Paradoxes
From GusWiki
Since the world itself is logically consistent, paradoxes only exist as cognitive phenomena: they reflect inconsistencies in our conceptualizations of the world. I make no hard distinction between paradoxes and arguments with counter-intuitive conclusions. Which intuitions are primary or derived is of no consequence. (See argument-mapping, intuition)
Contents |
List of paradoxes
Probability and Statistics
-:Two-envelopes paradox: the solution I know is a point in favor of Subjectivist Bayesianism.
Simpson's Paradox: the inferred relationship between two variables depends on the variables you're conditioning on. Pearl says: "any statistical relationship between two variables may be reversed by including additional factors in the analysis". This highlights the need for careful thinking about causality. Observing an instance of Simpson's Paradox is evidence that one's "control variables" are not independent of each other (and you are lucky to find out!). Simpson's Paradox cannot occur when all variables are directly manipulated.
Decision Theory
-:St. Petersburg paradox is an argument against the norm of maximizing expected utility.(especially in one-shot situations)
Other
-:Banach-Tarski paradox: the Axiom of Choice gives you a recipe for reassembling one orange into two oranges of the same size. However, as you might expect, the pieces are non-constructible (otherwise you wouldn't need AC).
-:Russell's Paradox: Russell's motivation for -:type theory.
