Making Ranking Theory Useful for Psychology of Reasoning
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Making Ranking Theory useful for Psychology of Reasoning Niels Skovgaard Olsen Making Ranking Theory useful for Psychology of Reasoning Dissertation zur Erlangung des akademischen Grades Doctor philosophiae (Dr.phil.) an der Geisteswissenschaftliche Sektion Fachbereich Philosophie vorgelegt von Niels Skovgaard Olsen Tag der mündlichen Prüfung: 17. November 2014 Referenten: Prof. Dr. Wolfgang Spohn Prof. Dr. Sieghard Beller Prof. Dr. Thomas Müller Abstract An organizing theme of the dissertation is the issue of how to make philosophical theories useful for scientific purposes. An argument for the contention is presented that it doesn’t suffice merely to theoretically motivate one’s theories, and make them compatible with existing data, but that philosophers having this aim should ideally contribute to identifying unique and hard to vary predictions of their theories. This methodological recommendation is applied to the ranking-theoretic approach to conditionals, which emphasizes the epistemic relevance and the expression of reason relations as part of the semantics of the natural language conditional. As a first step, this approach is theoretically motivated in a comparative discussion of other alternatives in psychology of reasoning, like the suppositional theory of conditionals, and novel approaches to the problems of compositionality and accounting for the objective purport of indicative conditionals are presented. In a second step, a formal model is formulated, which allows us to derive quantitative predictions from the ranking-theoretic approach, and it is investigated which novel avenues of empirical research that this model opens up for. Finally, a treatment is given of the problem of logical omniscience as it concerns the issue of whether ranking theory (and other similar approaches) makes too idealized assumptions about rationality to allow for interesting applications in psychology of reasoning. Building on the work of Robert Brandom, a novel solution to this problem is presented, which both opens up for new perspectives in psychology of reasoning and appears to be capable of satisfying a range of constraints on bridge principles between logic and norms of reasoning, which would otherwise stand in a tension. i Zusammenfassung Ein Leitmotiv dieser Dissertation ist die Fragestellung, wie man philosophische Theorien für empirische Wissenschaften nutzbar machen kann. Es wird ein Argument dafür aufgezeigt, dass es nicht genügt, seine Theorie theoretisch zu motivieren und sie mit bestehenden Befunden kompatibel zu machen, sondern dass man vielmehr dafür Sorge zu tragen hat, dass es möglich ist, Vorhersagen abzuleiten, die schwer zu variieren sind und von den bestehenden Theorien nicht geteilt werden. Diese methodologische Empfehlung wird in Bezug auf den rang-theoretischen Ansatz zu Konditionalsätzen angewendet, welcher die epistemische Relevanz und das Ausdrücken von Gründen in der Semantik von Konditionalsätzen betont. In einem ersten Schritt wird dieser Ansatz gegenüber bestehenden Alternativen, wie etwa der suppositionellen Theorie von Konditionalsätzen, theoretisch motiviert. Dabei wird unter anderem ein neuer Lösungsansatz für das Problem der Kompositionalität und das Problem des objektiven Behauptungs-Charakters indikativer Konditionalsätze angeboten. In einem zweiten Schritt wird ein mathematisches Modell formuliert, das uns erlaubt, quantitative Vorhersagen von dem rang-theoretischen Ansatz abzuleiten und es wird eingehend erörtert, welche neuen empirischen Fragestellungen damit verknüpft sind. Abschließend wird das sogenannte Problem der logischen Omniszienz ausführlich behandelt, da es die Frage aufwirft, ob die Rangtheorie (und ähnliche Ansätze) auf zu idealisierten Rationalitätsannahmen beruht, um für die Psychologie des Denkens attraktiv zu sein. Aufbauend auf der Theorie Robert Brandoms wird dabei ein neuer Lösungsansatz angeboten. Dieser vermag es sowohl, neue Perspektiven für die Psychologie des Denkens zu eröffnen, als auch einer Menge scheinbar widerstreitender Forderungen, die an Brückenprinzipien zwischen Logik und Normen des Denkens gestellt werden, gerecht zu werden. ii Table of Contents Preface ..................................................................................................................................................... vii I On How to make Philosophical Theories useful for Scientific Purposes ............................ 1 1 Introduction ........................................................................................................................................... 2 2 The Uniqueness Constraint ................................................................................................................... 4 3 Hard to Vary Predictions ....................................................................................................................... 7 4 Examples from Psychology of Concepts .............................................................................................. 9 5 Generating Predictions ........................................................................................................................ 18 Appendix 1: Sampling Spaces and Prior Probability Distributions ...................................... 22 II Motivating the Relevance Approach to Conditionals ............................................................... 35 1 Introduction ......................................................................................................................................... 36 1.1 The Horseshoe Analysis ..................................................................................................................... 36 1.2 The Suppositional Theory of Conditionals ........................................................................................... 38 1.3 The Relevance Approach ................................................................................................................... 42 2 The Semantics/Pragmatics Distinction ............................................................................................... 44 2.1 Reason Relations as Part of the Sense Dimension of Meaning ............................................................... 46 2.2 On Semantic Defects ......................................................................................................................... 48 3 Objective Purport and Compositionality ............................................................................................ 53 3.1 The Normative Foundation of Perceived Objective Purport ................................................................. 56 3.2 Comparative Remarks ........................................................................................................................ 59 III Making Ranking Theory Useful for Experimental Psychology ............................................ 69 1 Introduction ......................................................................................................................................... 70 2 Arguments against the Infinitesimal Translation ................................................................................ 70 2.1 Introducing Ranking Theory .............................................................................................................. 70 2.2 Implications for the Probability Scale .................................................................................................. 73 2.3 Ramifications for the Applications of Ranking Theory .......................................................................... 76 iii 2.4 Dilemma ........................................................................................................................................... 78 3 Extending Ranking Theory by Logistic Regression ............................................................................ 79 3.1 Logistic Regression ............................................................................................................................ 80 3.2 Logistic Regression and Ranking Theory ............................................................................................. 82 3.3 The Conditional Inference Task.......................................................................................................... 84 3.4 Introducing Qualitative Constraints on the Free Parameters .................................................................. 92 3.5 Deriving Predictions from the Logistic Regression Model ..................................................................... 93 3.6 The Ramsey Test & the Suppositional Theory of Conditionals .............................................................. 99 Appendix 2: An Alternative Taxonomy of Reason Relations ............................................... 103 IV The Logistic Regression Model and the Dual Source Approach ....................................... 109 1 Introduction ....................................................................................................................................... 110 2 The Dual Source Approach ............................................................................................................... 110 2.1 A Mathematical Implementation ....................................................................................................... 113 2.2 Using the Logistic Regression Model to model the Content Component .............................................. 116 2.2.1 Comparing the Logistic Regression Model