Robert May

As the history of analytic philosophy is written, Gottlob Frege sits among the pantheon, one of the core creators of a novel way of philosophical thinking. It is a way of thinking that is notably infused with logical and semantic insights that are original to Frege. The source of these insights is well known. They arise in the context of logicism, Frege’s mathematical project that unfolded in a body of thought punctuated by three seminal works, Begriffsschrift of 1879, Die Grundlagen der Arithmetik of 1884, and the two volumes of Grundgesetze der Arithmetik, published in 1893 and 1903. In these works, Frege sets out to show that arithmetic can be reduced to logic; more technically, that (a version of) the Peano-Dedekind axioms are derivable as theorems in a definitional extension of impredicative second-order logic. To achieve this goal, Frege introduced both a new logic and a new semantics; the conceptual apparatus that Frege brought to bear in these works, and in an accompanying series of classic essays, including most famously “On Sense and Reference,” has animated philosophical thought ever since

The LOGICAL FORM of a sentence (or utterance) is a formal representation of its logical structure; that is, of the structure which is relevant to specifying its logical role and properties. There are a number of (interrelated) reasons for giving a rendering of a sentence's logical form. Among them is to obtain proper inferences (which otherwise would not follow; cf. Russell's theory of descriptions), to give the proper form for the determination of truth-conditions (e.g. Tarski's method of truth and satisfaction as applied to quantification), to show those aspects of a sentence's meaning which follow from the logical role of certain terms (and not from the lexical meaning of words; cf. the truth-functional account of conjunction), and to formalize or regiment the language in order to show that it is has certain metalogical properties (e.g. that it is free of paradox, or that there is a sound proof procedure).

1. Nathan Salmon paper is entitled with a question: are general terms rigid? He asks this question in way of engaging the issue of the extension of the notion of rigidity beyond the domain of singular terms. While singular terms has been the province of most of the discussion of this rigidity since Naming and Necessity, it is well known that Kripke saw the notion extending to at least certain general terms such as terms for natural kinds. Scott Soames has recently weighed in on this issue in the latter chapters of his book Beyond Rigidity. His conclusion is that although there are significant overlaps in the properties of singular and general terms, there is no direct extension of rigidity to the general terms, and that rigid designation is properly applied only to singular terms. Salmon disagrees. His view, based in part of views dating back to his book Reference and Essence, is that there is an extension to be had, one which allows the application of the standard Kripkean characterization of rigidity to be applied to both sorts of terms. Central to his thesis is a claim about the status of certain definite descriptions. In these remarks, I will try to outline the issues to which NS is reacting, and the proposal he posits in response. I will then consider in a more critical light his claim about definite descriptions, bringing to bear considerations of their grammar.