Deducing the Principal Principle

This chapter gives two distinct justifications of the Principal Principle (PP) for Humean objective chances (HOCs). The first justification is “consequentialist” in nature: it shows that in practical decision-making, an agent who has to make bets on repeated chancy events of type A, and who knows the chance of A but has no better information (the scenario of PP), will do better setting her credence equal to the chance of A than she can do with any other, significantly different, betting strategy. The second justification shows that an epistemic agent meeting the conditions for application of PP is irrational—logically incoherent, in fact—if she sets her credence to a level substantially different from the chance. This argument is an adaptation of one originally offered by Colin Howson and Peter Urbach (1993) to justify the PP for von Mises–style hypothetical frequentism. It is shown that the argument works better in support of HOC than it did in support of frequentism.

Chance and Causation

Causality and objective probability are often linked. Some philosophers have tried to characterize objectively chancy setups as incomplete, partial causes of the various possible outcomes the setup may yield. Other philosophers have proposed probabilistic theories of causation, defining a cause c for an effect e as a factor whose presence raises the objective probability of e. Neither of these links is, overall, defensible. Nonetheless, it is clear that there is some link between causation and probability, as is shown with a simple vignette. Analyzing the vignette shows that one should link causation with subjective probability. It is proposed that the strongest general principle that links causation and probability is a Cause-Probability Principle (CPP), which says (roughly) that when an agent learns that a cause c for an effect e has been introduced or put into action, then her subjective probability for the occurrence of e should be at least as high as it was beforehand.

Humean Objective Chance

In this chapter, Humean objective chance (HOC) is laid out and discussed using a number of examples. The theory can be summarized as follows: Chances are constituted by the existence of patterns in the mosaic of events in the world. These patterns are such as to make the adoption of credences identical to the chances rational in the absence of better information, if one is obliged to make guesses or bets concerning the outcomes of chance setups. The full set of objective chances in our world is a Best System composed of many kinds of chances, at various levels of scale and with varying kinds of support in the Humean base. What unifies all the chances is their ability to play the role of guiding credence, as codified in the Principal Principle. The Best System(s) involved in HOC are, as with Lewis, determined by a balance of simplicity and strength and fit; through examples, the right way to understand these notions is sketched. HOC is explicitly pragmatic and is tied to the needs and capacities of limited rational agents.

Macro-Level and Micro-Level Chances

This chapter discusses conceptual problems that may arise if we think of the Best System as giving us two (potentially) different chances for the same macroscopic event: one that arises by mathematical entailment out of chancy microphysics, and a second one that is in the system because it supervenes directly on the pattern of events at the macro level. Given the pragmatic approach of HOC, such dual-chance-value situations could exist, though there are formidable conceptual difficulties about how to derive probabilities for macroscopic event-types from micro-level chance laws. It is argued that if such dual-value situations exist in the Best System, one would have reason to apply PP to the macro-level chance rules, but not to the micro-derived chances. The discussion reveals a heretofore hidden limitation of both HOCs themselves, and the validity of the arguments from chapter 4 justifying PP. But the limitation is of no practical consequence.

Undermining

The problem of undermining is an apparent contradiction that arises when Humean chances and the Principal Principle come together. This chapter gives a full discussion of, and resolution of, the undermining/contradiction problem for Humean chance. First, the problem is laid out and earlier attempts to resolve it are shown to be insufficient. It is then argued that the correct way to overcome the undermining problem is via a revised form of the Lewis-Hall response, which involves making a small amendment to the Principal Principle (PP) itself. The amendment is seen to be simpler and better justified than the one Lewis and Hall suggested. The modified version of the PP can be seen to be essentially identical, in all practical scenarios, to the original PP.

Metaphysical Preliminaries

The book argues that objective chance facts are grounded on the existence of patterns in the events found in our world’s Humean Mosaic (HM); and the chance facts so grounded will later be seen to be apt for guiding rational credences (subjective probabilities) in the way captured by the Principal Principle (PP). But what is this HM? What does it contain, and what does it leave out? What understanding of time is presupposed? The rest of the chapter discusses the idea of considering objective chance facts to be primitives of some sort, as most propensity views hold, or to be based on primitively (irreducibly) chancy laws of nature. After an extended attempt to explore what it could mean to postulate primitive chances or chancy laws, it is argued that no acceptable answer can be given. A tacit invocation of PP helps explain why philosophers often think they understand the meaning of primitive chance claims. The invocation of the PP is illegitimate, though, because there is no way to show that a bare primitive posit deserves to guide credence in the way captured by PP.

Humean Chance in Physics

Some of the most compelling examples of the existence of truly objective probabilities come from physics, in particular quantum physics and statistical mechanics. So it is crucial to the overall success of HOC that it be compatible with the objective probabilities found in these theories. First, objective probabilities in classical (Boltzmannian) statistical mechanics (SM) are discussed. It is shown that HOC does capture the central probabilistic postulates of SM, and indeed that it may do so in two distinct ways. Second, objective probabilities in standard, non-relativistic quantum mechanics (QM), the context in which the notion that fundamental physics is at bottom chancy first became widely accepted, are discussed. It is shown that HOC is especially apt for capturing the probabilities of QM; other accounts may do equally well (though some clearly do not), but none can do the job better.

From Lewisian Chance to Humean Chance

This chapter introduces David Lewis’ highly influential views on objective chance, from his 1980 treatment of objective chance and the Principal Principle (PP) to his 1994 Humean Best System analysis of chance. Some unfortunate consequences of Lewis’ theory are discussed: (1) if the Best System of laws for the world has no probabilistic laws in it, then there are no objective chances in the world. (2) Physical determinism is incompatible with non-trivial objective chances. (3) Events in the past are “no longer chancy.” It is argued that a good account of chance can and should reject all three of these consequences. But two pillars of Lewis’ approach remain valid. First, his contention that the ability to demonstrably play the chance role captured by the PP is crucial for any account of the nature of objective chance. And second, his intuition that a Best System approach in which chance facts supervene on patterns in the Humean Mosaic is a promising approach vis-à-vis allowing such a demonstrable grounding of the PP.