5. Relative Propositions.

A relative proposition is one whose parts are connected by a particle expressing relation; as,

Books are valuable, in so far as they are useful.

6. Causal Propositions.

A causal proposition is one whose parts are connected by a particle asserting that one of them is the cause of the other; as,

Cæsar defeated Pompey, because his army was better disciplined.

Or indicating that one of them is not the cause of the other;

as,

All events are necessary, because they were decreed by fate. A causal proposition is contradicted by denying the causation.

7. Comparative Propositions.

A comparative proposition is one which expresses the agreement or disagreement of a predicate and subject with each other in a greater or less degree; as,

The Greeks were more polished than the Romans.
The Christian religion is preferable to the Mahometan.

8. Exclusive Propositions.

An exclusive proposition is one which asserts that the predicate so agrees with the subject as to agree with it only; as, Victoria alone is Queen of England.

The Platonists were the only school of philosophers who maintained the immortality of the soul.

a There is a difference between the words alone and only, for 'only' implies that there is no other of the same kind, while alone' imports being unaccompanied with any other.

Exclusive propositions are false, if the predicate does not agree with the subject, or if it agrees with more subjects than

one.

9. Exceptive Propositions.

An exceptive proposition is one which expresses the agreement or disagreement of the subject with the predicate, except in some part of it; as,

All except the wise men are mad.

All but the pious are foolish.

The falsehood of an exceptive proposition is shown in the same way as in an exclusive.

10. Inceptive and Desitive Propositions.

Inceptive and desitive propositions are those in which something is said to begin or end; as,

After the death of the Gracchi, Rome ceased to be free.

SECTION IV.

CONDITIONAL SYLLOGISMS.

A syllogism is said to be conditional when either its major or minor premiss is expressed under a condition, or both the major and minor.

a An exclusive proposition may be changed into a synonymous exceptive, and in the change the subject of the exclusive becomes the excepted part of the exceptive. If the exclusive be affirmative, the exceptive will be negative, and vice versa, for an affirmative exclusive asserts that the predicate agrees with the subject alone, which is the same thing as to say, that the predicate disagrees with all except that subject; and this is a negative exceptive. Thus the exclusive-' Men are the only animals that reason'-when expressed in the form of an exceptive, will be, 'No animals but men reason.'-Walker, p. 80.

b An inceptive becomes desitive by using the desitive verb for the inceptive, and instead of the state after, the change declaring the state before, and similarly the desitive may become inceptive.-Walker, p. 80.

Conditional syllogisms are consequently of three kinds :— 1. When one of the premisses is conditional, and the conclusion absolute. In this case the major must be the conditional proposition.

2. When one of the premisses is conditional and the conclusion conditional. In this case the minor must be the conditional proposition.

3. When both major and minor propositions are conditional. In this case the conclusion must also be conditional.

When the major proposition is alone conditional, the conclusion is absolute, for this reason, that in the minor the part which asserts or denies the condition is put absolutely, and thus prevents the condition from entering the conclusion.

In conditional syllogisms of this kind, legitimate conclusions may be obtained in two ways:

1. From the position of the antecedent to the position of the consequent, e. g.

If the Christian miracles are credible, the Christian doctrines are true;

But the Christian miracles are credible; therefore,

The Christian doctrines are true.

In this example we proceed from the position of the antecedent to the position of the consequent. An argument of this kind is said to be constructive, or as it is technically termed in the modus ponens.

2. From the remotion of the antecedent to the remotion of the consequent, e. g.

If Atheists are in the right, then the world exists without a cause;

But the world does not exist without a cause; therefore, Atheists are not in the right.

In this example we proceed from the remotion of the consequent to the remotion of the antecedent. An argument of

this kind is said to be destructive, or, as it is technically termed, in the modus tollens.

The conclusiveness of each of these processes of reasoning is obvious. In the former example it is asserted in the major, that the consequent follows from the antecedent, and consequently, if the antecedent be true, the consequent must be true. In the latter example, the consequent is denied, or, in other words, is not true; and hence the antecedent from which it follows cannot be true.

In examples like the foregoing, where the major alone is conditional, we must consider the minor as the true proposition, for it is absolutely posited; and the conclusion, therefore, depends for its truth on the truth of the minor.

It may be remarked, that the removal of the antecedent or consequent does not merely signify the denial of it; but the contradiction of it, for the mere denial of it by a contrary proposition, will not make a true syllogism, e. g.

If every creature is reasonable, every brute is reasonable; But no brute is reasonable; therefore,

No creature is reasonable.

But if we put the minor in this form, viz.,

Every brute is not reasonable,

then it will follow legitimately in the conclusion, that Every creature is not reasonable.

It may be remarked, also, that when the antecedent and consequent are negative, they are removed by an affirmative,

as

If there be no God, then the world does not exhibit creative wisdom;

a If the absolute premiss assert the falsehood of the consequent, we must take care to make the conclusion the contradictory, not the contrary of the antecedent. For we can only infer that the antecedent is false, but are not thence warranted to assert the truth of its contrary.-Walker's Commentary.

But the world does exhibit creative wisdom; therefore,
There is a God.

But while, in conditional syllogisms of this description, there are two legitimate modes of reasoning, there are also two illegitimate modes,

1. When we proceed from the remotion of the antecedent to the remotion of the consequent.

In illustration, let us take the following example:

If Mahometanism be true, idolatry is sinful;

But Mahometanism is not true; therefore,
Idolatry is not sinful.

It is clear that in this example we cannot proceed from the remotion of the antecedent to the remotion of the consequent, for the sinfulness of idolatry is not affected by the truth or non-truth of Mahometanism.

2. When we proceed from the position of the consequent to the position of the antecedent.

In illustration, let us take the following example :

If states have great standing armies, they are powerful.
But this state is powerful; therefore,

This state has great standing armies.

It is obvious that in this example we cannot proceed from the position of the consequent to the position of the antecedent for great standing armies do not necessarily prove the internal power of a state.

When the subject of the antecedent and consequent is the same, a conditional syllogism may be changed into a categorical one, e. g.

If Cæsar be a king, he must be honoured;

But Cæsar is a king; therefore,

He must be honoured;