The basic question of ontology is “What exists?”. The basic question of metaontology is: are there objective answers to the basic question of ontology? Here ontological realists say yes, and ontological anti-realists say no. (Compare: The basic question of ethics is “What is right?”. The basic question of metaethics is: are there objective answers to the basic question of ethics? Here moral realists say yes, and moral anti-realists say no.) For example, the ontologist may ask: Do numbers exist? The Platonist (...) says yes, and the nominalist says no. The metaontologist may ask: is there an objective fact of the matter about whether numbers exist? The ontological realist says yes, and the ontological anti-realist says no. Likewise, the ontologist may ask: Given two distinct entities, when does a mereological sum of those entities exist? The universalist says always, while the nihilist says never. The metaontologist may ask: is there an objective fact of the matter about whether the mereological sum of two distinct entities exists? The ontological realist says yes, and the ontological anti-realist says no. Ontological realism is often traced to Quine (1948), who held that we can determine what exists by seeing which entities are endorsed by our best scientific theory of the world. In recent years, the practice of ontology has often presupposed an ever-stronger ontological realism, and strong versions of ontological realism have received explicit statements by Fine (this volume), Sider (2001; this volume), van Inwagen (1998; this volume), and others. (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Ontological Pluralism is the view that there are different modes, ways, or kinds of being. In this paper, I characterize the view more fully (drawing on some recent work by Kris McDaniel) and then defend the view against a number of arguments. (All of the arguments I can think of against it, anyway.).

Intuitionists and classical logicians use in common a large number of the logical axioms, even though they supposedly mean different things by the logical connectives and quantifiers — conquans for short. But Wittgenstein says The meaning of a word is its use in the language. We prove that in a definite sense the intuitionistic axioms do indeed characterize the logical conquans, both for the intuitionist and the classical logician.

Understanding the Infinite is a loosely connected series of essays on the nature of the infinite in mathematics. The chapters contain much detail, most of which is interesting, but the reader is not given many clues concerning what concepts and ideas are relevant for later developments in the book. There are, however, many technical cross-references, so the reader can expect to spend much time flipping backward and forward.