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The categories of knowledge that shaped philosophy for centuries are now being challenged by modern intellectual technologies. LLMs automate not only routine reasoning but also creative tasks, questioning the classical notions of truth, justification, and authorship.

Our intellectual tradition finds itself in a pre-formal stage, where epistemology is descriptive but lacks operational tools. As Newtonian calculus once transformed physics from qualitative speculation into a predictive science, so too do we now require a calculus of knowledge. Constructing a foundational ontology is the necessary first step toward this transformation.

The roots of epistemology lie in the opposition between Plato’s rationalism and Aristotle’s empiricism. Plato privileged eternal ideas grasped by reason, while Aristotle grounded cognition in sensory experience and induction. This debate shaped philosophy for two millennia.

The modern period saw Descartes anchor knowledge in the clarity of reason, while Locke and Hume emphasized experience, with Hume’s skepticism exposing the fragility of causality and induction. Kant sought a synthesis: knowledge is a fusion of empirical data and a priori structures such as space, time, and categories. Hegel and the German Idealists expanded this into dialectical development.

By the 19th century, science itself became the arbiter of truth. Positivism declared that only empirical science yields genuine knowledge, relegating philosophy to the role of systematizer of scientific results.

The 20th century opened with logical positivism, which sought to reconstruct philosophy in the image of science. The Vienna Circle’s verification principle reduced meaningful statements to those empirically verifiable. Yet the principle undermined itself and rendered scientific laws meaningless.

This collapse gave rise to new approaches. Popper emphasized falsifiability rather than verification. Kuhn showed that science advances through paradigm shifts, not linear accumulation. Lakatos refined this with “research programmes,” while Feyerabend argued that no single method governs knowledge—“anything goes.”

Thus, epistemology shifted from a search for certainty to recognition of science as historical, social, and dynamic.

Contemporary epistemology embraces pluralism. Knowledge is not homogeneous: Ryle distinguished “knowing-that” from “knowing-how”; Polanyi revealed the inarticulable domain of tacit knowledge; feminist and social epistemologies highlighted situated perspectives and epistemic injustice.

Grayling describes a paradox of knowledge: the more we discover, the more we realize our ignorance. Our theories, like maps, simplify reality; our viewpoints remain limited, and our interpretations reflect our own horizons.

Epistemology today is descriptively rich yet formally weak. It resembles physics before its mathematization—full of observations but lacking a rigorous calculus of transformation.

Knowledge is not solely mental but always mediated—by media, technology, activity, and interpretation.

To work with knowledge, we need not only epistemology but ontology, whose dual meaning is crucial.

In philosophy, ontology asks: what exists, and in what categories? Aristotle’s Categories was the first systematic classification of modes of being. An ontology of knowledge, in this sense, investigates the fundamental components and forms of knowledge itself.

In computer science, ontology is defined by Gruber as a “formal, explicit specification of a shared conceptualization.” Here, ontology is a technical artifact: a structured, machine-readable model of concepts, properties, and relations within a domain. Its purpose is clarity and interoperability between humans and machines.

These two senses are inseparable. A robust computational ontology must rest on philosophical foundations, lest it remain superficial. John Sowa exemplifies this synthesis. His conceptual graphs merge the precision of predicate logic with the intuitiveness of semantic networks, while drawing on Peirce’s semiotics to anchor technical systems in meaning.

Thus, ontology is both metaphysical and practical. For the age of LLMs, this duality becomes decisive: we must construct ontologies that are philosophically rigorous and computationally usable in order to describe, analyze, and technologize hybrid human–machine knowledge.

For centuries, philosophers sought a “logic of discovery,” but Hume’s critique undermined induction, and Popper relegated discovery to psychology, restricting philosophy to justification.

Kuhn and the sociology of science restored history and community to the process: paradigms shift through crises and revolutions, and facts are socially constructed.

Today, discovery itself is technologized. AI systems analyze vast data, generate hypotheses, and function as intellectual partners. LLMs assist in brainstorming, code generation, and uncovering connections. The challenge is to describe these hybrid processes of knowledge creation with an adequate ontology.

Logic was long seen as the path to a universal calculus of knowledge. Aristotle’s syllogistics, Leibniz’s characteristica universalis, Frege’s predicate logic, and Russell’s Principia Mathematica all pursued the dream of reducing thought to formal rules. Logical positivism attempted to realize this dream by cleansing philosophy of ambiguity.

Yet three limitations proved decisive:

Logic remains indispensable in fields like verification, databases, and engineering ontologies. But it never achieved the role of a universal language of knowledge. LLMs operate not by strict logical deduction but by generating coherence through statistical patterns in high-dimensional vector spaces.. Where logic sought certainty, LLMs provide patterns. This shift demands a new formal ontology capable of describing a probabilistic calculus of meaning.

The emergence of LLMs reframes debates about grounding, hallucination, and understanding. They generate ungrounded yet coherent text, embodying “statistical knowledge” distinct from referential knowledge. Their value emerges in hybrid interaction: humans supply grounding, while LLMs amplify by exploring high-dimensional semantic spaces.

Understanding should no longer be posed as a binary (“do machines understand?”). Instead, it should be described through measurable capacities: contextual adaptation, analogical transfer, coherence, and pragmatic alignment. In hybrid systems, these operations combine into genuine processes of knowledge creation.

Knowledge in vector spaces is probabilistic, dispositional, and gradient-based. What is needed is a calculus not of truth but of dispositions—describing how statistical patterns become meaningful through human interpretation.

Unlike the positivist search for an ideal language, this project does not aim to eliminate ambiguity. It seeks instead a formal apparatus for analyzing a new language-game: the practice of human–LLM interaction.

Constructing a formal ontology of knowledge requires three approaches in reciprocal illumination:

1_Conceptual analysis of philosophical traditions and categories.

2_Empirical analysis of real human–LLM interactions in research, law, and creative work.

3_Computational analysis of vector space structures and transformations.

This combined methodology can yield a foundational ontology that is philosophically grounded, empirically validated, and computationally tractable. It will provide the language to describe, design, and technologize processes of hybrid knowledge creation.

From Plato to positivism to pluralism, epistemology has traveled far but remains pre-formal. Logic, philosophy of science, and hermeneutics each brought insights but fell short of providing a calculus of knowledge.

LLMs reveal this limitation with clarity, showing how the absence of formal tools adequate to hybrid cognition demands the construction of a new ontology. By distinguishing knowledge-as-representation from knowledge-as-statistical-pattern, and by formalizing operations such as synthesis, grounding, and amplification, we can begin to develop a science of knowledge suited to our technological moment.

The intellectual heritage of centuries remains indispensable, but we now face an epistemological imperative: to build the conceptual frameworks needed to navigate the hybrid reality of human–machine thought.

[1] Aristotle (c. 350 BCE/1938). The Organon. H. P. Cooke & H. Tredennick (Trans.). Cambridge, MA: Harvard University Press.

[2] Bender, E. M., Gebru, T., McMillan-Major, A., & Shmitchell, S. (2021). On the dangers of stochastic parrots: Can language models be too big? . In Proceedings of the 2021 ACM Conference on Fairness, Accountability, and Transparency (pp. 610–623).

[3] Carnap, R. (1928). Der logische Aufbau der Welt. Berlin: Weltkreis-Verlag.

[4] Comte, A. (1830–1842). Cours de philosophie positive. Paris: Bachelier.

[5] Descartes, R. (1641/1996). Meditations on First Philosophy. J. Cottingham (Trans.). Cambridge: Cambridge University Press.

[6] Feyerabend, P. (1975). Against Method. London: New Left Books.

[7] Frege, G. (1892). Über Sinn und Bedeutung. Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50.

[8] Fricker, M. (2007). Epistemic Injustice: Power and the Ethics of Knowing. Oxford: Oxford University Press.

[9] Gadamer, H.-G. (1960/2004). Truth and Method. J. Weinsheimer & D. G. Marshall (Trans., 2nd rev. ed.). Continuum.

[10] Gettier, E. (1963). Is justified true belief knowledge? Analysis, 23(6), 121–123.

[11] Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik, 38, 173–198.

[12] Grayling, A. C. (2021). The Frontiers of Knowledge: What We Know About Science, History and the Mind. London: Viking.

[13] Gruber, T. R. (1993). A translation approach to portable ontology specifications. Knowledge Acquisition, 5(2), 199–220.

[14] Haraway, D. (1988). Situated knowledges: The science question in feminism and the privilege of partial perspective. Feminist Studies, 14(3), 575–599.

[15] Hegel, G. W. F. (1807/1977). Phenomenology of Spirit. A. V. Miller (Trans.). Oxford: Oxford University Press.

[16] Hume, D. (1748/2007). An Enquiry Concerning Human Understanding. P. Millican (Ed.). Oxford: Oxford University Press.

[17] Kant, I. (1781/1998). Critique of Pure Reason. P. Guyer & A. W. Wood (Trans.). Cambridge: Cambridge University Press.

[18] Kuhn, T. S. (1962/2012). The Structure of Scientific Revolutions (50th Anniversary Edition). Chicago: University of Chicago Press.

[19] Lakatos, I. (1978). The Methodology of Scientific Research Programmes. Cambridge: Cambridge University Press.

[20] Latour, B. (1987). Science in Action. Cambridge, MA: Harvard University Press.

[21] Leontiev, A. N. (1978). Activity, Consciousness, and Personality. Englewood Cliffs, NJ: Prentice-Hall.

[22] Leroi-Gourhan, A. (1964). Le Geste et la Parole. Paris: Albin Michel.

[23] Locke, J. (1689/1975). An Essay Concerning Human Understanding. P. H. Nidditch (Ed.). Oxford: Oxford University Press.

[24] McLuhan, M. (1964). Understanding Media: The Extensions of Man. New York: McGraw-Hill.

[25] Mitchell, M. (2019). Artificial Intelligence: A Guide for Thinking Humans. Farrar, Straus and Giroux.

[26] Mitchell, M. (2021). Why AI is harder than we think. arXiv preprint arXiv:2104.12871.

[27] Ong, W. J. (1982/2012). Orality and Literacy (30th Anniversary Edition). London: Routledge.

[28] Plato (c. 369 BCE/1921). Theaetetus. H. N. Fowler (Trans.). Cambridge, MA: Harvard University Press.

[29] Polanyi, M. (1966). The Tacit Dimension. Garden City, NY: Doubleday.

[30] Popper, K. (1934/2002). The Logic of Scientific Discovery. London: Routledge.

[31] Ricoeur, P. (1981). Hermeneutics and the Human Sciences: Essays on Language, Action and Interpretation. J. B. Thompson (Ed. & Trans.). Cambridge University Press.

[32] Russell, B., & Whitehead, A. N. (1910–1913). Principia Mathematica. Cambridge: Cambridge University Press.

[33] Ryle, G. (1949). The Concept of Mind. London: Hutchinson.

[34] Searle, J. R. (1980). Minds, brains, and programs. Behavioral and Brain Sciences, 3(3), 417–457.

[35] Searle, J. R. (1990). Is the brain’s mind a computer program? Scientific American, 262(1), 26–31.

[36] Shchedrovitsky, G. P. (1997). Philosophy, Methodology, Science. Moscow: School of Cultural Politics.

[37] Simondon, G. (1958). Du mode d’existence des objets techniques. Paris: Aubier.

[38] Sowa, J. F. (2000). Knowledge Representation. Pacific Grove, CA: Brooks/Cole.

[39] Stiegler, B. (1998). Technics and Time, 1. R. Beardsworth & G. Collins (Trans.). Stanford: Stanford University Press.

[40] Vallor, S. (2016). Technology and the Virtues: A Philosophical Guide to a Future Worth Wanting. Oxford: Oxford University Press.

[41] Vygotsky, L. S. (1978). Mind in Society. Cambridge, MA: Harvard University Press.

[42] Wittgenstein, L. (1921/2001). Tractatus Logico-Philosophicus. London: Routledge.

[43] Wittgenstein, L. (1953). Philosophical Investigations. Oxford: Blackwell.