Abstract of Logic, Book 2 · Chapter 11
CHAP. XI. Of Induction, Enthymeme, and Example.
Ax. 1. AN Induction is a Syllogiſm in which one Extreme is concluded by the other of the Medium; alſo defined a Progreſs from Singulars to Univerſals.
1. §. An Induction is ſo called, becauſe by thoſe things which are certain, it induces the Mind of the Hearer to believe thoſe that are Uncertain. Now an Induction collects the greateſt Extreme, that is, the Predicate of the Medium by the other Extreme, that is, the Subject, and all thoſe things that are like unto it. So in an Induction, for Inſtance, it's proved, that Animals void of Bile are long-liv'd; becauſe a Man, a Horſe, an Aſs, &c. are long-liv'd.
2. § When an Induction is ſaid to be a Progreſs from Singulars to Univerſals, the Words muſt not be too ſtrictly taken; For there are two ſorts of it, as thus explained, viz. one by which the Genus is collected of the Species's, or Univerſal of Singulars; and the other in which the Whole of the Parts. Examples of which are to be met with almoſt in every good Author. Thus Ariſtotle Book 8. of his Ethicks, Cap. 1. proves Friendſhip neceſſary to Men: To the Rich, becauſe it Exerciſes their Charity, and conſerves a Proſperous Fortune; Poor, becauſe their Refuge and Supply; Old Men, that they may be reverenced; and what cannot by themſelves be done by reaſon of their Infirmities, may be done by others that are their Friends. Youth, for fear they commit Sin; Vigorous Age, that it may perform famous Enterpriſes, &c. and this is an Induction of the firſt kind, and properly a Progreſſion from Singulars to Univerſals, or at leaſt, leſs Univerſals to more. But an Example of the other it would be, if one ſhould prove the Holy Scriptures to be divinely inſpired, becauſe the Law, the Prophets, the Goſpels, and Writings of the Holy Apoſtles, &c. are divinely inſpir'd; and this would be but improperly called a Progreſſion from Singulars to Univerſals; and ſo of like Inſtances.
Ax. 2. That the Induction may be firm, all the Singulars are to be numbered up, that from thence the Univerſals, or alſo all the Parts, that from hence the Whole may be concluded.
Ax. 3. Or if this be too troubleſome after an Enumeration of ſeveral, it may be ſubjoyn'd that the Ratio of the reſt is the ſame or ſome ſuch like.
1. §. So Horace intending to prove that no Men were content with their Lots, after he had affirmed that neither Merchant, Knight nor Husbandman, nor Lawyer were content with their Lots, he ſumms up all in this manner, viz. that Inſtances of this kind are ſo numerous, that it would weary even the Talkative Fabius, to recite them, &c.
Ax. 7. An Induction is everted, when an unlike Example can be given, and that is termed an Inſtance.
1. §. For Example; If any one ſhould collect that any part of the Body ſhould be cut off if ſo ill affected, as that there ſhould be no hopes of its Recovery, and there were Danger that the whole ſhould be infected by it, becauſe the Foot, the Hand, the Ear in ſuch a Caſe is to be cut off, it may be anſwered, that in the reſt of the Parts omitted there is another Ratio: For it would be a Ridiculous thing to cut off the Head for the Preſervation of the reſt of the Body; and if mention had been made alſo of the Head in the Induction, no body would have granted that that Part, tho' evilly affected, ſhould have been cut off. And thus much of Induction or a Syllogiſm of Induction.
Ax. 8. A Syllogiſm farther may be divided into Perfect and Imperfect. A Perfect is that in which nothing is wanting.
Ax. 9. An Imperfect, in which there is ſome Propoſition, as the Enthymeme; or ſome Part of the Argument, as, Example.
1. §. An Enthymeme, ſays Ariſtotle, is an imperfect Syllogiſm, Example, Induction.
Ax. 10. An Enthymeme is a Syllogiſm maimed or mutilated, of one Propoſition.
Ax. 11. And therefore conſiſts of two, of which the former is called the Antecedent, the latter the Conſequent.
Ax. 12. Now if the Subject of the Conſequent be put into the Antecedent, the Major is ſuppreſs'd; if the Predicate, the Minor; whether the one or the other, the Enthymeme may be reduc'd to a Categorical, by adding the Propoſition wanting.
Ax. 13. If neither the Subject, nor Predicate of the Conſequent, be in the Antecedent, the Major is ſuppreſs'd; and that being added, the Enthymeme is reduc'd to an Hypothetical Syllogiſm, or Syllogiſm of Suppoſition.
1. §. Now this Mode of Arguing or Argumentation, is ſo call'd from a Greek Word, ſignifying to think; becauſe one of the Propoſitions is expreſs'd and the other not, &c.
Now in this Enthymeme, for Example,
A Covetous Man wants; therefore a Covetous Man is not rich; the Subject of the Conſequent, is put into the Antecedent, from whence it is to be collected, that the Major is wanting; which being added, it will be a full Syllogiſm in this manner. No Rich Man wants; Every Covetous Man wants: And therefore no Covetous Man is Rich. But let us fee another: He that ſins not, is not the Author of Sin: And therefore God is not the Author of Sin. Here the Predicate of the Conſequent is expreſſed in the Antecedent, and therefore the Minor is wanting; which being added, it will be ſuch a Syllogiſm as this: He that does not ſin, is not the Author of Sin: God does not ſin: And therefore God is not the Author of Sin, &c. Add a Third to theſe, viz. Virtue makes happy: And therefore Vice miſerable. Here neither the Subject nor the Predicate of the Conſequent is expreſs'd in the Antecedent: And therefore the Major is wanting, which being added, it will make an Hypothetical Syllogiſm in this manner, viz. If Virtue makes happy, then Vice makes miſerable: But Virtue makes happy: And therefore Vice makes miſerable, &c.
Ax. 14. Now an Example is, when one Extreme is ſhewn to be in the Medium by the Reſemblance which it has to the other Extreme.
1. §. That is, when the Major Extreme or the Predicate is collected to be in the Medium by ſome Example, which is like unto the Third, that is, the Subject. For Example conſiſts in four Terms, out of which are made two Ratiocinations; one Perfect, in which out of a Univerſal Major is collected ſome Particular; the other Imperfect, in which out of a Particular like to the Subject of the Concluſion brought, is collected a Propoſition Univerſal containing the Similitude of both Particulars, and was the Major of the Firſt Ratiocination. For Example; Let the greater Extreme be this; It is Pernicious; The Medium, To wage War upon our Neighbours; The Minor, The Athenians wage War upon the Thebans; The Simile, The Thebans wage War upon the Phocenſes, or Citizens of Phoce in Boeotia. Of the which we may make this like Argumentation Exemplary. To wage War upon Neighbburs is pernicious; but if the Athenians infer or wage War upon the Thebans, they wage War upon Neighbours; and therefore if the Athenians wage War upon the Thebans it is pernicious. Add we to this Ratiocination ſome Example; and by that we may confirm the Major Propoſition, viz. that it proved pernicious to the Thebans their waging War with the Phocenſes, or Citizens of Phoce: But that was waging War upon Neighbours; and therefore to wage War upon Neighbours is pernicious. Here now is concluded the Predicate of the Medium by ſomething which is like unto the Subject of the Preceding Syllogiſm.
2. §. Now indeed an Example does not neceſſarily conclude; becauſe it proceeds from a Particular to a Univerſal: It perſuades yet and begets Opinion, and that upon this Foundation, viz. That the like ſhould agree to the like, is meet and reaſonable. In fine, it perſuades, if examined, that the Medium agrees with the Subject, as here, viz. that for the Athenians to wage War upon the Thebans was for them to wage War upon their Neighbours, and that the Predicate agrees to that which is like unto it, viz. that it was pernicious to the Thebans to wage War upon the Phocenſes. &c. And ſo we come to the Twelfth Chapter, viz. that of,