To appear in The Review of Metaphysics. 1 Review of Ontology and the Ambitions of Metaphysics* CHAD CARMICHAEL Indiana University–Purdue University Indianapolis In this book, Hofweber advances the thesis that quantifiers like 'something' and 'everything' have two senses: internal and external. He argues that, in the internal sense of 'something', but not the external sense, something is a proposition, something is a property, and something is a natural number. He claims that the external sense, but not the internal sense, is relevant to metaphysics. Thus, he endorses a form of nominalism-what he calls restricted nominalism (289-90)- by denying that these things exist in the sense relevant to metaphysics. However, Hofweber does think that ordinary objects "like rocks, houses, bottles, people, and so on" (183) are among all of the things in both the internal and the external sense. Hofweber distinguishes his two readings of 'something' (and related expressions) by appeal to examples involving apparently empty names. For example, he points out (67) that an exchange like this seems felicitous: * Thomas Hofweber. Ontology and the Ambitions of Metaphysics. Oxford University Press, 2016, xvi + 368 pp. 2 A: I know Fred admires someone, but I don't remember who. B: Oh, it's Sherlock Holmes. A: That's right, Fred admires Holmes. Given this, it is not implausible that 'Fred admires someone' is true, and that this is so because Fred admires Holmes. But surely, Hofweber thinks, there's at least some sense in which it is false that someone is Holmes. So, Hofweber concludes, the sense of 'someone' in which it is true that Fred admires someone must be different from the sense of 'someone' in which it is false that someone is Holmes. These are the internal and external senses, respectively. Hofweber advocates restricted nominalism on the basis of arguments for what he calls internalism about discourse concerning numbers, properties, and propositions. Internalism about F-talk is the thesis that expressions apparently referring to Fs "are not broadly referring expressions" and that quantifiers in the relevant discourse are "used in their internal reading" (107). He argues that, if internalism is true about F-talk, then Fs do not exist in the external sense, since in that case none of the terms in our F-talk externally refer. Hofweber argues for internalism about talk about numbers, properties, and propositions by careful attention to the use we make of terms in the relevant discourses. For instance, consider the case of number talk. Number terms like 'two' can occur both as singular terms ('The number of beers is two') and as adjectives ('There are two beers'). Hofweber argues that the singular term use of 'two' in this case is not intended to refer to a platonic entity, but rather that its purpose is to produce a pragmatic focus effect that emphasizes the quantitative aspects of the content. Having argued that, for this and other reasons, the purpose of 'two' is not to refer to anything, he thinks that it follows that the quantifier in this discourse is the internal one. Hofweber suggests that his arguments for internalism in each of the indicated domains lead to further insights into epistemological and metaphysical questions about the relevant domains. On the basis of his case for internalism about these three domains, for example, he argues for what he calls rationalism: the view that arithmetic is "a discipline carried out by thinking alone" (156). And 3 he argues for a thesis he calls conceptual idealism: the view that "what can be said or thought about reality depends on us" (257) and that "every truth can be stated by us, in our present language" (xiii). He also applies his framework to some much-discussed problems in metaontology, offering answers to the question whether ontology is easy or hard, whether it has a distinctively philosophical subject matter, and whether it has any important contributions to make to our understanding of the world. He closes the book with a critique of some currentlyfashionable approaches to the nature of ontology involving notions of fundamentality. I struggled throughout the book with the question why the external sense of 'something' is the one that we should care about in metaphysics. Hofweber's answer seems to be that only what exists in the external sense is "in the world" (70) or "in the domain" (77), is a subject of reference (103), and exists in a nontrivial sense (92). Unfortunately, this explanation is unsatisfying. Insofar as 'something' is subject to two interpretations, it is plausible that 'the world' and 'the domain' and 'reference' are all subject to two related interpretations as well. Indeed, Hofweber admits that 'reference' has these two senses (104). Given this, Hofweber's explanation of the metaphysical significance of external existence is just the claim that externally existent things are objects of external reference, are members of the external domain, and are externally worldly, while things that exist merely internally have none of these features. This is manifestly unilluminating: if we wonder-as I think we should-why external existence is the only metaphysically important notion of existence, then we should equally wonder why the "external" notions of reference, domain, and world are the important notions. And, to this question, I think Hofweber provides no answer at all. Furthermore, traditional concerns about his sort of view suggest that internal existence might actually be of some metaphysical interest: concerns about consistency, for example, in connection with examples like 'Meinong believed in the round square, so he believed in something', or examples like 'Russell was interested in the internally non-existent golden mountain, so he was interested in something'. If we treat these examples as Hofweber proposes to treat the Holmes 4 example above, we are led to contradiction. These concerns seem particularly pressing given that Hofweber accepts a similar argument for the internal existence of the largest prime number (151). Despite these reservations, the book is full of interesting arguments and insights, and it should be on the reading list for anyone interested in the metaontological matters that have received so much recent attention.