Towards a Flexible Bayesian and Deontic Logic of Testing Descriptive and Prescriptive Rules Explaining Content Effects in the Wason Selection Task Dissertation zur Erlangung des Doktorgrades der Mathematisch-Naturwissenschaftlichen Fakultäten der Georg-August-Universität Göttingen vorgelegt von Dr. Momme von Sydow (PhD) aus Konstanz am Bodensee Göttingen, 2006 D 7 Referent: Professor Dr. Michael R. Waldmann Korreferentin: Professorin Dr. Margarete Boos Tag der mündlichen Prüfung: 4. Mai 2006 „Cum deus calculat et cogitationem exercet, fit mundus“ (When God calculates and develops thought, he creates the world) G. W. Leibniz, 1765 [1996, 25] The Wason Selection Task is „probably the most intensive studied task in the psychology of reasoning […], which has raised more doubts over human rationality than any other psychological task“ M. Oaksford and N. Chater, 1998, 173, 174 The copyright of this thesis rests with the author. (c) Momme v. Sydow, Göttingen, 2006 Abstract v Abstract Research on the Wason selection task (WST) has raised fundamental doubts about the rationality of human hypothesis testing and added to the development of both domain-specific and domain-general theories of reasoning. This work proposes a rational but domain-specific synthesis aimed at integrating converging lines of research in the WST debate. For this synthesis two realms are distinguished, that of testing descriptive rules (hypotheses) and that of testing prescriptive rules (prescripts). For both realms, accounts are proposed that have normative aspects, but also domain- specific aspects. For the testing of descriptive hypotheses, a flexible Bayesian logic is developed, which is opposed to the falsificationist research program and builds on previous Bayesian accounts (on Oaksford and Chater, 1994, 2003, in particular). However, instead of advocating a universal Bayesian model a knowledge-based account is pur- sued which may explain the negative results of previous experiments. Additionally, the Bayesian treatment of conditionals is extended to other logical connectors. For the testing of conditional prescripts, a flexible deontic logic is proposed which draws more fully on the deontic logic of prohibitions, obligations and permissions than previous accounts. Moreover, this is combined with a goal-based, but systematic, mechanism of cooperator and cheater detection. Twelve experiments largely support the predictions of the proposed account. In two experiments the different strategies for testing descriptive or prescriptive rules were investigated. In seven experiments, positive support for the Bayesian account was obtained by actively introducing the preconditions of the models. Additionally, different Bayesian models of a conditional were distinguished and first evidence for a Bayesian logic of different connectors was obtained. In three experiments, the deontic logic of checking prescripts and its interaction with the goals of cheater or cooperator detection (including double foci) was investigated. The results cannot be explained by other current theories of the selection task, such as mental model theory, social contract theory, or pragmatic resoning theory, but do at least necessitate substantial extensions of these theories. In contrast, the results support the flexible Bayesian and deontic logic of testing descriptive and prescriptive rules. Kurzreferat vi Kurzreferat Die Wasonsche Informationswahlaufgabe (WST) ließ fundamentale Zweifel an der Rationalität menschlichen Hypothesentestens aufkommen und inspirierte die Ent- wicklung sowohl domänenspezifischer als auch domänenübergreifender Theorien des Denkens. In dieser Arbeit wird ein Synthesevorschlag entwickelt, der auf der einen Seite domänenspezifisch ist, auf der anderen Seite aber einen rationalen Ansatz darstellt. Um Anomalien in der WST-Debatte erklären zu können, wird dabei zwischen dem Prüfen deskriptiver und präskriptiver Aussagen unterschieden. Für das Prüfen deskriptiver Aussagen wird eine flexible Bayessche Logik entwickelt, die im Gegensatz zum falsifikationistischen Forschungsprogramm steht und auf vorangehende bayessche Ansätze (insbesondere auf Oaksford und Chater, 1994, 2003) aufbaut. Statt eines universellen Bayesschen Ansatzes wird ein wissensbasierter Ansatz vertreten, der die negativen Resultate früherer Forschung erklären könnte. Zudem wird der Bayessche Ansatz von Konditionalen auf andere logische Junktoren übertragen. Für die Testung präskriptiver Konditionalaussagen wird eine flexible deontische Logik vorgeschlagen. Diese umfaßt eine deontischen Logik von Verpflichtungen, Erlaubnissen und auch Verboten, die mit einem zielabhängigen, aber systematischen, Mechanismus der Cheater- und Cooperator-Detection kombiniert wird. In zwölf Experimenten konnten die meisten Vorhersagen des Ansatzes bestätigt werden. In zwei Experimenten wurde der Unterschied des Prüfens deskriptiver und präskriptiver Aussagen untersucht. In sieben Experimenten konnte der Bayessche Ansatz bestätigt werden, indem die Modellvoraussetzungen in der Instruktion absichtlich induziert wurden. Zudem wurden erste Evidenzen für unterschiedliche Effekte verschiedener Bayesianischer Modelle und für eine Bayessche Logik des Hypothesentestens vorgelegt. In drei Experimenten wurde die deontische Logik präskriptiver Aussagen und ihre Interaktion mit den Zielen Cheater oder Cooperator Detection (auch mit Doppelfokus) untersucht. Die Ergebnisse können nicht von anderen Theorien des WST (wie der Mental Model Theorie, der Social Contract Theory oder der Pragmatic Reasoning Schema Theorie) erklärt werden, sondern machen zumindest deren Erweiterung notwendig. Die Ergebnisse stützen den hier vertretenen Ansatz einer flexiblen bayesschen und deontischen Logik des Testens deskriptiver und präskriptiver Aussagen. Table of Contents vii Table of Contents 0 Introduction............................................................................................................1 PART I WASON SELECTION TASK AND THEORIES OF HYPOTHESIS TESTING....................................................................................................3 1 The Wason Selection Task and the Falsificationist Logic of Hypothesis Testing.....................................................................................................................3 1.1 The Structure of the Wason Selection Task....................................................3 1.2 The Traditional Solution for the WST: Formal Logic and Falsificationism .5 The Logical Interpretation of Hypotheses..........................................................................5 The Falsificationist Norm of Testing If-Then Hypotheses.................................................6 1.3 Early Results and Doubts Over Human Rationality – The Two Anomalies of the WST ..........................................................................................................7 The First Anomaly: The Predominance of Confirmatory Selection Patterns .....................8 The Second Anomaly: Content Effects ..............................................................................9 2 The Main Psychological Theories of the WST: A Normative or a Domain- specific Approach?...............................................................................................10 2.1 Mental Logic Theory ....................................................................................10 2.2 Mental Model Theory ...................................................................................11 2.3 Pragmatic Reasoning Schema Theory ..........................................................13 2.4 Social Contract Theory .................................................................................14 2.5 Relevance Theory .........................................................................................17 2.6 A Remark on the Research Agenda of Part II and Part III ...........................18 PART II TOWARDS A FLEXIBLE BAYESIAN LOGIC OF TESTING DESCRIPTIVE RULES..........................................................................19 3 Philosophical Considerations: The Problem of Induction and a Knowledge- Based Bayesian Account......................................................................................21 3.1 The Fundamental Problem of Induction .......................................................22 The Notion of Induction...................................................................................................22 Hume’s Fundamental Problem of Induction ....................................................................23 Falsificationism as Proposal to Solve the Problem of Induction......................................26 Falsificationism Falsified? – The Fundamental Problem of Falsification........................27 Criticism of Falsificationism Restricting its Domain of Applicability ......................27 The Fundamental Problem of Falsification................................................................28 Broad’s Contribution........................................................................................................31 The Probabilistic Nature of Induction........................................................................31 Table of Contents viii The Unresolved Problem of the Assumed Uniformity of Nature...............................31 Discussion of Broad’s Essentialist Solution of the Problem......................................32 Synduction – Knowledge and Induction ..........................................................................32