Online research in philosophy

This is the sequel to my "Fifteen Arguments Against Finite Frequentism" (Erkenntnis 1997), the second half of a long paper that attacks the two main forms of frequentism about probability. Hypothetical frequentism asserts: The probability of an attribute A in a reference class B is p iff the limit of the relative frequency of A's among the B's would be p if there were an infinite sequence of B's. I offer fifteen arguments against this analysis. I consider various frequentist responses, which I argue ultimately fail. I end with a positive proposal of my own, 'hyper-hypothetical frequentism', which I argue avoids several of the problems with hypothetical frequentism. It identifies probability with relative frequency in a hyperfinite sequence of trials. However, I argue that this account also fails, and that the prospects for frequentism are dim.

The starting point in the development of probabilistic analyses of token causation has usually been the naïve intuition that, in some relevant sense, a cause raises the probability of its effect. But there are well-known examples both of non-probability-raising causation and of probability-raising non-causation. Sophisticated extant probabilistic analyses treat many such cases correctly, but only at the cost of excluding the possibilities of direct non-probability-raising causation, failures of causal transitivity, action-at-a-distance, prevention, and causation by absence and omission. I show that an examination of the structure of these problem cases suggests a different treatment, one which avoids the costs of extant probabilistic analyses.

In order to comprehend the world around us and construct explaining theories for this purpose, we need a conception of physical probability, since we come across many (apparently) probabilistic phenomena in our world. But how should we understand objective probability claims? Since pure frequency approaches of probability are not appropriate, we have to use a single case propensity interpretation. Unfortunately, many philosophers believe that this understanding of probability is burdened with significant difficulties. My main aim is to show that we can treat propensity as a theoretical concept that exhibits many similarities to other theoretical concepts, and its difficulties are not insuperable if we make explicit some general presuppositions of scientific practice and apply them to propensities. At least this is true if we formulate the right bridge principle for propensity and rely on further methodological rules in dealing with propensity assertions to make them empirically testable.

The aim of this paper is to distinguish between, and examine, three issues surrounding Humphreys's paradox and interpretation of conditional propensities. The first issue involves the controversy over the interpretation of inverse conditional propensities — conditional propensities in which the conditioned event occurs before the conditioning event. The second issue is the consistency of the dispositional nature of the propensity interpretation and the inversion theorems of the probability calculus, where an inversion theorem is any theorem of probability that makes explicit (or implicit) appeal to a conditional probability and its corresponding inverse conditional probability. The third issue concerns the relationship between the notion of stochastic independence which is supported by the propensity interpretation, and various notions of causal independence. In examining each of these issues, it is argued that the dispositional character of the propensity interpretation provides a consistent and useful interpretation of the probability calculus.

A conception of probability as an irreducible feature of the physical world is outlined. Propensity analyses of probability are examined and rejected as both formally and conceptually inadequate. It is argued that probability is a non-dispositional property of trial-types; probabilities are attributed to outcomes as event-types. Brier's Rule in an objectivist guise is used to forge a connection between physical and subjective probabilities. In the light of this connection there are grounds for supposing physical probability to obey some standard set of axioms. However, there is no a priori reason why this should be the case.

The prime concern of this paper is with the nature of probability. It is argued that questions concerning the nature of probability are intimately linked to questions about the nature of time. The case study here concerns the single case propensity interpretation of probability. It is argued that while this interpretation of probability has a natural place in the quantum theory, the metaphysical picture of time to be found in relativity theory is incompatible with such a treatment of probability.

Von Mises thought that an adequate account of objective probability required a condition of randomness. For frequentists, some such condition is needed to rule out those sequences where the relative frequencies converge towards definite limiting values, and where it is nevertheless not appropriate to speak of probability … [because such a sequence] obeys an easily recognizable law (von Mises, Probability, Statistics, and Truth). But is a condition of randomness required for an adequate account of probability, given the existence of decisive arguments against frequentism? To put it another way: is it characteristic of the probability role that probability should have a connection to randomness? I will answer this question in the negative.

Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness (PIF), which defines fitness in terms of a conception of probability known as “propensity”. However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness. First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects. I argue that much of the probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism’s effects. Second, I argue in favor of the view that organism effect propensities either don’t exist or are not part of the basis of fitness, because they usually have values close to 0 or 1. More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed.