Contradictions and falling bridges: what was Wittgenstein’s reply to Turing?

Ásgeir Berg Matthíasson*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, I offer a close reading of Wittgenstein's remarks on inconsistency, mostly as they appear in the Lectures on the Foundations of Mathematics. I focus especially on an objection to Wittgenstein's view given by Alan Turing, who attended the lectures, the so called ‘falling bridges’-objection. Wittgenstein's position is that if contradictions arise in some practice of language, they are not necessarily fatal to that practice nor necessitate a revision of that practice. If we then assume that we have adopted a paraconsistent logic, Wittgenstein's answer to Turing is that if we run into trouble building our bridge, it is either because we have made a calculation mistake or our calculus does not actually describe the phenomenon it is intended to model. The possibility of either kind of error is not particular to contradictions nor to inconsistency, and thus contradictions do not have any special status as a thing to be avoided.

Original languageEnglish
Pages (from-to)537-559
Number of pages23
JournalBritish Journal for the History of Philosophy
Issue number3
Publication statusPublished - 2021

Bibliographical note

Publisher Copyright:
© 2020 BSHP.

Other keywords

  • Alan Turing
  • inconsistency
  • lectures on the foundations of mathematics
  • Ludwig Wittgenstein
  • Paradoxes


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