Epistemic closure under deductive inference: What is it and can we afford it?

Assaf Sharon, Levi Spectre*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in known premises. The first strategy, while effective, retains little of the original idea-conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson's safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson's theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge.

Original languageEnglish
Pages (from-to)2731-2748
Number of pages18
JournalSynthese
Volume190
Issue number14
DOIs
StatePublished - Sep 2013
Externally publishedYes

Keywords

  • Chance
  • Epistemic probability
  • Infallibilism
  • Inference
  • Knowledge
  • Knowledge safety
  • Lottery propositions
  • Modus ponens
  • Multi premise closure
  • Single premise closure

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