Online research in philosophy

Works of music don’t appear to be concrete objects; but they do appear to be created by composers, and abstract objects don’t seem to be the kind of things that can be created. In this paper I aim to develop an ontological position that lets us salvage the creativity intuition without either adopting an ontology of created abstracta or identifying musical works with concreta. I will argue that there are no musical works in our ontology, but nevertheless the English sentences we want to hold true are literally true. I rely on a meta-ontological view whereby ‘a exists’ can be true without committing us to an entity that is a. This meta-ontological view is illustrated by its application to the familiar example of the statue and the clay. I argue that my account of musical ontology fares better on the balance of costs and benefits than its rivals.

I am attracted to a radically minimal ontology. Many of the entities we quantify over in everyday speech do not, I hold, really exist. Complex objects are one such case: there is no mereology in reality – our ontology is one of entities lacking proper parts. However, I do not want to embrace an error-theory of talk about tables, chairs, etc: it is, even speaking strictly and literally, true to say such things exist. Rather, I suggest, we should view the (strict and literal) truth of such claims as not bringing an ontological commitment to tables, chairs, etc. It is true to say that there are such things; but that it is true does not commit us to admitting such things into our ontology. The purpose of this paper is to further elucidate this metaontological view and to defend it from some recent objections.

According to the familiar Quinean understanding of ontological commitment, (1) one undertakes ontological commitments only via theoretical regimentations, and (2) ontological commitments are to be identified with the domain of a theory’s quantifiers. Jody Azzouni accepts (1), but rejects (2). Azzouni accepts (1) because he believes that no vernacular expression carries ontological commitments. He rejects (2) by locating a theory’s commitments with the extension of an existence predicate. I argue that Azzouni’s two theses undermine each other. If ontological commitments follow from predications of existence, then ontological commitments can be expressed in the vernacular via negative existential sentences.

On the truthmaker view of ontological commitment [Heil (From an ontological point of view, 2003); Armstrong (Truth and truthmakers, 2004); Cameron (Philosophical Studies, 2008)], a theory is committed to the entities needed in the world for the theory to be made true. I argue that this view puts truthmaking to the wrong task. None of the leading accounts of truthmaking—via necessitation, supervenience, or grounding—can provide a viable measure of ontological commitment. But the grounding account does provide a needed constraint on what is fundamental. So I conclude that truthmaker commitments are not a rival to quantifier commitments, but a needed complement. The quantifier commitments are what a theory says exists, while the truthmaker commitments are what a theory says is fundamental.

My aim is to show that theories which try to construct truthmakers out of objects and properties/relations alone are not tenable: The Frege–Wittgenstein idea of incompleteness does not yield truthmakers. Armstrong’s theory of partial identity and the theory of moments, i.e., of non-transferable properties, yield truthmakers, but these theories have counter-intuitive consequences. I conclude that the notion of a truthmaker makes ontological demands beyond objects and properties/relations and propose that truthmakers are exemplification relations which are necessarily tied to objects and properties/relations.

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage.

In this paper I examine the objection to truthmaker theory, forcibly made by David Lewis and endorsed by many, that it violates the Humean denial of necessary connections between distinct existences. In Sect. 1 I present the argument that acceptance of truthmakers commits us to necessary connections. In Sect. 2 I examine Lewis’ ‘Things-qua-truthmakers’ theory which attempts to give truthmakers without such a commitment, and find it wanting. In Sects. 3–5 I discuss various formulations of the denial of necessary connections and argue that each of them is either false or compatible with truthmaker theory. In Sect. 6 I show how the truthmaker theorist can resist the charge that they are committed to necessary exclusions between possible existents. I conclude that there is no good objection to truthmaker theory on the grounds that it violates the Humean dictum.

This bulletin contains a summary of the main topics of discussion in truthmaker theory, namely: the definition of truthmakers, problems with Truthmaker Necessitarianism and Truthmaker Maximalism, the ontological burden of truthmakers and the recalcitrant topic of truthmakers for negative truths.

Discourse carries thin commitment to objects of a certain sort iff it says or implies that there are such objects. It carries a thick commitment to such objects iff an account of what determines truth-values for its sentences say or implies that there are such objects. This paper presents two model-theoretic semantics for mathematical discourse, one reflecting thick commitment to mathematical objects, the other reflecting only a thin commitment to them. According to the latter view, for example, the semantic role of number-words is not designation but rather the encoding of cardinality-quantifiers. I also present some reasons for preferring this view.

Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of the indispensability argument.