Logical Form

The notion of the logical form of an expression E is shown to be a semantic notion that can be derived from the notion of the structured meaning of E. This simple idea can be traced to categorial grammars, and it is implicitly used by Richard Montague. We argue that a most fine-grained tool for defining structured meaning can be found in Pavel Tichý’s Transparent Intensional Logic (TIL). Structured meanings of expressions are identified with abstract procedures, known as TIL constructions, expressed by the expressions. We construe concepts as closed constructions, and present a method of seeking the best semantic analysis (identical to the structured meaning) of a given expression. The method terminates in a complete lattice over the set of possible analyses; which analysis is the best one must, however, be relativized to a conceptual system. This relativization concerns primitive concepts of the conceptual system within which the semantic analysis is set. Our main thesis is: Every well-formed expression E of the language under analysis can be associated with a logical form that is unambiguously derived from the structured meaning of E. 1 The problem of adequate explication Logic is formal in the sense that all arguments of the same form as logically valid arguments are also logically valid and hence truth-preserving. (M. Goméz – Torrente) The goal of logic is to discover the entailment relation wherever it holds. The urgency of this task becomes obvious as soon as logic is applied to analyzing natural language expressions, because the historically developed grammatical structure of a natural language hides the logical form that underlies the given expressions. Our intuition is that the more fine-grained the analysis, the more instances of entailment are discovered. The question whether an analysis is better 116 Marie Duží, Pavel Materna (because more fine-grained) than another one is thus connected with the task of explicating the notion logical form. In this paper we present a method that makes it possible to find the most fine-grained analysis of an expression. The following question should be answered first: Let E be an expression of a natural language. Can we speak about the (unambiguously determined) logical form of E? Peregrin in [23, p. 1] presents an argument against what he calls a “metaphysical” conception of logic, according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our actual reasoning. In contrast, he argues that it is always an empirical question whether a given mathematical structure really does capture a principle of reasoning. More generally, he argues that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question. Indeed, from the viewpoint of general linguistics, the fact that an expression denotes just what it denotes (in the given language) is contingent: Linguistics is an empirical science, so the logical form of an expression is something what must be discovered in the “the realm of the formal“ (see [23]); thus, what we call logical analysis of language, LANL (see, e.g., [17, 19]) should accept the following principle ([30], [31, pp.801-842]): The notion of a code presupposes that prior to, and independently of, the code itself there is a range of items to be encoded in it. Hence. . .meanings cannot be conceived of as products of the language itself. They must be seen as logical rather than linguistic structures, amenable to investigation quite apart from their verbal embodiments in any particular language. To investigate logical constructions in this way is the task of logic. The linguist’s brief is to investigate how logical constructions are encoded in various vernaculars. So LANL is based on some study of logical structures and their properties and relations, and this activity is devoid of any empirical factor. As soon as the results of the logical investigation are applied (or made available to application) to the search for the logical form of an expression, we must be aware of the hypothetical character of this application. It is linguists who should participate in checking the adequacy of the proposal. All the same, LANL cannot be reduced to making particular proposals. Richard Montague [21] was the first to demonstrate the possibility of building up a logical system that makes it possible to systematically put forward logical constructions as logical (as opposed to grammatical) forms of a fragment of English. Here we will outline another systematic tool for the same project as Montague’s: Transparent Intensional Logic (TIL). (See, e.g., [29, 31]). We should, however, mention David Lewis and his [16], which makes two points that are important w.r.t. some trends in ‘post-analytic’ semantics: i) Lewis speaks about the “pleasing finitude that prevents Markerese semantics from dealing with the relations between symbols and the world of nonG. Sica (ed.) Essays on the Foundations of Mathematics and Logic ©2005 Polimetrica International Scientific Publisher Monza/Italy