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selves. The character of a creator agrees to God, and worship agrees to a creator, therefore worship agrees to God.
The foundation of all negative conyulsions is this, that where one of the two proposed ideas agrees with a third idea, and the other disagrees with it, they must needs disagree so far also with one another; as, if no finners are happy, and if angels are happy, then angels are not finners.
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 inItances which have been just mentioned.
In the constitution of a syllogism two things may be considered, (viz.) the matter and the form of it.
The matter of which a syllogism is made up, is three propositions ; 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 propofitions 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 difposed in two propositions in such a manner as to thew the connection between the major and minor term in the conclufion ; for which reason the middle term itfcif is sometimes called the ar.gument.
The proposition which contains the predicate of the conclusion, connected with the middle term, is usually called the major propofition, whereas the minor propofition connects the middle term with the subject of the conclusion, and is sometimes called the afiumption.
Note, This exact distinction of the several parts of a fyllogism, and of the major and minor terms connected with the middle term, in the major and minor propofitions, does chiefly beloug to simple or categorical fyllo
gisins, of which we shall speak in the next chapter, though, all syllogifms, whatsoever have something ana- · logical to it.
Note farther, that the major proposition is generally placed first, and the minor fecond, and the conclusion in the last place, where the syllogism is regularly composed and represented.
The form of a fyllogism 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 art 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 casual 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 propofitions do not appear, or are not placed in regular forms. ·
OF THE VARIOUS KINDS OF SYLLOGISMS, WITH PARTIL
. CULAR RULES RELATING TO THEM.
CYLLOGISMS are divided into various kinds either A 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 Syllogismsy both negative and
afirmative. ACCORDING to the question which is to be Di proved, so syllogisms are divided into universal
affirmitive, universalnegative, particularaffirmative, and particular negative. This is often called a division of Tyllogisms drawn from the conclufions; for so many forts of conclusions there may be which are marked with the letter 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 fin 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 in. justice; therefore no perfecution for conscience sake can be pleasing to God.
Particular affirmitive, 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 are founded is this ; whatsoever is affirmed or denied universally of any idea, may be af. firmed or denied of all the particula: kinds of beings which are contained in the extension of that universal idea. So the desert of death is affirmed universally of fin, and an unlawful wish is one particular kind of fin, which is contained in the universal idea of fin; there. fore the desert of death may be affirmed concerning an unlawful wish: and so of the rest.
Note, In the doctrine of syllogisms, a fingular and an indefinite propofition are ranked among universals, as was before observed in the doctrine of propositions.
Of plain, fimple Syllogifms and their rules. THE next division of syllogisms is into single and
A compound. This is drawn from the naiure 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 syllogifms, for distinction's fake, may be dis vided into * simple, complex and 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 evidenta ly 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 fought with diligence ; prudence is a human virtue; therefore prudence is to be sought diligently.
Note, Though the terms of propofitions may be complex; yet where the composition of the whole ar-gument is thus plain, simple, and regular, it is properly calied a simple fyllogism, since the complection 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 neceffary to mention these ax. ioms before-hand, for the use of those who will enter into the speculative reason of all these rules.
Axiom 1. Particular propositions are contained in universals, and may be inferred from them; but universals are not contained in particulars, nor can be in. ferred from them.
Axiom 2 In all univerfal propositions, the subject is universal : in all particular propositions, the subject is particular.
Axiom 3. In all affirmative propositions, the predia cate has no greater extension than the subject ; for its extension is reftrained by the subject, and therefore it is always to be, esteemed as a particular idea. It is by inere accident, if it ever be taken universally, and cannot happen but in such universal or singular propofitions as are reciprocal.
* As ideas and propofitions are divided into single and compound, and single are subdivided into simple and comples; so there are the same divisions and sub-divisions applied to syllogilms.
Axicin. 4. The predicate of a negative propofition is always taken universally, for in its whole extenfion 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.
Rule 1. The middle term must not be taken twice particularly, but once at leat universally. For if the middle term be taken for two different parts or kinds of the fame universal idea, then the subject of the conclufion is compared with one of these parts, and the predicate with another part, and this will never thew whether that subject and predicate agree or disagree : there will then be four distinct terms in the syllogism, 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 fame men who are spoken of in the major and minor propofitions.
Rule 1. The terms in the conclufion must never be talen more univerfully than they are in the premises. The reason is derived from the firit axiom, that generals can never be inferred from particulars.
Rule III. A negative conclufion cannot be proved by two afirmative premises. For when the two terms of the conclusions are united or agree to the middle term, it does not follow by any means that they disagree with one another. · Rule IV. If one of the premises be negative, the concluion must be negative. For if the middle term be denied of either part of the conclusion, it may thew that the terms of the conclusion disagree, but it can never hew that they agree.
Rule V. If either of the premises be particular, the conclufioil must be particular. This may be proved for the moit 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 uni vertals.