Tolerant reasoning: nontransitive or nonmonotonic?

Pablo Cobreros, Paul Egré, Dave Ripley, Robert van Rooij

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific consequence relations in relation to those, which we call: strict-to-tolerant entailment, pragmatic-to-tolerant entailment, and pragmatic-to-pragmatic entailment. The first two are nontransitive, whereas the latter two are nonmonotonic.

Original languageEnglish
Pages (from-to)S681-S705
Number of pages25
JournalSynthese
Volume199
Issue numberSuppl 3
DOIs
Publication statusPublished - Dec 2021
Externally publishedYes

Keywords

  • Noncontractive consequence
  • Nonmonotonic consequence
  • Nontransitive consequence
  • Pragmatic reasoning
  • Sorites paradox
  • Strict–tolerant logic
  • Vagueness

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