Online research in philosophy

In this work Henry Kyburg presents his views on a wide range of philosophical problems associated with the study and practice of science and mathematics. The main structure of the book consists of a presentation of Kyburg's notions of epistemic probability and its use in the scientific enterprise i.e., the effort to modify previously adopted beliefs in the light of experience. Intended for cognitive scientists and people in artificial intelligence as well as for technically oriented philosophers, the book also provides a general overview of the philosophy of science for the non-philosopher by one of the leading authorities in the field.

In this paper I attempt to tie together a longstanding dispute between Henry Kyburg and Isaac Levi concerning statistical inferences. The debate, which centers around the example of Petersen the Swede, concerns Kyburg's and Levi's accounts of randomness and choosing reference classes. I argue that both Kyburg and Levi have missed the real significance of their dispute, that Levi's claim that Kyburg violates Confirmational Conditionalization is insufficient, and that Kyburg has failed to show that Levi's criteria for choosing reference class are problematic. Rather, the significance of the Petersen case is to show that other aspects of their respective systems are defective: for Levi his account of credal judgments other than direct inference, and for Kyburg his explanation of how indexes are associated with a body of knowledge.

The system presented by the author in The Logical Foundations of Statistical Inference (Kyburg 1974) suffered from certain technical difficulties, and from a major practical difficulty; it was hard to be sure, in discussing examples and applications, when you had got hold of the right reference class. The present paper, concerned mainly with the characterization of randomness, resolves the technical difficulties and provides a well structured framework for the choice of a reference class. The definition of randomness that leads to this framework is simplified and clarified in a number of respects. It resolves certain puzzles raised by S. Spielman and W. Harper in their contributions to Profiles: Henry E. Kyburg, Jr. and Isaac Levi (R. Bogdan (ed.) 1982).

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.

At least one of these conceptions of probability underlies any theory of statistical inference (or, to use Neyman's phrase, 'inductive behavior'). ...

Henry Kyburg’s lottery paradox (1961, p. 197) arises from considering a fair 1000 ticket lottery that has exactly one winning ticket. If this much is known about the execution of the lottery it is therefore rational to accept that one ticket will win. Suppose that an event is very likely if the probability of its occurring is greater than 0.99. On these grounds it is presumed rational to accept the proposition that ticket 1 of the lottery will not win. Since the lottery is fair, it is rational to accept that ticket 2 won’t win either—indeed, it is rational to accept for any individual ticket i of the lottery that ticket i will not win. However, accepting that ticket 1 won’t win, accepting that ticket 2 won’t win, . . . , and accepting that ticket 1000 won’t win entails that it is rational to accept that no ticket will win, which entails that it is rational to accept the contradictory proposition that one ticket wins and no ticket wins.