The Art of Logic, Book 3 · Part 6
The Properties peculiar to the second Figure now follow, which are comprehended in three Canons.
1. The second Figure is (foreign) most sit to refute with; for it disjoyneth two diverse things, because they agree not in one third.
2. In the second Figure the Major must alway be Universal, even as in the first Figure.
3 In the second Figure, may be no meer affirmants.
The Proprieties of the third Figure, are four, set down in four Canons.
1. The proceeding of the third Figure is, for the most part, from the straighter to the larger. Therefore Logicians say, the first figure hath process foreign: the third, foreign.
2. The Minor must always be affirmant.
3. The whole and entire consequent of the Minor must needs be inferred in the conclusion, and put in the place of the Antecedent; for if it be maimed, or in part, all is troubled, and there are four Terms. As, Whole Christ is every where; whole Christ consisteth of the Godhead and the Manhood; therefore the Manhood is every where. Yea, though the Matter be good, the Form may be evil; as, God is the God of the living; God is the God of Abraham: therefore, Abraham liveth. Here, in the Conclusion, the Consequent of the Minor is impaired; which whole is not Abraham, but the God of Abraham. The Argument then must not be in the third, but the first Figure; thus, They, of whom God is God, do live; but God yet, is the God of Abraham; therefore he liveth: the Major followeth, because to be God, is to exercise Divine properties in the Object; and in whom such things are done, he must needs exist.
4. The Conclusion in the third Figure, is never Universal. And hitherto, of a perfect Syllogism.
Animperfect Syllogism, is, which hath an imperfect dispositionImperfect Syllogism. of Syllogistical Form.
And it is
Direct. f
Indirect. g
g Indirect, is which concludeth by indirect or absurd.
And it is
Primary. a
Secondary. b
Primary, is, when the adversary by the contradictory ofa the conclusion which he denyeth, and by the complication of a proposition manifestly true and granted, is driven to an absurdity.
The Canons hereof are seven.
1. Let the contradictory be taken of the conclusion which the adversary denyeth.
2. Let a contradiction be assumed manifestly true, and which the adversary cannot deny; and let that be placed instead of the Major.
3. Let the contradictory of the conolusion be put instead of the Minor: and thereupon with the Major manifestly true, let be inferrd an absurd conclusion.
4. From the absurd conclusion inferred, go back to the absurd proposition, or contradictory of the first conclusion.
5. The falshood of the Minor being shewed by the force of the contradictory principle, let it be shewed that the first conclusion is true, as, that whereto the Minor is contradictorily opposed; for example, Arians deny this conclusion, The Holy Ghost is God. I take the contradictory, The Holy Ghost is not God, but a Creature: and thus I infer, The spirit of God is not God, but a Creature; therefore, the The spirit of God is without God. This Conclusion is absurd; for no spirit is without that whose spirit it is: therefore Paul saith plainly, The spirit of God is in God. Therefore either the Major or Minor is absurd; not the Major, for it is manifest, the creatures are without the Creator; therefore the Minor: And therefore the right conclusion is true, which is opposed to this Minor.
6 Therefore a Syllogism leading to absurdity, is faulty either when the Major is infirm, or the conclusion not absurd or opposed to a true conclusion.
7 A Syllogism leading to absurdity, much urgeth in disputing, and hath the chief use in shewing the verity of principles, and specially of those conclusions which are nigh to principles, so as they cannot well be proved by demonstration.
Secondary, is, which by the Adversaries grant of concontradictories, inferreth the denyall of the same by it self; as, No Naturall body is infinite; some body, viz. Christs, by the Ubiquitaries opinion is infinite: therefore some body, viz. Christs, is not a body.
A direct, imperfect Syllogism, is, 1 Enthymema. 2 Consecution of sentences. 3 Induction. 4 Sorites
1 An Enthymema is a Syllogism wherein one of the premises is kept in.
The Canons are three.
1 In an Enthymema; the first proposition is called the antecedent, the other the consequent.
2 It may easily be made a Syllogism by adding the proposition that wanteth.
3 Which of the premises is wanting, may easily be judged by the conclusion; whereof, if the attribute (or latter part) appear not in the antecedent; the Major is wanting: if the subject (or first part) appear not, the Minor is wanting; as, a living creature moveth; therfore man moveth. Here wants the Minor; for this word man appeareth not in the antecedent. A man is aliving creature; therefore he moveth; Here wants the Major; for the attribute in the conclusion, moveth, appeareth not in the antecedent.
Consecution of sentences, is, when without disposition of the Mean, one sentence followeth another.
And it is
Consentanie. a
Dissentanie. b
Consentanie, is, when the consecution procedeth by consent of the sentences; Namely by conversion, inclusion, and other naturall Relations of the Sentences.a
The Canons hereof are nine.
1 The converting to the converted▪ in all kinds of conversion, followeth rightly: as, No Infidel eats Christs body; therefore, None that eats Christs body is an Infidel.
2 That inference which is made from a contrary sense is neer kin to conversion by contrary placing: as, Vertue is to be praised, therefore, Vice is to be dispraised.
3 From the Superiour or Universall unto the Inferior or Particular distributely there is a good consecution: as, All sinners repenting finde mercy: Therefore all great sinners repenting do finde mercy. But from one particular to another, it followeth not rightly; As to say: Some sin is not forgiven in the life to come, therefore some sin is forgiven in the life to come.
4 From the affirmative of a finite consequent (or attribute) followeth the Negative of an infinite consequent: as man is just, therefore man is not not-just.
5 From the affirmative of an infinite consequent followeth the Negative of a finite consequent, if the antecedent be capable of the habit: as, Man is not just, therefore neither is he just, neither un just. But of an infant it followes not, he is not just, therefore he is unjust; for he is not capable.
6 From a conjoyned consequent are inferred things divided, where there is no ambiguity nor repugnancy in the adject: as, Man is a living sensible body; Therefore man is a body, man is living, man is sensible. But it follows not, a Carkase is a dead man, therefore it is a man; For between a Carkase and a man there is a repugnancy.
7 From two or mo disjoyned consequents that cleave together by themselves, and are taken without ambiguity, we may infer conjoyned things: as, Man is a body, and he is mixt, and he is living, and he is sensible; therefore, man is a living mixt sensible body. But it followeth not if one say; This man is a Musitian, and he is good, therefore he is a good Musitian; because Musitian and good, cleave together by accident; And there is ambiguity in the word good, which may be understood either of Moral good, or of perfection of Arts. Neither is this right to say; This servant is a father, and he is thine; therefore, he is thy father; For there is ambiguity in the word thing.
8 From an exclusive to an Universal of transposed terms, is a good consequence. As, OnelyOnly man can laugh▪ therefore whatsoever can laugh is a man.
9 From the removing of the one immediate member, unto the exclusive, is a good consequence: As, We are not justified by works: therefore by faith onelyonly.
Dissentany consecution, is, when from the truth of the oneb of the opposites is understood the falshood of the other; and contrary from the falshood of the one, the truth of the other. As, It is true that some man is not chosen to life: therefore, It is false that every man is chosen to life. It is true that every Christian man is to be baptized: therefore, it is false that no Christian Infant is to be baptized.
Induction is either
Principal. a
Lesse principal. b
Principal, is, when from many singulars, or particulars,a there is drawn a general conclusion.
The Canons hereof are three.
1 An Induction standing of particular propositions, may bring in all the particulars: As if one would prove that Wine heateth, he may reckon up all sorts of Wine in the World, as French, Spanish, Rhenish, European, Asian, Affrican Wine, &c.
2 When singulars are infinite, it is enough to alledge some chief, with addition of this clause, Neither can an unlike example be shewn: As Paul in Heb. 11. to prove that all that are saved, are not saved but by faith, alledgeth Abel, Enoch, Noah, Abraham, Isaac, Jacob, Joseph, &c. and at last saith, There are many moe examples; Neither can any be shewed unlike to those.
3 An Induction may be made a Syllogism of the first Figure, by putting in the place of the Major such a proposition in which the consequent of the conclusion is spoken of all particulars or singulars (reckoned up or understood) as of the mean; and adding a Minor, in which the same particulars or singulars are spoken of the Antecedent (or first part) of the conclusion. As, Spanish, French, Rhenish, and all Wines do heat. All Wine is Spanish, French, Rhenish, &c. therefore, all Wines do heat.
Lesse Principal Induction, is, when one or two singularsb are induced, or when one is proved by another: As, Abraham was justified by faith: therefore, other godly are so justified also.
Sorites is an imperfect Syllogism, wherein the consequent of the first proposition is made the Antecedent of the second; and so forward as by a chain, until at length the last consequent be spoken of the Antecedent of the first propoposition: foreign an heap, foreign a coacervator, an heaper together. This is called a Stoical argument.
The Canons are five.
1 The reason of the consequence in a Sorites is both the connexion of the subordinates in the same predicament, and also the coherence of the causes and effects by themselves.
For Example. A man is an animal, an animal is a sensual body, a sensuall body is living, that that is living is mixt, that that is mixt is a substance: therefore, a man is a substance; also, Rom. 8. All foreknown are predestinate, all predestinate are called, all called are justified, all justified are glorified: therefore, all foreknown are glorified.
2 When terms not subordinate are confounded, and causes by themselves are mixt with causes by accident, the Sorites is naught: as, Of evil manners spring good Laws, good Laws are worthy of praise, things worthy of praise are to be desired: therefore, Evil manners are to be desired. This conclusion is naught; for evil manners are not causes of themselves of good Lawes, but by accident.
3 A denial makes a faulty Sorites, when it cannot be reduced to some figure; and begetteth either both premises negant, or a negant Minor in the first figure: otherwise when there is a good connexion of negative consequents or attributes, Negative Sorites are not simply to be rejected; as, Affliction bringeth patience, patience bringeth experience, experience brings forth hope, hope makes not ashamed, therefore affliction makes not ashamed.
4 When a particular proposition in a Sorites it put in the second or third place, or when the particular negant is put in any place, the Sorites is naught; for the Major is particular, or the Minor negant in the first Figure.
5 In a Sorites, the Antecedent or first part of the conclusion is the Minor term, the consequent the Major; the other which besides these are found in a Sorites, are Means; and look how many Means, so many Syllogisms.
An imperfect Syllogism also, is either
Simple.A compound or hypothetical Syllogism.
Compound.
Simple, which consisteth of simple Propositions; of which we have heard before.
Compound, is, which consisteth of a compound Proposition, called also hypothetical, and foreign.
And it is either
1 Conditional.
2 Disjunctive.
Conditional, whose Major is Conditional or Hyprthetical.
The Canons hereof are seven.
1 An Hypothetical Syllogism, consists of antecedent and consequent: the antecedent is of the first part of the Proposition; the consequent of the latter.
2 The Union of antecedent and consequent, is called the reason of the consequent, which is the very form of an hypothetical Syllogism; and therefore if it cannot be granted, the hypothetical Syllogism must needs be faulty.
3 That Hypothetical Syllogism is good, which may be reduced to a good simple Syllogism; for as the perfect is always the measure of the unperfect, so a simple Syllogism is the measure of a compound.
4 Therefore in an Hypothetical Syllogism, from the assumption of the antecedent to the conclusion of the consequent, the inference is of force, but not from the assumption or putting of the consequent, to the putting of the antecedent; for so in the second figure should be meer affirmants; as, If Infidels be grafted into Christ, they eat his flesh: But they eat his flesh; therefore they are grafted into Christ. The Argument is not of force.
5 From removing the consequent to the removing of the antecedent, the inference is of force; but not from the destruction of the antecedent to the destruction of the consequent; for so there should be a minor negant in the first figure: as, If he be a man, he hath reason; but he is not a man: therefore he hath not reason. The Conclusion is true, but it followeth not of the premisses formally, but by accident onelyonly.
6 When an Hypothetical hath three terms in the first Proposition, it is easily reduced to a Categoricall (or simple) Syllogism; for the reason of the consequence being granted, is put for the Major in a simple Syllogism, and then the Minor followeth of its own accord; as, If the Heaven be hot, it may be corrupted by another body: the reason of the consequence is, Every hot thing may be corrupted with another body that is cold; but it is not corruptible; therefore neither is it hot. Here of make a simple Syllogism in the second figure, thus▪ Every hot thing is corruptible. Heaven is not corruptible: therefore Heaven is not hot.
7 But when four terms are in the first Proposition, the reduction is hard and laborious, because the reason of the consequence cannot so easily be rendered by a simple Proposition: as, I… Justice be by the Law, Christ died in vain; But Christ died not in vain: therefore Justice is not by the Law. Here are four terms in the first Proposition.
2 A Disjunctive Syllogism is, which hath the first Proposition a Disjunctive.
And it is either
Uniform. c
Biformed, or a Dilemma. d
Uniform, is, which of members disjoyned takes away thec one to put the other, or puts the one to take away the other. as, Either we are justified by faith, or by works: not by works; therefore by Faith.
The Canons hereof are two.
1 The whole force of the consequence in a disjoyned Syllogism, consists in the opposition and disjunction of the parts, whereupon that must needs be naught whose parts are subordinate: as, We have instruction either from God, or from our teachers; but it is from God; therefore not from our teachers. The disjunction is naught, for it disjoyneth things subordinate.
2 A right disjunction, requires a full enumeration of parts: if therefore a third part can be given, or a fourth, the disjunction is naught: as, Heaven is either Hot or Cold: but it is not cold; therefore it is hot,
Here the first proposition hath an imperfect enumeration; for we should adde, or else it is without all Elementary quality.
A Biformed disjunctive is, that when a disjunction of parts is made, which soever be granted, the adversary is fast:d it is called a Dilemma foreign, as it were foreign, twice taken and taking; also an Horned Syllogism, and a Crocodiline Syllogism. As, Johns Baptism is either of God or of men. If of God, why do we not receive it? If of men, we are in danger of the people which count him a Prophet.
The Conons hereof are four.
1 The force of consequence in a Dilemma dependeth on the ful enumeration of the disjoyned members, and the convenient removing of them both.
2 The Dilemma hath no force, if there be not a full disjunction, but a third or fourth member may be given.
3 It is also without force if both members be granted, as making nothing against us. As the Jews reasoned against Christ: Tribute must be given to Cesar, o… unto God; If to God, then not to Caesar, and this is Treason: If to Caesar, then not to God, and this is Sacriledge. Our Saviour answereth by granting both, Give to Caesar that which is Caesars, and to God that which is Gods.
4 Finally, A Dilemma hath no force if it may be turned and returned upon the adversary.
Often also in the undertaking of a Dilemma, they are faulty in evil consequence, and then we must answer by denying the consequence, as, Infants which while they are a Baptizing, do cry and resist, either they understand, or not: If they understand not, neither beleeve they; and therefore should not be baptized: If they understand, they are Sacrilegious that oppugne Gods Institution.
Here be evil consequences in both branches; for it followeth not, That Infants do beleeve, although they understand not explicitely what there is done. Neither followeth it, That they are Sacrilegious and repugne Gods Ordinance though they cry and struggle; for they stuggle not against the water as it is an holy sign, or with formal reason; but as it is a cold Element oftensive to their tender body. Even as a godly man that loves no wine, doth naturally abhor the wine which is in the Lords Supper; but he abhors it only as it is wine, and not as it is a Sacred signe of Christs blood.
And thus much of a Syllogism Formal, or commonly considered.
A Special or Material Syllogism, is, which is restrained unto certain conditions of matter.
And it is either
True.
Apparent.
True, is, when not only the form, but also the matter of it is good.
And is either
Notional. a
Real. b
A notionall Syllogism, is, whose conclusion and premisesa have some second Notion or term of Logick.
The Canons hereof are two.
Of which the first for foreknowledge of the conclusion.
The latter is for finding out of the mean.
1. Every simple Notion handled in the first part of Logick comes into the conclusion of a National Sillogism; for every second Notion may be compared with the first. We ask, Whether time and place be words conjoyned or absolute? Whether the Genus of sin be an action, or the Genus of faith be knowledge? Whether Antichrist is to be one singular person? Whether faith be proper to the Elect? Whether persons in the Trinity be really, modally, or formally distinguished, and so of all other points. So as there is great use of a Notional Syllogism.
2. The Mean term for a notional Syllogysm, is easily taken from the nature and properties of that second Notion, of which question is made in the conclusion; so as from the first part of Logick the Canons of every second Notion may be put for the Major in the Syllogism, and then let the assumption be made affirmative or negative.
For example. It is asked, Whether an action be the genus of sin, or not. For a denyal, there is found out a mean term, from the nature and properties of a good genus. As by this Canon. No subject is the genus of that whereof it is the subject. l. 4. Top. cap. 6. But an action is the subject whereto sin cleaveth; therefore it is not the genus of sin.
Again, It is asked, Whether good works be the cause of Justification. Take for Major this Canon of a cause; No cause is after the effect; but good works are after Justification; for the person must first be justified and please God before he can do any good work: therefore good works are not the cause. And so of all other Notions, with their Canons treated of in the first part of Logick, wherby appeareth the great use of those Rules: and that there needs here no long discourse of a Notional or topical Syllogism.