With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

Another title in the reissued Oxford Classic Texts in the Physical Sciences series, Jeffrey's Theory of Probability, first published in 1939, was the first to develop a fundamental theory of scientific inference based on the ideas of Bayesian statistics. His ideas were way ahead of their time and it is only in the past ten years that the subject of Bayes' factors has been significantly developed and extended. Until recently the two schools of statistics were distinctly different and set apart. (...) Recent work has changed all that and today's graduate students and researchers all require an understanding of Bayesian ideas. This book is their starting point. (shrink)

The central question of this paper is: are deterministic and indeterministic descriptions observationally equivalent in the sense that they give the same predictions? I tackle this question for measure-theoretic deterministic systems and stochastic processes, both of which are ubiquitous in science. I first show that for many measure-theoretic deterministic systems there is a stochastic process which is observationally equivalent to the deterministic system. Conversely, I show that for all stochastic processes there is a measure-theoretic deterministic system which is observationally equivalent (...) to the stochastic process. Still, one might guess that the measure-theoretic deterministic systems which are observationally equivalent to stochastic processes used in science do not include any deterministic systems used in science. I argue that this is not so because deterministic systems used in science even give rise to Bernoulli processes. Despite this, one might guess that measure-theoretic deterministic systems used in science cannot give the same predictions at every observation level as stochastic processes used in science. By proving results in ergodic theory, I show that also this guess is misguided: there are several deterministic systems used in science which give the same predictions at every observation level as Markov processes. All these results show that measure-theoretic deterministic systems and stochastic processes are observationally equivalent more often than one might perhaps expect. Furthermore, I criticise the claims of the previous philosophy papers Suppes (1993, 1999), Suppes and de Barros (1996) and Winnie (1998) on observational equivalence. (shrink)

Leslie Graves, Barbara Horan and Alex Rosenberg (1999) have argued that the process of evolution is really deterministic, so we should be instrumentalists about our probabilistic evolutionary theory. I criticize the consistency of their view. I argue that because they are realists towards multiple theories (quantum mechanics and macrophysics) their arguments against realism for another scientific theory fail. The main point of this paper is critical, but in order to set up this criticism I explore the ramifications of realism for (...) multiple theories. Finally, I offer a brief metaphysical justification for realism about multiple theories. This view justifies realism for evolutionary theory, which has been defended by Robert Brandon and Scott Carson (1996). (shrink)

Evolutionary theory (ET) is teeming with probabilities. Probabilities exist at all levels: the level of mutation, the level of microevolution, and the level of macroevolution. This uncontroversial claim raises a number of contentious issues. For example, is the evolutionary process (as opposed to the theory) indeterministic, or is it deterministic? Philosophers of biology have taken different sides on this issue. Millstein (1997) has argued that we are not currently able answer this question, and that even scientific realists ought to remain (...) agnostic concerning the determinism or indeterminism of evolutionary processes. If this argument is correct, it suggests that, whatever we take probabilities in ET to be, they must be consistent with either determinism or indeterminism. This raises some interesting philosophical questions: How should we understand the probabilities used in ET? In other words, what is meant by saying that a certain evolutionary change is more or less probable? Which interpretation of probability is the most appropriate for ET? I argue that the probabilities used in ET are objective in a realist sense, if not in an indeterministic sense. Furthermore, there are a number of interpretations of probability that are objective and would be consistent with ET under determinism or indeterminism. However, I argue that evolutionary probabilities are best understood as propensities of population-level kinds. (shrink)

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. (shrink)

I argue that there are non-trivial objective chances (that is, objective chances other than 0 and 1) even in deterministic worlds. The argument is straightforward. I observe that there are probabilistic special scientific laws even in deterministic worlds. These laws project non-trivial probabilities for the events that they concern. And these probabilities play the chance role and so should be regarded as chances as opposed, for example, to epistemic probabilities or credences. The supposition of non-trivial deterministic chances might seem to (...) land us in contradiction. The fundamental laws of deterministic worlds project trivial probabilities for the very same events that are assigned non-trivial probabilities by the special scientific laws. I argue that any appearance of tension is dissolved by recognition of the level-relativity of chances. There is therefore no obstacle to accepting non-trivial chance-role-playing deterministic probabilities as genuine chances. (shrink)

Do the sciences aim to uncover the structure of nature, or are they ultimately a practical means of controlling our environment? In Instrumental Biology, or the Disunity of Science, Alexander Rosenberg argues that while physics and chemistry can develop laws that reveal the structure of natural phenomena, biology is fated to be a practical, instrumental discipline. Because of the complexity produced by natural selection, and because of the limits on human cognition, scientists are prevented from uncovering the basic structure of (...) biological phenomena. Consequently, biology and all of the disciplines that rest upon it--psychology and the other human sciences--must aim at most to provide practical tools for coping with the natural world rather than a complete theoretical understanding of it. (shrink)

Probability and indeterminism have always been core philosophical themes. This paper aims to contribute to understanding probability and indeterminism in biology. To provide the background for the paper, it will first be argued that an omniscient being would not need the probabilities of evolutionary theory to make predictions about biological processes. However, despite this, one can still be a realist about evolutionary theory, and then the probabilities in evolutionary theory refer to real features of the world. This prompts the question (...) of how to interpret biological probabilities which correspond to real features of the world but are in principle dispensable for predictive purposes. This paper will suggest three possible interpretations. The first interpretation is a propensity interpretation of kinds of systems. It will be argued that backward probabilities in biology do not present a problem for this propensity interpretation. The second interpretation is the frequency interpretation. Third, I will suggest Humean chances are a new interpretation of probability in evolutionary theory. Finally, this paper discusses Sansom’s argument that biological processes are indeterministic because probabilities in evolutionary theory refer to real features of the world. It will be argued that Sansom’s argument is not conclusive, and that the question whether biological processes are deterministic or indeterministic is still with us. (shrink)

This chapter unfolds a central philosophical problem of statistical mechanics. This problem lies in a clash between the Static Probabilities offered by statistical mechanics and the Dynamic Probabilities provided by classical or quantum mechanics. The chapter looks at the Boltzmann and Gibbs approaches in statistical mechanics and construes some of the great controversies in the field — for instance the Reversibility Paradox — as instances of this conflict. It furthermore argues that a response to this conflict is a critical choice (...) that shapes one's understanding of statistical mechanics itself, namely, whether it is to be conceived as a special or fundamental science. The chapter details some of the pitfalls of the latter ‘globalist’ position and seeks defensible ground for a kind of ‘localist’ alternative. (shrink)

This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...) on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason's theorem and Conway and Kochen's recent 'free will theorem', are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. (shrink)