Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Negation and Identity in a Modal Mode Theory

Juan Afanador

Abstract

This piece threads substructurality and modality into a negation that activates the downside of equivalence and identity in a fibrational framework. The piece is a working through of negation and contradiction as type-theoretic/categorial objects, towards an immanent critique of the subtending univalent paradigm. Although this is not the terminus of the piece, i wish to try and delineate the epistemic and intra-mundane problematics intertwined therewith. The piece's terminus is a mode theory of an intuitionistic modal logic that internalises a restriction on the Double Negation Elimination rule.

Negation and Identity in a Modal Mode Theory

Abstract

This piece threads substructurality and modality into a negation that activates the downside of equivalence and identity in a fibrational framework. The piece is a working through of negation and contradiction as type-theoretic/categorial objects, towards an immanent critique of the subtending univalent paradigm. Although this is not the terminus of the piece, i wish to try and delineate the epistemic and intra-mundane problematics intertwined therewith. The piece's terminus is a mode theory of an intuitionistic modal logic that internalises a restriction on the Double Negation Elimination rule.
Paper Structure (1 section, 1 theorem)

This paper contains 1 section, 1 theorem.

Key Result

Proposition 1

There exists, at least, one mode $A\in \mathbf{Struct}$, such that the canonical morphism of the symmetric closed monoidal category $\langle \mathbf{Struct}, \pentagodot, I, \to \rangle$ is not an isomorphism.

Theorems & Definitions (1)

  • Proposition 1