Notes on Logic and Probability
Notes for the course PHIL 171: Reasoning for humans: Clear thinking in an uncertain world.
There are 5 sections introducing logic and probability:
- Introduction - Introduction to the study of reasoning. Topics include: declarative sentences, propositions, arguments, inference patterns, logical form
- Logic - Introduction to propositional logic (also called sentential logic). Topics include: Boolean connectives (), truth tables, tautologies, contradictions, satisfiability, mutually exclusive formulas and validity.
- 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.
- Probability - Introduction to probability. Topics include: stochastic truth tables, conditional probability, Kolmogrov axioms, law of total probability, evidential support, independence.
- 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.