Consider the following causal exclusion principle: For all distinct properties F and F* such that F* supervenes on F, F and F* do not both cause a property G. Peter Menzies and Christian List have proven that it follows from a natural conception of causation as difference-making that this exclusion principle is not generally true. Rather, it turns out that whether the principle is true is a contingent matter. In addition, they have shown that in a wide range of empirically (...) ordinary cases, it follows that F* causes G and F does not. These cases plausibly include instances where F* is a mental property and F and G are physical properties. If this is the right conception of causation, it therefore turns out that the physical world is not causally closed. In this paper I show that there is an alternative conception of causation as difference-making that does not have the same consequences. Whether the physical world is causally closed therefore turns out to depend, inter alia, on which conception of difference-making is correct. I give a number of arguments for the alternative conception of difference-making. (shrink)

Causal theories of action, perception and knowledge are each beset by problems of so-called ‘deviant’ causal chains. For each such theory, counterexamples are formed using odd or co-incidental causal chains to establish that the theory is committed to unpalatable claims about some intentional action, about a case of veridical perception or about the acquisition of genuine knowledge. In this paper I will argue that three well-known examples of a deviant causal chain have something in common: they each violate Yablos proportionality (...) constraint on causation. I will argue that this constraint provides the key to saving causal theories from deviant chains. (shrink)

If counterfactual dependence is sufficient for causation and if omissions can be causes, then all events have many more causes than common sense tends to recognize. This problem is standardly addressed by appeal to pragmatics. However, Carolina Sartorio [2010] has recently raised what I shall argue is a more interesting problem concerning omissions for counterfactual theories of causation—more interesting because it demands a more subtle pragmatic solution. I discuss the relationship between the idea that causes are proportional to their effects, (...) the idea that causation is contrastive, and the question of the dimensions along which causal explanations should be evaluated with respect to one another. (shrink)

A cause is proportional to its effect when, roughly speaking, it is at the right level of detail. There is a lively debate about whether proportionality is a necessary condition for causation. One of the main arguments against a proportionality constraint on causation is that many ordinary and seemingly perfectly acceptable causal claims cite causes that are not proportional to their effects. In this paper, I suggest that proponents of a proportionality constraint can respond to this objection by developing an (...) idea that is present in Yablo’s early work on proportionality, but which has strangely been ignored by both Yablo and others in the subsequent debate. My suggestion is that proportionality—and, indeed, causation itself—is relative to a domain of events. At the metaphysical level, this means that the causal relation has an extra relatum—namely, a domain of events. At the level of language, it introduces a new way in which causal claims are context-sensitive: what is expressed by a causal claim depends on the contextually relevant domain of events. As I argue, this suggestion allows us to accommodate the truth of ordinary causal claims while extending the explanatory benefits of a proportionality constraint. (shrink)

This paper critically examines Timothy Williamson’s claim that knowledge figures essentially in explanations of behavior. Since this claim implies that knowledge is causally efficacious in bringing about actions, it plays a key role in Williamson’s case for knowledge being a mental state. I first discuss a central example of Williamson, in which a burglar ransacks a house. I dispute Williamson’s claim that the best explanation of the burglar’s behavior invokes the burglar’s state of knowledge as he enters the house, by (...) arguing that there is a better explanation that only mentions the burglar’s beliefs. Since the reasons that explain the superiority of my proposed explanation generalize, I conclude that one does not have to invoke a subject’s state of knowledge to explain behavior. Nevertheless, Williamson’s explanation is superior to belief-based explanations if one only considers facts that obtain before the action takes place. In the final part of the paper, I argue that this fact does not help Williamson’s case for considering knowledge as a mental state. (shrink)

In a previous paper, an elementary and thoroughly arithmetical proof of Fermat’s last theorem by induction has been demonstrated if the case for “n = 3” is granted as proved only arithmetically (which is a fact a long time ago), furthermore in a way accessible to Fermat himself though without being absolutely and precisely correct. The present paper elucidates the contemporary mathematical background, from which an inductive proof of FLT can be inferred since its proof for the case for “n (...) = 3” has been known for a long time. It needs “Hilbert mathematics”, which is inherently complete unlike the usual “Gödel mathematics”, and based on “Hilbert arithmetic” to generalize Peano arithmetic in a way to unify it with the qubit Hilbert space of quantum information. An “epoché to infinity” (similar to Husserl’s “epoché to reality”) is necessary to map Hilbert arithmetic into Peano arithmetic in order to be relevant to Fermat’s age. Furthermore, the two linked semigroups originating from addition and multiplication and from the Peano axioms in the final analysis can be postulated algebraically as independent of each other in a “Hamilton” modification of arithmetic supposedly equivalent to Peano arithmetic. The inductive proof of FLT can be deduced absolutely precisely in that Hamilton arithmetic and the pransfered as a corollary in the standard Peano arithmetic furthermore in a way accessible in Fermat’s epoch and thus, to himself in principle. A future, second part of the paper is outlined, getting directed to an eventual proof of the case “n=3” based on the qubit Hilbert space and the Kochen-Specker theorem inferable from it. (shrink)

I present a problem for theories of explanation, concerning explanations involving disjunctive properties. The problem is particular acute for the explanatory non-fundamentalist, according to whom non-fundamental scientific explanations are sometimes superior to fundamental physical explanations. I criticise solutions to the problem due to Woodward, Strevens and Sober, and Lewis, and then defend a solution inspired by an account of non-fundamental laws recently defended by Callender and Cohen.