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UT PSY 394U - Lecture Notes

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General PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatKeeping Penguins from DrowningDaniel BonevacNovember 15, 2007Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatGeneral PrinciplesIBirds fly.IAcids are corrosive.IHandguns are dangerous.IPromises ought to be kept.IWhat goes up must come down.IPotatoes contain vitamin C.IAccident victims who are cool to the touch may be in shock.IBulbs that do not light are burned out and should be replaced.Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatIntensionalityIPrinciples are not extensionalIThey are more than accidental generalizationsICars moveICars in my driveway are at least 15 years old.IAcids are corrosiveIAcids are in the cabinet on the leftDaniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatNot UniversalIPrinciples are not universalIThere are cars that don’t moveIThere are birds that don’t flyIThere are handguns that aren’t dangerousIThere are promises that shouldn’t be keptIThere are potatoes that don’t contain vitamin CDaniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatNot NecessaryIPrinciples are not necessaryIThere are possible worlds in which it is not true thatICars moveIBirds flyIHandguns are dangerousIPromises should be keptIPotatoes contain vitamin CDaniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatDangerous InferencesIInferring particular conclusions from them is dangerousIThe truth of a principle does not guarantee the truth of aparticular conclusion drawn from itBirds flyTweety is a bird∴ Tweety fliesIThe argument is nevertheless reasonableDaniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatDispositions and Scientific ReasoningIReasoning using disposition terms shares these featuresIIf placed in a magnetic field, iron filings form a characteristicpatternIThese iron filings are placed in a magnetic fieldI∴ These iron filings form a characteristic patter nIBut what if they are glued to the table?IObjects of a fixed mass accelerate at a rate proportional to theforce applied to themIThis object has a fixed massIA force is applied to itI∴ This object accelerates at a rate proportional to that forceIBut what if it is glued to the table? Subject to another force?What if there is friction?Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatMonotonicityIClassical logic is monotonic in the sense thatX |= B =⇒ X ∪ Y |= B.IAdding premises, that is, never turns a valid argument into aninvalid one.IIn a deductively valid argument, the truth of the premisesguarantees the truth of the conclusion, no matter whatadditional information might come to hand.Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatNonmonotonicityIThere is reason to think that much common sense reasoningis nonmonotonic.IAdding premises sometimes leads us to withdraw conclusionsthat we would have drawn from more limited information.Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatTweetyIConsider a simple case of modus ponens:Tweety is a bird.If Tweety is a bird, Tweety flies.∴ Tweety flies.IThis seems acceptable.Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatTweetyIBut suppose we learn further that Tweety is a penguin.IWe are no longer inclined to draw the conclusion that Tweetyflies.Tweety is a bird.If Tweety is a bird, Tweety flies.Tweety is a penguin.∴ Tweety flies.*Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatCountermodelsITo analyze such arguments, we need a different, defeasibleconcept of implication.IThe classical notion of implication forces monotonicity.ISay that X |= A iff there are no models in which everysentence in X is true but A is false.ISay, in other words, that X |= A iff there are nocounterexamples to X ; A .IThis definition guarantees monotonicity, for there is no way toextend that information in X to yield ¬A.Daniel Bonevac Keeping Penguins from DrowningGeneral PrinciplesMonmonotonic LogicBenchmark ProblemsDefeasible ConditionalsBenchmark Problems SolvedThe Penguin PrincipleThe Drowning ProblemA Possible Fix, and a Fix of ThatCountermodelsITo define a defeasible implication relation, we need to allowcounterexamples.IExtending the information in X may indeed yield ¬A.IOf course, if counterexamples are rampant, then theargument should count as invalid even defeasibly.IWe want to say, very roughly, that X defeasibly implies A iffcounterexamples to X ; A are sufficiently


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UT PSY 394U - Lecture Notes

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