The psychology of conditionals
Conditionals  indicative, counterfactual, deontic, and others  are central to the study of reasoning in linguistics, logic, philosophy, and psychology. These classes will cover the history of research on conditionals in the psychology of reasoning, and will introduce new Bayesian and probabilistic approaches, which have recently had a major impact on psychological theories about, and experiments on, human reasoning in general and conditional reasoning in particular. The new approaches recognize that most of this reasoning takes places in contexts of uncertainty. Most human inferences are not from arbitrary assumptions, but rather from uncertain premises, and lead finally to belief revision and updating, and to decision making. A central topic in this new research has been the hypothesis, originally proposed in logic and philosophy, that the probability of the natural language conditional, P(if A then B), is the conditional probability of B given A, P(BA). This relationship, P(if A then B) = P(BA), is fundamental in a Bayesian account of reasoning, and the latest research on it with be introduced and examined.
Class 1: The psychology of conditional reasoning: An introduction
The different types of conditional in natural language: indicative, counterfactual, deontic, and others.
Early experiments in the psychology of reasoning: the "defective" truth table, the selection task, and inferences from arbitrary assumptions. Apparent biases in this reasoning: confirmation and belief biases.
Critical examination of early psychological theories of this reasoning: mental logic and mental model theories.
Class 2: The probability of indicative conditionals
The reasons for taking a probabilistic approach to the study of reasoning: most human reasoning is not from arbitrary assumptions, but from uncertain premises. The premises are uncertain beliefs or are possibilities relevant to decision making, and the results are belief revision or updating, and effective decisions.
Conditionals are basic in reasoning. An inference from premises to a condition can be turned into a conditional, if premises then conclusion, and reasoning from a possible antecedent, as a premise, to a consequent, as a conclusion, can justify a conditional.
Uncertain conditional premises are probable to a degree less than certainty, but what is the probability of a conditional? The first experiments on this question used frequency distributions, but this limitation can be overcome. The general finding is that people judge the probability of a natural language conditional, P(if A then B), to be the conditional probability of B given A, P(BA). There are possible limitations of to this finding: missinglink conditionals.
A conditional that satisfies the relation, P(if A then B) = P(BA), is called a probability conditional. Why a probability conditional cannot be a Stalnaker/Lewis conditional. How to account for the meaning of a probability conditional: the Ramsey test and de Finetti and Jeffrey tables.
Class 3: Probability and conditional reasoning
Assessing inferences from uncertain premises in a Bayesian approach: generalizing consistency to coherence and classical validity to probabilistic validity, pvalidity.
Using coherence and pvalid inferences to study nonconditional inferences: &elimination and the conjunction fallacy. Another example: orintroduction.
Inferences that are valid for the truthfunctional material conditional but not pvalid for the probability conditional: the "paradoxes" of the material conditional. Inferring if A then B from notA, and from B. Strengthening the antecedent: inferring if A & B then C from if A then C.
Monotonicity and pvalidity: pvalidity is monotonic but the probability conditional is nonmonotonic.
Inferences that are valid for the truthfunctional material conditional and pvalid for the probability conditional: modus ponens (MP) and modus tollens (MT). Inferences that are invalid for the truthfunctional material conditional and pinvalid for the probability conditional: affirming the consequent (AC) and denying the antecedent.
The importance of the andtoif inference (also called centering), inferring if A then B from A & B, for theories of conditionals.
Class 4: Counterfactuals
The distinction between indicative and counterfactual conditionals: what exactly is it? Does a counterfactual, if A were the case then B would be, entail notA, or does the use of such a counterfactual by a speaker pragmatically suggest that notA holds? MP and the andtoif inference are relevant to answering these questions.
Possible worlds and counterfactuals: the Stalnaker/Lewis accounts. The psychological findings on people's judgments about possible worlds reviewed: counterfactuals and the emotions of regret and relief.
Probability judgments about counterfactuals: does P(if A were the case then B would be) = P(BA) hold for counterfactuals?
Counterfactuals and causation: Bayes nets and interventions. How MP and the andtoif inference are again relevant to this topic.
