The use of probability theory is widespread in our daily life as well as in scientific theories. In virtually all cases, calculations can be carried out within the framework of classical probability theory. A special exception is given by quantum mechanics, which gives rise to a new probability theory: quantum probability theory. This dissertation deals with the question of how this formalism can be understood from a philosophical and physical perspective. The dissertation is divided into three parts. In the first (...) part, the formalism of quantum probability theory and its relation to quantum mechanics is presented. The second part considers the possibility of reformulating quantum probability theory to embed it within classical probability. Mathematically, this possibility overlaps with the possibility of the existence of hidden variables theories of quantum mechanics: theories that attempt to solve fundamental problems in quantum mechanics by introducing additional physical properties of systems. The conclusion of this part is that, although classical reformulations of quantum probability theory are formally possible, they offer little insight into the formalism of quantum probability theory itself. The third part regards a more direct investigation of quantum probability theory. A reformulation of quantum probability theory is obtained by constructing a quantum logic on the basis of empirical non-probabilistic predictions of quantum mechanics. In this reformulation quantum probability functions are conditional probability functions on an algebra of propositions about measurements and measurement outcomes. (shrink)

Whether there exist causal relations between guns firing and people dying, between pedals pressed and cars accelerating, or between carbon dioxide emissions and global warming, is typically taken to be a mind-independent, objective, matter of fact. However, recent contributions to the literature on causation, in particular theories of contrastive causation and causal modelling, have undermined this central causal platitude by relativising causal facts to models or to interests. This thesis flies against the prevailing wind by arguing that we must pay (...) greater attention to which elements of our causal talk vary with context and which elements track genuine features of the world around us. I will argue that once these elements are teased apart we will be in a position to better understand some of the most persistent problems in the philosophy of causation: pre-emption cases, absence causation, failures of transitivity and overdetermination. The result is a naturalist account of causation, concordant with the contextual variability we find in our ordinary causal talk, and parsimonious with respect to the theoretical entities posited. (shrink)

Jonathan Schaffer introduced a new type of causal structure called 'trumping'. According to Schaffer, trumping is a species of causal preemption. Both Schaffer and I have argued that causation has a contrastive structure. In this paper, I analyze the structure of trumping cases from the perspective of contrastive causation, and argue that the case is much more complex than it first appears. Nonetheless, there is little reason to regard trumping as a species of causal preemption.

Much of the philosophical literature on causation has focused on the concept of actual causation, sometimes called token causation. In particular, it is this notion of actual causation that many philosophical theories of causation have attempted to capture.2 In this paper, we address the question: what purpose does this concept serve? As we shall see in the next section, one does not need this concept for purposes of prediction or rational deliberation. What then could the purpose be? We will argue (...) that one can gain an important clue here by looking at the ways in which causal judgments are shaped by people‘s understanding of norms. (shrink)

Questions about the metaphysics of causation may be usefully divided as follows. First, there are questions about the nature of the causal relata, including (1.1) whether they are in spacetime immanence), (1.2) how fine grained they are individuation), and (1.3) how many there are adicity). Second, there are questions about the metaphysics of the causal relation, including (2.1) what is the difference between causally related and causally unrelated sequences connection), (2.2) what is the difference between sequences related as cause to (...) effect, and those related as effect to cause or as joint effects of a common cause direction), and (2.3) what is the difference between sequences involving the cause, and those involving mere conditions selection). (shrink)

The basic idea of counterfactual theories of causation is that the meaning of causal claims can be explained in terms of counterfactual conditionals of the form “If A had not occurred, C would not have occurred”. While counterfactual analyses have been given of type-causal concepts, most counterfactual analyses have focused on singular causal or token-causal claims of the form “event c caused event e”. Analyses of token-causation have become popular in the last thirty years, especially since the development in the (...) 1970's of possible world semantics for counterfactuals. The best known counterfactual analysis of causation is David Lewis's (1973b) theory. However, intense discussion over thirty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of counterfactuals. Recent years have seen a proliferation of different refinements of the basic idea to achieve a closer match with commonsense judgements about causation. (shrink)

“Probabilistic Causation” designates a group of theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes change the probabilities of their effects. This article traces developments in probabilistic causation, including recent developments in causal modeling. A variety of issues within, and objections to, probabilistic theories of causation will also be discussed.

When two rocks shatter the window at once, what causes the window to shatter? Is the throwing of each individual rock a cause of the window shattering, or are the throwings only causes collectively? This question bears on the analysis of causation, and the metaphysics of macro-causation. I argue that the throwing of each individual rock is a cause of the window shattering, and generally that individual overdeterminers are causes.

There are some necessary conditions on causal relations that seem to be so trivial that they do not merit further inquiry. Many philosophers assume that the requirement that there could be no temporal gaps between causes and their effects is such a condition. Bertrand Russell disagrees. In this paper, an in-depth discussion of Russell’s argument against this necessary condition is the centerpiece of an analysis of what is at stake when one accepts or denies that there can be temporal gaps (...) between causes and effects. It is argued that whether one accepts or denies this condition, one is implicated in taking on substantial and wide-ranging philosophical positions. Therefore, it is not a trivial necessary condition of causal relations and it merits further inquiry. (shrink)

Understanding probabilities as something other than point values has often been motivated by the need to find more realistic models for degree of belief, and in particular the idea that degree of belief should have an objective basis in “statistical knowledge of the world.” I offer here another motivation growing out of efforts to understand how chance evolves as a function of time. If the world is “chancy” in that there are non-trivial, objective, physical probabilities at the macro-level, then the (...) chance of an event e that happens at a given time is \ until it happens. But whether the chance of e goes to one continuously or not is left open. Discontinuities in such chance trajectories can have surprising and troubling consequences for probabilistic analyses of causation and accounts of how events occur in time. This, coupled with the compelling evidence for quantum discontinuities in chance’s evolution, gives rise to a “continuity bind” with respect to chance probability trajectories. I argue that a viable option for circumventing the continuity bind is to understand the probabilities “imprecisely,” that is, as intervals rather than point values. I then develop and motivate an alternative kind of continuity appropriate for interval-valued chance probability trajectories. (shrink)

there is a substantial range of C1, C2, … of different not-too- distant alterations of C and a range E1, E2, of alterations of E, at least some of which differ, such that if C1 had occurred, E1 would have occurred, if C2 had occurred, E2 would have occurred and so on (Lewis 2000).

In order to keep matters brief, I shall assume knowledge of my Mind paper and Sungho Choi’s paper printed before this brief response (Noordhof 1999; Choi 2002). Sungho Choi claims that the example I gave to motivate my formulation of the ‘actual events’ clause fails to motivate it and that the formulation, in fact, contains a redundant element, namely my appeal to supersets. I think he is right that my example doesn’t work. However, I think he is wrong that the (...) actual events clause contains a redundant element. The second case he discusses provides the motivation we need. (shrink)

I argue that Lewis's counterfactual theory of causation, given his treatment of counterfactuals in terms of world-comparative similarity faces insuperable problems in the form of the problem of effects and the problem of epiphenomena.

Orthodox physicalism has a problem with mental causation. If physics is complete and mental events are not identical to physical events (as multiple-realisation arguments imply) it seems as though there is no causal work for the mental to do. This paper examines some recent attempts to overcome this problem by analysing causation in terms of counterfactuals or conditional probabilities. It is argued that these solutions cannot simultaneously capture the force of the completeness of physics and make room for mental causation.

Analyses of singular causation often make use of the idea that a cause increases the probability of its effect. Of particular salience in such accounts are the values of the probability function of the effect, conditional on the presence and absence of the putative cause, analysed around the times of the events in question: causes are characterized by the effect’s probability function being greater when conditionalized upon them. Put this way, it becomes clearer that the ‘behaviour’ of probability functions in (...) small intervals about the times in question ought to be of concern. In this article, I make an extended case that causal theorists employing the ‘probability raising’ idea should pay attention to the continuity question. Specifically, if the probability functions are ‘jumping about’ in ways typical of discontinuous functions, then the stability of the relevant probability increase is called into question. The rub, however, is that sweeping requirements for either continuity or discontinuity are problematic and, as I argue, this constitutes a ‘continuity bind’. Hence more subtle considerations and constraints are needed, two of which I consider: utilizing discontinuous first derivatives of continuous probability functions, and abandoning point probability for imprecise probability. _1_ Introduction _2_ Probability Trajectories and Continuity _2.1_ Probability trajectories _2.2_ Causation as discontinuous jumps _2.3_ Against systematic discontinuity _3_ Broader Discontinuity Concerns _4_ The Continuity Bind _4.1_ Retaining continuity with discontinuous first derivatives _4.2_ Imprecise probability trajectories _5_ Concluding Remarks Appendix. (shrink)

Abstract In Causing Actions, Pietroski defends a distinctive view of the relationship between mind and body which he calls Personal Dualism. Central to his defence is the Argument from Differential Vagueness. It moves from the claim that mental events have different vagueness of spatiotemporal boundaries from neural events to the claim that mental events are not identical to neural events. In response, I argue that this presupposes an ontological account of vagueness that there is no reason to believe in this (...) context. I further argue that Pietroski's reasons for rejecting the possibility that mental events are vaguely constituted from neural events are inadequate. I go on to show how Pietroski's Personal Dualism is ill-equipped to deal with the problem of mental causation because of its apparently necessary appeal to ceteris paribus laws. (shrink)