Complex demonstrative phrases, in English, are phrases such as “that woman in the department” and “that car on the corner”. They are of particular interest to philosophers for two related reasons. The first involves the problem of intentionality. If there are phrases that are candidates for “latching directly onto the world”, it is such phrases, and their “simple” counterparts, as in the occurrences of “that” in “that is nice”. As a result, philosophers interested in intentionality from the sense data theorists to contemporary philosophers of mind have devoted considerable attention to the question of how a demonstrative thought links to its object. The second reason involves issues in semantics and the philosophy of language. In the course of investigations into the model theory for modal logic in the 1950s and 1960s, philosophers recognized that the simplest way to treat terms was as modally rigid, namely as designating their actual designations relative to any possible world in which they existed, and nothing else in other worlds. It was soon recognized (by David Kaplan and others) that this semantic property could be elegantly explained by the assumption that the semantics of singular terms reflects the role of singular terms in linking representations directly to the world. If the semantic contribution of a singular term to a thought is simply the object it denotes, and the thought is the object of modal evaluation, then the modal rigidity of the class of terms falls out as a consequence. Demonstrative phrases, both simple and complex, have always been taken to be among the paradigms for this picture of reference, which has come to be known as “the direct reference” model.
     In Complex Demonstratives: A Quantificational Account, Jeffrey King challenges the assimilation of complex demonstratives to the direct reference model, and does so by challenging their assimilation to the category of singular terms. The first chapter is devoted to a battery of powerful arguments against the direct reference account. The two basic pieces of data King discusses are as follows. First, there are what King calls “No Demonstration, No Speaker Reference” [NDNS] cases, such as “That hominid who discovered how to start fires was a genius”, said by someone with no clue of who discovered how to start fires. King argues that such uses of complex demonstratives are not rigid, contra the direct reference account of them. The second, and equally damning class of cases for the direct reference account are what King calls “Quantifying In” [QI] cases. Such examples include “Most skiers remember that first black diamond run they attempted to ski”, or the reading of "That professor who brought in the biggest grant in each division will be honored" in which "each division" has scope over the complex demonstrative phrase. In QI cases, the denotation of a complex demonstrative varies as a function of the values introduced by an higher quantifier. Given the framework assumed, it is fairly straightforward to show that if any of this data is taken at face-value, the direct reference account of complex demonstratives is false, and so in the fifth and final chapter, King presents a series of arguments against those who appeal to an ambiguity in “that” in an attempt to reject the data he presents.
    In the second chapter, King presents three different quantificational analyses of complex demonstratives. According to the view he eventually adopts, the lexical meaning of the word “that” is a four-place relation, which King describes as “_and_are uniquely_in an object x and x is_”. Relative to a context, the second argument place of this relation is filled by a property that is determined by the intentions of the speaker. If the user of the demonstrative has a perceptual intention to refer to an object b, the second argument place is filled the property of being identical to b. If the user has a descriptive intention to refer to any object that satisfies a property P, then the second argument place is filled by the property P. The third argument place is filled by a relation between properties. When the speaker has a perceptual intention to refer to a particular object, the relation in question is of the form “being jointly instantiated in world w and time t”. When the speaker has a merely descriptive intention, the relation is of the form “being jointly instantiated.” Thus contextually saturated, the resulting relation is, like those expressed by the other quantificational determiners ("every", "some"), a two-place relation between properties.
    For example, suppose Jane, in world w and at time t, utters "That apple is shiny", when perceptually presented with a particular apple, call it A. According to King, the first argument place of "that" is filled by the property expressed by the nominal complement "apple", and the fourth argument place of "that" is filled by the property of being shiny (these are the two syntactically represented arguments of "that"). Since Jane has a perceptual intention to refer to A, the second argument place of the relation expressed by "that" is filled by the property being identical to A. For the same reason, the third argument place of the relation expressed by "that" in this context is filled by the relation of being jointly instantiated in w and t. The semantic content of Jane's utterance is, then, that applehood and being identical to A are jointly instantiated in w and t in an object x and x is shiny. This proposition is true relative to an arbitrary possible world w' and time t' just in case there is an object in w' and t' that is identical to A and is an apple in the actual world w and the time of utterance t, and is shiny in w' and t'. On this account, the actual world is a constituent of the proposition expressed by many uses of sentences containing complex demonstratives. It is worth mentioning that, as a result, it is subject to a variation of the criticism Scott Soames has leveled against "actualized" definite description theories of names (as King recognizes; see the discussion in footnote 28 on pp. 183-4).
    The remainder of the chapter is devoted to explaining how King’s favored theory can account for the whole range of data upon which all previous theories falter. For example, if the speaker has a merely descriptive intention to refer to an object with a complex demonstrative, then the proposition expressed by her utterance of a sentence containing it will contain the relation between properties of being jointly instantiated as the relation that fills the third argument place of the relation expressed by "that". Since this is not the relation of being jointly instantiated in the world and time of utterance, the proposition expressed by the speaker will not be indexed to the actual world and time. This predicts that a complex demonstrative will not behave like a rigid designator in modal evaluation, when the speaker has only a descriptive intention. As a result, King can provide a smooth account of NDNS uses of complex demonstratives.
    In the third chapter, King considers the interaction of complex demonstratives with operators that engage in semantically significant scope relations with quantificational elements. The thought here is that if complex demonstratives do give rise to the sort of scope ambiguities that uncontroversially quantificational determiner phrases do, that provides more evidence that they are also quantificational determiner phrases. Again, King provides compelling data for his claim (King strengthens these arguments in his fifth chapter, when he produces good syntactic evidence that complex demonstratives, even when used with perceptual intentions to refer to salient objects, behave syntactically like uncontroversially quantificational phrases). In the fourth chapter, King treats a variety of “loose ends”, such as the interaction of quantifier domain restriction with his quantificational treatment of complex demonstratives. King also argues that, on his semantics, the demonstrative element in a complex demonstrative (at least relative to a context) shares some of the important model theoretic properties that quantificational determiners are alleged to share cross-linguistically.
    To my knowledge, NDNS uses of complex demonstratives are completely novel with King. Philosophers before King have discussed QI uses of complex demonstratives. But some of them have not fully grasped their import. For example, in Barry Taylor (1980), Taylor argues from the felicity of "There is someone who loathes that denigrator of his" to the King-like conclusion that the demonstrative element in a complex demonstrative is best treated as a binary quantifier. But upon closer inspection, Taylor's discussion does not involve the relevant reading of this sentence (nor does his semantics produce it). Taylor rather discusses a reading of it according to which the value of the complex demonstrative is fixed in context, but the value of the nominal complement "denigrator of his" varies with the values of the variables quantified over by the initial quantifier (Ibid., p. 195). Had Taylor considered cases such as "Every man loathes that first denigrator of his", he might have realized the generality of the problem. The first paper I know of that clearly recognizes the threat QI cases pose for the direct reference account of complex demonstratives is Stephen Neale (1993), where he produces an ungrammatical version of a QI sentence (Ibid., p. 107; as King notes, Neale also cites a grammatical case of a QI sentence, due to Jamie Tappenden, in a footnote).
    The methodology of arguing from the possibility of quantifying into an expression to the conclusion that it is not a referring expression was employed in Gareth Evans (1979), where Evans argued from the possibility of quantifying into definite descriptions (as in his example "The father of each girl is good to her") to the conclusion that definite descriptions are not referring expressions. Evans concluded that the existence of such examples "does not constitute a knock-down argument against treating descriptions as referring expressions" (Ibid.), but rather only strongly suggests this conclusion. In contrast, King takes the existence of QI cases to provide a decisive refutation of the thesis that complex demonstratives are referring expressions.
    Interestingly, both Evans and King are correct. In the structured proposition framework assumed in King's book, where direct reference is characterized in terms of the contribution of (only) an object to a structured proposition, the existence of QI uses of the sort envisaged by Evans and King for a class of expressions does provide a decisive argument against the thesis that the expressions in that class are directly referential. But in a truth-conditional semantics, one could maintain that the reference relation is relativized to a sequence, and so preserve the thesis that such expressions are referring in the face of QI uses. This is the only case I have uncovered in which the assumption of the structured proposition framework may bias King's topic, and it does so rather innocently. Still, it is worth bearing in mind that the assumption of a structured proposition framework rather than a truth-conditional semantics may affect the strength of various arguments; the choice of framework is not a neutral one.
    King works out his theory in an extraordinarily rigorous manner. It would be worthwhile to see similarly worked out versions of alternative views, to see if they would be any less complex. King briefly discusses in a footnote one theory, that of Ernie Lepore and Kirk Ludwig, that could perhaps be altered to account for the data. Another alternative to King's account that has been insufficiently explored is the view that “that” expresses, as Irene Heim and Angelika Kratzer have argued “the” does, a function from properties to objects. This latter theory does seem to be able to account for the data discussed by King without emendation.
    In this book, Jeffrey King has produced the most carefully argued and linguistically astute study of complex demonstratives yet written. It is already required reading for experts in the field, but its lucidity makes it amenable to the relative novice as well.

Evans, G. (1979): "Reference and Contingency", The Monist 62.2: 161-189.
Neale, S. (1993): "Term Limits", Philosophical Perspectives, 7: Language and Logic, Ridgeview Publication. pp. 89-123.
Taylor, B. (1980): "Truth-Theory for Indexical Languages", in M. Platts (ed.), Reference, Truth and Reality, Routledge & Kegan Paul: 182-198.