I&C SCI 6B Lecture Notes - Lecture 4: Universal Instantiation, Universal Generalization, General Idea

• School: UC-Irvine
• Department: Information and Computer Science
• Course: I&C SCI 6B
• Professor: Wayne Hayes

Document Summary

Argument: a sequence of premises leading to a conclusion; valid is the truth of the premises necessarily implies the conclusion. Form: the form of the argument is the actual sequence of propositions leading to the conclusion. To ensure the argument is valid requires using accepted rules of inference (the rules can be verified by truth tables) Modus pomens (mode that affirms; aka law of detachment): the tautology (p^(p->q))-> (cid:930) (cid:857)(cid:933)h(cid:918) (cid:933)h(cid:931)(cid:918)(cid:918) (cid:917)(cid:928)(cid:933)(cid:932) (cid:932)(cid:933)a(cid:927)(cid:917) (cid:919)(cid:928)(cid:931) (cid:1490)(cid:933)h(cid:918)(cid:931)(cid:918)(cid:919)(cid:928)(cid:931)(cid:918)(cid:1491)(cid:858) Fallacies: an invalid argument where a tautology is surreptitiously (secretly/accidentally) replaced by a contingency, as if the contingency were always true. Rain (p) implies clouds (q) ^ clouds (q) -> rain (p) << this is a fallacy. Just clouds isn"t enough to make this statement true; this is. If it"s raining, there are clouds overhead (true) If there are clouds overhead, it"s raining (sometimes true) Example: [(p->q^not p] -> not q >> denying the hypothesis.