A Little About Logic


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MICHAEL LEVIN A LITTLE ABOUT LOGIC Logic.is the abstract-study of argument. Since philosophy is both highly abstract and concerned with arguments, philosophers take a keen interest in this subject. The best approach to logic is to reflect that arguments may be criticized in two ways. Sometimes when we say "That's a bad argument," wc mean that one or more of its premises arc incorrect. Should someone reason that Nebraska has a major canal because the Panama Canal is in Nebraska, you would probably say, "That's ridiculous - the Panama Canal is not in Nebraska." An argument can go wrong in another way, however. Its premises may be impeccable, but the reasoning by which they (allegedly) lead to the conclusion is faulty. For instance: P(remise). Bram Stoker's novel Dracula is contains a great deal of vampire lore. Therefore, C(onclusion). Bram Stoker must have been a vampire. The premise is true; Dracula does contain a lot about vampires. However, it is a mistake, or fallacy, to infer from this that its author must have been a vampire; after all, Moby Dick contains a great deal about whales, but Herman Melville was not a whale. Or else, someone might reason this way: . , t PI . All fishermen are liars. P2 . John is a lim', Therefore, C. John is a fisherman. You might at first see nothing wrong with this inference, hut a moment's reflection shows that C docs not follow from P I and P2 Even if all
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Introduction fishermen are liars, there may be other liars as well, for instance golfers. "PI and P2 are consistent with lohn being a mendacious golfer rather than a fisherman. Some fallacies arc so easily identified they have acquired names: the one just illustrated is calling affirming the consequent. Formal logic identifies patterns of reasoning that reliably lead from premises to conclusion. We arc all familiar with such patterns, which are readily recognizable when laid out, For instance, if X, Y, Z, ... stand for any sentences whatever, it is clear that the pattern of reasoning called hypothetical syllogism, namely PI. If X then Y. P2. If Y then Z. Therefore, C. If X then Z. is good reasoning. To say this reasoning is "good" means that, if premises P I and P2 are both true, the conclusion must be true. It is impossible for both "If X then Y" and "If Y then Z" to be true, yet "If X then Z" be false. Another pattern with this agreeable property is the disjunctive syllogism: PI . X or Y. P2. Not X. Therefore, c.Y. Once again, it is impossible for both premises to be true while the conclusion is false. If the alternatives are X and Y, and X is ruled out, only Y remains. The property illustrated by hypothetical syllogism and disjunctive syllogism is called validity: A pattern is valid when, given that all its premises arc true, its conclusion must be true. Particular arguments arc valid when their patterns are valid. Thus P I. Manitoba is either in the US or Canada. P2.
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