If two particular propositions differ in quality they are subcontraries; as

I Some Vine is a Tree. These may be both true together, O Some Vine is not a Tree. S but they can never be both false. Both particular and universal propositions which agree in quality, but not in quantity, are called subaltern, though these are not properly opposite, as

Or thus:

A Every Vine is a Tree.
I Some Vine is a Tree.

E No Vine is a Tree.

O Some Vine is not a Tree.

The canons of subaltern propositions are usually reckoned these three; namely, (1.) If an universal proposition be true, the particular will be true also, but not on the contrary. And, (2.) If a particular proposition be false, the universal must be false too, but not on the contrary. (3.) Subaltern propositions, whether universal or particular, may sometimes be both true and sometimes both false.

The conversion of propositions, is when the subject and predicate change their places with preservation of the truth. This may be done with constant certainty in all universal negatives and particular affirmatives: as no spirit is an animal, may be converted, no animal is a spirit; and some tree is a vine, may be converted, some vine is a tree,. But there is more of formal trifling in this sort of discourse than there is of solid improvement, because this sort of conversion arises merely from the form of words, as connected in a proposition, rather than from the matter.

Yet it may be useful to observe, that there are some propositions, which by reason of the ideas or matter of which they are composed, may be converted with constant truth: such are those propositions whose predicate is a nominal or real definition of the subject, or the difference of it, or a property of the fourth kind, or a superlative degree of any property or quality whatsoever; or in short wheresoever the predicate and the subject have exactly the same extension, or the same comprehension; as, every vine is a tree bearing grapes; and every tree bearing grapes is a vine: religion is the truest wisdom; and, the truest wisdom is religion; Julius Cæsar was the first Emperor of Rome; and, the first Emperor of Rome was Julius Cæsar." These are the propositions which are properly convertible, and they are called reciprocal propositions.

SECT. IV. Of pure and modal Propositions.

ANOTHER division of propositions among the scholastic writers, is into pure and modal. This may be called (for distinction-sake) a division according to the predicate.

When a proposition merely expresses that the predicate is connected with the subject, it is called a pure proposition; as, every true christian is an honest man: But when it includes also the way and manner wherein the predicate is connected with the subject, it is called a modal proposition; as, when I say, it is necessary that a true christian should be an honest man.

Logical writers generally make the modality of this proposition to belong to the copula, because it shews the manner of the connection between the subject and predicate. But if the form of the sentence as a logical proposition be duly considered, the mode itself is the very predicature of the proposition, and it must run thus: that a true christian should be an honest man is a necessary thing, and then the whole primary proposition is included in the subject of the modal proposition.

There are four modes of connecting the predicate with the subject, which are usually reckoned upon this occasion, namely, necessity and contingency, which are two opposites; possibility and impossibility, which are also opposites; as, "it is necessary that a globe should be round: that a globe be made of wood or glass, is an unnecessary or contingent thing: it is impossible that a globe should be square, it is impossible that a globe may be made of water."

With regard to the modal propositions which the schools have introduced, I would make these two remarks:

I. These propositions in English are formed by the resolution of the words, must be, might not be, can be, and cannot be, into those more explicate forms of a logical copula and predicate, is necessary, is contingent, is possible, is impossible: for it is necessary that a globe should be round, signifies no more than that a globe must be round.

II. Let it be noted, that this quadruple modality is only an enumeration of the natural modes or manners wherein the predi cate is connected with the subject: we might also describe several moral and civil modes of connecting two ideas together, namely, lawfulness and unlawfulness, conveniency, and incon veniency, &c. whence we may form such modal propositions as these it is unlawful for any person to kill an innocent man: it is unlawful for christians to eat flesh in Lent: to tell all that we think is expedient for a man to be affable to his neighbour is very convenient, &c.

There are several other modes of speaking whereby a predicate is connected with a subject: such as it is certain, it is doubtful, it is probable, it is improbable, it is agreed, it is granted, it is said by the ancients, it is written, &c. all which will form other kinds of modal propositions.

But whether the modality be natural, moral, &e: yet in

all these propositions it is the mode is the proper predicate, and all the rest of the proposition, except the copula (or word is) belongs to the subject; and thus they become pure propositions of a complex nature, of which we shall treat in the next section; so that there is no great need of making modals of a distinct sort.

There are many little subtleties which the schools acquaint us with concerning the conversion and opposition and equipollence of these modal propositions, suited to the Latin or Greek tongues, rather than the English, and fit to pass away the idle time of a student, rather than to enrich his understanding. SECT. V. Of single Propositions, whether simple or complex.

WHEN we consider the nature of propositions, together with the formation of them, and the materials whereof they are made, we divide them into single and compound.

A single proposition is that which has but one subject and one predicate; but if it has more subjects, or more predicates, it is called a compound proposition, and indeed it contains to or more propositions in it.

A single proposition (which is also called categorical) may be divided again into simple and complex*.

A purely simple proposition is that whose subject and predicate are made up of single terms; as virtue is desirable: every penitent is pardoned: no man is innocent.

When the subject or predicate, or both, are made up of complex terms, it is called a complex proposition; as every sincere penitent is pardoned: virtue is desirable for its own sake: no man alive is perfectly innocent.

If the term which is added to the subject of a complex proposition be either essential or any way necessary to it, then it is called explicative, for it only explains the subject; as, every mortal man is a son of Adam. But if the term added to make up the complex subject does not necessarily or constantly belong to it, then it is determinate, and limits the subject to a particular part of its extension; as, every pious man shall be happy. In the first proposition the word mortal is merely explicative: in the second proposition the word pious is determinative.

Here note, that whatsoever may be affirmed or denied concerning any subject, with an explicative addition, may be also affirmed or denied of that subject without it, as we may boldly say, every man is a son of Adam, as well as every mortal

As simple ideas are opposed to complex, and single ideas to compound, so propositions are distinguished in the same manner: the English tongue, in this respect having some advantage above the learned languages, which have no usual word to distinguish single from simple.

:

man but it is not so, where the addition is determinative, for we cannot say, every man shall be happy, though every pious mau shall be so.

In a complex proposition the predicate or subject is sometimes made complex by the pronouns who, which, whose, to whom, &c. which make another proposition; as, every man who is pious shall be saved: Julius, whose sirname was Cæsar, overcame Pompey: bodies, which are transparent, have many pores. Here the whole proposition is called the primary or chief, and the additional proposition is called an incident proposition. But it is still to be esteemed in this case merely as a part of the complex term; and the truth or falsehood of the whole complex proposition is not to be judged by the truth or falsehood of the incident proposition, but by the connection of the whole subject with the predicate. For the incident proposition may be false and absurd, or impossible, and yet the whole complex proposition may be true; as, a horse which has wings might fly over the Thames.

Beside this complexion which belongs to the subject or predicate, logical writers used to say, there is a complexion which may fall upon the copula also; but this I have accounted for in the section concerning modal propositions; and indeed it is not of much importance whether it were placed there or here.

SECT. VI. Of compound Propositions.

A COMPOUND proposition is made up of two or more subjects or predicates, or both; and it contains in it two or more propositions, which are either plainly expressed, or concealed and implied.

The first sort of compound propositions are those wherein the composition is expressed and evident, and they are distinguished into these six kinds, namely, copulative, disjunctive, conditional, causal, relative, and discretive.

I. Copulative propositions, are those which have more subjects or predicates connected by affirmative or negative conjunctions; as "riches and honour are temptations to pride: Cæsar conquered the Gauls and the Britons: neither gold nor jewels will purchase immortality." These propositions are evidently each of them may be resolved into two propositions, namely, riches are temptations to pride; aud honour is a temptation to pride; and so the rest.

comp

The truth of copulative propositions depends upon the truth of all the parts of them; for if Cæsar had conquered the Gauls, and not the Britons, or the Britons, and not the Gauls, the second copulative proposition had not been true.

Here note, Those propositions, which cannot be resolved. into two or more simple propositions, are not properly copulative, though two or more ideas be connected and coupled by such conjunctions, either in the subject or predicate; as, " two and three make five: majesty and meekness do not often meet the sun, moon, and stars are not all to be seen at once." Such propositions are to be esteemed merely complex, because the predicate cannot be affirmed of each single subject, but only of all of them together as a collective subject.

II. Disjunctive propositions, are when the parts are disjoined or opposed to one another by the disjunctive particles; as, it is either day or night: the weather is either shining or rainy: quantity is either length, breadth, or depth.

The truth of disjunctives depends on the necessary and immediate opposition of the parts; therefore only the last of these examples is true; but the two first are not strictly true, because twilight is a medium between day and night; and dry cloudy weather is a medium between shining and raining.

III. Conditional or hypothetical propositions, are those whose parts are united by the conditional particle if'; as, if the sun be fixed the earth must move; if there be no fire, there will be no smoke.

Note, The first parts of these propositions, or that wherein the condition is contained, is called the antecedent, the other is called the consequent.

The truth of these propositions depends not at all on the truth or falsehood of their two parts, but on the truth of the cons nection of them; for each part of them may be false, and yet the whole proposition true; as, if there be no providence, there will be no future punishment.

IV. Causal propositions are, where two propositions are joined by causal particles; as, "houses were not built that they might be destroyed: Rehoboam was unhappy because he fol lowed evil council."

The truth of a causal proposition arises not from the truth of the parts, but from the causal influence that the one part of it has upon the other; for both parts may be true, yet the proposition false, if one part be not the cause of the other.

Some logicians refer reduplicative propositions to this place, as men, considered as men, are rational creatures, that is, because they are men.

V. Relative propositions have their parts joined by such particles, as express a relation or comparison of one thing to another; as," when you are silent, I will speak as much as you are worth, so much shall you be esteemed as is the father, so is the son: where there is no tale-bearer, contention will cease."