Aspects of a Theory of Singular Reference: Prolegomena to a Dialectical Logic of Singular Terms

Dissertation, University of California, Los Angeles (1982)

Abstract

The difficulties encountered by attempts to treat identity as a relation between an object and itself are well-known: "...the sentence 'The morning star is...the morning star' is analytic and a truism, while...'The morning star is the evening star' is synthetic and represents a 'valuable extension of our knowledge'... But if {the morning star} and {the evening star} are the same object, and identity is taken as a relation holding between this object and itself, then it is impossible to explain how the two sentences can differ in cognitive content... ". Russell's solution to these difficulties rejects the identification of logical with grammatical form, in effect denying that such sentences assert relations between the morning star and itself. The logical representations which the Russellian proposes, contain quantifiers, predicate letters, and individual variables, but no expressions standing for particulars. The Fregean solution, while admitting logical representations whose nominal expressions stand for particulars, insists that the meaning of such expressions is different from their reference. Frege-Russell analyses thus both deny that the morning star is involved qua particular in the meaning of the sentences in question. ;Rather than replace the morning star as ontological subject of these sentences, I suggest that their difference in meaning arises from the kind of particular that the identity-relation relates--a particular which, unlike its Frege-Russell counterpart, is two-sided and multi-faceted. Such a particular requires an ambiguous singular term. In Chapter 1, I utilize such a term to provide a surfacist account of belief-context ambiguity requiring neither differences in relative scope nor distinctions between sense and reference. In Chapter 2, I go on to provide an account of negative existentials, necessity- and identity-statements which resolves philosophical problems that Russell-Frege analyses only avoid. To solve these problems, I show that it is necessary to reject two canons of philosophical logic, the Law of Identity and the Indiscernibility of Identicals

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William Greenberg
University of Puerto Rico

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