Online research in philosophy

In this paper I examine a cluster of concepts relevant to the methodology of truth theories: ‘informative definition’, ‘recursive method’, ‘semantic structure’, ‘logical form’, ‘compositionality’, etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.

Postmodernists claim that there is no truth. However, the statement 'there is no truth' is self-contradictory. This essay shows the following: One cannot state the idea 'there is no truth' universally without creating a paradox. In contrast, the statement 'there is truth' does not produce such a paradox. Therefore, it is more logical that truth exists.

This paper examines the question of the extensional correctness of Tarskian definitions of logical truth and logical consequence. I identify a few different informal properties which are necessary for a sentence to be an informal logical truth and look at whether they are necessary properties of Tarskian logical truths. I examine arguments by John Etchemendy and Vann McGee to the effect that some of those properties are not necessary properties of some Tarskian logical truths, and find them unconvincing. I stress the point that since the hypothesis that Tarski's definitions are extensionally correct is deeply entrenched, the burden of proof is still on the shoulders of Tarski's critics, who have not lifted the burden.

An important debate in the current literature is whether “all truth-conditional effects of extra-linguistic context can be traced to [a variable at; LM] logical form” (Stanley, ‘Context and Logical Form’, Linguistics and Philosophy, 23 (2000) 391). That is, according to Stanley, the only truth-conditional effects that extra-linguistic context has are localizable in (potentially silent) variable-denoting pronouns or pronoun-like items, which are represented in the syntax/at logical form (pure indexicals like I or today are put aside in this discussion). According to Recanati (‘Unarticulated Constituents’, Linguistics and Philosophy, 25 (2002) 299), extra-linguistic context can have additional truth-conditional effects, in the form of optional pragmatic processes like ‘free enrichment’. This paper shows that Recanati’s position is not warranted, since there is an alternative line of analysis that obviates the need to assume free enrichment. In the alternative analysis, we need Stanley’s variables, but we need to give them the freedom to be or not to be generated in the syntax/present at logical form, a kind of optionality that has nothing to do with the pragmatics-related optionality of free enrichment.

It is commonly assumed that the conception of truth defended by Frege in his mature period is characterized by the view that truth is not the property denoted by the predicate 'is true', but the object named by true sentences. In the present paper, I wish to make plausible an alternative interpretation according to which Frege's conception is characterized by the view that truth is what is expressed in natural language by the "form of the assertoric sentence". So construed, truth is neither an object (like the True) nor a property (like the Bedeutung of the predicate 'is true') but something of a very special kind that belongs to the same logical category as the logical relations (like subsumption). The main argument justifying this interpretation is that Frege's explication of truth does not hold of the True, but only of truth, considered as what is expressed by the form of the assertoric sentence.

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.

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.

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.

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).