study 3: nonstandard syllogisms
Syllogisms Containing More Than 3 Terms
1st Argument:
2nd Argument
Both arguments, above, have more than three terms each. So, the first task is to reduce the number of terms to three, if possible, making certain that each term is used in the same sense. This can be accomplished quite easily by obverting the second premise of the first argument and the first premise and the conclusion of the second argument.
Phase 1, First Example:
Phase 2, First Example:
1st Argument:
- All inexpensive things are poorly constructed.
- All German cars are expensive.
- .:. No poorly constructed things are German cars.
2nd Argument
- Some of the stolen books are not replaceable.
- No irreplaceable things are deductible.
- .:. Some of the stolen books are non-deductible.
Both arguments, above, have more than three terms each. So, the first task is to reduce the number of terms to three, if possible, making certain that each term is used in the same sense. This can be accomplished quite easily by obverting the second premise of the first argument and the first premise and the conclusion of the second argument.
Phase 1, First Example:
- All inexpensive things are poorly constructed.
- No German cars are inexpensive. (by obversion)
- .:. No poorly constructed things are German cars.
Phase 2, First Example:
- Major: No German cars are inexpensive.
- Minor: All inexpensive things are poorly constructed.
- .:. No poorly constructed things are German cars.
Phase 1, Second Example:
Now change the order of the premises in each argument.
Phase 2, Second Example:
- Some of the stolen books are irreplaceable. (by obversion)
- No irreplaceable things are deductible.
- .:. Some of the stolen books are not deductible. (by obversion)
Now change the order of the premises in each argument.
Phase 2, Second Example:
- Major: No irreplaceable things are deductible.
- Minor: Some of the stolen books are irreplaceable.
- .:. Some of the stolen books are not deductible.
The Five Rules
Rule 1: Two premises in both of which the middle term is undistributed do not imply a conclusion.
Rule 2: Two premises with undistributed terms having a conclusion which distributes those same terms do not imply a conclusion.
Rule 3: Two affirmative premises do not imply a negative conclusion.
Rule 4: Two negative premises do not imply a conclusion.
Rule 5: An affirmative and negative pair of premises does not imply an affirmative conclusion.
Rule 1: Two premises in both of which the middle term is undistributed do not imply a conclusion.
Rule 2: Two premises with undistributed terms having a conclusion which distributes those same terms do not imply a conclusion.
Rule 3: Two affirmative premises do not imply a negative conclusion.
Rule 4: Two negative premises do not imply a conclusion.
Rule 5: An affirmative and negative pair of premises does not imply an affirmative conclusion.
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