Online research in philosophy

Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic structure, because they differ in the placement of the logical constants “every” and “some”. By contrast, the sentences Every girl loves some boy. and Every boy loves some girl. are thought to have the same logical form, because “girl” and “boy” are not logical constants. Thus, in order to settle questions about logical form, and ultimately about which arguments are logically valid and which sentences logically true, we must distinguish the “logical constants” of a language from its nonlogical expressions.

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).

The ninth included paper is now fully, formally published with volume number and page numbers, and the second page of the Table of Contents reflects that change, as well.

Following Popper on the measure of content, we will combine the concept of logical probability, developed in the nineteenth century, with logical form, and we will answer some objections of Elias to the systematization of Popper's idea by Bar-Hillel and Carnap. We were led along this path by a novel by Isaac Asimov, the biochemist, medical school professor, science fiction writer, and popular science writer—a true polymath with over 400 books to his credit. Elias was concerned that Bar-Hillel and Carnap's theory of semantic content had no philosophical import, no unique properties, and no applications. We will suggest three areas of philosophical import, a unique property based on differences as explained by Peter Milne, and some applications in the general area of abstracting or summarization. We will also suggest that automated language-to-logical-form converters are feasible, necessary for the achievement of various ends, and desirable for the achievement of other ends. In the entire discussion of logical form, we will rely entirely on modern, classical (i.e., two-valued, truth-functional) logic alone, including that most vexatious of connectives, "if." We will close our work with an argument referred to in favor of > from our earlier work, in particular, and truth-functionality, more generally. The connection between the material on content in the first part of this book and the material on a truth-functional approach to logical form in the second part of this book is that the former material presupposes that a certain subset of declarative language is, in fact, truth-functional, a view that is particularly hard to defend for "if," and it is just that defense that is taken up in the second part. This book consists of ten published pieces, as well as three introductory units, and three concluding sections or units.

Carruthers’ argument depends on viewing logical form as a linguistic level. But logical form is typically viewed as underpinning general purpose inference, and hence as having no particular connection to language processing. If logical form is tied directly to language, two problems arise: a logical problem concerning language acquisition and the empirical problem that aphasics appear capable of cross-modular reasoning.

Consider the following argument: All men are mortal; Socrates is a man; therefore, Socrates is mortal. Intuitively, what makes this a valid argument has nothing to do with Socrates, men, or mortality. Rather, each sentence in the argument exhibits a certain logical form, which, together with the forms of the other two, constitute a pattern that, of itself, guarantees the truth of the conclusion given the truth of the premises. More generally, then, the logical form of a sentence of natural language is what determines both its logical properties and its logical relations to other sentences. The logical form of a sentence of natural language is typically represented in a theory of logical form by a well-formed formula in a ‘logically pure’ language whose only meaningful symbols are expressions with fixed, distinctly logical meanings (e.g., quantifiers). Thus, the logical forms of the sentences in the above argument would be represented in a theory based on pure predicate logic by the formulas ‘∀x(Fx ⊃ Gx)’, ‘Fy’, and ‘Gy’, respectively, where ‘F’, ‘G’, and ‘y’ are all free variables. The argument’s intuitive validity is then explained in virtue of the fact that the logical forms of the premises formally entail the logical form of the conclusion. The primary goal of a theory of logical form is to explain as broad a range of such intuitive logical phenomena as possible in terms of the logical forms that it assigns to sentences of natural language.

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.

This work contains Peter Long's important essay, Logic, Form and Grammar , which resolves many difficulties for the logical form of an argument where the reasoning is hypothetical. Also included are two essays on classical problems in philosophical logic, relating to logical form and formal relations.