Coherence and p-validity : Deduction from uncertain premises

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Table of contents

Part 1. Introduction
Chapter 1. Introduction
1.1 Types of reasoning
1.2 Types of statements
1.3 Research questions
1.4 Outline of the thesis
Part 2. Theoretical background
Chapter 2. Binary theories of reasoning and their accounts of conditionals
2.1 Classical logic
2.2 The material conditional
2.3 The truth conditions of the material conditional plus conditions of assertability: Grice and Jackson
2.3.1 Grice
2.3.2 Jackson
2.4 Possible world semantics: Stalnaker and Lewis
2.4.1 Stalnaker
2.4.2 Lewis
2.5 The triviality results
Chapter 3. Probabilistic theories of reasoning and probability conditionals
3.1 Why represent degrees of belief with probabilities?
3.2 Which interpretation of probability?
3.2.1 The frequentist interpretation
3.2.2 The logical interpretation
3.2.3 The subjectivist interpretation
3.3 How can we measure degrees of belief, and why would we want them to be coherent?
3.3.1 Measuring beliefs by measuring actions
3.3.2 Dutch book arguments
3.4 Coherence and p-validity: Deduction from uncertain premises
3.5 Probability conditionals
3.6 Conditionals and validity
3.7 Uncertain reasoning beyond deduction: Dynamic reasoning
3.8 Empirical evidence for the probabilistic approach
3.8.1 Evidence for reasoning from uncertain premises
3.8.2 Evidence for the probability conditional
Chapter 4. Alternatives to the probabilistic approach in psychology
4.1 Mental model theory (MMT)
4.1.1 Conditionals in MMT
4.1.2 Reasoning with conditional syllogisms in MMT
4.1.3 Mental models and probabilities
4.1.4 New MMT
4.2 Dual-component theories
4.2.1 « Logic » vs. « belief » in dual-component theories
4.2.2 Breaking the association of « logic » to type 2 and « belief » to type 1 processes
4.2.3 Breaking the « logic » vs. « belief » dichotomy itself
4.3 Research question
Part 3. Experiments
Chapter 5. Experiments 1 to 4: Coherence above chance levels
5.1 Methodological points relevant across experiments
5.1.1 Above-chance coherence
5.1.2 Linear mixed models
5.2 Experiment 1: Ifs and ors
5.2.1 Method
5.2.2 Results and discussion
5.2.3 General discussion
5.3 Experiment 2: Ifs, ands, and the conjunction fallacy
5.3.1 Overview of the conjunction fallacy
5.3.2 Ifs and ands
5.3.3 Method
5.3.4 Results and discussion
5.3.5 General discussion
5.4 Experiments 3 and 4: Intuition, reflection, and working memory
5.4.1 Experiment 3
5.4.2 Experiment 4
5.4.3 General discussion
Chapter 6. Experiments 5 to 7: Quantitative comparisons of degrees of belief
6.1 Experiment 5: At the edge vs. the centre of the coherence interval
6.1.1 Method
6.1.2 Results and discussion
6.1.3 General discussion
6.2 Experiment 6: Higher vs. lower than the premise probabilities
6.2.1 Method
6.2.2 Results and discussion
6.2.3 General discussion
6.3 Experiment 7: Certain premises and binary paradigm instructions
6.3.1 Method
6.3.2 Results and discussion
6.3.3 General discussion
Chapter 7. Experiments 8 and 9: Response variance
7.1 Experiment 8: Coherence interval width and response confidence
7.1.1 Varying location and width of coherence intervals
7.1.2 Measuring people’s sensitivity to location and width
7.1.3 Method
7.1.4 Results and discussion
7.1.5 General discussion
7.2 Experiment 9: Sensitivity to the variance of distributions
7.2.1 Method
7.2.2 Results and discussion
7.2.3 General discussion
Chapter 8. Experiment 10: Probability preservation properties
8.1 Method
8.2 Results and discussion
8.3 General discussion
Part 4. General discussion
Chapter 9. General discussion
9.1 The findings obtained across experiments
9.1.1 Coherent responses to MT
9.1.2 Changing responses to AC and DA
9.1.3 Conditionals, or-introduction, and the conjunction fallacy
9.1.4 Comparing above-chance coherence between inferences
9.1.5 The effect of an explicit inference task and working memory
9.1.6 Certain vs. uncertain premises, probabilistic vs. binary paradigm instructions
9.1.7 Factors with no systematic effect on above-chance coherence
9.1.8 The precision of people’s degrees of belief
9.1.9 The variance of belief distributions
9.1.10 P-validity matters over and above coherence
9.2 Conclusions
9.3 Implications for belief bias and dual-component theories
9.4 Limits of deduction and dynamic reasoning
9.5 Where next?
9.5.1 Dynamic reasoning
9.5.2 Counterfactuals, generals, and universals
9.5.3 Coherence and rationality
References