Other immediate inferences aside from the traditional square of opposition is the conversion of propositions, which involves the following:
1) conversion,
2) obversion, and
3) contraposition.
Conversion
This type of inference is done by simply interchanging the subject and predicate terms of the proposition with reference to the distribution of each term.
Conversion is very much valid on E and I propositions where the totality or partiality of exclusion and inclusion of both S class and P class are identical. Its application is limited or this type of inference is not applicable to all types of propositions. Thus, applying conversion to the four propositions yields the following result:
Take note that the qualities of the propositions above are the same. Also, it is invalid to apply conversion in particular negative (O) propositions because it is tantamount to inferring that something must be true to all members of a class because it is true to some members.
Obversion
Obversion is another immediate inference which can be correctly performed by following the two guidelines:
- By replacing the predicate terms of the statement with its class complement. The complement of a class is the class of all things that are not members of that class, that is, the complement of P is non-P, and vice versa; and
- By changing the quality of the statement, that is, if the statement is affirmative, then we make it negative, and if the statement is negative, we make it affirmative. Please note that only the quality of the statement is changed; the quantity should be left as is.
Thus, applying obversion to the four propositions yields the following result:
Contraposition
Other immediate inferences are done by combining conversion and obversion. And one of the combinations is called contraposition, which is done by obverting, converting, and then obverting again. So, to get the contrapositive of a universal affirmative (A) proposition “All S are P”, we can have “No S are non-P” by obversion and “No non-P are S” by applying conversion to the obvertend, and finally, “All non-P are non-S” by applying again obversion to the converse of the obverted proposition. Put simply, the process involves the following:
- Replacing the subject term by the complement of the predicate term; and
- Replacing the predicate terms by the complement of its subject term.
The table below will make this point clearer.
Exercises
Instruction: Give, where possible, the converse, obverse, and contrapositive of each of the propositions below.
- Rizal’s mother is a feminist.
- Some feminist arguments are not valid.
- Some nonatheist people attend church.
- All graduates of PMA are commissioned officers of the AFP.
- No reptiles are warm-blooded animals.
- Some robbers are honest persons who are forced to steal to feed their family.
- Some clergymen are not abstainers.
- All geniuses are weird.
- Some soldiers are not patriotic.
- Some non-Filipinos are communists.