Departmental Research Seminar with Dr Matthew Duncome

Title: The Horns Paradox

Abstract: Ancient Greek dialectic, Socratic-style dialectic, involved two participants with asymmetric roles. One posed questions and the other would affirm or deny the content of the question by saying ‘yes’ or ‘no’. The questioner aims to commit the answerer to something unsupportable, typically an inconsistency; the answerer aims to avoid this. But many questions come with presuppositions. So, if the answerer is restricted to ‘yes’ or ‘no’ answers, it is not always clear what they are committed to with that answer. Questioners may pose ‘loaded questions’, which have unsupportable commitments as presuppositions.

The loaded question that became canonical, and seeming formed the basis of a paradoxical argument, was ‘Have you lost your horns?’. This argument was variously attributed to Eubulides, a student of Euclides of Megara and rival of Aristotle, who is also credited with the Liar and Sorites paradoxes; Diodorus Cronus, a leading dialectician around c.300; and Chrysippus, the third head of the Stoic school. It is somewhat puzzling why anyone would take seriously the Horns. After all the solution is so obvious as to barely need stating: just refuse to answer ‘yes’ or ‘no’! It certainly does not seem as philosophically profound as the Liar or Sorites.

In this paper, I aim to give a reconstruction of an early version of this paradox based on our ancient sources, and try to understand the paradox in the context of dialectical practice after Socrates. I will argue that Eubulides likely originated a dialectical version of the Horns, which involved a loaded question in the context of a Socratic-style dialectic. Wheeler has suggested that Eubulides originated the Horns to support a thesis of Eleatic semantics, namely, questions and statements with negative existential presuppositions are meaningless. I reject this, and suggest that Eubulides developed the puzzle as a response to Aristotle’s solution to some similar fallacies.  Diodorus and Chrysippus inherit the puzzle and can block the conclusion while retaining the structures of dialectic, in particular the equivalent rule that there is no middle path between yes or no because of their views on the conditional.