Paradoxes, Probability, and Rational Choice
Not every surprising conclusion is a contradiction. First specify the sample space, available information, and decision rule; then decide what remains philosophically unsettled.
Learning objectives
- Identify inconsistent premises in a formal paradox.
- Compute a simple conditional probability.
- Distinguish prediction from causation and risk from ambiguity.
Recommended sequence
- Sorites: When Does a Heap Begin? — Start with a vague predicate.
- The Liar Paradox — Contrast vagueness with self-reference.
- Russell’s Paradox — Examine unrestricted set formation.
- The Monty Hall Problem — Track the host’s conditional behavior.
- Bertrand’s Random Chord Paradox — Compare different randomization procedures.
- Sleeping Beauty — Identify the disputed updating principle.
- The St. Petersburg Paradox — Separate expected money from utility.
- Newcomb’s Problem — Contrast causal and evidential recommendations.
- The Ellsberg Paradox — Compare known risks with ambiguous probabilities.
Read each article’s scenario first, write an initial answer, and then read the interpretations and sources. Spend as long as useful; there is no required schedule.
Reflection questions
- Which disputes disappear once assumptions are explicit?
- When should a seemingly irrational preference lead us to revise a normative model?
Final synthesis activity
Create a two-part worksheet: a fully specified probability puzzle with a calculation, and a decision problem with competing rules. Explain why the first has a determinate answer under its premises while the second may retain a substantive dispute.
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