In this paper it is contended, against a challenging recent interpretation of Frege, that Frege should be credited with the first semirigorous formulation of semantic theory. It is argued that the considerations advanced against this contention suffer from two kinds of error. The first involves the attribution to Frege of a skeptical attitude towards the truth-predicate. The second involves the sort of justification which these arguments assume a classical semantic theory attempts to provide. Finally, it is shown that Frege was (...) in fact mindful of the need for the relevant sort of justification. (shrink)

In §§28-31 of his Grundgesetze der Arithmetik, Frege forwards a demonstration that every correctly formed name of his formal language has a reference. Examination of this demonstration, it is here argued, reveals an incompleteness in a procedure of contextual definition. At the heart of this incompleteness is a difference between Frege's criteria of referentiality and the possession of reference as it is ordinarily conceived. This difference relates to the distinction between objectual and substitutional quantification and Frege?s vacillation between the two.

In §§28-31 of his Grundgesetze der Arithmetik, Frege forwards a demonstration that every correctly formed name of his formal language has a reference. Examination of this demonstration, it is here argued, reveals an incompleteness in a procedure of contextual definition. At the heart of this incompleteness is a difference between Frege’s criteria of referentiality and the possession of reference as it is ordinarily conceived. This difference relates to the distinction between objectual and substitutional quantification and Frege’s vacillation between the two.

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell's Paradox being derivable in it.This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege's Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, Q, is (...) relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell’s Paradox being derivable in it.This system is, except for minor differ...

In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantical notions such as reference and truth. I argue here Frege did make very serious use of semantical concepts. I argue, first, that Frege had reason to be interested in the question how the axioms and rules of his formal theory might be justified and, second, that he explicitly commits himself to offering a justification that appeals to the (...) notion of reference. I then discuss the justifications Frege offered, focusing on his discussion of inferences involving free variables, in section 17 of Grundgesetze, and his argument, in sections 29-32, that every well-formed expression of his formal language has a unique reference. (shrink)

Some philosophers, notably Professors Quine and Geach, have stressed the analogies they see between pronouns of the vernacular and the bound variables of quantification theory. Geach, indeed, once maintained that ‘for a philosophical theory of reference, then, it is all one whether we consider bound variables or pronouns of the vernacular'. This slightly overstates Geach's positition since he recognizes that some pronouns of ordinary language do function differently from bound variables; he calls such pronouns ‘pronouns of laziness'. Geach's characterisation of (...) pronouns of laziness has varied from time to time, but the general idea should be clear from a paradigm example: A man who sometimes beats his wife has more sense than one who always gives in to her.The pronouns ‘one’ and ‘her’ go proxy for a noun or a noun phrase in the sense that the pronoun is replaceable in paraphrase by simple repetition of its antecedent. (shrink)

Some philosophers, notably Professors Quine and Geach, have stressed the analogies they see between pronouns of the vernacular and the bound variables of quantification theory. Geach, indeed, once maintained that ‘for a philosophical theory of reference, then, it is all one whether we consider bound variables or pronouns of the vernacular'. This slightly overstates Geach's positition since he recognizes that some pronouns of ordinary language do function differently from bound variables; he calls such pronouns ‘pronouns of laziness'. Geach's characterisation of (...) pronouns of laziness has varied from time to time, but the general idea should be clear from a paradigm example: A man who sometimes beats his wife has more sense than one who always gives in to her.The pronouns ‘one’ and ‘her’ go proxy for a noun or a noun phrase in the sense that the pronoun is replaceable in paraphrase by simple repetition of its antecedent. (shrink)