Russell’s Notion of Scope

Mind 114 (456):1005-1037 (2005)
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Abstract

Despite the renown of ‘On Denoting’, much criticism has ignored or misconstrued Russell's treatment of scope, particularly in intensional, but also in extensional contexts. This has been rectified by more recent commentators, yet it remains largely unnoticed that the examples Russell gives of scope distinctions are questionable or inconsistent with his own philosophy. Nevertheless, Russell is right: scope does matter in intensional contexts. In Principia Mathematica, Russell proves a metatheorem to the effect that the scope of a single occurrence of a description in an extensional context does not matter, provided existence and uniqueness conditions are satisfied. But attempts to eliminate descriptions in more complicated cases may produce an analysis with more occurrences of descriptions than featured in the analysand. Taking alternation and negation to be primitive (as in the first edition of Principia), this can be resolved, although the proof is non-trivial. Taking the Sheffer stroke to be primitive (as proposed by Russell in the second edition), with bad choices of scope the analysis fails to terminate

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Saul Kripke
CUNY Graduate Center

Citations of this work

The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - 2019 - Philosophy and Phenomenological Research 99 (1):81-114.
Quantifying In From a Fregean Perspective.Seth Yalcin - 2015 - Philosophical Review 124 (2):207-253.
An Argument For Necessitism.Jeremy Goodman - 2016 - Philosophical Perspectives 30 (1):160-182.

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References found in this work

On Denoting.Bertrand Russell - 1905 - Mind 14 (56):479-493.
Reference and Definite Descriptions.Keith S. Donnellan - 1966 - Philosophical Review 75 (3):281-304.
Uber Sinn und Bedeutung.Gottlob Frege - 1892 - Zeitschrift für Philosophie Und Philosophische Kritik 100 (1):25-50.

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