Axiometry: Prolegomena to a Metric Science of Value (Transcendental Foundations and Formal Architecture – Part I)
Year: 2026
Type: preprint
Abstract: This article constitutes Part I of a foundational series establishing Axiometry as a formal science of value. Its principal aim is to overcome the contemporary stagnation of axiology, diagnosed as a persistent confusion between the ontological substrate of value and its operative functioning. Unlike classical approaches (Scheler, Hartmann, R. S. Hartman), which describe value as a static quality or a logical adequation, this work proposes an axiomatic architecture that models how values originate, actualize, and reorganize themselves within cognitive, affective, and social experience. The theoretical core of the volume is constructed in four fundamental movements. First, it postulates and demonstrates—through a transcendental argument by reductio ad absurdum—the necessity of the Axon (α) as the minimal and irreducible unit of valuative donation, establishing Principle 0 (F1). Second, it defines the Principle of Phenomenal Donation (F2), which articulates the asymmetric relation between the pure axon and its concrete manifestation in the noema (η), modulated by the state of the phenomenon. Third, it enunciates the Principle of Axiometric Correlation (PAC) (F3), formalizing apprehension as an irreducible correlation—via the operator ⊕—between the valuing noesis of the subject (Nν) and the axon of the phenomenon, confirming Frondizi's thesis that value exists "for someone and in relation to something." Fourth, from this correlation and the definition of operative conditionings, it derives the General Theorem of Phenomenological Coupling (F6), whose general equation integrates the subject's paradigmatic context and the concrete state of the phenomenon to model the phenomenological variability of value comprehension. To render these principles operative, the article develops an intersubjective social and cognitive ontology. It introduces the Paradigmatic Space (PS) as a shared field of meanings, norms, and affective dispositions that conditions what can be recognized as valuable, distinguishing from it the Paradigmatic World (PWs) as the subject's personal, weighted instance of that space. It defines the paradigm as a tuple ⟨Lemma, Emochemical Conditioning⟩ and formalizes concrete apprehension through the gamma function (γ), which transforms tensional coupling into attributive and qualitative predicates subject to the Paradigmatic Conditions of Actualization (PCA). It also anticipates the concept of the neotrope as an intervention that alters the ontological state of a system, preparing the ground for Part II. As the closing of this first installment, the text delineates the field of Pure Axiometry, indicating that the social crystallization of value—the passage from individual predicates to stable ordinal and cardinal values—will be addressed in Part II ("From Abstraction to Semiotic Paraosmosis") and applications to social systems in Part III. It does not seek, therefore, to close a system, but to inaugurate a formal, interdisciplinary research program that transforms the study of value into a modelable science. The appendices complement the central architecture with technical developments: Appendix A formalizes the minimal conditions for the existence of the Axon and its qualitative and dispositional completeness; Appendix B systematizes the relational structure of the paradigm and the Paradigmatic Space; Appendix C clarifies the noetic-noematic isomorphism in dialogue with the Husserlian tradition; Appendix D expands the typology of states of being into a four-valued supra-Boolean algebra and proves the Completeness Theorem of the Phenomenological System S₅; and Appendix E sketches the Axiometric Hyperspace (Ξ) as an integrative framework for a future cartography of value. Erratum Previous versions of this description employed the spelling Axion as the result of an undetected machine-translation error. The correct denomination of the concept is AXON (from the Greek ᾍΞΩΝ [Axón], meaning 'axis' or 'axis of rotation'). The Axon constitutes, in effect, the fundamental axis upon which the entire architecture of Axiometry turns.
Author: García Delgado, Marx Agustin
Language: English
Subfield: Experimental and Cognitive Psychology
Field: Psychology
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W7203635134
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