David Liggins

According to a popular ‘explanationist’ argument for moral or mathematical realism the best explanation of some phenomena are moral or mathematical, and this implies the relevant form of realism. One popular way to resist the premiss of such arguments is to hold that any supposed explanation provided by moral or mathematical properties is in fact provided only by the non-moral or non-mathematical grounds of those properties. Many realists have responded to this objection by urging that the explanations provided by the higher-level, moral and mathematical, properties are informative in a way in which their supposed replacements are not, and that this is because moral and mathematical properties are multiply realizable. This chapter responds to this manoeuvre by proposing a way in which moral and mathematical explanations might preserve the distinctive import that multiple realizability brings, without committing those who accept them to the existence of moral and mathematical properties.

Ascriptions of truth give rise to an explanatory asymmetry. For instance, we accept ‘ is true because Rex is barking’ but reject ‘Rex is barking because is true’. Benjamin Schnieder and other philosophers have recently proposed a fresh explanation of this asymmetry : they have suggested that the asymmetry has a conceptual rather than a metaphysical source. The main business of this paper is to assess this proposal, both on its own terms and as an option for deflationists. I offer a pair of objections to the proposal and defend them from counter-objections. To conclude, I discuss how else to explain the asymmetry, and set out the implications for deflationism and correspondence theories of truth.

Do numbers exist? Do properties? Do possible worlds? Do fictional characters? Many metaphysicians spend time and effort trying to answer these and other questions about the existence of various entities. These inquiries have recently encountered opposition: a group of philosophers, drawing inspiration from Aristotle, have argued that many or all of the existence questions debated by metaphysicians can be answered trivially, and so are not worth debating. Our task is to defend existence questions from the neo-Aristotelians' attacks.

Some philosophers deny the existence of composite material objects. Other philosophers 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.

Truthmaker theory promises to do some useful philosophical work: equipping us to argue against phenomenalism and Rylean behaviourism, for instance, and helping us decide what exists (Lewis 1999, 207; Armstrong 1997, 113-119). But it has proved hard to formulate a truthmaker theory that is both useful and believable. I want to suggest that a neglected approach to truthmakers – that of Ian McFetridge – can surmount some of the problems that make other theories of truthmaking unattractive. To begin with, I’ll outline some of the most prominent accounts of truthmaking in the current literature. Then the second part of the paper will explain McFetridge’s theory and argue for its superiority over these accounts.

Restrictionism is a response to the Liar and other paradoxes concerning truth. Restrictionists—as I will call proponents of the strategy—respond to these paradoxes by giving up instances of the schema <p> is true iff p. My aim is to show that the current unpopularity of restrictionism is undeserved. I will argue that, whilst cautious versions of the strategy may face serious problems, a radical and previously overlooked version of restrictionism provides a strong and defensible response to the paradoxes.