When people want to identify the causes of an event, assign credit or blame, or learn from their mistakes, they often reflect on how things could have gone differently. In this kind of reasoning, one considers a counterfactual world in which some events are different from their real-world counterparts and considers what else would have changed. Researchers have recently proposed several probabilistic models that aim to capture how people do (or should) reason about counterfactuals. We present a new model and (...) show that it accounts better for human inferences than several alternative models. Our model builds on the work of Pearl (2000), and extends his approach in a way that accommodates backtracking inferences and that acknowledges the difference between counterfactual interventions and counterfactual observations. We present six new experiments and analyze data from four experiments carried out by Rips (2010), and the results suggest that the new model provides an accurate account of both mean human judgments and the judgments of individuals. (shrink)

The logical interpretation of probability, or "objective Bayesianism'' – the theory that (some) probabilities are strictly logical degrees of partial implication – is defended. The main argument against it is that it requires the assignment of prior probabilities, and that any attempt to determine them by symmetry via a "principle of insufficient reason" inevitably leads to paradox. Three replies are advanced: that priors are imprecise or of little weight, so that disagreement about them does not matter, within limits; that it (...) is possible to distinguish reasonable from unreasonable priors on logical grounds; and that in real cases disagreement about priors can usually be explained by differences in the background information. It is argued also that proponents of alternative conceptions of probability, such as frequentists, Bayesians and Popperians, are unable to avoid committing themselves to the basic principles of logical probability. (shrink)

The relationship between machine learning and the philosophy of science can be classed as a dynamic interaction: a mutually beneficial connection between two autonomous fields that changes direction over time. I discuss the nature of this interaction and give a case study highlighting interactions between research on Bayesian networks in machine learning and research on causality and probability in the philosophy of science.

Donald Gillies is one of the pioneers in the philosophical analysis of artificial intelligence (AI). In his recent book, Gillies (1996) not only makes a new and rapidly developing field of science accessible to philosophers; he also introduces philosophical topics relevant to researchers in AI and thereby helps establish a dialogue between the two disciplines. His book clearly and convincingly demonstrates the fruitful interplay between AI and philosophy of science.

This paper is divided into two parts. In the first part , I will describe briefly how advances in artificial intelligence in the 1970s led to the crucial problem of handling uncertainty, and how attempts to solve this problem led in turn to the emergence of the new theory of Bayesian networks. I will try to focus in this historical account on the key ideas and will not give a full account of the technical details. Then, in the second part (...) , I will consider the implications of these new results for the long-standing controversy between Bayesians and non-Bayesians. (shrink)