their quality into four, which are marked or denoted by the letters A E, 1, 0, thus: Universal affirmative Particular affirmative Particular negative according to these old Latin rhymes Asserit A, negat E, verum generaliter ambæ ; This may be exemplified by these two ideas, a vine and a tree. A Every vine is a tree. E No vine is a tree. 1 Some vine is a tree. O Some vine is not a tree. The logicians of the schools have wirtten many large trifies concerning the opposition and conversion of propositions. It will be sufficient here to give a few brief hints of these things, that the learner may not be utterly ignorant of them. Propositions which are made of the same subject and predicate are said to be opposite, when that which is denied in one is affirmed in the other, either in whole or in part, without any consideration whether the propositions be true or no. If they differ both in quantity and quality, they are said to be contradictory; as, A Every vine is a tree. O Some vine is not a tree. If two universals differ ries; as, A Every vine is a tree. These can never be both true, or both false at the same time. in quality, they are contra These can never be both If two particular propositions differ in quality, they are subcontraries. The reader should remember here, that a proposition according to its quantity is called universal or particular, and ac cording to its quality it is either affirmative or negative. I Some vine is a tree. O Some vine is not a tree These ay be both true together, 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, A Every vine is a tree. I Some vine is a tree. Or thus: E No vine is a tree. O Some vine is not a tree. The canons of subalternate propositions are usually reckoned these three, viz. (1.) If any 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, 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 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 conver ted 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 Caesar. 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 manuer 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 subject and predicate. But if the form of the sentence, as a logical proposition, be duly considered, the mode itself is the very predicate 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 up on this occasion, (viz.) necessity and contingency which are two opposites, possibility and impossibility which are also two 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 should be of water. With regard to the modal propositions which the schools have introduced, I would make these two remarks: Remark 1. These propositions in English are formed by the resolution of the words, must be, might not be, can be, and caunot be, unto those more explicate form of a logical copula and predicate, is necessary, is contingent, is impossible, is possible: for it is necessary that a globe should be round, signifies no more than that a globe must be round. Remark 2. Let it be noted that this quadruple modality is only an enumeration of the natural modes or manners wherein the predicate is connected with the subject: we might also describe several moral and civil modes of connecting two ideas together, (viz.) lawfulness and unlawfulness, conveniency and inconveniency, &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 inexpe dient: 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, &c. 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 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 it contains two or more propositious 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 thy complex subject does not necessarily or constantly belong to it, then it is determinative, 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 man: but it is not so where the addition is determinative, so we cannot say, every man shall be happy, though every pious man shall be so. As simple ideas are opposed to complex, and single ideas to compound, 30 propositions are distinguished in the manner: the English tongue in this respect having some advantage above the learned languages, which have no usual word to distinguish single from simple, |