According to a widespread view in metaphysics and philosophy of science (the “Dependence Thesis”), all explanations involve relations of ontic dependence between the items appearing in the explanandum and the items appearing in the explanans. I argue that a family of mathematical cases, which I call “viewing-as explanations”, are incompatible with the Dependence Thesis. These cases, I claim, feature genuine explanations that aren’t supported by ontic dependence relations. Hence the thesis isn’t true in general. The first part of the paper (...) defends this claim and discusses its significance. I argue, for example, that many mathematical explanations are apparently compatible with Dependence, so the existence of counterexamples is interesting and non-obvious. The second part of the paper considers whether viewing-as explanations occur in the empirical sciences, focusing on the case of so-called fictional models (such as Bohr’s model of the atom). It’s sometimes suggested that fictional models can be explanatory even though they fail to represent actual worldly dependence relations. Whether or not such models explain, I suggest, depends on whether we think scientific explanations necessarily give information relevant to intervention and control. (shrink)

Abstract This article examines the little-explored remarks on verification in Wittgenstein's notebooks during the period between 1930 and 1932. In these remarks, Wittgenstein connects a verificationist theory of meaning with the notion of logical multiplicity, understood as a space of possibilities: a proposition is verified by a fact if and only if the proposition and the fact have the same logical multiplicity. But while in his early philosophy logical multiplicities were analysed as an outcome of the formal properties of simple (...) objects and simple signs, Wittgenstein in the early 1930s connects the notion of logical multiplicity with the notion of ways of seeing. I will argue that the relevant ways of seeing are closely similar to seeing-as or aspect seeing. According to Wittgenstein's view in the early 1930s, logical multiplicities are part of our perceptual experience of propositions and facts. In this sense, the verification relation depends on how we experience propositions and facts as being surrounded by a logical space of possibilities. Strikingly, Wittgenstein's way of thinking about the verification relation offers solutions to a set of seemingly intractable problems connected with the versions of verificationism developed by members of the Vienna Circle. (shrink)