Robert May

Over the years, I’ve been asked many times what “logical form” is, as applied to natural language. This is a natural enough question to address to me; after all, I’ve written a book titled Logical Form, and I’ve been asked to write any number of papers on the topic. This question, it seems to me, is certainly a “big” question, and big questions deserve big answers. I must admit, however, to being somewhat baffled as to how to do this satisfactorily, since big answers to big questions unfortunately tend to the trivial. With a nod to Wittgenstein, logical form has always seemed to me to be something that you know it when you see it; it is clear enough when it pops up, but one is hard pressed to say just what it is, to define it. This is so even though the meanings of the words “logical” and “form” seem straightforward enough; what I find puzzling is how the first word is supposed to modify the second. What is it that makes a form logical, as opposed to something else that is not logical? This, it seems to me, is a very hard question to answer indeed, for if we cannot contrast logical form with some other type of form, then every form (or no form) is a logical form, and we have arrived at the triviality previously mentioned.

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.