General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Keeping Penguins from Drowning Daniel Bonevac November 15 2007 Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That General Principles I Birds fly I Acids are corrosive I Handguns are dangerous I Promises ought to be kept I What goes up must come down I Potatoes contain vitamin C I Accident victims who are cool to the touch may be in shock I Bulbs that do not light are burned out and should be replaced Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Intensionality I I Principles are not extensional They are more than accidental generalizations I I I I Cars move Cars in my driveway are at least 15 years old Acids are corrosive Acids are in the cabinet on the left Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Not Universal I Principles are not universal I I I I I There are cars that don t move There are birds that don t fly There are handguns that aren t dangerous There are promises that shouldn t be kept There are potatoes that don t contain vitamin C Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Not Necessary I I Principles are not necessary There are possible worlds in which it is not true that I I I I I Cars move Birds fly Handguns are dangerous Promises should be kept Potatoes contain vitamin C Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Dangerous Inferences I Inferring particular conclusions from them is dangerous I The truth of a principle does not guarantee the truth of a particular conclusion drawn from it Birds fly Tweety is a bird Tweety flies I The argument is nevertheless reasonable Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Dispositions and Scientific Reasoning I Reasoning using disposition terms shares these features I I I I I I I I I If placed in a magnetic field iron filings form a characteristic pattern These iron filings are placed in a magnetic field These iron filings form a characteristic pattern But what if they are glued to the table Objects of a fixed mass accelerate at a rate proportional to the force applied to them This object has a fixed mass A force is applied to it This object accelerates at a rate proportional to that force But what if it is glued to the table Subject to another force What if there is friction Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Monotonicity I Classical logic is monotonic in the sense that X B X Y B I Adding premises that is never turns a valid argument into an invalid one I In a deductively valid argument the truth of the premises guarantees the truth of the conclusion no matter what additional information might come to hand Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Nonmonotonicity I There is reason to think that much common sense reasoning is nonmonotonic I Adding premises sometimes leads us to withdraw conclusions that we would have drawn from more limited information Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Tweety I Consider a simple case of modus ponens Tweety is a bird If Tweety is a bird Tweety flies Tweety flies I This seems acceptable Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Tweety I But suppose we learn further that Tweety is a penguin I We are no longer inclined to draw the conclusion that Tweety flies Tweety is a bird If Tweety is a bird Tweety flies Tweety is a penguin Tweety flies Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Countermodels I To analyze such arguments we need a different defeasible concept of implication I The classical notion of implication forces monotonicity I Say that X A iff there are no models in which every sentence in X is true but A is false I Say in other words that X A iff there are no counterexamples to X A I This definition guarantees monotonicity for there is no way to extend that information in X to yield A Daniel Bonevac Keeping Penguins from Drowning General Principles Monmonotonic Logic Benchmark Problems Defeasible Conditionals Benchmark Problems Solved The Penguin Principle The Drowning Problem A Possible Fix and a Fix of That Countermodels I To define a defeasible implication relation we need to allow counterexamples I Extending the information in X may indeed yield A I Of course if counterexamples are rampant then the argument should count as invalid even defeasibly I We want to say very roughly that X defeasibly implies A iff counterexamples to X A are sufficiently rare Daniel Bonevac Keeping Penguins from
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