Let us now review the four different

kinds of propositions.  The first form

is called the contrary.  Its formula

is one of the following.  Either, 'All A

is B' or 'No A is B'.  It is obvious

that the two propositions cannot both be

true, and we therefore would do well

to remember the axiom.

Contrary propositions may both be false.  They cannot both be true.

While the first item, 'contrary propositions may both be false', is obvious,

it is necessary to be on one's guard, for a false reasoning sometimes assumes

that while contrary propositions 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, Archbishop Whately gives the following illustration:

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.

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'.

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

'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 Colossians 1 we learn that principalities and powers are among

those which have been reconciled by the cross.  In the second chapter of

Colossians we learn that principalities and powers were among those that were

spoiled and stripped 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

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 Colossians 1, but great reticence over the passage that occurs in

Colossians 2.