Toward a new formulation of Solipsism

Abstract: The paper proposes a formal approach to ontological solipsism based on a system of quasi-equational axioms (S1–S5), where solipsism is defined as a relationship between Ego (I) and Datum (D), where existence (E) is their particular sum (E = I + D). The author constructs a mathematical space of solipsisms (SOLIP) as a set of pairs (I, D) and introduces a two-level ordering: between abstraction classes (according to the value of E) and within classes (lexicographically). The model is enhanced with the concept of the Turing Subject – a finite automaton (I) which interacts with an infinite tape (D), allowing self-awareness to be operationalised as recursion. As a result of interpreting a certain Hilbert’s axiom, a more comprehensive model of solipsism is formulated in the form of the Solipsistic Subject. This interdisciplinary approach integrates the elements of logic, computational theory, and ontology, offering novel tools for analysing solipsism as a formal system.