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Unformatted text preview: 5.4-Reducing the Number of Terms
All photographers are non-writers. Some editors are writers. Therefore, some non-photographers are not non editors. This syllogism is not in standard form because it has 6 terms: photographers editors writers non-photographers non-editors non-writers 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 non-W. Some E are W. Some non-P are not non-E. 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 non-W. Some E are W. Some non-P are not non-E. Reduced argument All W are non-P. Some W are not non-E. Some non-P are not non-E. 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 non-E. All W are non-P. Some non-P are not non-E. 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 non-B. All A are non-B. Some A are not non-B. Some A are non-B. Contraposition: All A are B. Some A are not B. All non-B are non-A. Some non-B are not non-A. ...
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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