This article is a critical review of Cocchiarella’s theory of reference. In conceptual realism, there are two central distinctions regarding reference: first, between active and deactivated use of referential expressions, and, second, between using referential expressions with and without existential presupposition. Cocchiarella’s normative restrictions on the existential presuppositions of reference lead to postulating two fundamentally different kinds of objects in conceptual realism: realia or concrete objects, on the one hand, and abstract intensional objects or nonexistents, on the other. According to Cocchiarella, nonexistents can be referred to only without existential presuppositions. However, referring to nonexistents with existential presuppositions is an ordinary human practice. To account for this fact, Cocchiarella’s normative theory of reference should be supplemented by a descriptive account of referring.

A personal view is presented of how metaphysics and ontology stand at the beginning of the twenty-first century, in the light of developments during the twentieth. It is argued that realist metaphysics, with serious ontology at its heart, has a promising future, provided that its adherents devote some time and effort to countering the influences of both its critics and its false friends.

Two fundamental categories of any ontology are the category of objects and the category of universals. We discuss the question whether either of these categories can be infinite or not. In the category of objects, the subcategory of physical objects is examined within the context of different cosmological theories regarding the different kinds of fundamental objects in the universe. Abstract objects are discussed in terms of sets and the intensional objects of conceptual realism. The category of universals is discussed in terms of the three major theories of universals: nominalism, realism, and conceptualism. The finitude of mind pertains only to conceptualism. We consider the question of whether or not this finitude precludes impredicative concept formation. An explication of potential infinity, especially as applied to concepts and expressions, is given. We also briefly discuss a logic of plural objects, or groups of single objects (individuals), which is based on Bertrand Russell’s (1903, The principles of mathematics, 2nd edn. (1938). Norton & Co, NY) notion of a class as many. The universal class as many does not exist in this logic if there are two or more single objects; but the issue is undecided if there is just one individual. We note that adding plural objects (groups) to an ontology with a countable infinity of individuals (single objects) does not generate an uncountable infinity of classes as many.