Symmetries and Asymmetries in Evidential Support

Several forms of symmetry in degrees of evidential support areconsidered. Some of these symmetries are shown not to hold in general. This has implications for the adequacy of many measures of degree ofevidential support that have been proposed and defended in the philosophical literature.     

Likelihoodism,Bayesianism, and relational confirmation

Likelihoodists and Bayesians seem to have a fundamental disagreement about the proper probabilistic explication of relational (or contrastive) conceptions of evidential support (or confirmation). In this paper, I will survey some recent arguments and results in this area, with an eye toward pinpointing the nexus of the dispute. This will lead, first, to an important shift in the way the debate has been couched, and, second, to an alternative explication of relational support, which is in some sense a “middle way” between Likelihoodism and Bayesianism. In the process, I will propose some new work for an old probability puzzle: the “Monty Hall” problem. Thanks to the participants of the Philosophy, Probability, and Modeling (PPM) Seminar at the University of Konstanz (especially Stephan Hartmann, Franz Huber, Wolfgang Spohn, and Teddy Seidenfeld), for a very fruitful discussion of an early draft of this paper in July, 2004. Since then, discussions and correspondences with Prasanta Bandyopadhyay, Luc Bovens, Alan Hájek, Jim Hawthorne, Jim Joyce, Jon Kvanvig (and other participants of his “Certain Doubts” blog, which had a thread on a previous draft of this paper), Patrick Maher, Sherri Roush, Richard Royall, Elliott Sober, Dan Steel, and an anonymous referee of Synthese has been very valuable.     

Updating: learning versus supposing

Bayesian orthodoxy posits a tight relationship between conditional probability and updating. Namely, the probability of an event A after learning B should equal the conditional probability of A given B prior to learning B. We examine whether ordinary judgment conforms to the orthodox view. In three experiments we found substantial differences between the conditional probability of an event A supposing an event B compared to the probability of A after having learned B. Specifically, supposing B appears to have less impact on the credibility of A than learning that B is true.     

Plantinga's Probability Arguments Against Evolutionary Naturalism

In Chapter 12 of Warrant and Proper Function , Alvin Plantinga constructs two arguments against evolutionary naturalism, which he construes as a conjunction E&N . The hypothesis E says that "human cognitive faculties arose by way of the mechanisms to which contemporary evolutionary thought directs our attention" (p. 220). With respect to proposition N , Plantinga (p. 270) says "it isn't easy to say precisely what naturalism is," but then adds that "crucial to metaphysical naturalism, of course, is the view that there is no such person as the God of traditional theism." Plantinga tries to cast doubt on the conjunction E&N in two ways. His "preliminary argument" aims to show that the conjunction is probably false, given the fact ( R ) that our psychological mechanisms for forming beliefs about the world are generally reliable. His "main argument" aims to show that the conjunction E&N is self-defeating – if you believe E&N , then you should stop believing that conjunction. Plantinga further develops the main argument in his unpublished paper "Naturalism Defeated" (Plantinga 1994). We will try to show that both arguments contain serious errors.     

Finding Missing Proofs with Automated Reasoning

This article features long-sought proofs with intriguing properties (such as the absence of double negation and the avoidance of lemmas that appeared to be indispensable), and it features the automated methods for finding them. The theorems of concern are taken from various areas of logic that include two-valued sentential (or propositional) calculus and infinite-valued sentential calculus. Many of the proofs (in effect) answer questions that had remained open for decades, questions focusing on axiomatic proofs. The approaches we take are of added interest in that all rely heavily on the use of a single program that offers logical reasoning, William McCune's automated reasoning program OTTER. The nature of the successes and approaches suggests that this program offers researchers a valuable automated assistant. This article has three main components. First, in view of the interdisciplinary nature of the audience, we discuss the means for using the program in question (OTTER), which flags, parameters, and lists have which effects, and how the proofs it finds are easily read. Second, because of the variety of proofs that we have found and their significance, we discuss them in a manner that permits comparison with the literature. Among those proofs, we offer a proof shorter than that given by Meredith and Prior in their treatment of ukasiewicz's shortest single axiom for the implicational fragment of two-valued sentential calculus, and we offer a proof for the ukasiewicz 23-letter single axiom for the full calculus. Third, with the intent of producing a fruitful dialogue, we pose questions concerning the properties of proofs and, even more pressing, invite questions similar to those this article answers.