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Eduction is a form of immediate inference which involves the act of drawing out the implied meaning of a given proposition. There are 4 kinds of eduction, namely:
- conversion,
- obversion,
- contraposition, and
- inversion
Conversion
Conversion refers to the formulation of a new proposition by way of interchanging the subject and the predicate terms of an original proposition, while retaining the quality of the original proposition. The original proposition is called the convertend, while the new proposition is called the converse. Let us consider the example below.
No plant is an animal.
Hence, no animal is a plant.
As is well known, the original proposition is called the “convertend”, while the new proposition is called the “converse”. And in the example above, it must be noted that the new proposition “No animal is a plant” is the implied meaning of the original proposition, that is, “No plant is an animal”.
There are two types of conversion, namely, simple and partial conversion.
Simple conversion is a type of conversion where the quantity of the convertend is retained in the conversion. It must be remembered that only universal negative (E) and particular affirmative (I) propositions can be converted through simple conversion.
Example 1:
No angels are mortals. (E)
Therefore, no mortals are angels. (E)
Example 2:
Some mortals are men. (I)
Therefore, some men are mortals. (I)
As already mentioned, only universal negative (E) and particular affirmative (I) propositions can be converted because in universal affirmative (A) propositions, the quantity of the predicate term in the convertend (which is particular) which becomes the subject term in the converse cannot be retained; while in particular negative (O) propositions, the subject term of the convertend, being made the predicate term of a negative proposition, would be changed from particular to universal. Let us consider the examples below:
Example 1:
All dogs are animals. (A)
Therefore, all animals are dogs. (A)
As we can see, the quantity of the predicate term “animals” in the original proposition, that is, the convertend, is particular because the proposition is affirmative. As we learned in the previous discussions, the predicate terms of all affirmative propositions are particular (while the predicate terms of all negative propositions are universal). Now, the quantity of the term “animals” which becomes the subject term in the converse is universal because of the universal signifier “all”. Hence, we cannot convert universal affirmative (A) propositions because, again, we cannot retain the quantity of the predicate term.
Example 2:
Some animals are not mammals. (O)
Therefore, some mammals are not animals. (O)
As we can see, the subject term of the convertend is particular because it is signified by the particular signifier “some”, but it becomes universal in the converse because it becomes the predicate term of a negative proposition. As mentioned above, the predicate terms of all negative propositions are always universal.
Partial conversion, on the other hand, is a type of conversion where the quantity of the convertend is reduced from universal to particular. Of course, partial conversion can only be applied to universal affirmative (A) and universal negative (E) propositions, where a universal affirmative proposition (A) is changed to particular affirmative (I) and a universal negative (E) proposition is changed to particular negative (O).
Let us consider the examples below.
Example 1:
All computers are gadgets. (A)
Therefore, some gadgets are computers. (I)
Example 2:
No computers are robots. (E)
Therefore, some robots are not computers. (O)
Obversion
Obversion refers to the formulation of a new proposition by retaining the subject and the quantity of the original proposition; however, the quality of the original proposition is changed and the predicate term is replaced by its contradictory. The original proposition is called the “obvertend”, while the new proposition is called the “obverse”. Please note that obversion is applicable to all types of categorical propositions. Let us consider the examples below.
Examples 1:
All men are mortal. (A)
Therefore, no men are immortal. (E)
Examples 2:
No giants are small creatures. (E)
Therefore, all giants are big creatures. (A)
Example 3:
Some men are mortal. (I)
Therefore, some men are not immortal. (O)
Example 4:
Some politicians are not corrupt individuals. (O)
Therefore, some politicians are non-corrupt individuals. (I)
Contraposition
Contraposition is the result of the combination of the principles of conversion and obversion. There are two types of contraposition, namely, partial and complete contraposition.
In partial contraposition, 1) the subject of the contraposit (that is, the new proposition) is the contradictory of the contraponend (that is, the original proposition); 2) the quality of the contraponend is changed in the contraposit; and 3) the predicate term in the contraposit is the subject term in the contraponend. Let us consider the example below.
Example 1:
All whales are mammals. (A)
Therefore, no non-mammals are whales. (E)
Example 2:
No police officers are drug addicts. (E)
Therefore, some non-drug addicts are police officers. (I)
Example 3:
Some students are not studious individuals. (O)
Therefore, some non-studious individuals are students. (I)
It must be noted that particular affirmative (I) propositions have no contraposits. Hence, we cannot apply contraposition to particular affirmative propositions. This is because contraposition involves to steps, namely: first, obversion, and then, second, conversion. Now, as we learned above, since the obverse of an “I” proposition is “O” proposition, then we cannot proceed because an “O” proposition does not have a converse.
In complete contraposition, on the other hand, 1) the subject term in the contraposit is the contradictory of the predicate term in the contraponend; 2) the quality of the contraponend is not changed in the contraposit; and 3) the predicate term in the contraposit is the contradictory of the subject term in the contraponend. Let us consider the examples below.
Example 1:
All whales are mammals. (A)
Therefore, all non-mammals are non-whales. (A)
Example 2:
No criminals are good people. (E)
Therefore, some evil people are not non-criminals. (O)
Example 3:
Some students are not studious. (O)
Therefore, some non-studious are not non-students. (O)
Inversion
Finally, in inversion, the subject and predicate terms of the new proposition are contradictories of the subject and predicate terms of the original proposition. And it must be noted that when doing inversions, we change the quantity of the invertend (that is, the original proposition); hence, inversions involve the changing of universal affirmative (A) propositions to particular affirmative (I) propositions, and universal negative (E) propositions to particular negative (O) propositions. Please note that particular affirmative (I) and particular negative (O) propositions do not have inverses.
There are two types of inversion, namely, partial inversion and complete inversion.
In partial inversion, the subject of the inverse (that is, the new proposition) is the contradictory of the subject of the invertend (that is, the original proposition). Let us consider the example below.
Example 1:
All priests are trustworthy. (A)
Therefore, some non-priests are not trustworthy. (O)
Example 2:
No dogs are feline. (E)
Therefore, some non-dogs are cats. (I)
In complete inversion, the subject and predicate of the new proposition are the contradictories of the subject and predicate of the original proposition. Let us consider the examples below.
Example 1:
Anything material is destructible. (A)
Therefore, some non-material things are indestructible. (I)
Example 2:
No wealthy person is financially insecure. (E)
Therefore, some non-wealthy persons are not financially non-insecure. (O)