Set Theory as the Unified Scheme for Physics

TL;DR

This paper proposes a set-theoretic framework called presets to unify physical descriptions, addressing paradoxes and enabling consistent integration of relativistic and quantum theories within a cognitive scheme.

Contribution

It introduces presets as a new set concept for physical objects, providing a unified cognitive scheme to reconcile relativistic and quantum theories.

Findings

Presets avoid logical paradoxes in physical descriptions.

Cognitive schemes based on presets unify relativistic and quantum observations.

Framework supports consistent integration of cosmological observations.

Abstract

The process of cognition is analysed to adjust the set theory to physical description. Postulates and basic definitions are revised. The specific sets of predicates, called presets, corresponding to the physical objects identified by an observer during cognition are introduced. Unlike sets, the presets are free of logical or set-theoretical paradoxes and may be consistently used in physical description. Schemes of cognition based on presets are considered. Being different logical systems, the relativistic and quantum theories, observations in modern cosmology cannot be consistently considered in one `unified physical theory', but they are in frames of introduced schemes of cognition.