The Art of Logic, Book 3 · Part 1 – Part 4
Of a Syllogism.
THE third part of Logick is busied in directingThe definition of Discourse. the Discourse.
Discourse is an act of the mind of man, moving it self forward from a known thing to an unknown, by a fit collation of things former and latter.
And it is either
Inferring.
Ordering.
Inferring Discourse is an action of mans mind by certain premised propositions proving another proposition, or improving it, by help of the Precepts of a Syllogism.
A Syllogism is considered, eitherforeign.
Commonly. a
Specially, in certain conditions of matter. b
A Syllogism commonly considered, is either perfectly soa called, or imperfectly.
Perfectly called, is, the disposition of three Propositions, wherein from the two former and better known, a thirdA Perfect Syllogism. more unknown or doubtful is fitly inferred, and gathered.
In this are to be considered the
Constitution.
Division.
A Syllogism is constituted of the
Material. m
Formal. n
The Material, is either 1. Simple, or 2. Compound.m
1. Simple are the Terms into which at last the Syllogism is resolved.
The Term is either the utmost or the mean.
The utmost or extream, is that which is put both in the Conclusion and in the Premises. And it is greater, or lesser.
The greater or Major, is the Consequent of the Conclusion,Major. always to be put in the first Proposition.
The lesser or Minor, is the Antecedent or Subject of theMinor. Conclusion, always to be put in the second Proposition.
The Mean, is, by means whereof the extreams are disposedMean. together.
The compound matter of a Syllogism, is a Proposition.
A Proposition, is either inferring or inferred.
Inferring, is, which inferreth the Conclusion: called therefore Premises: and it is either the major or minor.
The Major, or greater, is, in which the greater extream is disposed with the Mean.
The Minor, or lesser, is, in which the lesse extreame is disposed with the Mean.
The Inferred, is that which is gathered from the Premises.
The Formal of a Syllogism, is the fit disposition of the… Mean with the extreams.
The disposition of the Mean ariseth from the finding of it out.
The finding out of the Mean, consists in two things. 1. The foreknowledge of the Conclusion. 2. The Collation of the extreams one with another.
1. The foreknowledge of the Conclusion, is either
Simple. a
Compound. b
Simple, is, when the nature and propriety is foreknowna of both the extreams, as well the Antecedent as the Consequent.
Of this Foreknowledge there are three Canons.
1. Let the Word or Voice of both extreams be diligently examined, what it is, and of what sort; and if it be doubtful, let it be carefully distinguished, and that distinction be presupposed in place of a Principle, as well for confirmation as refutation.
2. Let it be observed, whether the extreams of the conclusion be universal or singular.
3. Let the causes, proprieties, and whole definition of both extreams be set down, either implicitely or expresly, as a certain and necessary Principle of the confirmation and refutation to come.
The Compound foreknowledge of the conclusion, is, when the nature, quality, and quantity thereof is considered.
The Canons hereof are seven:
1. Let the conclusion or state of the controversie be rightly informed.
2. Let a compound or Hypothetical, never be put in the place of a conclusion, but only a Simple or Categorical.
3. That conclusion is more easily proved, which may be concluded in many figures and moods; And that which can be but in few, is harder to be proved.
4. An universal affirmative is hardly proved, not easily refuted.
5. An universal negative is easily proved, hardly refelled.
6. A particular affirmant is more easily proved, more hardly refelled.
7 A particular negant is easie to prove, most hard to refute.
2. Now followeth the taking of the mean by Collation of the extreams.
The mean or medium, is either Perfectly so called or Imperfectly.
Perfectly called, is that simple Term which being taken from the nature of both extreams, either knitteth or disjoyneth them one with another.
Hereof, are three Canons.
1. Every mean is taken from the Terms of both extreams in the conclusion, as well the natural, as the repugnant Terms; therefore he that would find a medium, must mind the general, the special, the causes, the accidents, the parts, the cognata, the opposites of both Terms in the conclusion.
2. What manner of mean is required to make a Syllogism of this or that quantity, the Vowel Letters in the Modes of every Figure, do evidently shew.
3. The mean, though it may be taken from the part of the antecedent as wel as of the consequent, yet that is counted more noble which is drawn from the nature of the consequent; As for example, a mean is to be found to prove this conclusion, Every man is an Animal; mind the nature of this consequent Animal, and from it take the property of it, which is sense; this agreeth with both Terms, and is an excellent mean, or Argument to prove the conclusion, thus, Every thing that hath sense is an Animal. Every man hath sense; therefore every man is an Animal.
4. One and the same mean for a diverse respect of the Antecedent or consequent, may be referred to diverse places of Inventiom; as for example, A man hath sense, because he is an Animal: This Argument in respect of the Antecedent man, is from the place of the genus; but in respect of the consequent, it is from the place of the subject; for an Animal is the proper subject of sense.
5. Store of Means or Arguments is gotten chiefly two ways: 1. By deducing both extreams one after another through the places of invention, as well contingent as necessary. 2. By discerning the principal means from the less principal; for example, take the consequent of thy opposed conclusion particularly, and lead it through the contingent places; argue and reason from the Notation of it, the likes, equales, conjugates, and the other contingent titles of places: which are at least 16. now thou hast so many Means. Then come to the others store-house of necessary places; and reason from the Genus, the difference, the subject and accident, the proper, the causes, and the other titles of necessary places, which are at least 17. Then do the like about the Antecedent of the proposed conclusion; and thus maist thou have for one Conclusion fifty Means or Arguments: but not the store of Arguments is to be respected so much as the weight or force of them; three or four sound Arguments are enough to prove any common Conclusion.
The Mean imperfectly so called, is when a Testimony, or speech of any Author is taken to prove the conclusion. This mean is called foreign inartificial, because testimonies want artificial force to prove any thing of themselves. It is called also the Place from authority, that is, the dignity of the speaket.
And thus much of the constitution of a Syllogism; Now followeth the division of it.
Of the three Figures of Syllogisms,
A Syllogism is divided by three Figures.
A Figure is the conformation of a Syllogism, according to the certain situation of the Mean term, and certain manners (or modes) of quantity and quality; Figura est foreign. Alexand.
A mode or manner, is a lawful constitution of Propositions in every figure, according to the quality and quantity.
And it is either
Principal.
Lesse Principal.
Principal, is, when the Propositions are general, that is, joyned with universals, or indefinite, or particular.
Less Principal, is, when the premises are singular.
The Figures of Syllogisms are three:
The first Figure, is, in which the mean or middle Term is the Antecedent (subject or foregoer) in the major or first proposition: and the consequent (Attribute or follower) in the minor or second Proposition.
The Modes of this Figure are four, called Barbara▪ Celarent, Darii, Ferio; these are but words of Art, and serve for no other meaning then that the vowel Letters in them denote the quality and quantity of the Propositions; a noteth an universal affirmative; e an universal negative. i Noteth a particular affirmative, and o noteth a particular negative.
As may be seen in the examples following.
Barbara.
Every sinner is subject to Gods wrath.
Every man is a sinner: therefore,
Every man is subject to Gods wrath.
Celarent.
No sinner deserveth Gods favour.
Every man is a sinner: therefore,
No man deserveth Gods favour.
Darii.
All sin is to be shunned.
Some pleasure is sin: therefore,
Some pleasure is to be shunned.
Ferio.
No sin giveth a man true comfort:
Some pleasure is sin: therefore,
Some pleasure giveth a man no true comfort.
A Singular Syllogism.
The promised Messias ought to die for the sins of the world.
Jesus Christ is the promised Messiah: Therefore,
He ought to die for the sins of the world.
The second Figure, is, in which the Mean or middle term is in both the Premises put in the place of the Consequent.
The Modes of this Figure are also four, Called, Cesare, Camestres, Festino, Baroco.
Cesare.
No true Christian loveth this worlds good:
Every covetous man loveth this worlds good: therefore,
No covetous man is a true Christian.
Camestres.
All righteousness pleaseth God.
No faith without works pleaseth God: therefore,
No faith without works is righteousness.
Festino.
No true Worship displeaseth God:
Some prayer displeaseth God: therefore,
Some prayer is not true worship.
Baroco.
All vertue deserveth praise:
Some love deserveth not praise: therefore,
Some love is not vertue.
Singular Syllogisms.
Jupiter Belus was an Assyrian.
Jupiter of the Poets was not an Assyrian: therefore,
Jupiter of the Poets, is not Jupiter Belus.
Jude Iscariot was a Traytor.
Jude that wrote the Epistle, was not a Ttaytor: therefore,
Jude that wrote the Epistle, was not Jude Iscariot.
The third Figure is, in which the Mean or Medium is put3. Figure. in the place of the Antecedent in both premises.
The Modes of this Figure are six.
Called, Darapti, Felapton, Disamis, Datisi, Bocardo, Ferison.
Darapti.
Every godly man is happy.
Every godly man is hated of the world; therefore,
Some that is hated of the world is happy.
Felapton.
No will worship pleaseth God.
All will-worship is the invention of man: therefore,
Some invention of man pleaseth not God.
Disamis.
Some man shall be saved,
Every man is a sinner: therefore,
Some sinner shall be saved.
Datisi.
Every holy man is loved of God.
Some holy man is afflicted of God: therefore,
Some that is afflicted of God, is loved of God.
Bocardo.
Some in the visible Church shall not be saved.
All in the visible Church professe Christ▪ therefore,
Some that profess Christ shall not be saved.
Ferison.
None whom God loveth are wretched.
Some whom God loveth are poor: therefore,
Some poor men are not wretched.
Singular Syllogisms:
Judas was not saved.
Judas was an Apostle: therefore,
Some Apostle was not saved.
Abraham entred into the Kingdom of Heaven.
Abraham was rich: therefore,
Some rich man entreth into the Kingdom of Heaven.
And thus much of the Species or Figures of a perfect Syllogism.
Now followeth the proprieties.