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

COMMENTARY.

For Example; To live, is said universally of Ani∣mal; as, every Animal lives: And Man is contain∣ed 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 univer∣sally 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 Hol∣land is in the Low-Countries, or Belgium, and that Ley∣den is in Holland, or that Leyden is not in England; since Belgium is not in England, and Leyden is in Bel∣gium: 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 accommo∣dated 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 them∣selves: 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 them∣selves 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 Ex∣amples:

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 Conclusi∣on, 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 Pre∣misses, 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 in∣ferred: 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 Pre∣misses.

1. §. That is, that which is predicated of the Me∣dium in the Premisses, ought to be so in the Conclusi∣on; 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 eve∣ry Man lives. For when the Site of the Extremes is otherwise in the Premisses than it is in the Con∣clusion, the Syllogism either concludes nothing, or indi∣rectly.

Ax. 11. Fifthly, From two Negatives, nothing is con∣cluded. 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 Ar∣gument, 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, joyn∣ed 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 se∣cond 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 no∣thing 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 Determi∣nate Individuals, of which Singulars consist, are not subject to the same Homonymy, or doubtful Significa∣tion.

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 Univer∣sal: If either of the Premisses be denying, the Con∣clusion 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; Where∣fore if any Debility adhere to the Premisses, it must necessarily pass into the Conclusion no less than here∣ditary 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 Fi∣gure 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 Pre∣misses 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 Pre∣misses 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 Pre∣misses, 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 Pre∣misses 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. Un∣der the Subject, when one from a Universal Conclu∣sion 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 col∣lect, 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 con∣tained under it; As, if any one out of this Syl∣logism,

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.