Therefore he ought to be worshiped. In this Example, the Major or first Proposition, is we fee conditional, and therefore the Syllogism itself is also of the kind, called by that Name. And here we are to observe, that all conditional Propofitions are made of two distinct Parts: one expreffing the Condition upon which the Predicate agrees or difagrees with the Subject, as in this now before us, if there is a God; the other joining or disjoining the faid Predicate and Subject, as here, he ought to be worshiped. The first of these Parts, or that which implies the Condition, is called the Antecedent; the second, where we join or disjoin the Predicate and Subject, has the Name of the Confequent.

Ground of Il

lation in con. ditional Syllo gisms.

V. THESE Things explained, we are farther to observe; that in all Propofitions of this kind, fupposing them to be exact in point of Form, the Relation between the Antecedent and Confequent, must ever be true and real; that is, the Antecedent must always contain some certain and genuine Condition, which neceffarily implies the Confequent: for otherwise, the Propofition itself will be false, and therefore ought not to be admitted into our Reasonings. Hence it follows, that when any conditional Proposition is assumed, if we admit the Antecedent of that Propofition, we must at the fame time neceffarily admit the Confequent; but if we reject the Consequent, we are in like manner bound to reject the Antecedent. For as the Antecedent always exprefles fome Condition, which neceffarily implies the Truth of the Consequent; by admitting the Antecedent we allow of that Condition, and therefore ought alfo to admit the Consequent. In like manner, if it appears that the Confequent ought to be rejected, the Antecedent evidently must be so too; because, as was just now demonstrated, the admitting of the Antecedent, would neceffarily imply the Admiffion also of the Confequent.

VI. FROM what has been faid it appears, that there are two Ways of arguing in bypothetical Syllogifms, which lead to a certain and unavoidable Conclufion. For as the Major is always a conditional Propofition, confifting of an Antecedent and a Consequent; if the Minor admits the Antecedent, it is plain that the Conclufion must admit the Confequent. This is called arguing from the Admiffion of the Antecedent to the Admiffion of the Consequent, and conftitutes that Mood or Species of hypothetical Syllogifms, which is diffinguished in the Schools by the Name of the Modus ponens, inafmuch as by it, the whole conditional Proposition, both Antecedent and Confequent, is established. Thus:

If God is infinitely wife, and acts with perfect Freedom, be
does nothing but what is best.

But God is infinitely wife, and acts with perfect Freedom:
Therefore he does nothing but what is best.

Here we fee the Antecedent or first Part of the conditional Propofition is efstablished in the Minor, and the Consequent or fecond Part in the Conclufion; whence the Syllogifm itself is an Example of the Modus ponens. But if now we on the contrary suppose, that the Minor rejects the Consequent, then it is apparent, that the Conclufion must also reject the Antecedent. In this Cafe we are said to argue from the Removal of the Consequent, to the Removal of the Antecedent, and the particular Mood or Species of Syllogifms thence arifing, is called by Logicians the Modus tollens; because in it, both Antecedent and Confequent, are rejected or taken away, as appears by the following Example.

If God were not a Being of infinite Goodness, neither would
be confult the Happiness of his Creatures.
But God does confult the Happiness of his Creatures :
Therefore he is a Being of infinite Goodness.

They include

VII. THESE two Species take in the whole Class of conditional Syllogifms, and include all the all the legiti poffible Ways of arguing that lead to a legitimate Conclufion; because we cannot here proceed by

mate Ways of Arguing.

-a contrary Process of Reasoning, that is, from the Removal of the Antecedent to the Removal of the Consequent, or from the establishing of the Confequent to the establishing of the Antecedent. For altho' the Antecedent always expresses fome real Condition, which once admitted neceffarily implies the Consequent, yet it does not follow that there is therefore no other Condition; and if so, then after removing the Antece dent, the Consequent may still hold, because of fome other Determination that infers it. When we fay: If a Stone is exposed Jome time to the Rays of the Sun, it will contract a certain De gree of Heat; the Proposition is certainly true, and admitting the Antecedent, we must also admit the Confequent But as there are other Ways by which a Stone may gather Heat, it will not follow, from the ceasing of the before-mentioned Condition, that therefore the Consequent cannot take place. In other Words, we cannot argue: But the Stone has not been exposed to the Rays of the Sun; therefore neither has it any Degree of Heat: inasmuch as there are a great many other Ways, by which Heat might have been communicated to it. And if we cannot argue from the Removal of the Antecedent to the Removal of the Consequent, no more can we from the Admiffion of the Confequent to the Admiffion of the Antecedent. Because as the Consequent may flow from a great Variety of different Suppofitions, the allowing of it does not determine the precife Supposition, but only that fome one of them muft take place. Thus in the foregoing Propofition, If a Stone is exposed some time to the Rays of the Sun, it will contract a certain Degree of Heat: Admitting the Consequent, viz. that it has contracted a certain Degree of Heat, we are not therefore bound to admit the Antecedent, that it has been fome time exposed to the Rays of the Sun; because there are many other Caufes whence that Heat may have proceeded. These two Ways of arguing therefore, hold not in conditional Syllogifms, Indeed, where the Antecedent expreffes the only Condition on which the Consequent takes place, there they may be applied with Safety; because where-ever that Condition is not, we are fure that neither can the Consequent be, and fo may arque from the Removal of the one to the Removal of the other; as on the contrary, where-ever the Consequent holds, it is certain that the Condition must also take place; which thews, that by establishing the Consequent, we at the fome time eftablish the Antecedent. But as this is a very particular Cafe, and that happens but feldom, it cannot be extended into a general Rule, and therefore affords not any steady and universal Ground of Reasoning upon the two foregoing Sutions.

1. As from the Major's being a conditional Prosition, we obtain the Species of conditional Syll rifms; fo where it is a disjunctive Propofitior the Syllogifm to which it belongs is alfo called Disjunctive, as in the following Example:

The Marner

of arguing Syllogifins.

in disjunctive

The World is either self-existent, or the Work of some finite, or of fome infinite Being.

But it is not jelf-existent, nor the Work of a finite Being: Therefore it is the Work of an infinite Being.

Now a disjunctive Propofition is that, where of several Predicates, we affirm one necessarily to belong to the Subject, to the Exclufion of all the rest, but leave that particular one undetermined. Hence it follows, that as foon as we determine the particular Predicate, all the rest are of course to be rejected; or if we reject all the Predicates but one, that one neceffarily takes place. When therefore in a disjunctive Syllogifm, the feveral Predicates are enumerated in the Major; if the Minor establishes any one of these Predicates, the Conclusion ought to remove all the rest; or if in the Minor, all the Predicates but one are removed, the Conclufion must neceffarily establish that one. Thus in the disjunctive Syllogifm given above, the Major affirms one of three Predicates to belong to the Earth, viz. Self-existence, or that it is the Work of a finite, or that it is the Work of an infinite Being. Two of these Predicates are removed in the Minor, viz. Self-existence, and the Work of a finite Being. Hence the Conclufion neceffarily ascribes to it the third Predicate, and affirms that it is the Work of an infinite Being. If now we give the Syllogifm another Turn, infomuch that the Minor may establish one of the Predicates, by affirming the Earth to be the Production of an infinite Being; then the Conclufion must remove the other two, asserting it to be neither self-existent, nor the Work of a finite Being. These are the Forms of Reasoning in these Species of Syllogifms, the Justness of which appears at first Sight; and that there can be no other, is evident from the very Nature of a disjunctive Propofition.

Imperfect or

IX. In the feveral Kinds of Syllogisms hitherto mutilated Syl. mentioned, we may observe, that the Parts are logisms. compleat; that is, the three Propofitions of which they confift, are represented in Form. But it often happens, that fome one of the Premiffes is not only an evident Truth, but also familiar and in the Minds of all Men; in which Cafe it is usually omitted, whereby we have an imperfect Syllogifm, that feems to be made up of only two Propositions: Should we for instance argue in this manner:

Every Man is mortal:

Therefore every King is mortal.

The Syllogifm appears to be imperfect, as confifting but of two Propofitions. Yet it is really compleat, only the Minot [Every King is a Man] is omitted, and left to the Reader to supply, as being a Propofition fo familiar and evident, that it cannot escape him.

X. THESE seemingly imperfect Syllogisms are Enthymemes. called Enthymemes, and occur very frequently in Reasoning, especially where it makes a Part of common Conversation. Nay there is a particuler Elegance in them, because not difplaying the Argument in all its Parts, they leave fomewhat to the Exercise and Invention of the Mind. By this Means we are put upon exerting ourselves, and feem to share in the Discovery of what is proposed to us. Now this is the great Secret of fine Writing, so to frame and put toge ther our Thoughts, as to give full Play to the Reader's Imagination, and draw him insensibly into our very Views and Courfo

Pot

eM

Course of Reasoning. This gives a Pleasure not unlike to that which the Author himself feels in compofing. It besides shortens Discourse, and adds a certain Force and Liveliness to our Arguments, when the Words in which they are conveyed, favour the natural Quickness of the Mind in its Operations, and a fingle Expreffion is left to exhibit a whole Train of Thoughts.

Ground of
Reasoning in
immediate

XI. But there is another Species of Reasoning with two Propofitions, which seems to be complete in itself, and where we admit the Conclufion without fuppofing any tacit or fuppreffed. Confequences. Judgment in the Mind, from which it follows fyllogistically. This happens between Propofitions, where the Connection is such, that the Admiffion of the one, neceffarily and at the first fight implies, the Admiffion alfo of the other. For if it so falls out, that the Proposition on which the other depends is felfevident, we content ourselves with barely affirming it, and infer that other by a direct Conclufion. Thus by admitting an universal Proposition, we are forced also to admit of all the particular Propofitions comprehended under it, this being the very Condition that constitutes a Proposition universal. If then that univerfal Proposition chances to be self-evident, the particular ones follow of course, without any farther Train of Reasoning. Whoever allows for instance, that Things equal to one and the fame Thing are equal to one another, must at the fame time allow, that two Triangles, each equal to a Square whose Side is three Inches, are also equal between themselves. This Argument therefore,

Things equal to one and the fame Thing are equal to one another:

1

Therefore these two Triangles, each equal to the Square of a
Line of three Inches, are equal betrveen themselves,

is complete in its Kind, and contains all that is neceffary to-
wards a just and legitimate Conclufion. For the first or uni-
verfal Proposition is felf-evident, and therefore requires no far-
ther Proof. And as the Truth of the Particular is infeparably
connected with that of the Univerfal, it follows from it by an
obvious and unavoidable Confequence.

XII. Now in all Cafes of this kind, where Propofitions are deduced one from another, on anuts, account of a known and evident Connection, we Now are faid to reason by immediate Consequence. Such

All reduciblé to Syl'ogifms of f Former other.

me one

a Coherence of Propofitions, manifeft at first fight, and forcing itself upon the Mind, frequently occurs in Reasoning. Logicians have explained at fome length, the feveral SuppofiCul! VOL. II.

K