Ernest Lepore and Kurt Ludwig: Donald Davidson's Truth Theoretic Semantics.
Donald Davidson's Truth Theoretic Semantics.
New York: Oxford University Press 2007.
US$75.00 (cloth ISBN-13: 978-0-19-929093-2); US$45.00 (ISBN-13: 978-0-19-956168-1).
We are finite beings with finite minds, and yet the expressive power of natural language is infinite. Indeed, as Mother Goose once demonstrated, constructing a seemingly unending series of nonsynonymous expressions is mere child's play: 'This is the house that Jack built', 'This is the malt that lay in the house that Jack built,' 'This is the rat that ate the malt that lay in the house that Jack built,' and so on, ad infinitum. Our ability to comprehend a potential infinity of nonsynonymous expressions suggests that natural language is compositional, consisting of a finite number of primitive expressions together with a finite number of recursive rules for constructing complex expressions from these primitives. This 'compositionality constraint' is one of the two germinal ideas from which Donald Davidson's semantic project grew, and it is the focus of Lepore and Ludwig's recent book.
As Lepore and Ludwig (L and L) explain in their introduction, a compositional meaning theory is only part of a complete theory of meaning. It explains how the meanings of complex expressions are inherited from their primitive parts; a complete theory must account for the meanings of these primitive parts. Having already written a book on Davidson's approach to the more ambitious project, L and L's focus in this book is exclusively on the more modest project. The early chapters contain a detailed explanation of Davidson's approach, and the chapters that follow apply this approach to parts of language thought to provide it with difficulties: quantifiers (Chapters 2 and 3), proper names and indexicals (Chapter 4), demonstratives (Chapters 4 and 5), quotation and indirect discourse (Chapters 6 and 11, respectively), adjectives and adverbs (Chapter 7), tense and temporal expressions (Chapters 8, 9, and 10), and non-declarative sentences (Chapter 12).
I have said that the compositionality constraint is one of the two inspirations of Davidson's project. The other is the realization that an axiomatic truth theory of the Tarskian variety meets this constraint. Tarski argued that an adequate theory of truth for a language would have to meet his 'Convention T'--generating for every sentence s in the language a theorem or 'T-sentence' of the form '(T) s is T iffp' where '"s" is replaced with a structural description of an object language sentence ... and ... "p" is replaced by a metalanguage sentence that translates it' (28). Because p translates s only if they have the same truth conditions, a theory satisfying Convention T would consist of a complete specification in the theory's metalanguage of the truth conditions for expressions in the object language. Davidson's insight was to see that such a theory could double as a compositional meaning theory, for, with some additional constraints, the predicate 'is T iff could be replaced with 'means that' while preserving truth. Davidson himself was never very clear about the nature of these ancillary constraints, but L and L suggest that 1) the axioms of the theory must be interpretive, where an axiom is interpretive if it 'gives the reference or truth conditions for an object language term using a metalanguage term that translates it' (34), and 2) T-sentences must be derived from axioms by means of canonical proofs, i.e. proofs that 'draw only on the content of the axioms to prove T-form sentences' (36). If the axioms of the theory are interpretive and derivations of the theorems rely only on their content, the theorems will be interpretive as well.
L and L construct a compositional meaning theory meeting all three constraints for what they call 'Simple English0'. Simple English0 contains a single predicate (is ambitious), two names (Caesar and Brutus), three logical constants (and, or, and not), parentheses, and spaces (29). As L and L demonstrate, with a few well-chosen axioms and rules of inference we are able to generate a T-sentence for each of the infinitely many expressions of Simple English,,. For example, the T-sentence for (S), 'Brutus is ambitious or Caesar is ambitious', can be generated from interpretive axioms (Al - A4) by means of a canonical derivation relying only on universal quantifier instantiation (UI), replacement of equivalent expressions (R), and substitution of identities (S).
(Al) The referent of 'Brutus' = Brutus.
(A2) The referent of 'Caesar' = Caesar.
(A3) For all x, 'x is ambitious' is true iff the referent of x is ambitious.
(A4) For all formulae p, q, 'p or q' is true iff p is true or q is true.
(Tl) 'Brutus is ambitious or Caesar is ambitious' is true iff 'Brutus is ambitious' is true or 'Caesar is ambitious' is true. (From A4 by UI)
(T2) 'Brutus is ambitious' is true iff the referent of 'Brutus' is ambitious. (A3, UI)
(T3) 'Caesar is ambitious' is true iff the referent of 'Caesar' is ambitious. (A3, UI)
(T4) 'Brutus is ambitious' is true iff Brutus is ambitious. (Al, T2, S)
(T5) 'Caesar is ambitious' is true iff Caesar is ambitious. (A2, T3, S)
(T6) 'Brutus is ambitious or Caesar is ambitious' is true iff Brutus is ambitious or Caesar is ambitious. (Tl, T4, T5, R)
Note that (T6) is the T-sentence for S.
The bulk of the book is dedicated to applying the compositional meaning theory embodied in Simple English,, to elements of natural language thought to be problematic for Davidson's approach. Solutions to these difficulties fall into two general categories: 1) dissolutions of the apparent problem by a clarification of Davidson's project, and 2) the introduction of technical maneuvers to render tractable seemingly intractable expressions. Chapter 4, for example, takes up the question of whether a truth theoretic approach can accommodate the Fregean intuition that names have senses. Truth theories, being extensional, would seem to have difficulties handling such intensional objects. Not so, according to L and L, for we have to keep in mind that the axioms of a compositional meaning theory will be interpretive. Thus, Fregean intuitions can be accommodated simply by choosing (A5) over (A6): (A5) 'The referent of "Samuel Clemens" = Samuel Clemens'; (A6) 'The referent of "Samuel Clemens" = Mark Twain'. This seems like cheating until we remember that a compositional meaning theory is intended to show only how the meanings of complex expressions depend on the meanings of their primitive parts. It is no part of such a theory to derive the meanings of these primitives from some more primitive source.
Chapter 11, in which L and L present a modified account of Davidson's paratactic account of indirect discourse, provides an example of the second strategy. Consider the following sentences: (1) 'Lois said that Superman flies'; (2) 'Lois said that Clark Kent flies'. Assuming that Clark Kent is identical to Superman, the embedded sentences have identical truth conditions, and yet (1) and (2) do not. These sorts of 'opaque contexts' present difficulties to any approach suggesting that an extensional truth theory can function as a meaning theory, for the embedded sentences seem to be contributing something more than their truth conditions. Davidson attempted to resolve the issue by suggesting a syntactically more perspicuous rendering of (1), namely (1*): 'Lois said that. Superman flies.' That is, a speaker who utters (1) is actually uttering two sentences, one of which is asserted, the other of which is exhibited. It is as if the speaker is saying 'Lois said that' while pointing to an inscription of 'Superman flies'. The inscription is referred to by the speaker, but is not part of the content of her assertion. Thus, any theory that can handle demonstratives can handle indirect discourse as well.
This book goes a long way toward working out the details of Davidson's project, and these details matter. However, they are not all that matters. There is one crucial question L and L never address. The argument for the compositionality constraint is psychological in nature. It is because our minds are finite and our language is not that a theory of the latter has to be compositional. Thus, one might expect that the meaning theory offered by L and L would also be psychological in nature, a description of what a speaker knows in knowing a language. However, L and L are clear that this is not their intent: 'there is no suggestion here that (a compositional meaning theory) is or must be a theory which speakers of the language know, explicitly or implicitly' (19). Rather, a compositional meaning theory 'aims to capture the structure of the dispositions of the speaker which constitute her competence in speaking and understanding speech in the language' (19-20). It is not clear what L and L mean by the 'structure of a disposition', and nothing they say in Chapter 13 on logical form provides much clarification. But if a meaning theory is not intended to provide a description of what speakers know in knowing a language, it is not clear why a theory of meaning has to meet the compositionality constraint. After all, any disposition that can be described by means of a compositional theory can be described by means of a non-compositional theory. So why prefer the former to the latter?
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|Publication:||Philosophy in Review|
|Article Type:||Book review|
|Date:||Oct 1, 2009|
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