Niels Skovgaard-Olsen

Ranking Theory and Conditional Reasoning

Ranking theory is a formal epistemology that has been developed in over 600 pages in Spohns recent book The Laws of Belief, which aims to provide a normative account of the dynamics of beliefs that presents an alternative to current probabilistic approaches. It has long been received in the AI community, but it has not yet found application in experimental psychology. The purpose of this paper is to derive clear, quantitative predictions by exploiting a parallel between ranking theory and a statistical model called logistic regression. This approach is illustrated by the development of a model for the conditional inference task using Spohns (2013) ranking theoretic approach to conditionals.

The problem of logical omniscience, the preface paradox, and doxastic commitments

The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case in particular is the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective.

Relevance differently affects the truth, acceptability, and probability evaluations of “and”, “but”, “therefore”, and “if–then”

ABSTRACT In this study, we investigate the influence of reason-relation readings of indicative conditionals and “and”/“but”/“therefore” sentences on various cognitive assessments. According to the Frege–Grice tradition, a dissociation is expected. Specifically, differences in the reason-relation reading of these sentences should affect participants’ evaluations of their acceptability but not of their truth value. In two experiments we tested this assumption by introducing a relevance manipulation into the truth-table task as well as in other tasks assessing the participants’ acceptability and probability evaluations. Across the two experiments, a strong dissociation was found. The reason-relation reading of all four sentences strongly affected their probability and acceptability evaluations, but hardly affected their respective truth evaluations. Implications of this result for recent work on indicative conditionals are discussed.

Bridging Ranking Theory and the Stability Theory of Belief

In this paper we compare Leitgeb’s stability theory of belief (Annals of Pure and Applied Logic, 164:1338-1389, 2013; The Philosophical Review, 123:131-171, [2014]) and Spohn’s ranking-theoretic account of belief (Spohn, 1988, 2012). We discuss the two theories as solutions to the lottery paradox. To compare the two theories, we introduce a novel translation between ranking (mass) functions and probability (mass) functions. We draw some crucial consequences from this translation, in particular a new probabilistic belief notion. Based on this, we explore the logical relation between the two belief theories, showing that models of Leitgeb’s theory correspond to certain models of Spohn’s theory. The reverse is not true (or holds only under special constraints on the parameter of the translation). Finally, we discuss how these results raise new questions in belief theory. In particular, we raise the question whether stability (a key ingredient of Leitgeb’s theory) is rightly thought of as a property pertaining to belief (rather than to knowledge).

Corrigendum to “The relevance effect and conditionals” [Cognition 150 (2016) 26–36]

The authors regret two mistakes in the above mentioned article. Neither of these two errors affects the conclusions in any way. The authors would like to apologize for any inconvenience caused. First, when combining the data from the four different conditions we overlooked that some participants had the same participant id. This led us to erroneously reduce our sample size in several cases by treating data from different participants as coming from the same participant. This error affected all results reported in the paper. All tests are in fact more powerful than reported. After correcting this error (updated manuscripts and analyses scripts are available at: https://osf.io/j4swp/ ) the pattern of significant and non-significant results remained the same with two exceptions. The two exceptions were the follow-up analyses of the relevance by conditional probability interaction for indicatives. The difference between NE and IR at the midpoint and far right end of the scale was now significant, both p = 0.049. In all other cases the pattern stayed the same and the correct p-values were mostly somewhat smaller than reported. In addition, the degrees of freedom reported throughout are too low, but the effect of this on reported parameter estimates is small. Second, instead of a reduced sample of 495 participants we used all 725 participants for our analyses of the pretest (as reported in the supplemental materials). For the full 725 participants the average Delta-p was 0.32 for the positive relevance conditions, −0.27 for the negative relevance conditions, and −0.01 for our irrelevance conditions.