Online research in philosophy

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).

This reissue, first published in 1971, provides a brief historical account of the Theory of Logical Types; and describes the problems that gave rise to it, its ...

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.

It has been much debated whether Tractarian objects are what Russell would have called particulars or whether they include also properties and relations. This paper claims that the debate is misguided: there is no logical category such that Wittgenstein intended the reader of the Tractatus to understand his objects either as providing examples of or as not providing examples of that category. This is not to say that Wittgenstein set himself against the very idea of a logical category: quite the contrary. However, where Russell presents his logical variety of particulars and the various types of universal, and Frege presents his of objects and the various types of function, Wittgenstein denies the propriety of such a priori expositions. Wittgenstein envisages a variety of logical types of entity but insists that the nature of these types is something to be discovered only through analysis.

Type-logical semantics studies linguistic meaning with the help of the theory of types. The latter originated with Russell as an answer to the paradoxes, but has the additional virtue that it is very close to ordinary language. In fact, type theory is so much more similar to language than predicate logic is, that adopting it as a vehicle of representation can overcome the mismatches between grammatical form and predicate logical form that were observed by Frege and Russell. The grammatical forms of ordinary language sentences consequently may be taken to be much less misleading than logicians in the first half of the 20th century often thought them to be. This was realized by Richard Montague, who used the theory of types to translate fragments of ordinary language into a logical language. Semantics is commonly divided into lexical semantics, which studies the meaning of words, and compositional semantics, which studies the way in which complex phrases obtain a meaning from their constituents. The strength of type-logical semantics lies with the latter, but type-logical theories can be combined with many competing hypotheses about lexical meaning, provided these hypotheses are expressed using the language of type theory.

We examine Carruthers’ proposal that sentences in logical form serve to create flexibility within central system modularity, enabling the combination of information from different modalities. We discuss evidence from aphasia and the neurobiology of input-output systems. This work suggests that there exists considerable capacity for interdomain cognitive processing without language mediation. Other challenges for a logical form account are noted.

On this conception, the semantic types of its primitive terms and their mode of combination determine the logical form of a sentence as it relates to determining under what conditions it is true. We develop this idea in the framework of truth-theoretic semantics. We argue that the semantic form of a declarative sentence in a language L is revealed by a (canonical) proof of its T-sentence in an interpretive truth theory for L. We give a precise characterization of sameness of logical form between any two declarative sentences in any two languages in terms of the notion of corresponding proofs in interpretive truth theories for the languages. We illustrate the utility of this approach with a number of examples. We then extend the characterization to non-declaratives in a generalization of truth-theoretic semantics that appeals to fulfillment conditions, of which truth conditions are one variety. On this approach, logical forms are not reified, and the notion of sameness of logical form is treated as conceptually basic. We discuss the relation of this conception of logical form to the project of identifying logical constants, reviewing two approaches, one of which takes topic neutrality as central, the other recursion. We argue that the project of identifying logical constants for the purposes of classifying together valid arguments is largely independent of that of identifying logical form of sentences, and urge an ecumenical approach to extending talk of logical constants beyond where it is currently well grounded.

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.

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.