The Art of Logic, Book 3 · Part 5
Of the Proprieties of a Syllogism.
The Proprieties of a Syllogism are either
General.
Special.
General, are which agree to all the Figures together.
And they are comprehended in these Canons.
1. The disposition of a Syllogism is called by the principles set in the mind of man, of which the first is that which is called Spoken of All, and of None; to wit, when any thing is said or denyed of the Universal, the same is also said or denyed of the particulars contained under it.
The other Principle is of proportion.
Whatsoever do agree in one third Term, do agree between themselves; and they that dis-agree in one third, disagree between themselves.
2. In a Syllogism three Terms are only disposed, not more, nor fewer: The fourth Term must needs trouble the frame: For the mean is referred unto two: And four Terms may either be expressed, or implyed in a doubtful word; For every doubtful word, is a double word. Neither can there be lesse then three Terms; For two extreams cannot be disposed and knit without a third mean; Not but that one Term repeated more effectually may stand for two Terms; as in this A man in extream poverty is yet a man.
3. The mean (or middle Term) may not come into the conclusion.
4. If Abstract Terms be confounded with Concrete: and Oblique cases, with Right; so as the Principle of the spoken Of all, Of none, be violated, or that there be four Terms, the Syllogism must needs be naught.
5. Let there be a right placing of consignificative, or exceptive, and restrictive words, lest that which pertains to the conclusion be plucked from it, or lest the particular restrictive be twice repeated in the premises; For if that be, it is meer trifling; As in this example, Good, as it is good, is lovely; Justice is good, as it is good, Ergo, &c.
6. A Syllogism consisting of meer particulars is naught. One Term must be universal, else 'tis against both those Syllogistical principles noted before in the first Canon of All, and of None, and agreeing in one third; Moreover in pure particulars there be four Terms; For the Major speaks of one subject, and the Minor of another; As Some man is rich, some man is learned, Therefore learned men are rich.
7. A Syllogism of meere Negatives is naught: For it is against the second Syllogistical principle, which will have the middle Term at least attributed to the one extream. Example, No Infidel pleaseth God; No Elect is an Infidel; Therefore, No Elect pleaseth God.
8. Let the Premises in a Syllogism have the same kind of Attribution, or Predication; that is, the major must not be proper, and the minor improper, or otherwise. As, Bread is eaten with the mouth; Bread is Christs body; Therefore, Christs body is eaten with the mouth: Here that which is attributed or spoken of the Bread, in the first proposition, is proper; in the 2d. figurative: the conclusion therefore is false.
9. The major and minor Term, must be brought into the conclusion, as they were disposed in the Premises, not changed or maimed; Therefore it is not right to say; All sinners repentant find mercy; Some men find not mercy; Therefore, some men are not finners: Here the conclusion is maimed, and is not as in the first proposition.
10. There must be no more in the conclusion then was in the premises.
11. The conclusion must imitate the more unworthy and weaker part that is premised: The worthiness is esteemed by the quality, and quantity; so that an Affirmative is always more worthy then a Negative, and an Universal then a Particular. It is therefore ill to reason thus; Some faithful are saved; Every faithful man is called; Therefore, every man that is called is saved. Here, of a particular Major is inferred a general conclusion; And it followeth not the weaker, but the stronger.
12. In a Syllogism, sometime by reason of the form, a true conclusion is gathered from false premises: But it is impossible for a false Conclusion to be gathered from true premises: Truth cannot be gathered from falshood▪ but by accident; as, Every man is a Living creature: Every man is a stone: therefore, Every man is a living creature: Here the conclusion is true, (by reason of the form) though both the premises be false.
13. Of one Syllogism rightly framed, many conclusions may be gathered. And this, four manner of ways.
1. By consequence; As, They that have communion with the Devil abide not in Christ, and consequently do not eat Christs body.
2. By conversion of propositions; As, No elect abideth in sin all his life; Every believer is an elect; Therefore, none that abideth in sin all his life, is a Believer.
3. By inclusion of one proposition in another; As, All the Elect believe in Christ; Some men believe not in Christ; Therefore some men are not Elect; Therefore also it is false that all men are Elect; For in proving the truth of the one part of the contradictory, the falshood of the other part is included and proved.
4. By descention, or undertaking a particular term under an Universal; As, All that conserveth society, is profitable; All vertue conserveth society; Therefore, all Vertue is profitable, Therefore every lawful contract (because it conserveth society) is profitable.
And thus much of the general properties, common to all the Figures. Now followeth the special.
Of these some pertain to the
Primary. Figure.
Secondary, Figure.
The properties of the primary Figure, are five, contained in so many Canons
1. The disposition (or frame) of the first Figure, is most perfect: And this for three causes.
1. Because the frame of this Figure most agreeth to natural sense, and the Syllogistical principles that are in all men, and is of all the most evident.
2. Because the Mean of this Figure, is indeed the Mean or middle in place and situation; whereas in other figures, it is the Mean foreign, and by reason of illation.
3. Because in this, all kind of conclusion may be gathered; Affirmative, Negative, Universal, and Particulars, which is done in none of the other Figures.
2. In the first figure there is a proceeding from Universals to Particulars, or from the Genus to the Species.
3. The major of the first Figure must alwaies be Universal.
4. The minor must alwaies be Affirmative.
5. The Antecedent of the minor proposition in the first figure, must be included in the Antecedent of the Major, as the Special in his General. This Canon is most profitable to be noted: For the whole frame, and form of this first figure is overthrown, if in the Antecedents of the major, and minor be two disjoyned things, and not subordinate one to another.
The properties of the secondary figures, are either common to both, as well the second as the third, or special to each one.
Common to both, is imperfection arising both from lesser evidence, and from placing of the mean with the extreams.
Imperfection requireth both
Reduction, and
Exposition.
Reduction, is the transforming of a Syllogism formed in the first or second Figure, into a Syllogism of the first Figure.
Reduction is either
Direct, or
Indirect.
1. Direct, is, which is done by the only transposing, or turning of the Propositions, the extreams of the conclusion remaining.
The Canons of this Reduction are eight.
1. Reduction of the second and third Figure unto the first, is not alwaies necessary; therefore not always carefully to be essayed.
2. The Consonants in the beginning and the midst, do shew the manner of Reduction.
3. The Consonanrs in the beginning are four; B C D F▪ shewing unto which Mode of the figure, every Mode of the second and third figure is to be reduced; Namely to that which beginneth with the same Consonant. As Cesare and Camestres are reduced to Celarent; Festino and Felapton unto Ferio; Disamis and Datisi unto Darii.
4. Also the four Consonants in the midst. C M P S, do shew by what Instrument the reduction is to be made, whether by Conversion, Transposition, or deduction unto impossible.
5. C, therefore noteth indirect Reduction, or that which is done by the Impossible, and is onelyonly in those words, Baroco and Bocardo.
6. M, noteth that there must be a transposition made of the propositions, the Minor in the place of the Major, and the Major in place of the Minor.
7. P, noteth conversion of the proposition by accident: to wit of the minor, into which the syllable having P, falleth, if the syllable of the modes be rightly distributed into the propositions.
8. S, sheweth that there must be a simple conversion made either of the Major, or the Minor, and the conclusion together: as this letter is hard, either in the first, or midle, or last syllable: For if it be heard in the first syllable, As Cesare, it noteth the simple conversion of the major; if in the midst, it notes the conversion of the minor: And if in the last, the conversion of the conclusion, as in Camestres it is twice heard, in the midst and the last, and therefore noteth the conversion to be made of the Minor and of the conclusion. As take the syllogism in Cesare.
Cessare.
No true Christian loveth the World,
Every covetous man loveth the World: therefore
No covetous man is a true Christian.
First the letter C sheweth it must be reduced to Celarent; S, in the first syllable shews the manner of reduction; to wit, by a simple conversion of the major, thus.
Celarent
None that loveth the world is a true Christian.
Every covetous man loveth the world: therefore,
No covetous man is a true Christian.
Indirect Reduction, is, when we shew the evidence of the Illation by absurdity of the contradiction to be admitted.
The Canons hereof are six.
1. Indirect Reduction hath place only in two Moods Baroco of the second, and Bocardo of the third Figure.
2 Indirect Reduction is made by concession, and by Assumption.
3. By concession, because the adversary granteth both premises, and yet denies the inference of the Conclusion.
4. The premises therefore, being granted, by supposition, the contradictory is to be taken of the conclusion, which is in the imper ect Syllogism, that is to be reduced.
5. The contradictory of the conclusion being taken, is put in the place of the Minor, if it be Baroco of the second Figure: and in place of the Major, if it be Bocardo of the third Figure: and so the Major in the second Figure, is alway left in his place, as the Minor in the third.
6. Hence is made the conclusion in the first Figure, wherein contradiction is made to the proposition left of the imperfect Syllogism; and so the adversary is driven to an absurdity, that is, to the contradictory of that proposition, which before he had granted as true.
And thus much of shewing the evidence by Reduction.
Exposition, is the declaration of a Syllogism formedforeign. with a middle Mean general Term in the third Figure, by a singular Mean contained under the general, as neerer to the sense; for example,
None of the Elect sin unto death.
Some of the elect sin grievously,
Therefore, Some that sin grievously, sin not to death.
Exposition of this may be made by singulars known unto us, as David, Peter, &c. David sinned not unto death; David sinned grievously; therefore, some grievously sinning, sin not to death.