Online research in philosophy

The experimental setup of the self-referential quantum measurement, jovially known as the ‘quantum suicide’ or the ‘quantum Russian roulette’ is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the apparent violation of this principle – relating objective probabilities and subjective chance – in this type of thought experiment is just an illusion due to the usage of some terms and concepts ill-defined in the quantum context. We conclude that even in the case that Everett’s (or some other ‘no-collapse’) theory is a correct description of reality, we can coherently believe in equating subjective credence with objective chance in quantum-mechanical experiments. This is in agreement with results of the research on personal identity in the quantum context by Parfit and Tappenden.

Some have argued that chance and determinism are compatible in order to account for the objectivity of probabilities in theories that are compatible with determinism, like Classical Statistical Mechanics (CSM) and Evolutionary Theory (ET). Contrarily, some have argued that chance and determinism are incompatible, and so such probabilities are subjective. In this paper, I argue that both of these positions are unsatisfactory. I argue that the probabilities of theories like CSM and ET are not chances, but also that they are not subjective probabilities either. Rather, they are a third type of probability, which I call counterfactual probability. The main distinguishing feature of counterfactual-probability is the role it plays in conveying important counterfactual information in explanations. This distinguishes counterfactual probability from chance as a second concept of objective probability.

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.

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.

This paper examines two mistakes regarding David Lewis’ Principal Principle that have appeared in the recent literature. These particular mistakes are worth looking at for several reasons: The thoughts that lead to these mistakes are natural ones, the principles that result from these mistakes are untenable, and these mistakes have led to significant misconceptions regarding the role of admissibility and time. After correcting these mistakes, the paper discusses the correct roles of time and admissibility. With these results in hand, the paper concludes by showing that one way of formulating the chance–credence relation has a distinct advantage over its rivals.

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.

[1] You have a crystal ball. Unfortunately, it’s defective. Rather than predicting the future, it gives you the chances of future events. Is it then of any use? It certainly seems so. You may not know for sure whether the stock market will crash next week; but if you know for sure that it has an 80% chance of crashing, then you should be 80% confident that it will—and you should plan accordingly. More generally, given that the chance of a proposition A is x%, your conditional credence in A should be x%. This is a chance-credence principle: a principle relating chance (objective probability) with credence (subjective probability, degree of belief). Let’s call it the Minimal Principle (MP).

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.

David Lewis's influential work on the epistemology and metaphysics of objective chance has convinced many philosophers of the central importance of the following two claims: First, it is a serious cost of reductionist positions about chance (such as that occupied by Lewis) that they are, apparently, forced to modify the Principal Principle--the central principle relating objective chance to rational subjective probability--in order to avoid contradiction. Second, it is a perhaps more serious cost of the rival non-reductionist position that, unlike reductionism, it can give no coherent explanation for why the Principal Principle should hold. I argue that both of these claims are fundamentally mistaken.