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A formal system for reasoning about assertibility, truth, and meaningfulness

Nik Weaver

TL;DR

This work proposes axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and proves the consistency of the resulting formal system.

Abstract

We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.

A formal system for reasoning about assertibility, truth, and meaningfulness

TL;DR

This work proposes axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and proves the consistency of the resulting formal system.

Abstract

We propose axioms governing the interaction of constructive assertibility and meaningfulness predicates with a self-applicative truth predicate characterized by the T-scheme, and we prove the consistency of the resulting formal system.

Paper Structure

This paper contains 4 sections, 3 theorems, 2 equations.

Table of Contents

  1. 1.
  2. 2.
  3. 3.
  4. 4.

Key Result

Theorem 3.1

ATM proves (a) $\mathbb{M}[L_1] \to \mathbb{A}[\dot{\bot}]$ (b) $\neg\neg\mathbb{M}[L_1]$ (c) $\mathbb{A}[L_2] \to \mathbb{A}[\dot{\bot}]$ (d) $\neg\neg\mathbb{A}[L_2]$.

Theorems & Definitions (6)

  • Theorem 3.1
  • proof
  • Theorem 4.1
  • proof
  • Corollary 4.1
  • proof