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

Ásgeir Berg Matthíasson

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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
Number of pages23
JournalBritish Journal for the History of Philosophy
VolumeLatest Articles
Early online date1 Oct 2020
Publication statusE-pub ahead of print - 1 Oct 2020


  • Paradoxes
  • Ludwig Wittgenstein
  • Alan Turing
  • Lectures on the foundations of mathematics
  • Inconsistency


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