirce) to model how externalization of thought (e.g., the Meno’s diagonal) enables internalization of structure and the production of new concepts; (4) Transdisciplinary synthesis drawing from philosophy of mathematics, epistemology of noise, cybernetics, and French epistemology to trace homologous structures of genesis (metastability, articulation, polarization); (5) Programmatic reconfiguration of the conceptual landscape to orient systematic philosophy toward real genetic conditions without relying on pre-given criteria or methods. No empirical data are collected; instead, the paper builds a meta-theoretical framework for thinking genesis.

- Real genesis is neither reducible to nor derivable from either member of traditional oppositions; it occurs in a generative thirdness—a disjunctive, abductive hinge that simultaneously produces and presupposes the poles (continuous/discrete, rational/empirical, transcendental/historical, etc.). - Abduction precedes and conditions deduction and induction in the genesis of knowledge, functioning as a context-sensitive deformation of frameworks spurred by surprise; diagrammatic reasoning exemplifies how such abductions externalize and stabilize new concepts. - In information-theoretic terms (Malaspina), novelty emerges within metastable tension between absolute uncertainty and complete redundancy; information/noise distinctions are processual and context-dependent, aligning with the broader thesis of genesis through suspended polarity. - Mathematical and philosophical absolutes are re-made through historical dialectical unfolding (Cavaillès/Lautman), enabling a convergence where contingency is rendered necessary by generative structures and operations. - A genetic realism places a normative-exigent demand on philosophy to self-ground its methods and criteria through creative acts at the hinge of genesis, resisting both dogmatic absolutism and naturalized relativism. - Reconfiguring the conceptual landscape around this genetic hinge rejuvenates systematic thought, offering a path to transform sedimented dualisms and to engage complex, multi-scalar realities without capitulating to relativism.

By locating the site of philosophical novelty in a generative thirdness, the paper addresses the impasse between relativism and absolutism: rather than choosing a pole, it shows how both are produced through an abductive-dialectical hinge that makes novelty possible. This framework reframes the research problem—how to think the absolute without dogmatism and the relative without nihilism—by proposing abduction and articulation as immanent processes that generate the very criteria and forms of thought. The significance lies in demonstrating homologies across domains (mathematics, epistemology of noise, diagrammatic cognition) where metastable tensions generate form. The approach clarifies how historical contingency and transcendental invariants co-produce each other, offering a systematic orientation that can inform philosophy of mathematics, epistemology, and transdisciplinary theory. In doing so, it promises renewed traction on conceptual deadlocks and a revitalized practice of systematic philosophy centered on creative self-grounding.

The paper contributes a programmatic account of real genesis as a generative thirdness—an abductive-dialectical hinge that articulates and produces traditional oppositions. It synthesizes insights from Cavaillès, Lautman, Châtelet, Peirce, Malaspina, and others to argue that novelty and meaning arise through metastable suspensions that render contingency necessary. The proposed genetic realism urges philosophy to reconfigure its conceptual landscape and to practice creative self-grounding without pre-given methods. Future research directions include: (1) further formalization of abductive hinges in mathematics and logic; (2) systematic development of diagrammatic and categorical tools to model articulation and polarization; (3) applications of the metastability framework to information theory, cognition, and scientific theory-change; (4) explorations of ethical and political implications of genetic self-grounding for transforming historical deadlocks.

The work is a conceptual and programmatic synthesis without empirical or formal proofs; it relies on interpretive readings and analogical homologies across disciplines. As no datasets or case studies are analyzed, generalizability depends on the persuasiveness of the philosophical reconstruction. The absence of a single, unified formal model of the genetic hinge may limit operationalization, and the speculative scope risks under-specifying criteria for distinguishing fruitful from misguided abductions.