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Eduction (Conversion of Propositions): Categorical Logic
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This lecture notes discusses the topic "conversion of propositions" or eduction in Categorical Logic.
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Eduction (Conversion of Propositions): Categorical LogicEduction 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:
1) conversion,
2) obversion,
3) contraposition, and
4) 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.
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