Monitio logica, or, An abstract and translation of Burgersdicius his logick by a gentleman.

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 U∣niversals.

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 A∣nimals 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. Ex∣amples of which are to be met with almost in e∣very good Author. Thus Aristotle Book 8. of his E∣thicks, Cap. 1. proves Friendship necessary to Men: To the Rich, because it Exercises their Charity, and conserves a Prosperous Fortune; Poor, because their Re∣fuge 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 Pro∣phets, the Gospels, and Writings of the Holy Apo∣stles, &c. are divinely inspir'd; and this would be but improperly called a Progression from Singulars to Univer∣sals; 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 Enume∣ration 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 Talka∣tive 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 affe∣cted, as that there should be no hopes of its Reco∣very, 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 an∣swered, 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 Pro∣position, as the Enthymeme; or some Part of the Argu∣ment, as, Example.

1. §. An Enthymeme, says Aristotle, is an imper∣fect 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 Con∣sequent.

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 Argumenta∣tion, 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 col∣lected, that the Major is wanting; which being ad∣ded, 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 an∣other: 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 Ante∣cedent,

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 hap∣py: And therefore Vice miserable. Here neither the Subject nor the Predicate of the Consequent is ex∣press'd in the Antecedent: And therefore the Major is wanting, which being added, it will make an Hy∣pothetical Syllogism in this manner, viz. If Virtue makes happy, then Vice makes miserable: But Virtue makes happy: And therefore Vice makes mi∣serable, &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 Par∣ticular; the other Imperfect, in which out of a Par∣ticular like to the Subject of the Conclusion brought, is collected a Proposition Universal containing the Si∣militude of both Particulars, and was the Major of the First Ratiocination. For Example; Let the greater Extreme be this; It is Pernicious; The Me∣dium, To wage War upon our Neighbours; The Mi∣nor, 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 Ex∣emplary. To wage War upon Neighbburs is per∣nicious; 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 Ra∣tiocination

some Example; and by that we may con∣firm the Major Proposition, viz. that it proved pernici∣ous to the Thebans their waging War with the Pho∣censes, or Citizens of Phoce: But that was waging War upon Neighbours; and therefore to wage War upon Neighbours is pernicious. Here now is con∣cluded the Predicate of the Medium by something which is like unto the Subject of the Preceding Syllo∣gism.

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 Medi∣um 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,