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Since the operations of conversion, obversion, and 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 Machiavellian political leaders are not enlightened individuals.
Therefore, some enlightened individuals are not Machiavellian political leaders.
The conclusion of Argument 1 is the of the premise.
The immediate inference in Argument 1 is:
Invalid and commits the fallacy of illicit conversion
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit contraposition
Argument 2
All naturally occurring phenomena are events that are bound by natural laws.
Therefore, all events that are not bound by natural laws are phenomena that are not naturally occurring.
The conclusion of Argument 2 is the of the premise.
The immediate inference in Argument 2 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 3
No horses from Alaska are Kentucky Derby winners.
Therefore, no Kentucky Derby winners are horses from Alaska.
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
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit conversion
Argument 4
Some human waste products are not biodegradable substances.
Therefore, some human waste products are non-biodegradable substances.
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
Valid and does not commit a formal fallacy
Invalid and commits the fallacy of illicit contraposition
Argument 5
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 5 is the of the premise.
The immediate inference in Argument 5 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
