The book makes two connected claims. The first is that nothing like acquaintance is needed for singular reference, in thought or language. The second is that this makes room for a new unification among a range of expressions: (i) indefinite and (ii) definite noun phrases, (iii) simple and (iv) complex demonstratives, and (v) proper names. Since acquaintance plays no significant role, it cannot make significant discriminations among these categories. They are unified by the fact that, at a certain level of description, all five kinds of expression function in the same way: ‘they single out objects by way of restricted quantification that is sometimes covert’ (36).

The authors (henceforth H&M) say, rightly, that Russell's notion of acquaintance, or derivatives from it, have played a very important role in much recent thinking about reference. For Russell, acquaintance was a conceptually unmediated relation between a mind and an object. Such an object had to be ‘demon-proof’ in that one could not suppose there to be an object when there was not – which meant, for Russell, that the paradigm object was a sense-datum. More recently, philosophers like Evans and McDowell have repudiated the Cartesian aspects of Russellian acquaintance, while retaining its essential core, making the paradigm relation between a thinker and an object the kind of information-transmitting path along which knowledge can flow. Despite this liberalization of Russell's notion, the shape of his distinction remains influential. On the one hand, one may think of an object ‘by description’, even when not related to it by the special relation, as most of us would think of the tallest spy. On the other hand, there is

Many thinkers have supposed that expressions like names and demonstratives are tailor-made to express thoughts of this distinctive, singular kind, whereas indefinite and definite descriptions can typically express only the more general thoughts.

H&M aim to undermine this distinction, and along with it the distinction among the kinds of expressions. Their most straightforward approach to showing that ‘acquaintance … is a dispensable relic of a bygone era in the philosophy of language and mind’ (25) is to provide examples in which our singular thought and reference is as genuinely singular as can be imagined, even though acquaintance is absent. A familiar kind of case is named future objects. H&M give a telling example, attributed to Robin Jeshion: Henry VIII orders a great warship to be constructed. It is to be called Henry Grace à Dieu. Some time later, having received no news from the shipyard, he declares ‘I'm going to Woolwich to visit Henry Grace à Dieu’. The ship has not causally impacted on Henry; rather, the causation has flowed in the other direction (Henry caused the ship to exist). Yet Henry seems able to think about the ship in a singular fashion.

The problem with using examples of this kind is that defenders of the distinction will simply deny that such thoughts are ‘as singular as can be’. They will say that Henry's use of the name involves him in no more than a descriptive thought, paraphrasable as ‘I'm going to visit the ship I ordered to be built and to be named Henry Grace à Dieu’. H&M offer two systematic chapters, in which the case for and against acquaintance is subjected to deeper and more theoretical scrutiny.

In Part II of the book, liberated from any need to find a special place for acquaintance, H&M consider the five types of expression to be unified. One of the trickiest is what they call ‘specific indefinites’. This turns out not to be a category of expression, but a way of using noun phrases, especially those of the form ‘an F’. The leading idea is that a use of an indefinite is specific when the speaker uses it with a definite object in mind. H&M consider various refinements of this thought, concluding that

When ‘an F’ is used specifically, the speaker's ‘restrictor’ is the predicate G (or the property of being G) that supplements ‘F’ to supply a more demanding, indeed unique, restriction. Thus far, definition. The doctrine about such uses delivers a truth condition:

I take it that ‘being about how things stand with that object’ means that whether or not the utterance is true depends upon how things are with that object. Putting the two claims together: for all objects x, among uses of indefinites, when and only when an utterance presupposes covert material uniquely restricting the indefinite's application to x, the utterance is true iff true of x.

There are seeming counterexamples. A female student, A, who has done very well in the test, asks her professor if any male student did better. The professor thinks B is male and did better; presupposing this (and so having B ‘in mind’), he responds:

In fact, B did worse, but C is a male student who alone did better than A and scored 96. Intuitively, what the professor said is true. Yet, by the first quotation (from page 129) his utterance appears to count as a specific use of the indefinite ‘a male student’, a use specific to B, and from the second (from page 136) it should be true iff B scored better than A, which he did not.

Subsequent chapters suggest that definite descriptions, demonstratives and names also have quantificational structure. The differences relate to the ways in which uniqueness is presupposed, and the manner and extent to which hearers are supposed to have access to the presupposed material.

As may be apparent from my discussion of indefinites, there is plenty of room for disagreement about some of the fine details of the views proposed. But I have considerable sympathy with many general features of the approach. For example, H&M acknowledge that ‘we allow our representational machinery to form a singular object representation even if we know there is no worldly object for that representation’ – in short, they allow for reference without a referent (see Sainsbury Reference Without Referents, OUP, 2005). (Admittedly, it is less clear how seriously H&M take the possibility: the expressions under discussion are often said quite generally to ‘single out objects’.) They also allow that our cognitive access to objects may pass through the thoughts of others: they call these ‘parasitic object representations’ (142). A simple example would be a case in which I tell you I am waiting for a friend and you go on to ask me questions about her. You may represent the friend simply as whatever friend of mine I was thinking or talking about; this ‘parasitic’ representation is a perfectly fine basis for communication and the transmission of knowledge, and obviously does not require anything like acquaintance, which they successfully show will not serve as the basis for a distinctive category of thought or talk.

This is quite a formidable book. Although there is little unclarity at the micro-level, although it is replete with ingenious and thought-provoking arguments and shows an extraordinary grasp of a wide and very complex literature, I was sometimes hard put to say how the various elements of the discussion were meant to fit together. H&M are writing for fellow professionals. If you are not already familiar with such phrases as ‘exceptional scope’, ‘phi-features of pronouns’, ‘singleton quantifier’, you will need to interrupt your reading (as I did) to acquire some background. You will also need somehow to deal with 549 footnotes over 248 pages. But there is a great deal to be learned from this book.