What question did this study set out to answer?

The aim is to show that standard number systems are determined by operational constraints from intelligence, according to Cognitional Mechanics.

May 12, 2026Open Access

Numbers as Necessary Structures of Intelligence: Axiomatically Selected Number Systems from Cognitional Mechanics

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Demonstrates that number systems arise from intelligence constraints, highlighting their structural necessity.

The aim is to show that standard number systems are determined by operational constraints from intelligence, according to Cognitional Mechanics.
Axiomatic exploration of number systems including ℕ, ℤ, ℚ, ℝ, and ℂ.
Analysis of selection order of number systems based on geometric-persistence and operational constraints.
Application of Galois theory to establish relationships between number systems.
ℝ is established as a unique ordered complete field prior to ℂ, based on Axiom 2.
Axioms 1 and 4 define ℕ, ℤ, and ℚ as minimal substructures necessary for distinguishability and reversibility.
The framework shows that numbers are generated from intelligence requirements rather than being discovered.

T.O. (2026) studied this question.

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