At the outset, it is worth recalling a sentence that exposes the inconsistency at the heart of contemporary thinking about mathematics and reality. Faggin notes that some have mistaken the mathematical description of the world for the world itself — as though a symbolic structure could replace ontology, as though language could become substance. This observation opens the space for relational epistemology, revealing how easily one confuses the map with the territory, the projection with what is projected, the description with what is described.
Relational epistemology begins from a simple yet fundamental premise: we do not know things; we know configurations of relations. This shift in perspective displaces the entire field of knowledge. A thing is not an autonomous entity but a momentary stabilisation of the relational field. Knowledge is access to a fragment of that field, to a portion of its dynamics, to a slice of its continuous movement. It is therefore necessarily partial — and its partiality does not arise from the limitations of the human mind but from the nature of relations themselves, which are never fully transparent.
In this sense, mathematics becomes a projection rather than an ontology. As a language, it describes relational stabilisations without ever reaching their source. As a creation of the mind, it attempts to grasp the structure of the field, yet captures only its representation, never the relation itself. Mathematics is clonable because it is symbolic; ontology is not clonable because it is relational. What can be written can be repeated; what is lived never repeats itself. Mathematics thus becomes an epistemological tool, not an ontological one — a map rather than a landscape.
At this point Boole enters, with remarkable clarity, noting that probability is an inference arising from partial knowledge. It is one of the purest sentences in the history of epistemology. Probability is not a property of the world — it is a property of our access to the world. If we knew all relations, all their couplings, levels and nonlinear dependencies, probability would vanish, replaced by certainty. Probability becomes a measure of the opacity of relations, not of their nature — epistemological rather than ontological.
Gödel completes this picture by showing the incompleteness of every descriptive system. A system cannot describe itself within itself, cannot grasp the entirety of its own structure while remaining both closed and complete. In relational epistemology this means that no full description of relations exists. There are only projections of relations, always incomplete. Mathematics cannot capture the whole of ontology, just as language cannot capture the whole of experience. This is not a flaw of language — it is a feature of relations, which always exceed their representations.
Relational epistemology therefore rests on four principles. First: knowledge is relational. Second: access to relations is always partial. Third: every description is a projection of relations into language. Fourth: no description encompasses the full structure of relations.
These principles form the foundation that allows one to move from epistemology to ontology, from description to structure, from projection to field.
In this way relational epistemology prepares the ground for the formalism of dynamic tautology. One must first separate description from ontology, so as not to mistake mathematics for reality. Then separate probability from relations, so as not to confuse ignorance with the nature of the world. Next separate projection from structure, so as not to mistake symbol for relation. Only then can one enter relational ontology — no longer a description but a system. Only then can one construct a formalism showing how relations generate successive states, how self‑reference becomes dynamics, how tautology passes into movement.
Here we have what becomes not only an introduction to relational epistemology but also the first step toward relational ontology — the place where knowledge is separated from being, the preparation for Chapter V, which will show mathematics as a projection of ontology rather than its substance. It is also the beginning of the path toward Chapter VI, where dynamic tautology will become a formal system.
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