On Denoting

Mind 114 (456):873 - 887 (2005)
Abstract
By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish three cases: (1) A phrase may be denoting, and yet not denote anything; e.g., `the present King of France'. (2) A phrase may denote one definite object; e.g., `the present King of England' denotes a certain man. (3) A phrase may denote ambiguously; e.g. `a man' denotes not many men, but an ambiguous man. The interpretation of such phrases is a matter of considerably difficulty; indeed, it is very hard to frame any theory not susceptible of formal refutation. All the difficulties with which I am acquainted are met, so far as I can discover, by the theory which I am about to explain
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Ofra Magidor (2009). Category Mistakes Are Meaningful. Linguistics and Philosophy 32 (6):553-581.
Michael Mckinsey (2009). Thought by Description. Philosophy and Phenomenological Research 78 (1):83-102.

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2010-03-24
In "On Denoting" (1905), Russell presents a theory of denotation which relies on the notion of a variable.  Russell says very little about variables in this paper.  He says only that they are "fundamental," and that they are "essentially and wholly undetermined" constituents of propositional functions.  I think I understand the role of this notion in Russell's theory, and why Russell says what he does about it,  He appeals to non-denoting elements in propositions in order to avoid having to interpret "a=b" as "a=a."  By using variables, he can claim that no elements in a propositional function serve the role of the denoting phrase.  For example, in the fully explicit presentation of "Scott is the author of Waverley," we do not find anything for which we could substitute the phrase "the author of Waverley."  The meaning of the denoting phrase is only found when we interpret the proposition as a whole, and cannot be found in any of its parts. 

My problem is, I don't know what it means to say ... (read more)
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