Abstract of Logic, Book 2 · Chapter 8 – Chapter 9
CHAP. VIII. Of the Laws, Rules and Proprieties of Syllogiſms.
Ax. 1. THE Neceſſity of Conſecution, which we call'd the Soul of Syllogiſm, leans upon certain Foundations and Rules; ſo certain and known that they cannot be deny'd by any one.
Ax. 2. Univerſal Syllogiſms affirming depend on the Rule or Dictum de omni, that is, all, which is this: Whatſoever is predicated Univerſally of any Univerſal; That is alſo predicated of all that are contain'd under that Univerſal.
COMMENTARY.
For Example; To live, is ſaid univerſally of Animal; as, every Animal lives: And Man is contained under Animal; as, every Man is an Animal: And therefore to live, may alſo be affirmed of Man; as, every Man lives, &c. And this is the Syllogiſm affirming in the firſt Figure.
Ax. 3. Syllogiſms univerſal denying lean upon the Rule of None, which is this: Whatſoever is univerſally denyed of any Univerſal, is alſo denyed of all which contain'd under that Univerſal.
1. §. For Example; Deny we Stone of Animal; as no Animal is a Stone: Now Man is contained under Animal: For every Man is an Animal; and therefore Stone muſt alſo be denyed of Man: For no Man is a Stone; and this is a Syllogiſm denying in the firſt Figure. As neceſſary therefore as it is for Leyden to be in the Low-Countries, or Belgium, when it appears that Holland is in the Low-Countries, or Belgium, and that Leyden is in Holland, or that Leyden is not in England; ſince Belgium is not in England, and Leyden is in Belgium: So neceſſary is it that the Concluſion ſhould follow from well and lawfully diſpoſed Premiſſes. Which will be more eaſily underſtood if the Dictum of All and None be Paraphraſtically propounded and accommodated to Syllogiſms in this manner, viz. Whatſoever Predicate is univerſally affirmed or Denyed of any Medium, that alſo is affirmed or denyed of that Subject, which is contained under that Medium, wherein there are three diſtinct Parts, of which the firſt repreſents the Major, ſecond the Concluſion, and third the Minor.
Ax. 4. Singular Syllogiſms depend upon this Maxim, whatever things agree in one ſingle Third: Thoſe alſo agree amongſt themſelves; and thoſe of which one agrees to any ſingle Third, the other not: Thoſe alſo agree not amongſt themſelves.
1. §. As for Inſtance; If two Trees are equal to the ſame Meaſure, it is rightly collected, that thoſe Trees are equal alſo amongſt themſelves: So alſo if it may be truly affirmed of David that he was a Prophet and a Manſlayer, it follows that ſome Prophet was a Manſlayer, and that in ſuch a Syllogiſm as this.
David was a Manſlayer:
David was a Prophet:
Some Prophet therefore was a Manſlayer, &c.
On the other ſide, whereas of two Beams, if one of them be agreeable to a certain Meaſure, the other not, it follows that they muſt be unequal amongſt themſelves: So alſo if it convene to Judas, that he was an Apoſtle, and not faithful to his Lord: It follows alſo that ſome Apoſtle was not faithful to his Lord; and that in ſuch a Syllogiſm as this.
Judas was not faithful to his Lord;
Judas was an Apoſtle:
Some Apoſtle therefore was not faithful to his Lord.
If there be two, of which neither agrees to any one Third; it is uncertain whether they agree amongſt themſelves or not.
Ax. 5. Thoſe Syllogiſms which are agreeable to theſe Rules, are true Syllogiſms, which diſſent from them Paralogiſms, or Vitious Syllogiſms: But,
Ax. 6. That the more eaſily true Syllogiſms may be diſcern'd from Paralogiſms, ſome Laws are to be obſerv'd, of which ſome are common to all; others peculiar to each Figure.
Ax. 7. The Common Laws are ſeven; and firſt, in a Syllogiſm there muſt be no more or leſs than three Terms.
1. §. This Law is preſcribed Book 1. Prior. Cap. 25. and is thus prov'd: A Queſtion has but two Terms, viz. Major and Minor, or Subject and Predicate: The Medium or Argument is taken from without; and that ought to be but one; as we have ſhewn, Cap. 6. of this Book. Tho'
2. §. It often happens that there are four Terms in a Syllogiſm when there ſeems to be but three; and that chiefly for three Cauſes: And firſt, becauſe ſome Word or Sentence in the Syllogiſm is doubtful; as in this Syllogiſm,
That which wants Beginning and End, is Eternal;
The World wants Beginning and End;
Therefore the World is Eternal.
There are four Terms, becauſe Beginning and End in the Major, are to be underſtood of Duration, in the Minor of Magnitude.
3. §. Secondly, becauſe Concretes are confounded with Abſtracts, or Abſtracts with Concretes, as in this Syllogiſm:
Whiteneſs is a Quality;
Snow is white:
Therefore Snow is a Quality.
4. §. Thirdly, becauſe the Caſes are chang'd in the Nouns, or Tenſes in the Verbs; as in theſe Examples:
All Servants are their own Maſters; That is, Servants of their own Maſters:
Davus is a Servant:
Therefore Davus is his own Maſter.
No Boy ever lived long;
Neſtor was a Boy:
Therefore Neſtor did not live long.
But if the ſame Mutation of Caſe or Time that is made in the Premiſſes, be made alſo in the Concluſion, it maketh not a Fourth Term: As appears from theſe Examples.
All Servants are of their Maſters;
Davus is a Servant:
Therefore Davus is of his Maſter, that is, belonging to him.
No Boy lived long;
Neſtor was a Boy:
Therefore Neſtor as a Boy, did not live long.
Ax. 8. The ſecond Law is, that there ſhould be no more nor leſs in the Concluſion than there was in the Premiſſes.
1. §. That is, The Extremes which were with the Medium diſpoſed in the Premiſſes, ſhould be ſo poſited in the Concluſion as they were in the Premiſſes, without any either Addition or Detraction: For if any thing be either added or withdrawn, there will be four Terms, as appears from the following Examples.
Thoſe which pleaſe God are happy;
All thoſe which are faithful pleaſe God:
All thoſe which are faithful therefore are happy and are afflicted with no Calamities.
All repenting Sinners are admitted into Favour;
Some Men are not admitted into Favour:
Some Men therefore are not Sinners.
For both Syllogiſms are Vitious: the firſt, becauſe there is more; and the ſecond, becauſe leſs in the Concluſion than there was in the Premiſſes.
Ax. 9. The third is, the Medium muſt not enter the Concluſion.
1. §. Vitious therefore are thoſe Syllogiſms in which either the whole, or Part of the Medium is included in it; For Example;
Every Horſe differs from a Man;
Socrates differs not from a Man;
Therefore Socrates differs not from a Horſe.
This Syllogiſm is bad, becauſe the Word Differ is Part of the Medium: For it ought to have been inferred: Therefore Socrates is not a Horſe, &c.
Ax. 10. The fourth is, the Extremes are ſo to be plac'd in the Concluſion as they were before in the Premiſſes.
1. §. That is, that which is predicated of the Medium in the Premiſſes, ought to be ſo in the Concluſion; and that which is ſubjected to the Medium in the Premiſſes, ought to be ſo in the Concluſion: Or if both Extremes are ſubjected, or both predicated, that ought to be predicated in the Concluſion, which is conjoyned with the Medium in the Major Propoſition; and that ſubjected which is conjoyn'd with the Medium in the Minor Propoſition; This Syllogiſm therefore is Vitious, viz.
Every Animal lives;
Every Man is an Animal:
Therefore every thing living is Man.
For the Inference ought to have been, Therefore every Man lives. For when the Site of the Extremes is otherwiſe in the Premiſſes than it is in the Concluſion, the Syllogiſm either concludes nothing, or indirectly.
Ax. 11. Fifthly, From two Negatives, nothing is concluded. Which Law leans upon this Reaſon, viz. that the Dictum of all requires both; and the Dictum of none, one affirmed Propoſition. This Syllogiſm therefore is Vitious
No Stone is an Animal;
No Man is a Stone:
No Man therefore is an Animal, &c.
2. §. And yet if the Negation be Part of the Argument, a good Syllogiſm may be made of two Negatives. For this Syllogiſm,
That which does not feel, is not an Animal;
A Plant does not feel:
A Plant therefore is not an Animal.
does rightly conclude; becauſe the Particle not, joyned with feel in the Major, did not make a Negation, but only render'd the Medium Infinite, and the ſame Force it ought to exerciſe in the Aſſumption or ſecond Propoſition: And therefore tho' the Minor be in Specie denying, yet is it taken for an Affirming, viz. of an infinite Predicate, &c.
Ax. 12. The Sixth is, that from two Particulars nothing is concluded.
1. §. Which depends upon this Reaſon, viz. that the Dictum of all and none, require either that both, or at leaſt one Propoſition be Univerſal. This Syllogiſm therefore is vicious.
Some Animal is a Man;
Some Animal is a Beaſt:
Some Beaſt therefore is a Man, &c.
2. §. That from two Singulars ſomething rightly may be concluded, and not from two Particulars, this is the reaſon; Uncertain Individuals, which compoſe particular Propoſitions, are Ambiguous; and therefore in Syllogiſms that conſiſt of pure Particulars, there are four Terms. But now Determinate Individuals, of which Singulars conſiſt, are not ſubject to the ſame Homonymy, or doubtful Signification.
Ax. 13. The ſeventh is, that the Concluſion ſhall follow the weaker or deterior Part.
1. §. Wherefore, ſince a Propoſition denying is deterior to an Affirming, and a Particular to an Univerſal: If either of the Premiſſes be denying, the Concluſion alſo muſt be ſo. And if either of them be Particular, the Concluſion alſo muſt be ſo: For the Propoſitions premis'd are the Cauſe of the Concluſion; but the Cauſe cannot be deterior to its Effect; Wherefore if any Debility adhere to the Premiſſes, it muſt neceſſarily paſs into the Concluſion no leſs than hereditary Diſeaſes do to Poſterity. This Rule extends it ſelf alſo to the Conditions of the Matter; ſo that if one of the Premiſſes be neceſſary, the other Contingent, the Concluſion alſo muſt be Contingent, as is taught Book 1. Prior. Cap. 21. And theſe Laws are general.
Ax. 14. The ſpecial Laws, are theſe three; and firſt, the Major of the firſt Figure muſt be always Univerſal, and the Minor Affirming.
1. §. This Law is collected out of Book 1. Prior. Cap. 4. And, therefore theſe Syllogiſms muſt be vitious.
Some Animal is a Beaſt;
Every Man is an Animal:
Every, or ſome Man therefore is a Beaſt.
Every Man is an Animal;
No Horſe is a Man:
Therefore no Horſe is an Animal.
But yet if the Negation be Part of the Medium, the Syllogiſm is not vitious, as we ſaid above.
Ax. 15. The ſecond is, that the Major of the ſecond Figure muſt be always Univerſal, and one of the Premiſſes denying.
1. §. And therefore theſe Syllogiſms are vitious.
Some Animal is a Man;
No Horſe is a Man:
Some Horſe therefore is not an Animal.
Every Man is an Animal;
Every Horſe is an Animal:
Every Horſe therefore is a Man.
Ax. 16. The third is, the Minor of the third Figure muſt be affirming, and the Concluſion Particular.
1. §. And therefore theſe Syllogiſms are vitious:
Every Animal lives;
No Animal is a Plant:
Therefore ſome Plant does not live.
Every Man is an Animal;
Every Man lives:
Every living thing therefore is an Animal.
Ax. 17. The Proprieties convening to Syllogiſms which are fram'd according to theſe Rules, are two, and the firſt is, from true Premiſſes nothing follows but what is true.
1. §. Concerning this Propriety Ariſtotle teaches Book 2. Prior, Cap. 2. And therefore if from true Premiſſes follows what is falſe, it is a Sign that the Form of the Syllogiſm is Vitious, and that there is a Tranſgreſſion againſt ſome of the above-ſaid Laws; and therefore this Syllogiſm,
Every Man is an Animal;
Every Horſe is an Animal:
Every Horſe therefore is a Man.
Is a Paralogiſm; becauſe a falſe Concluſion is collected from true Premiſſes; and that, becauſe both the Premiſſes are affirming in the ſecond Figure. But now if the Form of the Syllogiſm be good, nothing hinders that a true Concluſion may be drawn from falſe Premiſſes, as in this Syllogiſm.
Every Stone is an Animal;
Every Man is a Stone:
Every Man therefore is an Animal.
For here the Form is good, and yet both the Premiſſes apparently falſe, and Concluſion true; but this happens by chance. But from true Premiſſes rightly diſpos'd, there never follows any thing which is falſe.
Ax. 18. The other Propriety is, that from one Syllogiſm rightly form'd many Concluſions may be drawn, and that either by Converſion of the Concluſion, or by Subalternation.
1. §. This Propriety is given us Cap. 1. of the ſame Book: For he who has prov'd, that every Man is an Animal, or no Man is a Stone, or ſome Plants are hurtful, he has by the ſame Premiſſes prov'd that ſome Animal is a Man, no Stone is a Man, and that ſomething noxious is a Plant, becauſe thoſe Concluſions may be converted into theſe, either by Accident or ſimply, &c.
2. §. Subalternation or Subſumption, happens under the Subject, or the Medium, or the Predicate. Under the Subject, when one from a Univerſal Concluſion infers a particular Propoſition which is contain'd in it. As if one having prov'd all Senſe to ariſe from a Reception of the Object, ſhould from thence collect, that the Sight alſo proceeded from the Reception of the Object. Under the Medium, when from a Major Univerſal of the firſt or third Figure, a Particular is inferr'd, which is contained in it; As if any one from this Syllogiſm,
Every Animal is nouriſhed;
Every Man is an Animal:
Every Man therefore is nouriſhed.
ſhould infer, that a Chameleon was nouriſhed. Under the Predicate, when from a Univerſal Major of the ſecond Figure a Particular is inferred, which is contained under it; As, if any one out of this Syllogiſm,
No inanimate Body is nouriſhed;
Every Plant is nouriſhed:
No Plant, therefore is inanimate.
ſhould infer, no Stones are nouriſhed; becauſe they are inanimate, &c.
CHAP. IX. Of the Declaration of the Second and Third Figure, by Reduction to the Firſt, and Expoſition ſo far as is neceſſary for our Purpoſe.
Ax. 1. THE Syllogiſms of the firſt Figure are more perfect than the reſt, for two Reaſons; Firſt, becauſe in that may be concluded all manner of Queſtions, whether Affirming, Denying, Univerſal, Particular,; whereas in the Second only Denying, and in the Third, Particular.
Ax. 2. Secondly, becauſe in that there appears the Neceſſity of the Syllogiſtical Sequel, and the Dictum of All and None, which in the reſt of the Figures are not ſo conſpicuous, but that they require a Declaration.
Ax. 3. Which Declaration is to be made, two ways, viz. by Reduction to the Firſt and by Expoſition.
Ax. 4. Reduction is either oſtenſive, or elſe by Way of Impoſſible.
Ax. 5. Reduction by Impoſſible is perform'd by one of the Premiſſes retaining, and the Concluſion's Contradiction being put in Place of the other.
Ax. 6. Oſtenſive by the Propoſitions being converted, or alſo tranſpoſed.
Ax. 7. To both which are of Uſe thoſe Conſonants, which are contained in the Names of the Modes, to be farther read of in Logicks; but too long here to recite.
Ax. 8. By Expoſition the Neceſſity of the Conſecution is declared, viz. in the third Figure. When in Place of the Medium Univerſal, there is taken a ſingular: As, ſuppoſe Ariſtotle, or ſome other Perſon inſtead of Man., which is contained under that Univerſal, by which to collect the ſame Concluſ… as,
1. §. For Example; a Syllogiſm in Datiſi, viz.
Every Man may err;
Some Man is a Philoſopher:
Some Philoſopher therefore may err.
If any one ſhould doubt this Illation, one may take a ſingular Medium: As, ſuppoſe Ariſtotle, or the like inſtead of Man, and make an Expoſitory Syllogiſm, with it in this manner, viz.
Ariſtotle might or could err;
Ariſtotle was a Man:
And therefore ſome Man might or could err.
Which Concluſion is therefore the more evident; becauſe it has a ſenſible Medium, in which Conform to that moſt evident Maxim, viz. Whatever things agree in the ſame ſingular Third; they alſo agree amongſt themſelves.
2. Syllogiſms of the ſecond Figure are not ſo well declared by Expoſition, becauſe the Medium in the Second, ought to be predicated; but a Singular cannot naturally be predicated, but only ſubjected. And thus far of the Geneſis, or manner of making of Syllogiſms.