Online research in philosophy

The goal of this paper is to sketch and defend a new interpretation or theory of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The subtitle obviously emulates the title of Lewis seminal 1980 paper A Subjectivist s Guide to Objective Chance while indicating an important difference in perspective. The view developed below shares two major tenets with Lewis last (1994) account of objective chance: (1) The Principal Principle tells us most of what we know about objective chance; (2) Objective chances are not primitive modal facts, propensities, or powers, but rather facts entailed by the overall pattern of events and processes in the actual world. But it differs from Lewis’ account in most other respects. Another subtitle I considered was A Humean Guide ... But while the account of chance below is compatible with any stripe of Humeanism (Lewis , Hume s, and others ), it presupposes no general Humean philosophy. Only a skeptical attitude about probability itself is presupposed (as in point (2) above); what we should say about causality, laws, modality and so on is left a separate question. Still, I will label the account to be developed “Humean objective chance”.

one's subjective probability for a proposition should conform to one's beliefs about that proposition's objective chance of coming true. David Lewis has argued (i) that this principle provides the defining role for chance; (ii) that it conflicts with his reductionist thesis of Humean supervenience, and so must be replaced by an amended version that avoids the conflict; hence (iii) that nothing perfectly deserves the name ‘chance’, although something can come close enough by playing the role picked out by the amended principle. We show that in fact there must be ‘chances’ that perfectly play what Lewis takes to be the defining role. But this is not the happy conclusion it might seem, since these ‘chances’ behave too strangely to deserve the name. The lesson is simple: much more than the Principal Principle—more to the point, much more than the connection between chance and credence—informs our understanding of objective chance. 1 Introduction 2 Preliminaries 3 Undermining futures and the New Principle 4 The Old Principle rescued? 5 The New Bug 6 Conclusion.

Lewis’ Principal Principle (PP) aims at clarifying the connection between chance (i.e. objective probability) and credence (i.e. subjective probability). It is generally assumed that the chance that an event will occur does not depend on our credence in the occurrence of that event. Nevertheless, chances constrain our credence, and Lewis’ PP is an attempt to capture this connection.

There are at least three core principles that define the chance role: (1) the Principal Principle, (2) the Basic Chance Principle, and (3) the Humean Principle. These principles seem mutually incompatible. At least, no extant account of chance meets more than one of them. I offer an account of chance which meets all three: L*-chance. So the good news is that L*-chance meets (1)–(3). The bad news is that L*-chance turns out unlawful and unstable.

The goal of this paper is to sketch and defend a new interpretation or 'theory' of objective chance, one that lets us be sure such chances exist and shows how they can play the roles we traditionally grant them. The account is 'Humean' in claiming that objective chances supervene on the totality of actual events, but does not imply or presuppose a Humean approach to other metaphysical issues such as laws or causation. Like Lewis (1994) I take the Principal Principle (PP) to be the key to understanding objective chance. After describing the main features of Humean objective chance (HOC), I deduce the validity of PP for Humean chances, and end by exploring the limitations of Humean chance.

Any adequate theory of chance must accommodate some version of David Lewis's ‘Principal Principle’, and Lewis has argued forcibly that believers in primitive propensities have a problem in explaining what makes the Principle true. But Lewis can only derive (a revised version of) the Principle from his own Humean theory by putting constraints on inductive rationality which cannot be given a Humean rationale.

A chance-credence norm states how an agent's credences in propositions concerning objective chances ought to relate to her credences in other propositions. The most famous such norm is the Principal Principle (PP), due to David Lewis. However, Lewis noticed that PP is inconsistent with many accounts of chance that attempt to reduce chance facts to non-modal facts. Those who defend such accounts of chance have offered two alternative chance-credence norms, both of which are consistent with reductionism about chance: the first is the New Principle (NP), formulated by Ned Hall and Michael Thau and grudgingly accepted by Lewis; and the second is Jenann Ismael's General Recipe (IP). However, while NP and IP are each consistent with the sort of reductionism that conflicts with PP, they are incompatible with one another. Thus, the question arises: Which should the reductionist favour? In this paper, I argue that the consequences of IP when coupled with a reductionist account are unacceptable, so we must accept NP. I conclude by considering two responses to my arguments.

Machine generated contents note: 1. The concept of chance; 2. The classical picture; 3. Ways the world might be; 4. Possibilities of thought; 5. Chance in phase space; 6. Possibilist theories of chance; 7. Actualist theories of chance; 8. Anti-realist theories of chance; 9. Chance in quantum physics; 10. Chance in branching worlds; 11. Time and evidence; 12. Debunking chance.

There’s a long history of discussion of probability in philosophy, but objective chance separated itself off and came into its own as a topic with the advent of a physical theory - quantum mechanics - in which chances play a central, and apparently ineliminable, role. In 1980 David Lewis wrote a paper pointing out that a very broad class of accounts of the nature of chance apparently lead to a contradiction when combined with a principle that expresses the role of chance in guiding belief. There is still no settled agreement on the proper response to the Lewis problem. At the time he wrote the article, Lewis despaired of a solution, but, although he never achieved one that satisfied him completely, by 1994, due to work primarily by Thau and Hall, he had come to think the problem could be disarmed if we fudged a little on the meaning of ‘chance’. I’ll say more about this below. What I’m going to suggest, however, is that the qualification is unnecessary. The problem depends on an assumption that should be rejected, viz., that using information about chance to guide credence requires one to conditionalize on the theory of chance that one is using. I’m going to propose a general recipe for using information about chance to guide belief that does not require conditionalization on a theory of chance at any stage. Lewis’ problem doesn’t arise in this setting.

The most important theories in fundamental physics, quantum mechanics and statistical mechanics, posit objective probabilities or chances. As important as chance is there is little agreement about what it is. The usual “interpretations of probability” give very different accounts of chance and there is disagreement concerning which, if any, is capable of accounting for its role in physics. David Lewis has contributed enormously to improving this situation. In his classic paper “A Subjectivist's Guide to Objective Chance” he described a framework for representing single case objective chances, showed how they are connected to subjective credences, and sketched a novel account what they are within his Humean account of scientific laws. Here I will describe these contributions and add a little to them.