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wrote : St Paul is an apostle: therefore christianity requires us to believe what St Paul wrote.
No human artist can make an animal; a Ay or a worm is an animal: therefore no human artist can make a fly or a worm.
The father always lived in London; the fon always lived with the father : therefore the son always lived in London.
The blossom foon follows the full bud; this peartree hath many full buds : therefore it will shortly have many biofloms.
One hail-itone never falls alone; but a hail-ftone fell juít now; therefore others fell with it.
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 historians wrote after Moses.*
Now the force of all these arguments is so 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 reaion of things, do really contain the conclusion that is deduced from them, which is a never-failing test of true syllogisms, as shall be shewn here-after.
The truth of most of these complex syllogisms may also be made to appear (if needful) by reducing them either to regular, simple syllogisins, or to some of the conjunctive syllogisms, which are described in the next fection. I will give an instance only in the first, and leave the reit to exercise the ingenuity of the reader.
The first argument may be reduced to a fyllogiin in Barbara, thus,
The sun is a senseless being;
* Perhaps some of these fyllogisms may be reduced to those which I call connexive afterwards; but it is of little moment to what ipe. cies they belong; for it is not any formal fet of rules, so much as the evidence and force of reason, that must deterinine the truth or falsehood of all such. fyllogisms.
less being. Though the conclusive force of this argument is evident without this reduction.
THOSE are called conjunctive syllogisms wherein N one of the premises, namely the major, has diftin&t parts, which are joined by a conjunction, or some such particle of speech. Most times the major or minor, or both, are explicitly compound propositions: and generally the major proposition is made up of two distinct parts or propositions, in such a manner, as that by the affertion of one in the minor, the other is either asserted or denied in the conclusion; or by the denial of one in the minor, the other is either asserted or denied in the conclusion. It is hardly possible indeed to fit any short definition to include all the kinds of them ; but the chief amongst them are the conditional syllogism, the disjunctive, the relative, and the connexive.
I. The conditional or hypothetical syllogisms is whose major, or minor, or both, are conditional propositions ; as, if there be a God, the world is governed by Providence; but there is a God : therefore the world is governed by Providence.
The syllogisms admit two sorts of true argumentation, where the major is conditional.
1. When the antecedent is asserted in the minor, that the consequence may be afferted in the conclusion; such is the preceding example. This is called arguing from the position of the antecedent to the position of the consequent.
2. When the consequent is contradicted in the minor proposition, that the antecedent may be contradicted
in the conclusion; as, if atheists are in the right, then the world exists without a cause ; but the world does not exist without a cause : therefore atheists are not in the right. This is called arguing from the removing of the consequent to the removing of the antecedent.
To remove the antecedent or consequent here does not merely signify the denial of it, but the contradiction of it; for the mere denial of it by a contrary proposition will not make a true syllogism, as appears thus : if every creature be reasonable, every brute is reasonable ; but no brute is reasonable : therefore no creature is reasonable. Whereas, if you say in the minor, but every brute is not reasonable : then it would follow truly in the conclusion : therefore every creature is not reasonable.
When the antecedent or consequent are negative propositions, they are removed by an affirmative; as, if there be no God, then the world does not discover creating wisdom; but the world does discover creating wisdom : therefore there is a God. In this instance the consequent is removed or contradicted in the minor, that the antecedent may be contradicted in the conclu. sion. So in this argument of St Paul, 1 Cor. xv. " If the dead rise not, Christ died in vain; but Christ did not die in vain : therefore the dead shall rise."
There are also two sorts of false arguing, viz. (1.) from the removing of the antecedent to the removing of the consequent; or, (2.) from the position of the consequent to the position of the antecedent. Examples of these are easily framed'; as,
(1.) If a minister were a prince, he must be honoured; but a minister is not a prince :
Therefore he must not be honoured.
(2.) If a minister were a prince, he must be honour. ed; but a minister muft be honoured :
Therefore he is a prince. Who fees not the ridiculous falsehood of both these fyllogisms ?
Observ. I. If the subject of the antecedent and the consequent be the same, then the hypothetical syllogism inay be turned into a categorical one; as, if Cæfar be a
king, he must be honoured ; but Cæsar is a king; therefore, &c. This may be changed thus; every king must be honoured ; but Cæfar is a king : therefore, &c.
Obferv. II. If the major proposition only be conditional, the conclusion is categorical: but if the mia nor or both be conditional, the conclusion is also conditional ; as, the worshippers of images are idolaters; if the Papists worship a crucifix, they are worshippers of an image : therefore, if the Papists worfhip a crucifix, they are idolaters. But this sort of syllogisms should be avoided as much as possible in disputation, because they greatly embarras a cause: the syllogisms whole major only is hypothetical, are very frequent, and used with great advantage.
II, A disjunctive fyllogisın is when the major proposition is disjunctive ; as, the earth moves in a circle or an ellipsis; but it does not move in a circle ; therefore it moves in an ellipsis.
A disjunctive syllogism may have many members or parts thus ; it is either spring, summer, autumn, or winter ; but it is not spring, autumn, or winter; therefore it is summer.
The true method of arguing here is from the affer. tion of one, to the denial of the rest, or from the denial of one or more, to the affertion of what remains ; but the major should be so framed that several parts of it cannot be true together, though one of them is evidently true.
III. A relative syllogism requires the major proposition to be relative; as, where Christ is, there shall his servants be ; but Christ is in heaven; therefore his servants shall be there also. Or, as is the captain, so are his soldiers ; but the captain is a coward : therefore his soldiers are so too.
Arguments that relate to the doctrine of proportion, must be referred to this head; as, as two are to four, so are three to six ; but two make the half of four : there. fore three make the half of six.
Besides these, there is another fort of syllogisms which
PART III. is very natural and common, and yet authors take very little notice of it, call it by an improper name, and deicribe it very defectively, and that is,
IV. A connective syllogism. This some have called copulative; but it does by no means require the major to be a copulative nor a compound proposition (according to the definition given of it, Part II. Chap II. bect. 6.) but it requires that two or more ideas be so connected either in the complex subject or predicate of the major, that if one of them be affirmed or denied in the minor, common sense will naturally thew us what will be the consequence. It would be very tedious and useless to frame particular rules about them, as will appear by the following examples, which are very various, and yet may be farther multiplied.
(1.) Meekness and humility always go together; Moses was a man of meekness: therefore Moles was also humble. Or we may form this minor, Pharaoh was no humble man; therefore he was not meek. .
(2.) No man can serve God and Mammon the covetous man serves Mammon : therefore he cannot serve God. Or the minor may run thus, the true Christian serves God; therefore he does not serve Mammon.
(3.) Genius must join with study to make a great man; Florino has genius but he cannot study : therefore Florino, will never be a great man. Or thus, Quintus studies hard but has no genius: therefore Quintus will never be a great man.
74.) Gulo cannot make a dinner without flesh and fish; there was no fish to be gotten to-day: therefore Gulo this day cannot make a dinner. . (5.) London and Paris are in different latitudes; the latitude of London is gi deg. 1 half; therefore this cannot be the latitude of Paris.
(6.) Joseph and Benjamin had one mother ; Rachel was the mother of Joseph : therefore she was Benjamin's mother too.
(7) The father and the son are of equal stature ; the father is six feet high : therefore the son is fix feet also,