The Fregean Notion of an Object
Dummett’s work on the problem of abstract objects reflects his commitment to the explanatory power of Frege’s new predicate logic and the associated thesis ‘that Frege’s analysis of language, and the semantics that goes with it, are basically correct’ (1973a, p. 474).1 Dummett claims, moreover, that the very notion of an ‘object’, ‘as it is now commonly used in philosophical contexts, is a modern notion, one first introduced by Frege’ (1973a, p. 471). Frege’s ‘modern’ notion of an object, Dummett suggests, is concomitant with the formalisation of natural language in the predicate calculus, for ‘it is only in relation to an analysis of that form that we understand the notion’ (1973a, p. 477). It is for this reason that ‘questions such as whether or not there are any abstract objects, what abstract objects there are, what abstract objects are and how we know that they exist, what is the criterion for their existence, where the dividing line comes between concrete and abstract objects, all these are modern questions’ (1973a, p. 471). In order to understand Dummett’s theory of abstract objects, therefore, it is necessary in the first instance to consider the conceptual presuppositions of Frege’s ‘modern’ notion of an object.
KeywordsAbstract Object Singular Term Predicate Logic Ontological Commitment Syntactic Category
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