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may be inferred from them but universals are not contained in particulars, nor can be inferred from them. 2. In alt univer: sal propositions, the subject is universal : in all particular pro. pusitions, the subject is particular. 3. In alt affirmative propo. sitions, 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 aceident, if it ever be taken universally, and cannot happen but in such universal or singular propositions as are reciprocal. 4. The predicate of a pegative proposition is always taken upivera sally, for in its whole extension it is denied of the subjeet. I we say no stone is vegetable, we deny all sorts of vegetation con cerning stones.
The Rules of simple, regular Syllogisms are these :
1. “ 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 kinds of the same universal idea, then tlae subject of the conclusion is compared with one of these parts, aud the predicate with another parts and this will never shem whether that subject and predicate agree or disagree : there will then be foor 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 beyer infer that some robber's are pious, for the upidulle term men being taken twice particularly, it is not the same men who are spoken of in the major and minor propositions.
İL. “ The terms in the copelasion must never be taken more universally than they are in the premises." The reason is de rived from the first axiom, that generals eat never be inferred from particulars.
WI.“ A negative conclasion cannot be proved by two affirStative premises." For when the two terms of the conclusion are united or agree to the middle term, it does not follow by any meas that they disagree from one another.
IV. “ If one of the premises be negative, the conclusion must be ocgative." For if the middle teren be denied of either part of the conclusion, it may shew that the terms of the conclusion disagree, but it can never slew that they agree.
V. * If either of the prennises be particolar, the conclusion must be particalat. This inay be proved for the most part from the firyt axiom.
"These two fast rules are sometimes united in this single sentence, The conclusion always follows the weaker part of the premises. Now negatives mod particulars are counted inferior to affirmatives and universals.
VI. “ Frau the negative premises nothing can be conclats
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, 6. 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 0, 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, 1, 0, to make three propositions amount to sixty-four ; but fiftyVOL. VII.
four of them are excluded from forming true syllogisms by the seven rules in the foregoing section; the remaining ten are variously diversified by figures and moods into fourteen syllogisms.
The figure of a syllogism is the proper disposition of the middle term with the parts of the question.
A mood is the regular determination of propositions according to their quantity and quality, that is, their universal or particular affirination or negation ; which are signified by certain artificial words wherein the consonants are neglected, and these four vowels, A, E, I, O, are only regarded.
There are generally counted three figures. In the first of them the middle term is the subject of the major proposition, and the predicate of the minor. This contains four moods, called, Barbara, Celarent, Darii, Ferio. And it is the excellency of this figure, that all sorts of questions or conclusions may be proved by it, whether A, E, 1, or 0, that is, universal or particular, affirmative or negative; as,
Bar-Every wicked man is truly miserable;
ba-All tyrants are wicked men ;
ra. Therefore all tyrants are truly miserable.
la-Covetous men are always in fear;
ri-Somne afflictions further our salvation;
i. Therefore some afflictions are good for us. se-Nothing that must be repented of is truly desirable; ri. Some pleasures must be repented of; o. Therefore there are some pleasures which are not truly
desirable. In the second figure the middle term is the predicate of botla the premises : this contains four moods, namely, Cesare, Camestres, Festino, Baroca, and it admits only of negative coaclusions'; as,
CeNo liar is fit to be believed ;
The third figure requires that the middle term be the sub. ject of both the premises. It has six moods, namely, Darapti, Felapton, Disamis, Datusi, Bocardo, Ferison : and it admits only of particular conclusions ; as,
Da-Whosoever loves God shall be saved ;
li. Therefore some who have imperfections shall be saved.
I leave the reader to form examples of the rest.
The moods of these three figures are comprised in four Latia verses.
Barbara, Celarent, Darii, Ferio, quoque primæ.
Adjungens Disamis, Datisi, Bocardo, Férison.
In the first figure the major proposition must always be universal, and the minor affirmative. In the second figure also the major must be universal, and one of the premises, together with the conclusion, must be negative. In the third figure the minor must be affirmative, and the conclusion always particular. There is also a fourth figure, wherein the middle term is predicated in the major proposition, and subjected in the minor: but this is a very indirect and oblique manner of concluding, and is never used in the sciences, nor in human life, and therefore I call it useless. Some logicians will allow it to be nothing else but a mere inversion of the first figure; the moods of it, namely, Baralipton, or Babari, Calentes, Dibatis, Fespamo, Fresisom, are not worthy to be explained by one example.
Sect. IV.--Of Complex Syllogisms. IT is not the mere use of complex terms in a syllogism that gives it this name, though one of the terms is usually complex ; but those are properly called complex syllogisms, in which the middle term is not connected with the whole subject, or the whole predicate in two distinct propositions, but is intermingled and compared with them by parts, or in a more confused manner, in different forms of speech ; as,
The sun is a senseless being ;
Therefore the Persians worshipped a senseless being. Here the predicate of the conclusion is worshipped a senseless being, part of which is joined with the middle term sun in the major proposition, and the other part in the minor. Though this sort of argument is confessed to be entangled or confused, and irregular, if examined by the rules of simple syllogisms: yet there is a great variety of arguments used in books of learning, and in common life, whose consequence is strong and evi. dent, and which inust be ranked under this head; as,
I. Erclusive propositions will form a complex argument; as, piolis men are the only favourites of heaven; true christians are favourites of heaven; therefore true christians are pious men. Or thus, hypocrites are not pious men; therefore hypocrites are not favourites of heaven.
II. Erceptive propositions will make such complex syllogisus; as, none but physicians came to the consultation, the
nurse is no physician; therefore the nurse came not to the consultation.
III. Or, Comparative propositions; as knowledge is better than riches : virtue is better than knowledge; therefore virtue is better than riches : or thus, a dove will fly a mile in a minute ; a swallow flies swifter than a dove; therefore a swallow will fly more than a mile in a minute.
IV. Or, Inceptive and desitive propositions; as, the fogs vanish as the sun rises ; but the fogs have not yet began to vanish ; therefore the sun is not yet risen.
V. Or Modal propositions; as, it is necessary that a Gene. ral understand the art of war; but Caius does not understand the art of war; therefore it is necessary Caius should not be a General : Or thus, A total eclipse of the sun would cause darkness at noon : it is possible that the moon at that time may totally eclipse the sun, therefore it is possible that the moon may cause darkness at noon.
Besides all these, there is a great number of complex sylTogisms which can hardly be reduced under any particular titles, because the forms of hainan language are so exceeding variQu8; as,
Christianity requires us to believe what the apostles wrote: St. Paul is an apostle , therefore christianity requires us to believe what St. Paul wrote.
No human artist can make an animal; a fy or a worm is an animal; therefore no human artist can make a fly or 3
The father always lived in London; the son always lived with the father ; therefore the son always lived in London.
The blossom soon follows the full bud; this pear-tree hath mapy full buds; therefore it will shortly have many blossoms.
One bail-stone never falls alone : but a bailstone fell jast now; therefore others fell with it. in Thunder seldom comes without lightning ; but it thundered yesterday; therefore probably it lightened also.
Moses wrote before the Trojan war; the first Greek historians wrote after the Trojan war; therefore the first Greek bistorians wrote after Moses.*
Now the force of all these arguments 18 $0 evident and (conclusive, that though the form of the syllogism be never so
irregular yet we are sure the inferences are just and true; for the premises, according to the reason of things, do really
* Perhaps sotne of these syllogistas may be reduced to those which I call “ connexive" sfterward, but is of little moment to wbat species" they Belong; for it is not any formal set of rules, so much as the evidence and force of reason, that must determine the truth or falsehood of all such syl. logistas.