ABSTRACTProbability judgements entail a conjunction fallacy if a conjunction is estimated to be more probable than one of its conjuncts. In the context of predication of alternative logical hypothesis, Bayesian logic provides a formalisation of pattern probabilities that renders a class of pattern-based CFs rational. BL predicts a complete system of other logical inclusion fallacies. A first test of this prediction is investigated here, using transparent tasks with clear set inclusions, varying in observed frequencies only. Experiment 1 uses data where (...) BL makes dominant predictions; Experiment 2's predictions were less clear, and we additionally investigated judgements about the second-most probable hypotheses. The results corroborated a pattern-probability account and cannot be easily explained by other theories of CFs. IFs were not limited to conjunctions, but rather occurred systematically for several logical connectives. Thus, pattern-based prob... (shrink)

The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I call the practical relevance principle. In (...) contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures. (shrink)

It is widely believed that one should not become more confident that all swans are white and all lions are brave simply by observing white swans. Irrelevant conjunction or “tacking” of a theory onto another is often thought problematic for Bayesianism, especially given the ratio measure of confirmation considered here. It is recalled that the irrelevant conjunct is not confirmed at all. Using the ratio measure, the irrelevant conjunction is confirmed to the same degree as the relevant conjunct, which, it (...) is argued, is ideal: the irrelevant conjunct is irrelevant. Because the past’s really having been as it now appears to have been is an irrelevant conjunct, present evidence confirms theories about past events only insofar as irrelevant conjunctions are confirmed. Hence the ideal of not confirming irrelevant conjunctions would imply that historical claims are not confirmed. Confirmation measures partially realizing that ideal make the confirmation of historical claims by present evidence depend strongly on the (presumably subjective) degree of belief in the irrelevant conjunct. The unusually good behavior of the ratio measure has a bearing on the problem of measure sensitivity. For non-statistical hypotheses, Bayes’ theorem yields a fractional linear transformation in the prior probability, not a linear rescaling, so even the ratio measure arguably does not aptly measure confirmation in such cases. (shrink)

“Naturalized epistemology” is a recent attempt to transform the theory of knowledge into a branch of natural science. Traditional epistemologists object to this proposal on the grounds that it eliminates the distinctively philosophical content of epistemology. In this thesis, I argue that traditional philosophers are justified in their reluctance to accept naturalism, but that their ongoing inability to refute it points to deeper problems inherent in traditional epistemology. I establish my thesis first by critiquing three versions of naturalism, showing that (...) each version either fails to implement its objectives consistently or starts from dubious objectives. “Optimistic naturalism” attempts to use naturalistic methods to give positive answers to traditional epistemological questions (such as by affirming that our beliefs can be justified). This fails because the form of traditional questions requires the concept “belief,” a concept that I argue naturalistic methodology cannot countenance (because of the severe constraints of naturalistic semantic theory). “Pessimistic naturalism,” the version advocated by Quine, is more consistent with naturalistic methodology, but fails because hidden behind its conclusions are assumptions (such as the underdetermination thesis) that cannot themselves be naturalized in the full context of scientific evidence. A final attempt to naturalize epistemology, deflationary naturalism, dispenses with traditional questions entirely, urging that the terms “knowledge” and “justification” be taken as mere pragmatic devices whose use can, nevertheless, be studied scientifically. Curiously, this view fails to take account of important facts about the actual use of those terms, as studied by psychologists. In the end, despite problems with each of these versions, traditional philosophers can learn something from their encounter with naturalism. In the course of showing how various naturalistic doctrines cannot themselves be naturalized, I identify the flaws in traditional epistemology (such as its reliance on a priorism, and its resulting inability to articulate a workable empirical foundationalist theory of justification) that make naturalism harder to challenge. These flaws must be corrected if philosophers are to preserve the autonomy of their discipline. (shrink)