David Liggins

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.

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 Introduction2 Yablo’s Expressionism3 Psychological Objections to Yablo’s Expressionism4 Introducing Belief Expressionism5 Objections and Replies5.1 Yablo’s likely response5.2 Charity6 Conclusion

There is a recent and growing trend in philosophy that involves deferring to the claims of certain disciplines outside of philosophy, such as mathematics, the natural sciences, and linguistics. According to this trend— deferentialism, as we will call it—certain disciplines outside of philosophy make claims that have a decisive bearing on philosophical disputes, where those claims are more epistemically justified than any philosophical considerations just because those claims are made by those disciplines. Deferentialists believe that certain longstanding philosophical problems can be swiftly and decisively dispatched by appeal to disciplines other than philosophy. In this paper we will argue that such an attitude of uncritical deference to any non-philosophical discipline is badly misguided. With reference to the work of John Burgess and David Lewis, we consider deference to mathematics. We show that deference to mathematics is implausible and that main arguments for it fail. With reference to the work of Michael Blome-Tillmann, we consider deference to linguistics. We show that his arguments appealing to deference to linguistics are unsuccessful. We then show that naturalism does not entail deferentialism and that naturalistic considerations even motivate some anti-deferentialist views. Finally, we set out deferentialism’s failings and present our own anti-deferentialist approach to philosophical inquiry.

in Robin Le Poidevin (ed.) Being: Developments in Contemporary Metaphysics. Cambridge: Cambridge University Press. Peter van Inwagen claims that there are no tables or chairs. He also claims that sentences such as ‘There are chairs here’, which seem to imply their existence, are often true. This combination of views opens van Inwagen to a charge of self-contradiction. I explain the charge, and van Inwagen’s response to it, which involves the claim that sentences like ‘There are tables’ shift their truth-conditions between different contexts of utterance. I present an alternative response which involves the negation of that claim, and argue that it is preferable to van Inwagen’s.

Thomas Hofweber argues that the thesis of direct reference is incompatible with physicalism, the claim that the nonphysical supervenes on the physical. According to Hofweber, direct reference implies that some physical objects have object-dependent properties, such as being Jones’s brother, which depend on particular objects for their existence and identity. Hofweber contends that if some physical objects have object-dependent properties, then Local-Local Supervenience (the physicalist doctrine on which he concentrates) fails. In this note, we argue that Hofweber has failed to show that the possession by physical objects of object-dependent properties implies the falsity of Local-Local Supervenience.

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.

A pretence theory of a discourse is one which claims that we do not believe or assert the propositions expressed by the sentences we utter when taking part in the discourse: instead, we are speaking from within a pretence. Jason Stanley argues that if a pretence account of a discourse is correct, people with autism should be incapable of successful participation in it; but since people with autism are capable of participiating successfully in the discourses which pretence theorists aim to account for, all these accounts should be rejected. I discuss how pretence theorists can respond, and apply this discussion to two pretence theories, Stephen Yablo's account of arithmetic and Kendall Walton's account of negative existentials. I show how Yablo and Walton can escape Stanley's objection