Bayesian probability

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.     

Mechanistic probability

I describe a realist, ontologically objective interpretation of probability, ??far-flung frequency (FFF) mechanistic probability??. FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world. Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities. I also argue that it??s a virtue rather than a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens.     

Pollock on probability in epistemology

In Thinking and Acting John Pollock offers some criticisms of Bayesian epistemology, and he defends an alternative understanding of the role of probability in epistemology. Here, I defend the Bayesian against some of Pollock's criticisms, and I discuss a potential problem for Pollock's alternative account.     

Conceptual fallacies in subjective probability

Subjective probability considered as a logic of partial belief succumbs to three fundamental fallacies. These concern the representation of preference via expectation, the measurability of partial belief, and the normalization of belief.     

Response force in RT tasks: Isolating effects of stimulus probability and response probability

Mattes, UIrich, and Miller (1997) found that as response probability decreases in a simple reaction time (RT) task, participants produce more forceful responses as well as longer RTs, suggesting a direct influence of preparatory processes on the motor system. In this previous study, however, response probability was confounded with stimulus probability, leaving open the possibility that response force was sensitive to stimulus- rather than response-related preparation. The present study was conducted to unravel the effects of stimulus and response probability. Experiment 1 manipulated stimulus probability and revealed that responses to a more probable stimulus are less forceful than responses to a less probable stimulus even when both stimuli require the same response. Experiment 2 demonstrated that this stimulus probability effect does not depend on the overall level of response probability. Experiment 3 showed an analogous effect for response probability when stimulus probability is kept constant. The complete pattern of results suggests that both stimulus probability and response probability affect the forcefulness of a response. It is argued that response probability exerts adirect influence on the motor system, whereas stimulus probability influences the motor system indirectly via premotoric adjustments.     

Possibility and probability

Conclusion De Finetti was a strong proponent of allowing 0 credal probabilities to be assigned to serious possibilities. I have sought to show that (pace Shimony) strict coherence can be obeyed provided that its scope of applicability is restricted to partitions into states generated by finitely many ultimate payoffs. When countable additivity is obeyed, a restricted version of ISC can be applied to partitions generated by countably many ultimate payoffs. Once this is appreciated, perhaps the compelling character of the Shimony argument will be less overwhelming and the attractiveness of de Finetti's more permissive attitude will become more apparent.I want to push the permissive tendency in de Finetti still further. It seems doubtful that RUIWC should be required as de Finetti apparently suggested. It is also excessively dogmatic and restrictive to require that the credal states of ideally situated rational agents be numerically definite (Levi 1974, 1980). And de Finetti's rejection of objectivism in statistics overreached itself when he dismissed objective probabilities as meaningless metaphysical artefacts (Levi 1986). In this respect, the philosophically most important lessons de Finetti has to teach us are to be found not in his celebrated representation theorem but in his discussions of the relations between 0-probability and possibility, conditional probability and countable additivity. Perhaps, the technical issues involved are remote and pedantic. But the attitude de Finetti sought to inculcate is of profound importance.Thanks are due to Teddy Seidenfeld whose comments have improved this paper substantially. He is not to blame for its lingering defects.     

Epistemology and probability

Probability is sometimes regarded as a universal panacea for epistemology. It has been supposed that the rationality of belief is almost entirely a matter of probabilities. Unfortunately, those philosophers who have thought about this most extensively have tended to be probability theorists first, and epistemologists only secondarily. In my estimation, this has tended to make them insensitive to the complexities exhibited by epistemic justification. In this paper I propose to turn the tables. I begin by laying out some rather simple and uncontroversial features of the structure of epistemic justification, and then go on to ask what we can conclude about the connection between epistemology and probability in the light of those features. My conclusion is that probability plays no central role in epistemology. This is not to say that probability plays no role at all. In the course of the investigation, I defend a pair of probabilistic acceptance rules which enable us, under some circumstances, to arrive at justified belief on the basis of high probability. But these rules are of quite limited scope. The effect of there being such rules is merely that probability provides one source for justified belief, on a par with perception, memory, etc. There is no way probability can provide a universal cure for all our epistemological ills.     

Indefinite probability statements

Conclusion Indefinite probability statements can be analysed in terms of statements which attribute probability to propositions. Therefore, there is no need to find a special place in probability theory for them; once we have an adequate account of statements that straightforwardly attribute probability to propositions, we will automatically have an adequate account of indefinite probability statements.