David Liggins

Abstract Expressionism and the Communication Problem

Some philosophers have recently suggested that the reason mathematics is useful in science is that it expands our expressive capacities. Of these philosophers, only Stephen Yablo has put forward a detailed account of how mathematics brings this advantage. In this article, I set out Yablo’s view and argue that it is implausible. Then, I introduce a simpler account and show it is a serious rival to Yablo’s. 1 Introduction 2 Yablo’s Expressionism 3 Psychological Objections to Yablo’s Expressionism 4 Introducing Belief Expressionism 5 Objections and Replies   5.1 Yablo’s likely response   5.2 Charity 6 Conclusion 1 Introduction 2 Yablo’s Expressionism 3 Psychological Objections to Yablo’s Expressionism 4 Introducing Belief Expressionism 5 Objections and Replies   5.1 Yablo’s likely response   5.2 Charity   5.1 Yablo’s likely response   5.2 Charity 6 Conclusion

Grounding and the indispensability argument

There has been much discussion of the indispensability argument for the existence of mathematical objects. In this paper I reconsider the debate by using the notion of grounding, or non-causal dependence. First of all, I investigate what proponents of the indispensability argument should say about the grounding of relations between physical objects and mathematical ones. This reveals some resources which nominalists are entitled to use. Making use of these resources, I present a neglected but promising response to the indispensability argument—a liberalized version of Field’s response—and I discuss its significance. I argue that if it succeeds, it provides a new refutation of the indispensability argument; and that, even if it fails, its failure may bolster some of the fictionalist responses to the indispensability argument already under discussion. In addition, I use grounding to reply to a recent challenge to these responses.

Good weasel hunting

The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four avenues for replying to Melia. We will argue that the three replies pursued in the literature so far are unpromising. We will then propose one new reply that is much more powerful, and—in the light of this—advise participants in the debate where to focus their energies.

Is ontological revisionism uncharitable

Abstract Some philosophers (‘nihilists’) deny the existence of composite material objects. Other philosophers (‘universalists’) hold that whenever there are some things, they compose something. The purpose of this paper is to scrutinize an objection to these revisionary views: the objection that nihilism and universalism are both unacceptably uncharitable because each of them implies that a great deal of what we ordinarily believe is false. Our main business is to show how nihilism and universalism can be defended against the objection. A secondary point is that universalism is harder to defend than nihilism.

Agnosticism about Ontology

Let ‘ontological realism’ be the view that ontological issues are intelligible, that they are substantial, and that they are resolvable. Different philosophers use the phrase ‘ontological realism’ in different ways. We use it in a relatively weak, accommodating sense. Some philosophers, such as Ted Sider, use ‘ontological realism’ to designate the view that there is a single most natural quantifier meaning. That is not part of our use of the term. We wish to build into the phrase no more than the above characterization.