Carl Hoefer

Our beliefs can have, or fail to have, a significant epistemic virtue: they can be true. What about our partial beliefs – that is, credences or subjective probabilities? Is there an epistemic virtue that credences can have or fail to have, whose nature or role with respect to credences is analogous to the role that truth has with respect to full beliefs? Van Fraassen argued in the 1980s that there is indeed such an analog virtue, and he claimed that it is calibration: our credences should match, or be in tune with, some appropriately chosen frequencies of events. For example, if your credence in the proposition ‘It will rain today’ is 0.3 for any day that starts out like today did, and in fact it does rain on approximately 30% of such days, then your credence level is well‐calibrated, and is vindicated by the actual frequency of rain.In an unpublished paper Alan Hájek rejects this calibrationist answer, and proposes instead that having credences in agreement with the relevant objective chances is what it is to have vindicated credences, in the relevant sense analogous to truth for full beliefs. Although there are problems that afflict both van Fraassen's and Hájek's proposals, I will argue that Hájek and the calibrationist are both largely right – although the calibrationist answer is at bottom more right. In section I will propose an account of being in tune with the world that divides types of propositions into a few different classes; for one of those classes, Hájek's answer is exactly right, while for the others the calibrationist account gives the right answer

On the face of it ‘deterministic chance’ is an oxymoron: either an event is chancy or deterministic, but not both. Nevertheless, the world is rife with events that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point. On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin toss it is determined whether it will land heads or tails.2 On the other hand, we commonly assign probabilities to the different outcomes a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics (which is still an important part of modern physics) assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved?

The topics of gravitational field energy and energy-momentum conservation in General Relativity theory have been unjustly neglected by philosophers. If the gravitational field in space free of ordinary matter, as represented by the metric g ab itself, can be said to carry genuine energy and momentum, this is a powerful argument for adopting the substantivalist view of spacetime.This paper explores the standard textbook account of gravitational field energy and argues that (a) so-called stress-energy of the gravitational field is well-defined neither locally nor globally; and (b) there is no general principle of energy-momentum conservation to be found in General Relativity. I discuss the nature and justification of the zero-divergence law for ordinary stress-energy, and its possible connection with the failure of General Relativity to realise Mach's principle.

Since the death of strong reductionism, philosophers of science have expanded the horizons of their understandings of the physical, mental, and social worlds, and the complex relations among them. To give one interesting example, John Dupre has endorsed a notion of downward causation: ‘higher-level’ events causing events at a ‘lower’ ontological level. For example, my intention to type the letter ‘t’ causes the particular motions experienced by all the atoms in my left forefinger as I type it. The proper explanation of the motions of an atom at the tip of my forefinger primarily involves my intentions, rather than the immediately preceding motions of other nearby atoms, or any other such particle–level events.

GRW Theory postulates a stochastic mechanism assuring that every so often the wave function of a quantum system is `hit', which leaves it in a localised state. How are we to interpret the probabilities built into this mechanism? GRW theory is a firmly realist proposal and it is therefore clear that these probabilities are objective probabilities (i.e. chances). A discussion of the major theories of chance leads us to the conclusion that GRW probabilities can be understood only as either single case propensities or Humean objective chances. Although single case propensities have some intuitive appeal in the context of GRW theory, on balance it seems that Humean objective chances are preferable on conceptual grounds because single case propensities suffer from various well know problems such as unlimited frequency tolerance and lack of a rationalisation of the principal principle.

The underdetermination of theory by evidence must be distinguished from holism. The latter is a doctrine about the testing of scientific hypotheses; the former is a thesis about empirically adequate logically incompatible global theories or "systems of the world". The distinction is crucial for an adequate assessment of the underdetermination thesis. The paper shows how some treatments of underdetermination are vitiated by failure to observe this distinction, and identifies some necessary conditions for the existence of multiple empirically equivalent global theories. We consider how empiricists should respond to the possibility of such systems of the world

Much is asked of the concept of chance. It has been thought to play various roles, some in tension with or even incompatible with others. Chance has been characterized negatively, as the absence of causation; yet also positively—the ancient Greek τυχη´ reifies it—as a cause of events that are not governed by laws of nature, or as a feature of the laws themselves. Chance events have been understood epistemically as those whose causes are unknown; yet also objectively as a distinct ontological kind, sometimes called ‘pure’ chance events. Chance gives rise to individual unpredictability and disorder; yet it yields collective predictability and order—stable long-run statistics, and in the limit, aggregate behavior susceptible to precise mathematical theorems. Some authors believe that to posit chances is to abjure explanation; yet others think that chances are themselves explanatory. During the Enlightenment, talk of ‘chance’ was regarded as unscientific, unphilosophical, the stuff of superstition or ignorance; yet today it is often taken to be a fundamental notion of our most successful scientific theory, quantum mechanics, and a central concept of contemporary metaphysics. Chance has both negative and positive associations in daily life. The old word in English for it, hazard, which derives from French and originally from Arabic, still has unwelcome connotations of risk; ‘chance’ evokes uncertainty, uncontrollability, and chaos. Yet chance is also allied with luck, fortune, freedom from constraint, and diversity. And it apparently has various practical uses and benefits. It forms the basis of randomized trials in statistics, and of mixed strategies in decision theory and game theory; it is appealed to in order to resolve problems of fair division and other ethical..

In a now-classic paper, Nancy Cartwright argued that the Humean conception of causation as mere regular co-occurrence is too weak to make sense of our everyday and scientific practices. Specifically she claimed that in order to understand our reasoning about, and uses of, effective strategies, we need a metaphysically stronger notion of causation and causal laws than Humeanism allows. Cartwright’s arguments were formulated in the framework of probabilistic causation, and it is precisely in the domain of (objective) probabilities that I am interested in defending a form of Humeanism. In this paper I will unpack some examples of effective strategies and discuss how well they fit the framework of causal laws and criteria such as CC from Cartwright’s and others’ works on probabilistic causality. As part of this discussion, I will also consider the concept or concepts of objective probability presupposed in these works. I will argue that Cartwright’s notion of a nomological machine, or a mechanism as defined by Stuart Glennan, is better suited for making sense of effective strategies, and therefore that a metaphysically primitive notion of causal law (or singular causation, or capacity, as Cartwright argues in (1989)) is not – here, at least – needed. These conclusions, as well as the concept of objective probabilities I defend, are largely in harmony with claims Cartwright defends in The Dappled World. My discussion aims, thus, to bring out into the open how far Cartwright’s current views are from a radically anti-Humean, causal-fundamentalist picture.

Classical statistical mechanics posits probabilities for various events to occur, and these probabilities seem to be objective chances. This does not seem to sit well with the fact that the theory’s time evolution is deterministic. We argue that the tension between the two is only apparent. We present a theory of Humean objective chance and show that chances thus understood are compatible with underlying determinism and provide an interpretation of the probabilities we find in Boltzmannian statistical mechanics