formed. Hence transformation is really nothing but a method of making more obvious and explicit, of bringing out into full relief, judgments that lurk in the background of consciousness when other judgments dealing with the same subject-matter are propounded.

There are two distinct ways of accomplishing this result. First, by establishing the relation of the subjectterm to the predicate-term, there is always implied the (negative) relation of that same subject-term to the contradictory of that same predicate-term; this may be brought out in a new judgment expressing the implied relation. This is called obversion, which consists in asserting a new judgment with the same subject-term as the original proposition. but with opposite quality, and with the contradictory of the original predicate-term as the new predicate. Hence in obversion only the predicate-term and copula are affected. Second, a judgment establishing a relation between the two ideas represented by the two terms of a proposition implies another judgment dealing with the same subject-matter, having the same quality, and keeping within the limits of the knowledge communicated in the original proposition, but bringing out explicitly how the predicate-term is related to the subject-term in respect to distribution. This is called conversion, which consists in interchanging the subject and predicate terms of the original proposition in the new proposition, with no change in quality. Since the original judgment contains the knowledge from which the new proposition is derived, the terms in the latter must never be distributed unless they were distributed in the former. There are two types of conversion:

one, conversion by limitation, or per accidens, is so called because the subject-term of the original proposition loses its distribution in becoming the predicate-term of the new proposition. The other type is called simple conversion because no change in distribution occurs. There is a third species of transformation called contraversion (also contraposition), which does not introduce any new operation, but simply combines the two already mentioned, first obverting the original proposition and then converting the proposition which results from obversion.

The proposition from which we start in transformation is called the obvertend, convertend, or contravertend, according to the process we contemplate. The derived proposition is called the obverse, converse, or contraverse, according to the process employed to obtain it.

Obversion is applicable to all four propositions. Conversion by limitation only is applicable to A, because the predicate-term of this proposition is not distributed, and must be kept undistributed as the subject-term of the new (I) proposition. Simple conversion is applicable to E and I because there is a balance in regard to the use of the two terms in these propositions, both being distributed in E and both undistributed in I. O cannot be converted because the undistributed subjectterm of the original proposition would have to become the distributed predicate-term of the derived proposition, thus violating the rule of conversion. Contraversion is applicable to all the propositions excepting I. I cannot be contraverted because the step of obversion would give O, and this cannot be submitted to the sec

ond step of conversion for reasons already explained. Though E is contravertible, this process is not often employed upon it because its contraverse is the same as the contraverse of its subalternate O.

The following table of examples will make the recent discussion clearer:

OBVERTEND

OBVERSION

OBVERSE

A, All voters are citizens,

E, No bats are birds,

I, Some insects are winged,

obverts into E, No voters are noncitizens.

obverts into A, All bats are non

birds.

obverts into O, Some insects are not non-winged.

O, Some men are not religious, obverts into I, Some men are non

religious.

Contravertend, A, All voters are citizens.
(Obverse, E, No voters are non-citizens.)
Contraverse, E, No non-citizens are voters.

Contravertend, E, No bats are birds.
(Obverse, A, All bats are non-birds.)
Contraverse, I, Some non-birds are bats.

Contravertend, O, Some men are not religious.
(Obverse, I, Some men are non-religious.)

Contraverse, I, Some non-religious creatures are men.

I is not contravertible.

The following table indicates the processes of transformation that are applicable to the several propositions:

PROCESSES OF TRANSFORMATION APPLICABLE TO THE FOUR

56. REASONS FOR TRANSFORMING PROPOSITIONS.— The student may wonder why we should be to all this trouble to transform the various propositions. The real utility of this manipulation of the judgment will not be fully understood until the subject of deductive reasoning is reached. But a hint may be given here. In the first place, it is a powerful aid to exact thought to know and understand just how much truth, besides that directly stated, is implied in a proposition which we utter or to which we give assent. In the second place, the thinking involved in following the possible transformation of propositions and seeing the limits thereto is an excellent mental discipline, which has a value analogous to that of reducing or simplifying algebraic

expressions. In the third place, the cogency of deductive reasoning may often be more clearly demonstrated when a propositional element of the deductive argument is transformed. Let it suffice here to warn the student that the complete mastery of this topic is an indispensable condition of successful work in the analysis of argument.

REFERENCES

Creighton, An Introductory Logic, Ch. VII.
Hyslop, Elements of Logic, Chs. IX and X.

Welton, Manual of Logic, Vol. I, Bk. III, Ch. II, and Ch. III, § 102.

Welton, The Logical Bases of Education, Ch. VII.

Hibben, Logic, Deductive and Inductive, Chs. XII, XIII, and

XIV.

REVIEW QUESTIONS

1. How much of the denotation of the subject-term is referred to in the A proposition? of the predicate-term?

2. How much of the denotation of the subject and predicate terms is referred to in the E proposition?

3. How much of the denotation of the two terms is referred to in the I?

4. How much of the denotation of the subject-term is taken in the O proposition? of the predicate-term?

5. Why are A and E called universal? I and O particular? 6. How does the knowledge of the predicate-term given us in the affirmative propositions compare with that given us in the negative propositions?

7. What do you understand by distribution, by a distributed term, and by an undistributed term?

8. How many distributions are possible in the proposition? 9. How many distributions occur in A? in E? in I? in O? 10. What kind of relationship exists between A and E, and what name is given to it? Answer the same questions in respect to A and O, O and A, E and I, I and E, A and I, I and A, E and O, O and E, I and Q.