Thought-Culture; Or, Practical Mental TrainingAtkinson, William Walker
Science
Thought-Culture; Or, Practical Mental Training
Atkinson, William Walker
Thought and thinking
In Conversion by Contraposition, there is a change in the position of
the negative copula, which shifts the expression of the quality. As for
instance, in the Particular Negative "Some animals are not horses," we
cannot say "Some horses are not animals," for that would be a violation
of the rule that "no term must be distributed in the converse which is
not distributed in the convertend," for as we have seen in the preceding
chapter: "In Particular propositions the _subject_ is _not_
distributed." And in the original proposition, or convertend, "animals"
is the _subject_ of a Particular proposition. Avoiding this, and
proceeding by Conversion by Contraposition, we convert the Convertend
(O) into a Particular Affirmative (I), saying: "Some animals are
not-horses;" or "Some animals are things not horses;" and then
proceeding by Simple Conversion we get the converse, "Some things not
horses are animals," or "Some not-horses are animals."
The following gives the application of the appropriate form of
Conversion to each of the several four kind of Judgments or
Propositions:
(A) _Universal Affirmative_: This form of proposition is converted by
Limited Conversion. The predicate not being distributed in the
convertend, it cannot be distributed in the converse, by saying "all."
("In affirmative propositions the _predicate_ is _not_ distributed.")
Thus by this form of Conversion, we convert "All horses are animals"
into "Some animals are horses." The Universal Affirmative (A) is
converted by limitation into a Particular Affirmative (I).
(E) _Universal Negative_: This form of proposition is converted by
Simple Conversion. In a Universal Negative _both terms are distributed_.
("In universal propositions, the _subject_ is distributed;" "In
negative propositions, the _predicate_ is distributed.") So we may say
"No cows are horses," and then convert the proposition into "No horses
are cows." We simply convert one Universal Negative (E) into another
Universal Negative (E).
(I) _Particular Affirmative_: This form of proposition is converted by
Simple Conversion. For _neither term is distributed_ in a Particular
Affirmative. ("In particular propositions, the _subject_ is _not_
distributed. In affirmative propositions, the _predicate_ is _not_
distributed.") And neither term being distributed in the convertend, it
must not be distributed in the converse. So from "Some horses are males"
we may by Simple Conversion derive "Some males are horses." We simply
convert one Particular Affirmative (I), into another Particular
Affirmative (I).
(O) _Particular Negative_: This form of proposition is converted by
Contraposition or Negation. We have given examples and illustrations in
the paragraph describing Conversion by Contraposition. The Particular
Negative (I) is converted by contraposition into a Particular
Affirmative (I) which is then simply converted into another Particular
Affirmative (I).
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