Summary It is maintained that the chance of an event happening is always a physical property of a system, measured by a process of derived measurement involving the two fundamental magaitudes—nuumber of events and number of trials. Chances are not measurable by a process of fundamental measurement. Bat the calculation of chances is analogous to fundamental measurement. It is usually theoretical, and is valuable only in so far as the calculated chances are confirmed by measurement. When a proposition concerns a system characterized by a chance, it may sometimes (but by no means always) be regarded as having a definite probability determined by that chance. The probability of propositions which do not concern systems characterized by chances has nothing to do with chance.
Summary It is maintained that the chance of an event happening is always a physical property of a system, measured by a process of derived measurement involving the two fundamental magaitudes—nuumber of events and number of trials. Chances are not measurable by a process of fundamental measurement. Bat the calculation of chances is analogous to fundamental measurement. It is usually theoretical, and is valuable only in so far as the calculated chances are confirmed by measurement. When a proposition concerns a system characterized by a chance, it may sometimes (but by no means always) be regarded as having a definite probability determined by that chance. The probability of propositions which do not concern systems characterized by chances has nothing to do with chance.
On a very intuitive way of thinking, if it is already determined that some event will happen, then there is no non-trivial chance of it failing to happen, and if it is already determined that some event will not happen, then there is no non-trivial chance of it happening. A different sort of worry that arises for an actual frequentist analysis of deterministic chance is that such an analysis seems unsuited to theories like Boltzmannian statistical mechanics or Bohmian mechanics insofar as those theories are supposed to describe the evolution of the Universe as a whole. It should be clear, then, that there are options available for understanding deterministic chance that are in keeping with several of the leading metaphysical analyses of chance. It is widely accepted that whatever chances are, they are to be contrasted with individual credences . According to classical statistical mechanics, the fundamental laws are Newtonian and thus deterministic.
The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned.I argue that this understanding of chances in quantum mechanics, despite being a part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers.
The chance of a physical event is the objective, single-case probability that it will occur. In probabilistic physical theories like quantum mechanics, the chances of physical events play the formal role that the values of physical quantities play in classical (deterministic) physics, and there is a temptation to regard them on the model of the latter as describing intrinsic properties of the systems to which they are assigned.I argue that this understanding of chances in quantum mechanics, despite being a part of the orthodox interpretation of the theory and the most prevalent view in the physical community, is incompatible with a very wide range of metaphysical views about the nature of chance. The options that remain are unlikely to be attractive to scientists and scientifically minded philosophers.
Abstract The concept of objective probability — chance — has three distinctive features: chances are measured by statistics, but only with high chance, increasing with the number of trials involved; when the chances of the outcomes of a chance process are known, even in the context of a single trial, then one's subjective probabilities — credences — in those outcomes should be set equal to those chances; and finally, chance processes involve uncertainty as to the outcomes of those processes. The second of these features is established for ratios in the squared norms of branches by the Born-rule theorem, proved in Chapter 8. This chapter shows that the first and third hold for those same quantities. All three characteristics of chance thus apply to branching in the Everett interpretation. In consequence, branching processes should be identified with chance processes, and ratios in the squared norms with chances.
The notion of objective probability or chance, as a physical trait of the world, has proved elusive; the identification of chances with actual frequencies does not succeed. An adequate theory of chance should explain not only the connection of chance with statistics, but with degrees of belief, and more broadly the entire phenomenology of (seemingly) chance events and their measurement. Branching structure in the decoherence-based many worlds theory provides an account of what chance is that satisfies all these desiderata, including the requirement that chance involves uncertainty.
Definitions The concept of probability is of considerable importance in optics, as in any situation in which the outcome of a given trial or measurement is uncertain. Under these conditions it is desirable to be able to associate a measure with the likelihood of the outcome or the event in question; such a measure is called the probability of the event. Several different definitions of probability have been adopted at various times in the past. The classical definition is based on an exhaustive enumeration of the possible outcomes of an experiment or trial. If the trial has N distinguishable, mutually exclusive outcomes, which are equally likely to occur, and if n out of these N possible outcomes have an attribute or characteristic that we call ‘success’, then the probability of success in any one trial is given by the ratio n/N . For example, if we roll a die, and if each of the six digits is equally likely to be on top when the die comes to rest, there are N = 6 distinguishable outcomes. If we identify success with an even number, for example, then since there are three different ways in which success can be achieved, it follows that the probability of success when the die is rolled is given by 3/6 = 1/2. Unfortunately, an exhaustive enumeration of all possibilities is not always feasible. Another common definition of probability is based on the notion of relative frequency of success.