In its main contemporary sense, nominalism is the thesis that abstract entities do not exist. Equivalently, it is the thesis that everything that does exist is a concrete object. Since there is no generally accepted account of the abstract-concrete distinction, and since it remains genuinely unclear how certain (putative) entities are to be classified, the content of modern nominalism is to some degree unsettled. Certain consequences of the view are, however, tolerably clear. For example, it is widely agreed that the objects of pure mathematics—numbers, sets, functions, abstract geometrical spaces, and so on—are to be classified as abstract. It is also widely agreed that certain objects of metaphysics and semantics—propositions, meanings, properties and relations, and so on—must be abstract if they exist at all. Modern nominalists thus commit themselves to rejecting these paradigmatic abstract entities and hence to rejecting any scientific, mathematical...