Disjunction
Aloni (Mari)
Source: Stanford Encyclopaedia of Philosophy, Winter 2016 Edition
Paper - Abstract

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Author’s Introduction

  1. In logic, disjunction1 is a binary connective (V) classically interpreted as a truth function the output of which is true if at least one of the input sentences (disjuncts) is true, and false otherwise. Its supposed connection with disjunctive words of natural language like or has long intrigued philosophers, logicians and linguists.
  2. In this entry we give an overview of logical and linguistic analyses of disjunction2 with focus on developments at the interface between logic and language.
    • Sections 1 and 2 present disjunction3 as a binary connective in classical logic and in a number of non-classical interpretations.
    • Section 3 discusses some basic facts concerning disjunctive words in natural language, and introduces a generalized, cross-categorial notion of disjunction4 as the join operator in a (Boolean) algebra.
    • Section 4 and 5 present Paul Grice’s account of the use of or in conversation and recent developments in the discussion on inclusive and exclusive uses of linguistic disjunctive words.
    • Finally, sections 6 and 7 introduce two recent non-classical accounts of linguistic disjunction5 and discuss applications to phenomena of free choice, disjunctive questions and counterfactuals with disjunctive antecedents.

Contents
  1. Disjunction6 in classical logic
  2. Non-classical variations
    • 2.1 Law of excluded middle and the principle of bivalence
      → 2.1.1 Disjunction7 in intuitionistic logic
      → 2.1.2 Disjunction8 in multi-valued logics
      → 2.1.3 Disjunction9 in dynamic semantics
      → 2.1.4 Disjunction10 in supervaluationism
      → 2.1.5 Disjunction11 in quantum logic
    • 2.2 Disjunctive syllogism and addition
  3. Disjunction12 in language
  4. Disjunction13 in conversation
  5. Inclusive and exclusive uses of or
  6. Modal accounts of disjunction14 and free choice
  7. Alternative-based accounts of disjunction15
    • 7.1 Inquisitive semantics
    • 7.2 Examples of linguistic applications
      → 7.2.1 Disjunction16 in the antecedent of a conditional
      → 7.2.2 Disjunction17 in questions

Comment:

See Stanford Encyclopedia of Philosophy: Disjunction.

Text Colour Conventions (see disclaimer)

  1. Blue: Text by me; © Theo Todman, 2020
  2. Mauve: Text by correspondent(s) or other author(s); © the author(s)



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