ࡱ> JLI5@ >bjbj22 "DXX<:${jjjjjjjj$1Rujjjjjjj5&&&j:jj&j&"&HHj^ PǮiHK0{HjHH"j0jj&jjjjjZ Z A Brief Introduction to Logic logicthe study of arguments argumenta collection of statements consisting of one or more premises and a conclusion valid argumentan argument for which it is impossible (inconceivable) that all of its premises are trueand (at the same time) its conclusion is false example Brad will pass the test only if he studies. (premise) If Brad goes to the fraternity party, then he will not study. (premise) Therefore, if Brad goes to the fraternity party he will not pass the test. (conclusion) Two types of arguments: 1. deductiveare intended to be valid 2. inductiveare not intended to be valid invalid argumenta deductive argument that is not valid example Brad will pass the exam only if he studies. (premise) If Brad goes to the fraternity party, then he will not study. (premise) Therefore, if Brad doesnt go to the fraternity, he will pass the exam. (conclusion) sound argumenta valid argument with true premises Therefore, to determine whether an argument is sound, we must answer two questions: (1) Is the argument valid? (2) Are all of the premises true? validity, soundness, and truth Even if the premises and conclusion of a deductive argument are all true, the argument may be invalid and unsound. example All mammals are animals. [true] Some animals are primates. [true] Therefore, all primates are mammals. [true] [argument is invalid (Why?) and unsound (Why?)] Even if the premises of a valid argument are false, the conclusion may be true. example Some mammals are reptiles. [false] All reptiles are cats. [false] Therefore, some mammals are cats. [true] [argument is valid (Why?) and unsound (Why?)] The conclusion of a sound argument must be true. (Why?) To analyze an argument is to present it in premise conclusion form, listing the premises and the conclusion. General Procedure for Testing the Validity of a Deductive Argument: 1. Identify the form of the argument. 2. Try to find an argument of the same form with true premises and a false conclusion. 3. If such an argument can be found, then the original argument is invalid. 4. If no such argument can be found, then either (1) the original argument is valid or (2) the tester is incompetent. inductive arguments not intended to be valid intended to convince us to accept conclusion examples I. Carol has observed 10,000 crows in the wild and all, without exception, were black. Therefore, all crows everywhere are black. II. 96% of all philosophy professors are underpaid. Lockhart is a philosophy professor. Therefore, Lockhart is probably underpaid. Some types of inductive arguments: generalization argument causal argument analogical argument generalization argument x1 has characteristics C1 and C2 x2 has characteristics C1 and C2 . . . xn has characteristics C1 and C2 Therefore, everything that has characteristic C1 also has characteristic C2. causal argument Event a1 of type X preceded event b1 of type Y. Event a2 of type X preceded event b2 of type Y. . . . Event an of type X preceded event bn of type Y. Therefore, events of type X are caused by events of type Y. analogical argument Each of x and y has characteristics C1, C2, , Cn x has characteristic Cn+1 Therefore, y also has characteristic Cn+1 Evaluating inductive arguments 1.Are the premises true? 2. If the premises were all true, would they give us sufficient reason to accept the conclusion? Steps in Analyzing and Evaluating Arguments 1. Analyze the argument: #1:;CD E O W X b    G H R Z [ o  + , / 3 M Q U X n o  h9"CJ OJQJaJ hN5CJ \aJ h9"CJaJh9"h9"CJ aJ h9"6CJ ]aJ h9"5CJ \aJ h9"h9"CJ aJ G;E X  H [ , o 8dd[$\$^8`gd9"dd[$\$^gd9"dd[$\$^gd9"hdd[$\$^hgd9" dd[$\$gd9"gd9"> :L^DT}&dd[$\$^gd9"dd[$\$^gdDdd[$\$^`gd9" dd[$\$gd9"8dd[$\$^8`gd9"dd[$\$^gd9"8:HJL`\^BDLZ2:STVZ|}$%&(,w|@BDR8PRVǼhDCJ aJ h9"5CJ \aJ h9"56CJ \]aJ h9"6CJ ]aJ h9"CJ aJ h9"CJaJh9"CJ OJQJaJ h9"G<  !:;<=>kgd9"dd[$\$^gdqdd[$\$^gdD dd[$\$gd9"dd[$\$^`gdD:<>Lz|~   $%&+,-/01FGHMNOkpqrstªªªªªªªªªªhDh9"6CJ H*]aJ hqhq6CJ aJ h9"6CJ ]aJ hD6CJ ]aJ h9"CJaJh9"CJ OJQJaJ h9"h9"CJ aJ hDCJ aJ A  )*+,234=>NOPXYZ     !FGJKQRSilmhqhq5CJ$aJ$hqh9"CJ H*aJ hqCJ aJ hDCJ aJ hqhq6CJ aJ h9"6CJ H*]aJ h9"6CJ ]aJ h9"CJ aJ h9"> 9:>kmq22222222222J3L3P3X3333333334"4R4T4V4d4444444455555ϺϮϮϮģhqh9"CJ aJ hq6CJ ]aJ h9"CJ OJQJaJ Uhqh9"h9"6CJ ]aJ hqCJ aJ h9"CJaJh9"CJ aJ hqh9"CJ$aJ$hqh9"5CJ$\aJ$>>dd[$\$^gdv dd[$\$gdDhdd[$\$^hgdv dd[$\$gd9"gd9"gd9"hdd[$\$^h`gd9"hdd[$\$^hgdqhdd[$\$^h`gdq Identify the main argument and the supporting arguments. List the premises and conclusion of each. Add any unstated premises and conclusions. 2. Classify each argument (main and supporting) as deductive or inductive. 3. Evaluate each deductive argument by determining whether the argument is valid whether the premises are all true [This may require considering prior evaluations of supporting deductive and inductive arguments.] 4. Evaluate each inductive argument by determining Whether the premises, if true, would adequately support the conclusion Whether the premises are all true The No Nitpicking Rule In evaluating someone else s argument, avoid nitpicking: Give the author s argument the most sympathetic interpretation possible. Add plausible premises that would strengthen the argument, even if not stated by the author. Remove any implausible premises that are not essential to the argument. Try to think of supporting arguments (not provided by the author) for any questionable premises.  prove : a very tricky word; it may mean to establish (as true) with complete certainty to establish (as true) with a very high probability to draw as the conclusion of a sound deductive argument to draw as the conclusion of a successful inductive argument Advice: Do not use  prove in discussing or writing about philosophy unless you explain exactly what you mean! 5$6&6(66666666666 7*7F7R7777777:8H8x8z8|888889L9N9P9^9t9999999 :~:::::,;.;0;>;;;;hDCJaJhDCJ OJQJaJ hDhDCJ aJ hD56CJ \]aJ hvCJ aJ h9"6]hqCJ aJ h9"6CJ ]aJ h9"CJaJh9"CJ OJQJaJ h9"h9"CJ aJ 8;;<<<$<<<<< ==(=*=6=====>>>ؾh9"hDhDCJ aJ hD6CJ ]aJ hDhDCJ OJQJaJ hvCJ aJ hDCJ aJ hDCJaJ 1h/ =!"#$%@@@ NormalCJ_HaJmH sH tH R`R 9" Heading 1dd@&[$\$5CJ0KH$\aJ0N`"N 9" Heading 2dd@&[$\$5CJ$\aJ$N`2N 9" Heading 3dd@&[$\$5CJ\aJDA@D Default Paragraph FontRi@R  Table Normal4 l4a (k@(No List4>`4 9"Titledd[$\$JC`J 9"Body Text Indentdd[$\$D;EXH[,o ,51 f . 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