Notes on Logic and Probability

Notes for the course PHIL 171: Reasoning for humans: Clear thinking in an uncertain world.

By Eric Pacuit (pacuit.org)

There are 5 sections introducing logic and probability:

1. Introduction - Introduction to the study of reasoning. Topics include: declarative sentences, propositions, arguments, inference patterns, logical form
2. Logic - Introduction to propositional logic (also called sentential logic). Topics include: Boolean connectives ($\wedge, \vee, \neg,\rightarrow, \leftrightarrow$), truth tables, tautologies, contradictions, satisfiability, mutually exclusive formulas and validity.
3. Logic and Reasoning - Patterns of reasoning in propositional logic. Topics include: valid/invalid inference rules, introduction to Boolean algebra, Venn/Euler diagrams, Wason selection task, Byrne suppression task, conditionals.
4. Probability - Introduction to probability. Topics include: stochastic truth tables, conditional probability, Kolmogrov axioms, law of total probability, evidential support, independence.
5. Probabilistic Inference - Introduction to reasoning with probabilities. Topics include: Conjunction Fallacy, Simpson's Paradox, Bayes Theorem, base-rate fallacy, Bayes nets, confirmation measures, paradox of the ravens.