Our Creator must be worshipped.
God is our Creator.

Therefore God must be worshipped.

The comparison of this third idea, with the two distinct parts of the question, usually requires two propositions, which are called the premises: the third proposition which is drawn from them is the conclusion, wherein the question itself is answered, and the subject and predicate joined either in the negative or the affirmative.

The foundation of all affirmative conclusions is laid in this general truth, that so far as two proposed ideas agree to any third idea, they agree also among themselves. The character of Creator agrees to God, and worship agrees to a Creator, there fore worship agrees to God.

The foundation of all negative conclusions is this, that where one of the two proposed ideas agree with the third idea, and the other disagrees with it, they must needs disagree so far also with one another; as, if no sinners are happy, and if angels are happy, then angels are not sinners.

Thus it appears what is the strict and just notion of a syllogism: It is a sentence or argument made up of three propositions, so disposed, as that the last is necessarily inferred from those which go before, as in the instances which have been just mentioned.

In the constitution of a syllogism two things may be consi dered, viz. the matter and the form of it.

The matter of which a syllogism is made up, is three pro positions; and these three propositions are made up of three ideas or terms variously joined. The three terms are called the remote matter of a syllogism; and the three propositions the proxime or immediate matter of it. The three terms are named the major, the minor, and the middle. The predicate of the conclusion is called the major term, because it is generally of a larger extension than the minor term, or the subject. The major and minor terms are called the extremes. The middle term is the third idea, invented and disposed in two propositions, in such a manner as to shew the connection between the major and minor term in the conclusion; for which reason' the middle term itself is sometimes called the argument.

That proposition which contains the predicate of the conclusion, connected with the middle term, is usually called the major proposition, whereas the minor proposition connects the middle term with the subject of the conclusion, and is sometimes called the assumption.

Note, This exact distinction of the several parts of a syllogism, and of the major and minor terms connected with the middle term in the major and minor propositions, does chiefly belong

to simple or categorical syllogisms, of which we shall speak in the next chapter, though all syllogisms whatsoever have something analogical to it.

Note farther, That the major proposition is generally placed first, and the minor second, and the conclusion in the last place, where the syllogism is regularly composed and represented.

The form of a syllogism is the framing and disposing of the premises according to art, or just principles of reasoning, and the regular inference of the conclusion from them.

The act of reasoning, or inferring one thing from another, is generally expressed and known by the particle therefore, when the argument is formed according to the rules of art; though in common discourse or writing, such causal particles as for, because, manifest the act of reasoning as well as the illative particles then and therefore; and wheresoever any of these words are used, there is a perfect syllogism expressed or implied, though perhaps the three propositions do not appear, or are not placed in regular form.

CHAP. II.—Of the various Kinds of Syllogisms, with particular Rules relating to them.

SYLLOGISMS are divided into various kinds, either according to the question which is proved by them, according to the nature and composition of them, or according to the middle term, which is used to prove the question.

SECT. I. Of universal and particular Syllogisms, both negative and affirmative.

ACCORDING to the question which is to be proved, so syllogisms are divided into universal affirmative, universal negative, particular affirmative, and particular negative. This is often called a division of syllogisms drawn from the conclusion; for so many sorts of conclusions there may be, which are marked with the letters A, E, I, O.

In an universal affirmative syllogism, one idea is proved universally to agree with another, and may be universally affirmed of it; as, every sin deserves death, every unlawful wish is a sin; therefore every unlawful wish deserves death.

In an universal negative syllogism, one idea is proved to disagree with another idea universally, and may be thus denied of it; as, no injustice can be pleasing to God; all persecution for "the sake of conscience is injustice; therefore no persecution for conscience sake can be pleasing to God.

Particular affirmative and particular negative syllogisms,

may be easily understood by what is said of universals, and there will be sufficient examples given of all these in the next

section.

The general principle upon which these universal and particular syllogisms is founded, is this, Whatsoever is affirmed or denied universally of any idea, may be affirmed or denied of all the particular kinds or beings, which are contained in the extension of that universal idea. So the desert of death is affirmed universally of sin, and an unlawful wish is one particular kind of sin, which is contained in the universal idea of sin, therefore the desert of death may be affirmed concerning an unlawful wish. And so of the rest.

Note, In the doctrine of syllogisms, a singular and indefinite proposition are ranked among universals, as was before observed in the doctrine of propositions.

SECT. II. Of plain, simple Syllogisms, and their Rules.

THE next division of syllogisms is into single and compound. This is drawn from the nature and composition of

them.

Single syllogisms are made up of three propositions, compound syllogisms contain more than three propositions, and may be formed into two or more syllogisms. Single syllogisms, for distinction's sake, may be divided into *simple, complex, aud conjunctive.

Those are properly called simple or categorical syllogisms, which are made up of three plain, single or categorical propositions, wherein the middle term is evidently and regularly joined with one part of the question in the major proposition, and with the other in the minor, whence there follows a plain single conclusion; as "every human virtue is to be sought with diligence: prudence is a human virtue; therefore prudence is to be sought diligently."

Note, Though the terms of propositions may be complex; yet where the composition of the whole argument is thus plain, simple, and regular, it is properly called a simple syllogism, since the complexion does not belong to the syllogistic form of it.

Simple syllogisms have several rules belonging to them, which being observed will generally secure us from false inferences; but these rules being founded on four general axioms, it is necessary to mention these axioms beforehand, for the use of those who will enter into the speculative reason of all these rules:

1. Particular propositions are contained in universals, and

As ideas and propositions are divided into single and compound, and single are subdivided into simple and complex; so there are the same divisions and subdivisious applied to syllogisms.

may be inferred from them; but universals are not contained in particulars, nor can be inferred from them. 2. In all universal propositions, the subject is universal: in all particular propositions, the subject is particular. 3. In all affirmative propositions, the predicate has no greater extension than the subject; for its extension is restrained by the subject, and therefore it is always to be esteemed as a particular idea. It is by mere accident, if it ever be taken universally, and cannot happen but in such universal or singular propositions as are reciprocal. ↓ The predicate of a negative proposition is always taken univer Bally, for in its whole extension it is denied of the subject. If we say no stone is vegetable, we deny all sorts of vegetation concerning stones.

The Rules of simple, regular Syllogisms are these:

I. "The middle term must not be taken twice particularly, but once at least universally." For if the middle term be taken for two different parts or kiuds of the same universal idea, then the subject of the conclusion is compared with one of these parts, and the predicate with another part, and this will never shew whether that subject and predicate agree or disagree: there will then be four distinct terms in the syllogisin, and the two parts of the question will not be compared with the same third idea; as if I say, some men are pious, and some men are robbers, I can never infer that some robbers are pious, for the middle term men being taken twice particularly, it is not the same men who are spoken of in the major and minor propositions.

II. "The terms in the conclusion must never be taken more universally than they are in the premises." The reason is derived from the first axiom, that generals can never be inferred from particulars.

III. "A negative conclusion cannot be proved by two affirmative premises.' For when the two terms of the conclusion are united or agree to the middle term, it does not follow by any means that they disagree from one another.

IV. "If one of the premises be negative, the conclusion must be negative." For if the middle term be denied of either part of the conclusion, it may shew that the terms of the conclusion disagree, but it can never shew that they agree.

V." If either of the premises be particular, the conclusion must be particular. This may be proved for the most part from the first axiom.

These two last rules are sometimes united in this single sentence, The conclusion always follows the weaker part of the premises. Now negatives and particulars are counted inferior to affirmatives and universals.

VI. "From two negative premises nothing can be conclud

ed." For they separate the middle term both from the subject and predicate of the conclusion, and when two ideas disagree to a third, we cannot infer that they either agree or disagree with each other. Yet where the negation is a part of the middle term, the two premises may look like negatives according to the words but one of them is affirmative in sense; as, "What has no thought cannot reason; but a worm has no thought; therefore a worm cannot reason." The minor proposition does really affirm the middle term concerning the subject, namely, a worm is what has no thought, and thus it is properly in this syllogism an affirmative proposition.

VII. "From two particular premises nothing can be concluded." This rule depends chiefly on the first axiom.

A more laborious and accurate proof of these rules, and the derivation of every part of them in all possible cases, from the fore-going axioms, require so much time, and are of so little importance to assist the right use of reason, that it is needless to insist longer upon them here. See all this done ingeniously in the Logic called the Art of Thinking, Part III. Chap. III, &c.

SECT. III.-Of the Moods and Figures of simple Syllogisms.

SIMPLE syllogisms are adorned and surrounded in the common books of Logic with a variety of inventions about moods and figures, wherein by the artificial contexture of the letters A, E, I, and O, men have endeavoured to transform Logic, or the Art of Reasoning, into a sort of mechanism, and to teach boys to syllogise, or frame arguments and refute them, without any real inward knowledge of the question. This is almost in the same manner as school-boys have been taught perhaps in their trifling years to compose Latin verses, that is, by certain tables and squares, with a variety of letters in them, wherein by counting every sixth, seventh, or eight letter, certain Latin words should be framed in the form of hexameters or pentameters; and this may be done by those who know nothing of Latin or of verses.

I confess some of these logical subtleties have much more use than those versifying tables, and there is much ingenuity discovered in determining the precise number of syllogisms that may be formed in every figure, and giving the reasons of them, yet the light of nature, a good judgment and due consideration of things, tend more to true reasoning than all the trappings of moods and figures. But lest this book be charged with two great defects and imperfections, it may be proper to give short hints of that which some logicians have spent so much time and paper upon.

All the possible compositions of three of the letters, A, E, I, O, to make three propositions amount to sixty-four; but fiftyVOL. VII.

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