<p>This paper shows how an inferentialist notion of content can be developed in such a way that it allows for an analogue of Frege’s hierarchy of senses as a response to Mates’s Puzzle. I argue that any plausible inferentialist conception of the objects of belief that wants to take Mates’s Puzzle at face value must allow for failures of the Cut rule. This follows from two premises, namely: (A) To take Mates’s Puzzle at face value, one must acknowledge that there can be sentences of the form “<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>” and “<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi\)</EquationSource> </InlineEquation>” that imply each other and, nevertheless, “<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(y\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="16" /> </InlineMediaObject> <EquationSource Format="TEX">\(\phi\)</EquationSource> </InlineEquation>” and “<InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq5.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(y\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(x\)</EquationSource> </InlineEquation> believes that <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11229_2025_5275_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi\)</EquationSource> </InlineEquation>” do not imply each other. (B) According to any plausible inferentialist conception of the objects of belief, two sentences express the same object of belief if they can be replaced for each other as premises and as conclusions <i>salva consequentia</i>.</p>

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An inferentialist approach to Mates’s Puzzle

  • Ulf Hlobil

摘要

This paper shows how an inferentialist notion of content can be developed in such a way that it allows for an analogue of Frege’s hierarchy of senses as a response to Mates’s Puzzle. I argue that any plausible inferentialist conception of the objects of belief that wants to take Mates’s Puzzle at face value must allow for failures of the Cut rule. This follows from two premises, namely: (A) To take Mates’s Puzzle at face value, one must acknowledge that there can be sentences of the form “ \(x\) believes that \(\phi\) ” and “ \(x\) believes that \(\psi\) ” that imply each other and, nevertheless, “ \(y\) believes that \(x\) believes that \(\phi\) ” and “ \(y\) believes that \(x\) believes that \(\psi\) ” do not imply each other. (B) According to any plausible inferentialist conception of the objects of belief, two sentences express the same object of belief if they can be replaced for each other as premises and as conclusions salva consequentia.