four of them are excluded from forming true syllogisms by the seven rules in the foregoing section; the remaining ten are variously diversified by figures and moods into fourteen syllogisms.

The figure of a syllogism is the proper disposition of the middle term with the parts of the question.

A mood is the regular determination of propositions according to their quantity and quality, that is, their universal or particular affirmation or negation; which are signified by certain artificial words wherein the consonants are neglected, and these four vowels, A, E, I, O, are only regarded.

There are generally counted three figures. In the first of them the middle term is the subject of the major proposition, and the predicate of the minor. This contains four moods, called, Barbara, Celarent, Darii, Ferio. And it is the excellency of this figure, that all sorts of questions or conclusions may be proved by it, whether A, E, I, or O, that is, universal or particular, affirmative or negative; as,

Bar-Every wicked man is truly miserable;
ba-All tyrants are wicked men ;

ra. Therefore all tyrants are truly miserable.
Ce-He that's always in fear is not happy;
la-Covetous men are always in fear;
rent. Therefore covetous men are not happy.
Da-Whatsoever furthers our salvation is good for us;
ri-Some afflictions further our salvation;

i. Therefore some afflictions are good for us.

Fe-Nothing that must be repented of is truly desirable;
ri. Some pleasures must be repented of;

o. Therefore there are some pleasures which are not truly
desirable.

In the second figure the middle term is the predicate of both the premises: this contains four moods, namely, Cesare, Camestres, Festino, Baroca, and it admits only of negative conclusions; as,

Ce-No liar is fit to be believed;

sa-Every good christian is fit to be believed;

re. Therefore no good christian is a liar.

The reader may easily form examples of the rest.

The third figure requires that the middle term be the sub. ject of both the premises. It has six moods, namely, Darapti, Felapton, Disamis, Datasi, Bocardo, Ferison: and it admits only of particular conclusions; as,

Da-Whosoever loves God shall be saved;

rap-All the lovers of God have their imperfections;
ti. Therefore some who have imperfections shall be saved.

I leave the reader to form examples of the rest.
The moods of these three figures are comprised in four
Latin verses.

Barbara, Celarent, Darii, Ferio, quoque primæ.
Cesare, Camestres, Festino, Baroco, secundæ.
Tertia Derapti, sibi vindicat, atque Felapton,
Adjungens Disamis, Datisi, Bocardo, Ferison.
The special rules of the three figures are these.

In the first figure the major proposition must always be universal, and the minor affirmative. In the second figure also the major must be universal, and one of the premises, together with the conclusion, must be negative. In the third figure the minor must be affirmative, and the conclusion always particular. There is also a fourth figure, wherein the middle term is predicated in the major proposition, and subjected in the minor: but this is a very indirect and oblique manner of concluding, and is never used in the sciences, nor in human life, and therefore I call it useless. Some logicians will allow it to be nothing else but a mere inversion of the first figure; the moods of it, namely, Baralipton, or Babari, Calentes, Dibatis, Fespamo, Fresisom, are not worthy to be explained by one example.

SECT. IV. Of Complex Syllogisms.

IT is not the mere use of complex terms in a syllogism that gives it this name, though one of the terms is usually complex ; but those are properly called complex syllogisms, in which the middle term is not connected with the whole subject, or the whole predicate in two distinct propositions, but is intermingled and compared with them by parts, or in a more confused manner, in different forms of speech; as,

The sun is a senseless being;

The Persians worshipped the sun;

Therefore the Persians worshipped a senseless being. Here the predicate of the conclusion is worshipped a senseless being, part of which is joined with the middle term sun in the major proposition, and the other part in the minor. Though this sort of argument is confessed to be entangled or confused, and irregular, if examined by the rules of simple syllogisms: yet there is a great variety of arguments used in books of learning, and in common life, whose consequence is strong and evident, and which inust be ranked under this head; as,

I. Exclusive propositions will form a complex argument; as, pious men are the only favourites of heaven; true christians are favourites of heaven; therefore true christians are pious men. Or thus, hypocrites are not pious men; therefore hypocrites are not favourites of heaven.

II. Exceptive propositions will make such complex syllogistas; as, none but physicians came to the consultation; the

nurse is no physician; therefore the nurse came not to the con sultation.

III. Or, Comparative propositions; as knowledge is better than riches: virtue is better than knowledge; therefore virtue is better than riches or thus, a dove will fly a mile in a minute; a swallow flies swifter than a dove; therefore a swallow will fly more than a mile in a minute.

IV. Or, Inceptive and desitive propositions; as, the fogs vanish as the sun rises; but the fogs have not yet began to vanish; therefore the sun is not yet risen.

V. Or Modal propositions; as, it is necessary that a General understand the art of war; but Caius does not understand the art of war; therefore it is necessary Caius should not be a General: Or thus, A total eclipse of the sun would cause darkness at noon it is possible that the moon at that time may totally eclipse the sun; therefore it is possible that the moon may cause darkness at noon.

Besides all these, there is a great number of complex syllogisms which can hardly be reduced under any particular titles, because the forms of human language are so exceeding vari

ous; as,

Christianity requires us to believe what the apostles wrote: St. Paul is an apostle; therefore christianity requires us to believe what St. Paul wrote.

No human artist can make an animal; a fly or a worm is an animal; therefore no human artist can make a fly or a

worm.

The father always lived in London; the son always lived with the father; therefore the son always lived in London.

The blossom soon follows the full bud; this pear-tree hath many full buds; therefore it will shortly have many blossoms.

One hail-stone never falls alone: but a hailstone fell just now; therefore others fell with it.

Thunder seldom comes without lightning; but it thundered yesterday; therefore probably it lightened also.

Moses wrote before the Trojan war; the first Greek historians wrote after the Trojan war; therefore the first Greek historians wrote after Moses.*

Now the force of all these arguments is so evident and conclusive, that though the form of the syllogism be never so irregular yet we are sure the inferences are just and true; for the premises, according to the reason of things, do really

Perhaps some of these syllogisms may be reduced to those which ! call "connexive" afterward, but is of little moment to what "species" they Velong; for it is not any formal set of rules, so much as the evidence and force of reason, that must determine the truth or falsehood of all such sylTugisms.

DO

contain the conclusion that is deduced from them, which is a never-failing test of a true syllogism, as shall be shewn hereafter.

The truth of most these complex syllogisms may also be made, to appear, if needful by reducing them either to regular, simple sollygisms, or to some of the conjunctive syllogisms, which are described in the next section. I will give an instance only in the first, and leave the rest to exercise the ingenuity of the reader. The first argument may be reduced to a syllogism in Barbara, thus,

The sun is a senseless being:

What the Persians worshipped is the sun;

being.

Therefore what the Persians worshipped is a senseless

Though the conclusive force of this argument is evident without the reduction.

:

SECT. V.-Of Conjunctive Syllogisms.

THOSE are called conjunctive Syllogisms, wherein one of the premises, namely the major, has distinct parts, which are joined by a conjunction, or some such particle of speech. Most times the major or minor, or both, are explicitly compound propositions and generally the major proposition is made up of two distinct parts or propositions, in such a manner, as that by the assertion of one in the minor, the other is either asserted or denied in the conclusion; or, by the denial of one in the minor, the other is either asserted or denied in the conclusion. It is hardly possible indeed to fit any short definition to include all the kinds of them; but the chief amongst them are the conditional syllogism, the disjunctive, the relative and the connexive.

I. The conditional, or hypothetical syllogism, is that whose major or minor, or both, are conditional propositions; as, If there be a God, the world is governed by providence; but there is a God; therefore the world is governed by Providence.

These syllogisms admit two sorts of true argumentation, whether the major is conditional.

1. When the antecedent is asserted in the minor, that the consequent may be asserted in the conclusion; such is the preceding example. This is called arguing from the position of the antecedent to the position of the consequent.

2. When the consequent is contradicted in the minor proposition, that the antecedent may be contradicted in the conclusion as, 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. This is called arguing from the removing of the consequent to the removing of the antecedent.

To remove the antecedent or consequent here, 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, as appears thus: "If every creature be reasonable, every brute is reasonable; but no brute is reasonable;" therefore no creature is reasonable. Whereas, if you say in the minor, but every brute is not reasonable, then it would follow truly in the conclusion, therefore every creature is not reasonable.

When the antecedent or consequent are negative propositions, they are removed by an affirmative; as, If there be no God, then the world does not discover creating wisdom; but the world does discover creating wisdom; therefore there is a God. In this instance the consequent is removed or contradicted in the minor, that the antecedent may be contradicted in the conclusion. So in this argument of St. Paul; 1 Cor. xv. If the dead rise not, Christ died in vain; but Christ did not die in vain: therefore the dead shall rise.

There are also two sorts of false arguing, namely, (1.) From the removing of the antecedent to the removing of the consequent; or, (2.) From the position of the consequent, to the position of the antecedent. Examples of these are easily framed; as,

(1.) If a minister were a prince he must be honoured; but a minister is not a prince :

Therefore he must not be honoured.

(2.) If a minister were a prince, he must be honoured; but a minister must be honoured;

Therefore he is a prince.

Who sees not the ridiculous falsehood of both these syllo

gisms?

Observ. I. If the subject of the antecedent and the consequent be the same, then the hypothetical syllogism may be turned into a categorical one; as, If Cæsar be a king he must be honoured; but Cæsar is a king; therefore, &c. This may be changed thus, Every king must be honoured; but Cæsar is a king; therefore, &c.

II. If the major proposition only be conditional, the conclusion is categorical: But if the minor or both be conditional, the conclusion is also conditional; as, the worshippers of images are idolators if the Papists worship a crucifix, they are worshippers of an image; therefore, if the Papists worship a crucifix, they are idolators. But this sort of syllogisms should be avoided as much as possible in disputation, because they greatly embarrass a cause: The syllogisms, whose major only is hypothetical, are very frequent, and used with great advantage.

III. A disjunctive syllogism is when the major proposition is