Online research in philosophy

The conjunction fallacy has been a key topic in debates on the rationality of human reasoning and its limitations. Despite extensive inquiry, however, the attempt of providing a satisfactory account of the phenomenon has proven challenging. Here, we elaborate the suggestion (first discussed by Sides et al., 2001) that in standard conjunction problems the fallacious probability judgments experimentally observed are typically guided by sound assessments of confirmation relations, meant in terms of contemporary Bayesian confirmation theory. Our main formal result is a confirmation-theoretic account of the conjuntion fallacy which is proven robust (i.e., not depending on various alternative ways of measuring degrees of confirmation). The proposed analysis is shown distinct from contentions that the conjunction effect is in fact not a fallacy and is compared with major competing explanations of the phenomenon, including earlier references to a confirmation-theoretic account.

Confirmation is commonly identified with positive relevance, E being said to confirm H if and only if E increases the probability of H. Today, analyses of this general kind are usually Bayesian ones that take the relevant probabilities to be subjective. I argue that these subjective Bayesian analyses are irremediably flawed. In their place I propose a relevance analysis that makes confirmation objective and which, I show, avoids the flaws of the subjective analyses. What I am proposing is in some ways a return to Carnap's conception of confirmation, though there are also important differences between my analysis and his. My analysis includes new accounts of what evidence is and of the indexicality of confirmation claims. Finally, I defend my analysis against Achinstein's criticisms of the relevance concept of confirmation.

The attempt to explicate the intuitive notions of confirmation and inductive support through use of the formal calculus of probability received its canonical formulation in Carnap's The Logical Foundations of Probability. It is a central part of modern Bayesianism as developed recently, for instance, by Paul Horwich and John Earman. Carnap places much emphasis on the identification of confirmation with the notion of probabilistic favorable relevance. Notoriously, the notion of confirmation as probabilistic favorable relevance violates the intuitive transmittability condition that if e confirms h and h' is part of the content of h then e confirms h'. This suggests that, pace Carnap, it cannot capture our intuitive notions of confirmation and inductive support. Without transmittability confirmation losses much of its intrinsic interest. If e, say a report of past observations, can confirm h, say a law-like generalization, without that confirmation being transmitted to those parts of h dealing with the as yet unobserved, then it is not clear why we should be interested in whether h is confirmed or not. The following paper rehearses these difficulties and then proposes a new probabilistic account of confirmation that does not violate the transmittability condition.

Confirmation functions are generally thought of as probability functions. The well known difficulties associated with the probabilistic confirmation functions proposed to date indicate that functions other than probability functions should be investigated for the purpose of developing an adequate basis for confirmation theory. This paper deals with one such function, the likelihood function. First, it is argued here that likelihood is not a probability function. Second, a proof is given that, in the limit, likelihood can be used to determine which of two observationally distinct hypotheses is true. Finally, a demonstration is given that, in the presence of a finite amount of experimental information, likelihood can serve as a good estimator of truth.

This paper attempts to clarify the meaning and significance of "qualitative confirmation". The need to do so is related to the fact that, without such a conceptualization, a large portion of the human sciences are relegated to a less than scientific status. Accordingly, "qualitative confirmation" is viewed as a proper subset of traditional confirmation theory. To establish such a case, a general Hempelian framework is utilized, but it is supplemented with two additional levels of confirmation. It is concluded that the final test for adequacy of such confirmation must rest on a subjective probability notion.