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. (shrink)

Frege's development of the theory of arithmetic in his Grundgesetze der Arithmetik has long been ignored, since the formal theory of the Grundgesetze is inconsistent. His derivations of the axioms of arithmetic from what is known as Hume's Principle do not, however, depend upon that axiom of the system--Axiom V--which is responsible for the inconsistency. On the contrary, Frege's proofs constitute a derivation of axioms for arithmetic from Hume's Principle, in (axiomatic) second-order logic. Moreover, though Frege does prove each of (...) the now standard Dedekind-Peano axioms, his proofs are devoted primarily to the derivation of his own axioms for arithmetic, which are somewhat different (though of course equivalent). These axioms, which may be yet more intuitive than the Dedekind-Peano axioms, may be taken to be "The Basic Laws of Cardinal Number", as Frege understood them. Though the axioms of arithmetic have been known to be derivable from Hume's Principle for about ten years now, it has not been widely recognized that Frege himself showed them so to be; nor has it been known that Frege made use of any axiomatization for arithmetic whatsoever. Grundgesetze is thus a work of much greater significance than has often been thought. First, Frege's use of the inconsistent Axiom V may invalidate certain of his claims regarding the philosophical significance of his work (viz., the establishment of Logicism), but it should not be allowed to obscure his mathematical accomplishments and his contribution to our understanding of arithmetic. Second, Frege's knowledge that arithmetic is derivable from Hume's Principle raises important sorts of questions about his philosophy of arithmetic. For example, "Why did Frege not simply abandon Axiom V and take Hume's Principle as an axiom?". (shrink)

In just a few years, children achieve a stable state of linguistic competence, making them effectively adults with respect to: understanding novel sentences, discerning relations of paraphrase and entailment, acceptability judgments, etc. One familiar account of the language acquisition process treats it as an induction problem of the sort that arises in any domain where the knowledge achieved is logically underdetermined by experience. This view highlights the cues that are available in the input to children, as well as childrens skills (...) in extracting relevant information and forming generalizations on the basis of the data they receive. Nativists, on the other hand, contend that language-learners project beyond their experience in ways that the input does not even suggest. Instead of viewing language acqusition as a special case of theory induction, nativists posit a Universal Grammar, with innately specified linguistic principles of grammar formation. The nature versus nurture debate continues, as various poverty of stimulus arguments are challenged or supported by developments in linguistic theory and by findings from psycholinguistic investigations of child language. In light of some recent challenges to nativism, we rehearse old poverty-of stimulus arguments, and supplement them by drawing on more recent work in linguistic theory and studies of child language. (shrink)

This chapter contains section titled: Hidden Tautologies Minimal Syntax.

Each sentence derives its meaning from what its component words mean and from its syntactic structure. And the thesis of this chapter is that this is so because the meaning‐property of a sentence is nothing over and above the property of being constructed in a certain way from primitives with certain meanings. In this explanation of how sentence meanings are ’composed’, absolutely nothing is presupposed about the source of word meaning. Thus the possibility of compositionality imposes no constraint on how (...) the meanings of words are engendered. In particular, we see that compositionality gives us no reason to accept Davidson's explication of meaning in terms of truth conditions. (shrink)