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.