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Unformatted text preview: 5.4Reducing the Number of Terms
All photographers are nonwriters. Some editors are writers. Therefore, some nonphotographers are not non editors. This syllogism is not in standard form because it has 6 terms: photographers editors writers nonphotographers noneditors nonwriters Since three of the terms are complements of the other three, the number of terms can be reduced to a total of three. We can use conversion, obversion, and contraposition, but we must use conversion only on E and I statements and contraposition only on A and O statements. Symbolized argument All P are nonW. Some E are W. Some nonP are not nonE. Reduced argument No P are W. Some E are W. Some E are not P. It is not necessary to eliminate the negated terms in order to reduce the number of terms. It is equally effective to convert certain nonnegated terms into negated ones. Symbolized argument All P are nonW. Some E are W. Some nonP are not nonE. Reduced argument All W are nonP. Some W are not nonE. Some nonP are not nonE. The reduced argument is once again equivalent to the original one, but now we must reverse the order of premises to put the syllogism into standard form: Some W are not nonE. All W are nonP. Some nonP are not nonE. The operations that are allowed are summarized as follows: Conversion: Obversion: No A are B. Some A are B. All A are B. No A are B. Some A are B. Some A are not B. No B are A. Some B are A. No A are nonB. All A are nonB. Some A are not nonB. Some A are nonB. Contraposition: All A are B. Some A are not B. All nonB are nonA. Some nonB are not nonA. ...
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This note was uploaded on 04/18/2008 for the course PHIL 1010 taught by Professor Canterbury during the Spring '08 term at Toledo.
 Spring '08
 Canterbury

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