Online research in philosophy

The term ‘logical form’ has been called on to serve a wide range of purposes in philosophy, and it would be too ambitious to try to survey all of them in a single essay. Instead, I will focus on just one conception of logical form that has occupied a central place in the philosophy of language, and in particular in the philosophical study of linguistic meaning. This is what I will call the classical conception of logical form. The classical conception, as I will present it in section 1, has (either explicitly or implicitly) shaped a great deal of important philosophical work in semantic theory. But it has come under fire in recent decades, and in sections 2 and 3 I will discuss two of the recent challenges that I take to be most interesting and significant.

We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use disjunction. Findings from studies of child language acquisition and from cross-linguistic research invite the conclusion that children do not learn to be logical—it comes naturally to them.

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.

Arguments from the Logical Problem of Language Acquisition suggest that since linguistic experience provides few negative data that would falsify overgeneral grammatical hypotheses, innate knowledge of the principles of Universal Grammar must constrain learners hypothesis formulation. Although this argument indicates a need for domain-specific constraints, it does not support their innateness. Learning from mostly positive data proceeds unproblematically in virtually all domains. Since not every domain can plausibly be accorded its own special faculty, the probative value of the argument in the linguistic case is dubious. In ignoring the holistic and probablistic nature of theory construction, the argument underestimates the extent to which positive data can supply negative evidence and hence overestimates the intractability of language learning in the absence of a dedicated faculty. While nativism about language remains compelling, the alleged Logical Problem contributes nothing to its plausibility and the emphasis on the Problem in the recent acquisition literature has been a mistake.

Natural language is full of patterns that appear to fit with general linguistic rules but are ungrammatical. There has been much debate over how children acquire these “linguistic restrictions,” and whether innate language knowledge is needed. Recently, it has been shown that restrictions in language can be learned asymptotically via probabilistic inference using the minimum description length (MDL) principle. Here, we extend the MDL approach to give a simple and practical methodology for estimating how much linguistic data are required to learn a particular linguistic restriction. Our method provides a new research tool, allowing arguments about natural language learnability to be made explicit and quantified for the first time. We apply this method to a range of classic puzzles in language acquisition. We find some linguistic rules appear easily statistically learnable from language experience only, whereas others appear to require additional learning mechanisms (e.g., additional cues or innate constraints).

Evidence is presented to show that the role of a generative grammar of a natural language is not merely to generate the grammatical sentences of that language, but also to relate them to their logical forms. The notion of logical form is to be made sense of in terms a natural logic, a logical for natural language, whose goals are to express all concepts capable of being expressed in natural language, to characterize all the valid inferences that can be made in natural language, and to mesh with adequate linguistic descriptions of all natural languages. The latter requirement imposes empirical linguistic constraints on natural logic. A number of examples are discussed.

Logic has its roots in the study of valid argument, but while traditional logicians worked with natural language directly, modern approaches first translate natural arguments into an artificial language. The reason for this step is that some artificial languages now have very well developed inferential systems. There is no doubt that this is a great advantage in general, but for the study of natural reasoning it is a drawback that the original linguistic forms get lost in translation. An alternative approach would be to develop a general theory of the natural logic behind human reasoning and human information processing by studying formal logics that operate directly on linguistic representations. That this is possible we will try to make plausible in this paper. It will turn out that one level of representation, that of Logical Form, can meaningfully be identified with the language of an existing and well-understood logic, a restricted form of the theory of types. It is not difficult to devise inference systems for this language, and it is thus possible to study reasoning systems that are based directly on language.

Recent research suggests that language evolution is a process of cultural change, in which linguistic structures are shaped through repeated cycles of learning and use by domain-general mechanisms. This paper draws out the implications of this viewpoint for understanding the problem of language acquisition, which is cast in a new, and much more tractable, form. In essence, the child faces a problem of induction, where the objective is to coordinate with others (C-induction), rather than to model the structure of the natural world (N-induction). We argue that, of the two, C-induction is dramatically easier. More broadly, we argue that understanding the acquisition of any cultural form, whether linguistic or otherwise, during development, requires considering the corresponding question of how that cultural form arose through processes of cultural evolution. This perspective helps resolve the “logical” problem of language acquisition and has far-reaching implications for evolutionary psychology.