Invariance as Criterion of Being: Logos as Operator of Distinguishability

This paper offers an ontological solution to the problem of “the unreasonable effectiveness of mathematics” (Eugene Wigner), arguing that mathematics and physical reality represent two manifestations of a single principle—Logos as operator of distinguishability. Logos is interpreted not as word or law, but as a formal mechanism ensuring the stability of distinctions across time and under transformations. Being is defined through invariance: to exist means to preserve distinguishability through change. The proposed concept unifies physics, mathematics, and epistemology under a common principle of realizability—through the formula ∀g ∈ G, g(r) = r, (0.1) where being is attributed only to those relations that are invariant with respect to some group of transformations. The novelty of this work consists in: • Eliminating the substantial understanding of things, replaced by a network ontology of distinctions; • Introducing a formalized criterion of being through invariance; • Explaining the effectiveness of mathematics as a direct consequence of the isomorphism of Logos in physical, mathematical, and cognitive dimensions; • Incorporating processuality—Logos is conceived not as static form, but as dynamic operator of stability in change. Thus, the paper proposes a fundamental ontology of distinguishability, capable of explaining the connection between existence, cognition, and conservation laws. Keywords: Logos, invariance, distinction, realizability, ontology, metamonism, symmetry, Noether’s theorem, category theory, philosophy of information