never be true of the same subject at the same time, for they are

contradictory. Nor can the propositions 'it may not be' and 'it cannot

not be' be at once true of the same subject.

The propositions which have to do with necessity are governed by the

same principle. The contradictory of 'it is necessary that it should

be', is not 'it is necessary that it should not be,' but 'it is not

necessary that it should be', and the contradictory of 'it is

necessary that it should not be' is 'it is not necessary that it

should not be'.

Again, the contradictory of 'it is impossible that it should be'

is not 'it is impossible that it should not be' but 'it is not

impossible that it should be', and the contradictory of 'it is

impossible that it should not be' is 'it is not impossible that it

should not be'.

To generalize, we must, as has been stated, define the clauses 'that

it should be' and 'that it should not be' as the subject-matter of the

propositions, and in making these terms into affirmations and

denials we must combine them with 'that it should be' and 'that it

should not be' respectively.

We must consider the following pairs as contradictory propositions:



It may be. It cannot be.

It is contingent. It is not contingent.

It is impossible. It is not impossible.

It is necessary. It is not necessary.

It is true. It is not true.

13



Logical sequences follow in due course when we have arranged the

propositions thus. From the proposition 'it may be' it follows that it

is contingent, and the relation is reciprocal. It follows also that it

is not impossible and not necessary.