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Logic & formalism papers 6 papers
Logicians, formal-methods and foundations readers. Formal systems and what they cannot say: Laws of Form and the calculus of indications, distinction and re-entry, self-reference, category theory, coalgebra and bisimulation, proof assistants, computability, formal ontology.
Category theory. Categories, functors and coalgebra Tagged papers: 32.
The Void Is Not False: Recovering the Unmarked State in Logic from the Calculus of Indications
A critique-first paper: Boolean logic and set theory reify the void (the unmarked state) into false and the empty set, committing a category error; false is a mark, the void is not a value. A reconstruction program (distinction-logic with inside/outside/oscillating states) is labeled conjecture with…
The Ontology of Boundary-Crossing: Spencer-Brown Cancellation Rule Defended
Systematic defense of Spencer-Brown Cancellation rule: establishes structural isomorphism with quantum measurement collapse via three-outcome dynamics (Varela 1975, corroborated by 29-schisms numerical search 2026). 4-level M-property justification framework. Boson-fermion observer analysis. 14…
Quantum Laws of Form
George Spencer-Brown's Laws of Form (1969) proposed the act of drawing a distinction as the primitive operation from which logic, mathematics, and physics can be constructed. This consolidation synthesizes known quantum correspondences, identifies 7 open problem categories, and proposes 4…
Category Error of the Ego
Epistemology represents the formal philosophical study of how humans acquire knowledge. This field investigates the fundamental differences between justified belief and mere subjective opinion. Applying this discipline to human identity reveals significant gaps in how we understand ourselves. The…
Universal Computational Topos
This work presents a comprehensive mathematical framework for understanding computational self-reference through the unification of hierarchical computational theories and meta-computational approaches. We establish that the Computational Trinity Principle—distinguishing Object, Model, and Meta…
Computo Ergo Sum
This paper resolves Hilbert’s sixth problem by introducing the Self-Computing Universe Framework (𝒞), a meta-axiomatic system positing that the universe is not merely described by mathematics but is a self-executing mathematical structure. While its six foundational axioms are expressed with the…
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