Online research in philosophy

Contrary to a claim made by Kaplan (Mind 114:933–1003, 2005) and Neale (Mind 114:809–871, 2005), the readings available to sentences containing definite descriptions embedded under propositional attitude verbs and conditionals do pose a significant problem for the Russellian theory of definite descriptions. The Fregean theory of descriptions, on the other hand, deals easily with the relevant data.

Russell argued, famously, that definite descriptions are not logical constituents of the sentences in which they appear. In neither of the following should we suppose that the definite description picks anything out: The King of France is bald The Prince of Wales is bald Since France is a republic, nothing could be picked out by the first; and if the semantic structures of each are the same, it cannot be the function of the second to pick anything out either. On the alternative semantics developed in his 1905 article 'On Denoting', definite descriptions do not have meaning in isolation; they have meaning only in the context of a whole sentence. Andrew Botterell and Robert Stainton have pointed out that this conclusion appears to be at odds with the phenomenon of unembedded definite descriptions, in which definite descriptions are uttered, meaningfully, without accompanying predicates. For example, it is possible to utter 'The last temptation' on its own and in doing so express a proposition (that a salient profiterole ought to be resisted, perhaps). Since definite descriptions can be used in this way, how can it be right to claim, with Russell, that they lack meaning in isolation? The present paper seeks to show how a Russellian semantics for definite descriptions (on a certain understanding of what is required for a semantics to be Russellian) is entirely compatible with the phenomenon of unembedded definite descriptions. In particular, Botterell and Stainton are wrong to think that generalized quantifier semantics is better able to cope with the phenomenon than a more authentically Russellian syncategorematic semantics.

A sentence containing a number of definite descriptions, each lying within the scope of its predecessor, is naturally read as asserting the uniqueness of a sequence of objects satisfying the descriptions. The project of providing a general uniform procedure for eliminating embedded definite descriptions that gets this and other logical forms right is impeded by several puzzles.

Definite descriptions, I shall argue, have two possible functions. 1] They are used to refer to what a speaker wishes to talk about, but they are also used quite differently. Moreover, a definite description occurring in one and the same sentence may, on different occasions of its use, function in either way. The failure to deal with this duality of function obscures the genuine referring use of definite descriptions. The best known theories of definite descriptions, those of Russell and Strawson, I shall suggest, are both guilty of this. Before discussing this distinction in use, I will mention some features of these theories to which it is especially relevant.

Taking a Russellian approach to descriptions, this paper aims to explain the nature of referring, the rationale for using definite descriptions referentially, the difference between referring to something and merely alluding to it or just describing it, specific uses of indefinite descriptions, and the pragmatic character of the referential-attributive distinction. Among the points defended are that definite descriptions do not have referential meanings, that using a description to refer identifies by implicitly conveying an identity, that one can describe a (singular) proposition without being in a position to grasp it, and that incomplete definite descriptions do not threaten Russell’s theory.

The view that plural reference is reference to a set is examined in light of George Boolos's treatment of second-order quantification as plural quantification in English. I argue that monadic second-order logic does not, in Boolos's treatment, reflect the behavior of plural quantifiers under negation and claim that any sentence that properly translates a second-order formula, in accordance with his treatment, has a first-order formulation. Support for this turns on the use of certain partitive constructions to assign values to variables in a way that makes Boolos's reading of second-order variables available for a first-order language and, with it, the possibility of interpreting quantification in an unrestricted domain.A first-order theory, T(D), is developed on the basis of Boolos's treatment of simple plural definite descriptions extended to Richard Sharvy's general theory of definite plural and mass descriptions. I introduce a primitive predicate, o, for the relation of the referent of a singular description to that of its plural. If o is simply added to T(D), is definable in T(D), and the result is inconsistent. If o is added to a theory with axioms for the fragment of T(D) I call D-mereology, the result is a natural basis for the development of a pluralized Zermelo set theory. This theory, however, is inconsistent in an unrestricted domain, unless it is recast as a second-order theory of sets interpreted in Boolos's way.

Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously if only because mathematicians take many-valued functions seriously. We assess the objection (by Russell, Frege and others) that many-valued functions are illegitimate because the corresponding terms are ambiguous. We also assess the various methods proposed for getting rid of them. Finding the objection ill-founded and the methods ineffective, we introduce a logical framework that admits plural reference, and use it to answer some earlier questions and to raise some more.

Descriptions are phrases of the form ‘an F’, ‘the F’, ‘Fs’ and ‘the Fs’. They can be indefinite (e.g., ‘an F’ and ‘Fs’), definite (e.g. ‘the F’ and ‘the Fs’), singular (e.g., ‘an F’, ‘the F’) and plural (e.g., ‘the Fs’, ‘Fs’). In English plural indefinite descriptions lack an article and are for that reason also known as ‘bare plurals’.

Descriptions are phrases of the form ‘an F’, ‘the F’, ‘Fs’, ‘the Fs’ and NP's F (e.g. ‘John's mother’). They can be indefinite (e.g., ‘an F’ and ‘Fs’), definite (e.g. ‘the F’ and ‘the Fs’), singular (e.g., ‘an F’, ‘the F’) or plural (e.g., ‘the Fs’, ‘Fs’). In English plural indefinite descriptions lack an article and are for that reason also known as ‘bare plurals’. How to account for the semantics and pragmatics of descriptions has been one of the central topics in philosophy for centuries. This entry focuses on the historical and contemporary philosophical debate about Bertrand Russell’s theory of descriptions and the theories that developed as responses to this theory.

The paper revisits Sharvy's theory of plural definite descriptions. An alternative account of plural definite descriptions building on the ideas of plural quantification and non-distributive plural predication is developed. Finally, the alternative is extrapolated to account for generic uses of definite descriptions.