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Lesson_Five_and_Test

# Lesson_Five_and_Test - LESSON 5 Categorical Logic Part 4...

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Section 9: Translating into Standard Form , Barker, pp. 54-58. ***Read the section, then the following additional comments. This section highlights both some of the strengths and weaknesses of categorical logic. The strength is that this form of logic can accommodate a surprising number of different assertions; many different sentences can be translated into standard form. The obvious weakness is that the result may be incredibly awkward. Nevertheless, we must be able to undertake these transformations. Following Barker’s analysis, we need to consider two steps in the translation process: translating the sentences into categorical form and translating the argument into a genuine syllogism. My comments will simply touch on a few highlights of the more unusual situations. Translating Sentences a) Individuals . Many terms in English refer not to classes of things, but singular individuals. For example, Kermit the Frog, Ozzie Osborne, the winner of the 1996 Olympic gold medal in the men’s decathlon, the town of Swayzee, etc., all refer to one and only one individual. The same thing may be true for events, such as the day when Richard Burton met Elizabeth Taylor or the sixth game of the 1995 World Series. Under the system we are using in this course, we translate these items as: “all frogs identical with Kermit,” “all people identical with Ozzie Osborne,” “all people who won the 1996 Olympic gold medal in the men’s decathlon,” “all towns identical to Swayzee,” “all times when Richard Burton met Elizabeth Taylor,” and “all games identical to the sixth game of the 1995 World Series.” Awkward? You bet; but it gets the job done. b) “Only.” How does one translate a sentence such as “Only people with a ticket can win the lottery”? Consider the two options: All people with tickets are winners of the lottery, and All winners of the lottery are people with tickets. 1 LESSON 5 Categorical Logic, Part 4

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As nice as the first option would be for participants in the lottery, the operators would never stand for it. Clearly the meaning is the second one; it restricts the potential winners to the class of people who have tickets. Thus Only X’s are Y’s translates as All Y’s are X’s. c) “Unless.” Similarly, a word such as “unless” must be seen as restricting the classes in the way in which it makes sense. So, if I say, Your car will stall unless you have gas in the tank, I am not saying: All times when your car stalls are times when you do not have gas in the tank; but All times when you do not have gas in the tank, are times when your car stalls.
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Lesson_Five_and_Test - LESSON 5 Categorical Logic Part 4...

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