Plato's dialogue Sophist undertakes to define a sophist. After six unsuccessful attempts, the Eleatic Stranger announces that the sophist has appeared in so many ways because he has a special skill: he makes people think he knows things he does not know; he deceives them into mistaking falsehoods for truths. To capture the essence of the sophist the inquirers must therefore explain falsehood, and especially false statement, the sophist's major weapon. Plato's analysis of falsehood is the topic of C.'s book.

C. gives a carefully argued interpretation of large stretches of the Sophist and summarises portions he treats in less detail, such as the divisions and definitions of the sophist which frame the dialogue at beginning and end (Chapter 1). He does not discuss the tantalising description of dialectic and the surrounding text (mentioned p. 116). With those chief exceptions, the book offers a comprehensive commentary, starting with the Greek text and C.'s translation, followed by a survey and assessment of the main competing interpretations accompanied by notes sorting the vast secondary literature (in English, German, French and Italian), enabling readers to see at a glance who agrees with whom on key interpretative issues. The philosophical analysis is aided by expert exegesis of textual issues. The introduction presents a concise overview of C.'s interpretation, and a final appendix gives a formal presentation of his reconstruction of Plato's analysis of true and false sentences.

C.'s interpretation is a version of M. Frede's, though C. agrees with L. Brown that Plato makes room for a ‘complete’ use of the verb ‘to be’ (existence) to handle sentences such as ‘Change is, because it partakes of being’ (Soph. 256a1) (p. 120). According to C., Plato in the Sophist distinguishes two ‘incomplete’ uses of the verb ‘to be’. In Plato's terminology, one specifies being auto kath' hauto (‘itself by itself’), the other being pros alla (‘in relation to others’) (255c13–e2, passage discussed pp. 144–9). C. calls the first the ‘definitional’ use, featured in such Platonic self-predications as ‘largeness is large’ and in definitions such as ‘man is a featherless biped animal’ (I invoke a whimsical definition from the Sophist's companion dialogue Statesman). According to C., a definitional sentence is available just in case the subject and complement in a sentence ‘x is y’ pick out kinds, and a definitional sentence is true just in case x and y are identical (p. 123). C. calls the second use of the verb ‘to be’ the ‘ordinary’ use, as in ‘Socrates is wise’. A sentence ‘x is y’ construed on its ‘ordinary’ reading is true, just in case x instantiates y; ‘x’ can pick out either a sensible particular or a kind. ‘Socrates is wise’ is true on the ordinary reading of ‘is’, because Socrates instantiates wisdom (p. 123).

In a densely argued section of the Sophist (topic of Chapter 4), Plato's Stranger develops machinery to use in his later analysis of the true sentence, ‘Theaetetus is sitting’, and the false sentence, ‘Theaetetus is flying’. He distinguishes five great kinds – change, stability, being, identity and difference – some of which can combine, some not; and then, selecting change as his subject, he systematically shows how change relates to each of the other four kinds. Change both is and is not each of the others, with one exception: change is neither stability nor stable (C. queries the exception, since all Platonic forms should be stable, but the entire section is premised on the claim that some kinds can combine and others not, and many of the Stranger's arguments presuppose that change and stability are opposites that cannot partake of each other). In any case, change is and is not each of the other three. For instance, change is identical and is not identical: change is identical because change is identical with itself, but change is not identical because it is different from identity. As C. construes these claims, the positive sentence uses ordinary ‘is’ (change instantiates identity in being identical with itself), while the negative uses definitional ‘is’ (change is not defined as identity).

While I agree with Frede and C. that Plato distinguishes different uses of ‘is’ and ‘is not’ in the Sophist, their interpretation of the pairs of sentences about change should give us pause, because it turns out that the positive statement ‘x is y’ always uses ordinary ‘is’, whereas the negative ‘x is not y’ always uses definitional ‘is’. The section offers no definitional instances of ‘x is y’. The Stranger certainly had the resources to supply positive definitional sentences, had he intended to articulate the Frede/C. distinction here. Examples are ready to hand even in the small domain of five great kinds, and one is available when sentences are limited to those about change. The self-predication ‘change is changing’ employs C.'s definitional ‘is’: the sentence is about kinds, and the kinds signified by subject and complement are identical. Given the absence of this self-predication, it seems unlikely that the Stranger's examples of ‘x is y’ and ‘x is not y’ are meant to display the difference between ‘ordinary’ and ‘definitional’ predication. On the contrary, the pairs of sentences use the same ‘is’ (it specifies being pros alla): ‘x is y’ is a positive predication, whereas ‘x is not y’ is a statement of non-identity whose explication relies on difference. According to the Stranger, the positive predication ‘change is identical’ states that change partakes of identity in relation to itself. The negative statement ‘change is not identical’ states that change partakes of difference from identity, i.e. the two kinds are not identical with each other (256a10–b4). Plato's Stranger is developing machinery to analyse negative predications and false statements later in the dialogue, and difference will perform a further role in that analysis. So far it accounts for non-identity only: x is not y, because x partakes of difference from y. He will extend his analysis to handle negative predications such as ‘Theaetetus is not flying’ – Theaetetus is not flying, because flying is different from (i.e. non-identical to) some feature of Theaetetus that excludes flying (viz. sitting) – and then to false statements such as ‘Theaetetus is flying’. The role of difference in statements of non-identity in the section on great kinds is a vital first step towards the Stranger's upcoming analysis of negative predication and falsehood.

C. would dispute my treatment of ‘Theaetetus is not flying’, which relies on what he calls the ‘quasi incompatibility’ interpretation of negation, according to which the negated item is different from (non-identical to) some feature of Theaetetus that excludes it (on an incompatibility range). Theaetetus is sitting, and his sitting excludes flying. In C.'s discussion of negation (Chapter 5), he favours for textual reasons what he calls the ‘extensional’ interpretation of negation, according to which Theaetetus is different from everything of which ‘flying’ is true (birds, insects, etc.) (p. 195), but when he treats false sentences in Chapter 6, he opts instead for the so-called ‘Oxford’ interpretation, according to which flying is different from all features belonging to/instantiated by Theaetetus – snub-nosed, clever, man, sitting, etc. C. has an ingenious way to reconcile the two interpretations (p. 240), but Plato would have a simpler, more convincing account if he interprets negation in the same way when he develops the machinery to deal with negative predication (257b1–258c6) and when he applies the machinery in his analysis of falsehood (261c6–264b10). The ‘quasi incompatibility’ interpretation suits both sections. C. rejects the view because he finds no explicit evidence for incompatibility ranges (pp. 190–2, 239). In fact, there is a nice piece of evidence in the Stranger's initial explication of negative predication (257b1–c4). According to the Stranger, when we call something ‘not large’, we do not mean the opposite of large (small); something not large could be equal or small. Largeness and smallness mark off an incompatibility range – size – and something not large has some definite size on that range different from largeness.

Further topics invite discussion, but perhaps I have said enough to indicate that C.'s book will stimulate productive debate. The book is a substantial contribution to the literature on Plato's Sophist. The final chapter on false sentences is particularly provocative and interesting.