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may both be false, one must be true. This, however, is a snare. Simply to deny that
"All A is B" does not, of necessity, admit that "No A is B".
Contrary propositions differ in quantity, quality, or both, and the truth or falsity of any
proposition depends on the subject-matter of the proposition.
Subject-matter may be (1) Necessary, or (2) Contingent.
For example, Whately
gives the following illustration:--
(1) NECESSARY MATTER.-- " `All islands are surrounded by water'. This must be
so, because the matter is necessary. To say `No islands are surrounded by water' or
`Some islands are not surrounded by water' is manifestly false."
(2) CONTINGENT MATTER.--" `Some islands are fertile': `Some are not fertile'.
These assertions are both true because the matter is contingent. If we use `All' or
`No' with contingent matter our propositions will be false. It is necessarily true that
all islands are surrounded by water; it is not necessarily true that all islands are
fertile, barren, sandy, rocky, etc., etc."
We trust the reader will not lightly set these things aside: to keep these principles well
before the mind will save from many snares. We arrive, therefore, at the following:--
All affirmatives, in necessary matter, are true, and negatives false.
All universals, in contingent matter, are false, and particulars are true.
"All" and "No", in contingent matter, render the proposition false. Many erroneous
doctrines will be found under this heading.
The second form of proposition is called the "Sub contrary". In this case, both
positive and negative may be true: they cannot, however, both be false. We must
therefore learn to distinguish these "sub contraries" from the ordinary contraries. The
formula for this proposition is "Some A is B". "Some A is not B." It is self-evident that
if some A is B then some A is not B. In Col. 1: we learn that principalities and powers
are among those which have been reconciled by the cross. In Col. 2: we learn that
principalities and powers were among those that were spoiled and stript off by the cross.
To use "all" in either of these cases will be evidently untrue. We must say:--
"Some principalities and powers were reconciled to God by the cross, and Some
principalities and powers were not reconciled to God by the cross."
If the reader will consult the writings of those who advocate universal reconciliation,
he will discover great prominence given to the passage that occurs in Col. 1:, but great
reticence over the passage that occurs in Col. 2:
We now come to what is called the "Contradictories". The formulæ are as follows:
"All A is B"; "Some A is not B", and "No A is B"; "Some A is B."
The rule to remember is that of two contradictory propositions, one must be true and
the other false. If it is true that "all men are sinners", then it is false to assert that "some
men are not sinners". If it be true to assert that "No men are righteous", then it is false to
affirm that "Some men are righteous". If, therefore, we discover that the Scriptures in