A paradox of rejection

Thomas N P A Brouwer*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
9 Downloads (Pure)


Given any proposition, is it possible to have rationally acceptable attitudes towards it? Absent reasons to the contrary, one would probably think that this should be possible. In this paper I provide a reason to the contrary. There is a proposition such that, if one has any opinions about it at all, one will have a rationally unacceptable set of propositional attitudes—or if one doesn’t, one will end up being cognitively imperfect in some other manner. The proposition I am concerned with is a self-referential propositional attitude ascription involving the propositional attitude of rejection. Given a basic assumption about what constitutes irrationality, and a few assumptions about the nature of cognitively ideal agents, a paradox results. This paradox is superficially like the Liar, but it is importantly different in that no alethic notions are involved at all. As such, it stands independent of the Liar and is not a ‘revenge’ version of it. After setting out the paradox I discuss possible responses. After considering several I argue that one is best off simply accepting that the paradox shows us something surprising and interesting about rationality: that some cognitive shortfall is unavoidable even for ideal agents. I argue that nothing disastrous follows from accepting this conclusion.

Original languageEnglish
Pages (from-to)4451-4464
Number of pages14
Issue number18
Early online date20 Sept 2014
Publication statusPublished - Dec 2014

Bibliographical note

I would like to thank Michael Bench-Capon, Jason Turner, Robbie Williams and Francesco Berto and audiences at Leeds, Manchester, Amsterdam and Aberdeen for comments on drafts of this material, as well as several anonymous referees. This paper was prepared within the 2013–15 AHRC project The Metaphysical basis of Logic: the Law of Non-Contradiction as Basic Knowledge (grant ref. AH/K001698/1).


  • Bilateralism
  • Dialetheism
  • Indeterminacy
  • Paradox
  • Propositional attitudes
  • Rationality
  • Rejection


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