SSH 105 Lecture Notes - Lecture 5: Counterexample, Modus Ponens, Modus Tollens
3 Dec 2018
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Document Summary
Sometimes, we can tell just from the logical form of an argument whether it is valid. Often when we try to decide what to believe or do we are faced with several options, and we reason by ruling them out one by one. A disjunction asserts that at least one of the disjuncts is true. A disjunction is inclusive if all of its disjuncts can be true at once. If you know that a disjunction is true, and you discover that one disjunct is not true then you can conclude that the other one must be true. This reasoning is a matter of ruling out possibilities. We start believing that either p or q is true; we rule out p; so we conclude, q must be true. Denying a disjunct where the disjunction is false will always lead to a false conclusion, even though the argument is valid. A disjunction is exhaustive when it includes all the possibilities.
