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4.4 8. Contraposition – Practice Given Statement: No non-S…
4.4
8. Contraposition – Practice
Given Statement: No non-S are non-P.
Truth Value of Given Statement: True
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: All S are non-P.
Truth Value of Given Statement: True
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: Some non-S are non-P.
Truth Value of Given Statement: True
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: Some S are non-P.
Truth Value of Given Statement: False
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: Some S are not P.
Truth Value of Given Statement: False
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: Some S are not non-P.
Truth Value of Given Statement: True
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: All S are P.
Truth Value of Given Statement: False
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
Given Statement: No S are P.
Truth Value of Given Statement: False
Contrapositive of Given Statement: .
Truth Value of Contrapositive:
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9. Illicit Conversion and Illicit Contraposition
Since the operations of conversion, obversion, and contraposition yield determinate truth values in some cases, some inferences whose conclusions depend on these operations are valid. Recall that a deductively valid argument is one in which the conclusion necessarily follows from the premise(s) and in which it is impossible for the conclusion to be false when you assume that the premises are true. An invalid deductive argument commits a formal fallacy. Two particular formal fallacies that are relevant to the preceding operations are the fallacy of illicit conversion and the fallacy of illicit contraposition. You can see the various forms of these two fallacies here.
Illicit Conversion
All A are B.
Therefore, All B are A.
Some A are not B.
Therefore, some B are not A.
Illicit Contraposition
Some A are B.
Therefore, some non-B are non-A.
No A are B.
Therefore, no non-B are non-A.
Since conversion yields determinate truth values only for the converses of E statements and I statements, an argument in which the premise is an A statement or an O statement, and in which the conclusion is the converse of the premise, is necessarily invalid. The operation of conversion does not guarantee that the converse of a true A statement or a true O statement is also true.
And since the operation of contraposition yields determinate truth values only for the contrapositives of A statements and O statements, an argument in which the premise is an E statement or an I statement, and in which the conclusion is the contrapositive of the premise, is necessarily invalid. The operation of contraposition does not guarantee that the contrapositive of a true E statement or a true I statement is also true.
For each of the following immediate inferences, indicate whether the conclusion is the converse, obverse, or contrapositive of the premise. Then use your knowledge of the operations of conversion, obversion, and contraposition to determine whether each immediate inference is valid or invalid. If the argument is invalid, indicate whether it commits illicit conversion or illicit contraposition.
Argument 1
Some traditional American breakfast foods are dishes that use eggs.
Therefore, some dishes that use eggs are traditional American breakfast foods.
The conclusion of Argument 1 is the of the premise.
The immediate inference in Argument 1 is:
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit contraposition
Invalid and commits the fallacy of illicit conversion
Argument 2
Some human waste products are not biodegradable substances.
Therefore, some human waste products are non-biodegradable substances.
The conclusion of Argument 2 is the of the premise.
The immediate inference in Argument 2 is:
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit contraposition
Invalid and commits the fallacy of illicit conversion
Argument 3
Some Machiavellian political leaders are not enlightened individuals.
Therefore, some enlightened individuals are not Machiavellian political leaders.
The conclusion of Argument 3 is the of the premise.
The immediate inference in Argument 3 is:
Invalid and commits the fallacy of illicit contraposition
Invalid and commits the fallacy of illicit conversion
Valid and does not commit a formal fallacy
Argument 4
Some extraterrestrial life forms are carbon-based life forms.
Therefore, some life forms that are not carbon-based are terrestrial life forms.
The conclusion of Argument 4 is the of the premise.
The immediate inference in Argument 4 is:
Invalid and commits the fallacy of illicit conversion
Invalid and commits the fallacy of illicit contraposition
Valid and does not commit a formal fallacy
Argument 5
Some sugarless gums are not good sources of vitamins.
Therefore, some bad sources of vitamins are not gums with sugar.
The conclusion of Argument 5 is the of the premise.
The immediate inference in Argument 5 is:
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit conversion
Invalid and commits the fallacy of illicit contraposition
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10. True/False Review and Chapter Summary
Use your knowledge of the operations of conversion, obversion, and contraposition to determine which of the following statements are true. Check all that apply.
When you are determining the proper term complement for a complex term, you must take into account the relevant scope of discourse.
If you perform the operation of contraposition on an A statement or an O statement, then the resulting contrapositive must have the same truth value as the original statement.
The operation of contraposition involves switching the subject term and the predicate term in a categorical proposition but does not involve replacing either term with its term complement.
The operation of obversion always yields an obverse with a truth value that is undetermined by the truth value of the original statement.
The converse of a false E proposition must be false also.
You should never assume a restricted scope of discourse when determining the term complement for a term.
The contrapositive of a true A proposition must be true also.
The converse of a false A proposition must be false also.
The operation of conversion involves switching the subject term and the predicate term in a categorical proposition.
Any immediate inference with a categorical proposition for a premise, and the obverse of that premise for a conclusion, will be deductively valid.
If you perform the operation of conversion on an A statement or an O statement, then the resulting converse must have the same truth value as the original statement.
The operation of obversion yields a determinate truth value when performed on any categorical proposition.
The obverse of a true I proposition must be false.
The obverse of a true I proposition must be true also.
The contrapositive of a true E proposition must be true also.
