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Infinite “Backward” Induction Arguments
Author(s) -
Sorensen Roy
Publication year - 1999
Publication title -
pacific philosophical quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.914
H-Index - 32
eISSN - 1468-0114
pISSN - 0279-0750
DOI - 10.1111/1468-0114.00084
Subject(s) - backward induction , iterated function , dilemma , surprise , mathematical economics , focus (optics) , epistemology , common knowledge (logic) , computer science , philosophy , mathematics , game theory , psychology , artificial intelligence , social psychology , mathematical analysis , physics , multimodal logic , optics , epistemic modal logic , description logic
A large family of paradoxical arguments have been subsumed under the label “backward induction arguments”. These include the iterated prisonerÃs dilemma, the centipede game, and the surprise test paradox. They are described as backward because they begin by considering a future hypothetical alternative, rule it out, and then rule out each predecessor. Thus they go backward in time ruling out finitely many alternatives. I present examples that go forward in time and eliminate infinitely many alternatives. These pose problems for solutions that focus on common knowledge assumptions.