If there are exceptions, it is still a rule : a probabilistic understanding of conditionals

Keine Regel ohne Ausnahme? : Ein probabilistischer Ansatz zu Konditionalen

  • Numerous recent publications on the psychological meaning of “if” have proposed a probabilistic interpretation of conditional sentences. According to the proponents of probabilistic approaches, sentences like “If the weather is nice, I will be at the beach tomorrow” (or “If p, then q” in the abstract version) express a high probability of the consequent (being at the beach), given the antecedent (nice weather). When people evaluate conditional sentences, they assumingly do so by deriving the conditional probability P(q|p) using a procedure called the Ramsey test. This is a contradicting view to the hitherto dominant Mental Model Theory (MMT, Johnson-Laird, 1983), that proposes conditional sentences refer to possibilities in the world that are represented in form of mental models. Whereas probabilistic approaches gained a lot of momentum in explaining the interpretation of conditionals, there is still no conclusive probabilistic account of conditional reasoning. This thesis investigates the potential of a comprehensiveNumerous recent publications on the psychological meaning of “if” have proposed a probabilistic interpretation of conditional sentences. According to the proponents of probabilistic approaches, sentences like “If the weather is nice, I will be at the beach tomorrow” (or “If p, then q” in the abstract version) express a high probability of the consequent (being at the beach), given the antecedent (nice weather). When people evaluate conditional sentences, they assumingly do so by deriving the conditional probability P(q|p) using a procedure called the Ramsey test. This is a contradicting view to the hitherto dominant Mental Model Theory (MMT, Johnson-Laird, 1983), that proposes conditional sentences refer to possibilities in the world that are represented in form of mental models. Whereas probabilistic approaches gained a lot of momentum in explaining the interpretation of conditionals, there is still no conclusive probabilistic account of conditional reasoning. This thesis investigates the potential of a comprehensive probabilistic account on conditionals that covers the interpretation of conditionals as well as conclusion drawn from these conditionals when used as a premise in an inference task. The first empirical chapter of this thesis, Chapter 2, implements a further investigation of the interpretation of conditionals. A plain version of the Ramsey test as proposed by Evans and Over (2004) was tested against a similarity sensitive version of the Ramsey test (Oberauer, 2006) in two experiments using variants of the probabilistic truth table task (Experiments 2.1 and 2.2). When it comes to decide whether an instance is relevant for the evaluation of a conditional, similarity seems to play a minor role. Once the decision about relevance is made, believability judgments of the conditional seem to be unaffected by the similarity manipulation and judgments are based on frequency of instances, in the way predicted by the plain Ramsey test. In Chapter 3 contradicting predictions of the probabilistic approaches on conditional reasoning of Verschueren et al (2005), Evans and Over (2004) and Oaksford & Chater (2001) are tested against each other. Results from the probabilistic truth table task modified for inference tasks supports the account of Oaksford and Chater (Experiment 3.1). A learning version of the task and a design with every day conditionals yielded results unpredicted by any of the theories (Experiments 3.2-3.4). Based on these results, a new probabilistic 2-stage model of conditional reasoning is proposed. To preclude claims that the use of the probabilistic truth table task (or variants thereof) favors judgments reflecting conditional probabilities, Chapter 4 combines methodologies used by proponents of the MMT with the probabilistic truth table task. In three Experiments (4.1 -4.3) it could be shown for believability judgments of the conditional and inferences drawn from it, that causal information about counterexamples only prevails, when no frequencies of exceptional cases are present. Experiment 4.4 extends these findings to every day conditionals. A probabilistic estimation process based on frequency information is used to explain results on all tasks. The findings confirm with a probabilistic approach on conditionals and moreover constitute an explanatory challenge for the MMT. In conclusion of all the evidence gathered in this dissertation it seems justified to draw the picture of a comprehensive probabilistic view on conditionals quite optimistically. Probability estimates not only explain the believability people assign to a conditional sentence, they also explain to what extend people are willing to draw conclusions from those sentences.show moreshow less
  • Zahlreiche aktuelle Publikationen über die psychologische Bedeutung der Worte „Wenn - dann“ schlagen eine probabilistische Interpretation von Konditionalen vor. Vertretern dieses probabilistischen Ansatz zufolge drücken Sätze der Form „Wenn das Wetter schön ist, dann bin ich morgen am Strand“ (oder „Wenn p, dann q“ in der abstrakten Version) eine hohe Wahrscheinlichkeit des Konsequenten (am Strand sein), gegeben den Antezedenten (schönes Wetter) aus. Menschen beurteilen demnach Konditionalsätze, indem sie die bedingte Wahrscheinlichkeit P(q|p) mit Hilfe eines Ramsey-Tests abschätzen (Evans & Over, 2004). Diese Sichtweise stellt einen Gegenentwurf zur bisher dominanten Theorie mentaler Modelle (Johnson-Laird, 1983) dar, die davon ausgeht, dass Konditionalsätze Aussagen über Möglichkeiten machen, die in Form mentaler Modelle repräsentiert werden. Obwohl probabilistische Ansätze in den letzten Jahren überzeugende Evidenz für eine probabilistische Interpretation von Konditionalen präsentiert haben, gibt es nochZahlreiche aktuelle Publikationen über die psychologische Bedeutung der Worte „Wenn - dann“ schlagen eine probabilistische Interpretation von Konditionalen vor. Vertretern dieses probabilistischen Ansatz zufolge drücken Sätze der Form „Wenn das Wetter schön ist, dann bin ich morgen am Strand“ (oder „Wenn p, dann q“ in der abstrakten Version) eine hohe Wahrscheinlichkeit des Konsequenten (am Strand sein), gegeben den Antezedenten (schönes Wetter) aus. Menschen beurteilen demnach Konditionalsätze, indem sie die bedingte Wahrscheinlichkeit P(q|p) mit Hilfe eines Ramsey-Tests abschätzen (Evans & Over, 2004). Diese Sichtweise stellt einen Gegenentwurf zur bisher dominanten Theorie mentaler Modelle (Johnson-Laird, 1983) dar, die davon ausgeht, dass Konditionalsätze Aussagen über Möglichkeiten machen, die in Form mentaler Modelle repräsentiert werden. Obwohl probabilistische Ansätze in den letzten Jahren überzeugende Evidenz für eine probabilistische Interpretation von Konditionalen präsentiert haben, gibt es noch keine überzeugende probabilistische Erklärung für konditionales Schließen. Die vorliegende Doktorarbeit leistet einen Beitrag zu einer umfassenden probabilistischen Theorie von Konditionalen, die die Interpretation und die Ziehung von Schlüssen aus Konditionalsätzen umfasst.show moreshow less

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Metadaten
Author:Sonja Maria Geiger
URN:urn:nbn:de:kobv:517-opus-13113
Advisor:Reinhold Kliegl
Document Type:Doctoral Thesis
Language:English
Year of Completion:2007
Publishing Institution:Universität Potsdam
Granting Institution:Universität Potsdam
Date of final exam:2007/04/13
Release Date:2007/04/25
Tag:Konditionalregeln; Logisches Denken; Mentale Modell Theorie; Probabilistische Theorie; Ramsey-Test
Deduction; Ramsey test; conditional reasoning; mental modell theory; probabilistic theory
RVK - Regensburg Classification:ER 940
RVK - Regensburg Classification:CP 4100
RVK - Regensburg Classification:CP 6500
Organizational units:Humanwissenschaftliche Fakultät / Institut für Psychologie
Dewey Decimal Classification:1 Philosophie und Psychologie / 15 Psychologie / 150 Psychologie