Crossing pictures of ‘determination’ in Wittgenstein's remarks on rule‐following

Philosophical Investigations 47 (1):32-52 (2023)
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Abstract

In PI 189, Wittgenstein's interlocutor asks, ‘But are the steps then not determined by the algebraic formula?’. Wittgenstein responds, ‘The question contains a mistake’. What is the mistake contained in the interlocutor's question? Wittgenstein's elaboration is neither explicit nor its intended upshot transparent. In this paper, I offer a reading on which the interlocutor's question arises from illicitly crossing different pictures of ‘determination’. I begin by working through Wittgenstein's machine analogy in PI 193, which illustrates picture‐crossing in our ways of talking about a machine. Using the lessons from this analogy, I show how the interlocutor's ‘mistake’ can be diagnosed in similar terms: their confusion about the power of a rule to determine its applications rests on mistakenly crossing a behavioural and a mathematical sense of ‘determine’—thereby concocting a mystifying picture of rule‐following.

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Philip Bold
University of Minnesota

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