The Idea of Truth in the Logic of Relational Development

Theory of Absolute Truth

2026

A mathematical model in which truth is revealed as a sequence of qualitative transitions in the logic of the subject's relational development with the world.

This theory introduces a vector measure of epistemic efficiency, based on three fundamental dimensions of the subject's cognitive and active capacity: Freedom, Strength, and Authorship.

Absolute Truth is the datum that makes a person freer, stronger, and more authorial. In practice, we work with true data — those that improve a person's life (increase their vector of efficiency). If a person uses true data, their life gradually becomes better. If they use false data, it gets worse.

Core Definitions

Vector of State

The state of an epistemic agent is described by the vector:

V = (F, P, A) ∈ ℝ³

where F — Freedom, P — Strength (Power), A — Authorship.

Partial Ordering

The space of states is endowed with the structure of a partial order:

V₁ ≼ V₂ ⇔ F₁ ≤ F₂ ∧ P₁ ≤ P₂ ∧ A₁ ≤ A₂

Mathematical Development of the Idea of Truth

1. Selection of the Vector Basis (F, P, A)

Any theory claiming operationality must rely on a minimal set of independent yet jointly sufficient parameters describing the subject's effectiveness.

The choice of precisely these three components — Freedom, Strength, and Authorship — is justified as follows:

Freedom (F) captures the horizon of possibilities (number of real alternatives + presence of an exit operator).
Strength (P) captures realizational power (availability of resources to actualize choice).
Authorship (A) captures the degree of causal attribution (the agent's ability to perceive themselves as the source of the result).

These three dimensions form a minimal basis system in which any qualitative improvement in the subject's state can be expressed as a non-decreasing vector.

2. Introduction of Partial Order

Unlike a total order, a partial order allows comparison only between states where dominance exists across all components simultaneously. This is important because:

Not all states are comparable. For example, an increase in freedom with a simultaneous decrease in authorship does not allow us to definitively say that one state is "better" than another. The partial order preserves this incomparability, which corresponds to real epistemic practice.

Formally, this is expressed through the relation ≼, which is reflexive, antisymmetric, and transitive, but not necessarily total.

3. Definition of Truth as a Monotonic Operator

Truth is defined as an operator T on the set of data such that:

V(T(x)) ≽ V(x) for all x, and ∃x : V(T(x)) ≻ V(x)

This definition directly follows from the requirement that truth must always be non-deteriorating (weakly increasing) and sometimes strictly improving. Such a definition automatically generates a filter in the partially ordered set of states.

4. Operationalization through the Evaluation Function σ

For practical applicability, a discrete approximation of the direction of vector change is introduced:

σ(x) = (ΔF, ΔP, ΔA) ∈ {−1, 0, +1}³

Each component of σ reflects a qualitative transition:

+1 — qualitative improvement in the given dimension
0 — absence of significant change
−1 — qualitative deterioration

Such quantization allows the subject to perform evaluation without needing precise measurement of F, P, A values, while preserving the mathematical rigor of the criterion.

5. Criterion of Truth and the Positive Cone

A datum x is considered true if and only if σ(x) lies in the positive cone K⁺, that is:

σ(x) ∈ K⁺ \ {0}, where K⁺ = {v | vᵢ ≥ 0 ∀i}

This is equivalent to stating that truth is any datum whose application does not lead to regression in any of the basic dimensions and provides strict progress in at least one.

6. Self-Verifiability as a Fixed Point

The theory possesses the property of self-verifiability because the application of its own statements to the subject's state does not decrease the vector V. Formally, this means that the theory is a fixed point of the operator T:

V(T(Theory)) ≽ V(Theory)

Thus, the theory not only describes truth but also satisfies its own criterion, which removes the problem of regress in justification.

Epistemological Justification

Homogeneity

A single criterion (vector growth) is applied to all types of data and levels of complexity.

∀ D (domain) : Criterion(D) = Growth(V)

Connectedness

The vector components are functionally interdependent; a change in one affects the others.

ΔF = f(ΔP, ΔA) ∧ ΔP = f(ΔF, ΔA) ∧ ΔA = f(ΔF, ΔP)

Complexity

The model allows for folding and unfolding — from the individual to the scientific community.

V_system = Σ V_i + Emergence

Structuredness

The space of states possesses a clear algebraic structure (a partially ordered vector space).

(S, ≼) — partially ordered set

Constructivity

Truth is not discovered but constructed through the sequential application of operators that increase the vector.

T(x) = x + δ, where δ ∈ K⁺ (positive cone)

Systematicity

The model views cognition as a holistic system, not a set of isolated statements.

Truth(System) ≠ Σ Truth(Parts)

Operational Method of Verification

For practical verification, an evaluation function is introduced:

σ(x) = (ΔF, ΔP, ΔA) ∈ {−1, 0, +1}³

Criterion of truth: A datum x is true if σ(x) belongs to the positive cone (all components ≥ 0 and at least one > 0).

Key Properties

Self-Verifiability

The application of the theory to its own statements leads to a non-decrease in the vector.

Amplification Loop

A subject who systematically applies true data increases their capacity to transmit conditions for the growth of F, P, and A to surrounding systems.

Proof of Truth

Final Formula of the Theory of Absolute Truth • 2026

Truth is an operator T such that for any datum x:

V(T(x)) ≽ V(x)

and there exists at least one datum for which the inequality is strict.

Full normalized vector space: multiple vectors showing monotonic growth after the application of Truth.

The theory satisfies its own criterion (self-verifiability) and generates a positive loop of epistemic efficiency amplification.

真 CHXD, HENYAKTSP