# Mind: April 2010, Vol. 119, No. 474.

There is No Easy Road to Nominalism, MARK COLYVAN

Hartry Field has shown us a way to be nominalists: we must purge our scientific theories of quantification over abstracta and we must prove the appropriate conservativeness results. This is not a path for the faint hearted. Indeed, the substantial technical difficulties facing Field's project have led some to explore other, easier options. Recently, Jody Azzouni, Joseph Melia, and Stephen Yablo have argued (in different ways) that it is a mistake to read ontological commitments simply from what the quantifiers of the best scientific theories range over. This paper argues that all three arguments fail and they fail for much the same reason; would-be nominalists are thus left facing Field's hard road.

What Are Mathematical Coincidences (and Why Does It Matter)? MARC LANGE

Although all mathematical truths are necessary, mathematicians take certain combinations of mathematical truths to be coincidental, accidental, or fortuitous. The notion of a "mathematical coincidence" has so far failed to receive sufficient attention from philosophers. This article argues that a mathematical coincidence is not merely an unforeseen or surprising mathematical result, and that being a misleading combination of mathematical facts is neither necessary nor sufficient for qualifying as a mathematical coincidence. The paper argues that although the components of a mathematical coincidence may possessa common explainer, they have no common explanation; that two mathematical facts have a unified explanation makes their truth noncoincidental. The essay goes on to suggest that any motivation we may have for thinking that there are mathematical coincidences should also motivate us to think that there are mathematical explanations, since the notion of a mathematical coincidence can be understood only in terms of the notion of a mathematical explanation. It further argues that the notion of a mathematical coincidence plays an important role in scientific explanation. When two phenomenological laws of nature are similar, despite concerning physically distinct processes, it may be that any correct scientific explanation of their similarity proceeds by revealing their similarity to be no mathematical coincidence.

The Internal Relatedness of All Things, JONATHAN SCHAFFER

The argument from internal relatedness was one of the major nineteenth century neo-Hegelian arguments for monism. This argument has been misunderstood, and may even be sound. The argument, as this article reconstructs it, proceeds in two stages: first, it is argued that all things are internally related in ways that render them interdependent; second, the substantial unity of the whole universe is inferred from the interdependence of all of its parts. The guiding idea behind the argument is that failure of free recombination is the modal signature of an integrated monistic cosmos.

Presuppositions and Local Contexts, PHILIPPE SCHLENKER

In the last thirty years, the problem of presupposition projection has been taken to provide a decisive argument for a dynamic approach to meaning, one in which expressions are not evaluated with respect to the global context of utterance, but rather with respect to a local context obtained by updating the global one with expressions that occur earlier in the sentence. The computation of local contexts is taken by dynamic analyses to follow from a generalization of the notion of belief update. This article argues that the dynamic approach is faced with a dilemma: in its pragmatic incarnation (Stalnaker), it is explanatory but not general; in its semantic incarnation (Karttunen and Heim), it is general but not explanatory. I suggest that the dilemma stems from a faulty understanding of local contexts, and I offer a new reconstruction of this notion which eschews belief update but offers a general and fully precise solution to the projection problem.

Borderline Hermaphrodites: Higher-order Vagueness by Example, ROY SORENSEN

The Pyrrhonian skeptic Favorinus of Arelata personified indeterminacy, cultivating his borderline status to undermine dogmatism. Inspired by the techniques of Favorinus, this article shows, by example, that "vague" has borderline cases. These concrete steps lead to a more abstract argument that "vague" has borderline borderline cases and borderline borderline borderline cases. My specimens are intended to supplement earlier nonconstructive proofs of the vagueness of "vague."
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