Simple Syllogifms have feveral Rules belonging to them, which being obferved, will generally fecure us from falfe Inferences: But thefe Rules being founded on four general Axioms, it is neceffary to mention thefe Axioms beforehand, for the Ufe of those who will enter into the fpeculative Reason of all thefe Rules.

Axiom 1. Particular Propofitions are contained in Universals, and may be inferred from them; but Univerfals are not contained in Particulars, nor can be inferred from them.

Axiom 2. In all univerfal Propofitions, the Subject is univerfal: In all particular Propofitions, the Subject is particular.

Axiom 3. In all affirmative Propofitions, the Predicate has no greater Extenfion than the Subject for its Extenfion is restrained by the Subject, and therefore it is always to be efteemed as a particular Idea. It is by mere Accident, if it ever be taken univerfally, and cannot happen but in fuch univerfal or fingular Propofitions as are reciprocal.

Axiom 4. The Predicate of a negative Propofition is always taken univerfally, for in its whole Extenfion it is denied of the Subject. If we say no Stone is vegetable, we deny all forts of Vegetation concerning Stones.

The Rules of fimple, regular Syllogifms are

these.

Rule I. The middle Term must not be taken twice particularly, but once at least univerfally. For if the middle Term be taken for two different Parts or Kinds of the fame univerfal Idea, then the Subject of the Conclufion is compared with one of

thefe

these Parts, and the Predicate with another Part, and this will never shew whether that Subject and Predicate agree or disagree : There will then be four distinɛt Terms in the Syllogism, and the two Parts of the Question will not be compared with the same third Idea; as if I say, some Men are pious, and some Men are Robbers, I can never infer that Some Robbers are pious, for the middle Term Men being taken twice particularly, it is not the same Men who are spoken of in the major and minor Propositions,

Rule II. The Terms in the Conclusion must never be taken more universally than they are in the Premisses. The Reason is derived from the first Axiom, that Generals can never be inferred from Particulars.

Rule III. A negative Conclusion cannot be proved by two affirmative Premisses. For when the two Terms of the Conclusion are united or agree to the middle Term, it does not follow by any Means that they disagree with one another.

Rule IV. If one of the Premisses be negative, the Conclusion must be negative. For if the middle Term be denied of either Part of the Conclufion, it may shew that the Terms of the Conclusion disagree, but it can never shew that they agree.

Rule V. If either of the Premisses be particular, the Conclusion must be particular. This may be proved for the most part from the first Axiom.

These two last Rules are fonietimes united in this single Sentence, The Conclusion always follows the weaker Part of the Premises. Now Negatives

and Particulars are counted inferior to Affirmatives and Univerfals.

Rule VI. From two negative Premiffes nothing can be concluded. For they feparate the middle Term both from the Subject and Predicate of the Conclufion, and when two Ideas difagree to a third, we cannot infer that they either agree or difagree with each other.

Yet where the Negation is a Part of the middle Term, the two Premiffes may look like Negatives according to the Words, but one of them is affirmative in Sense; as, What has no Thought cannot reafon; but a Worm has no Thought; therefore a Worm cannot reafon. The minor Propofition does really affirm the middle Term concerning the Subject, (viz.) a Worm is what has no Thought, and thus it is properly in this Syllogifm an affirmative Propofition.

Rule VII. From two particular Premiffes, nothing can be concluded. This Rule depends chiefly on the firft Axiom.

A more laborious and accurate Proof of these Rules, and the Derivation of every Part of them in all poffible Cases, from the foregoing Axioms, require fo much Time, and are of fo little Importance to affift the right Use of Reason, that it is needless to infift longer upon them here. See all this done ingeniously in the Logick called, the Art of Thinking, Part iii. Chap. iii. &c.

SECT,

SECT. III.

Of the Moods and Figures of fimple Syllogifms.

Imple Syllogifms are adorned and furrounded in the common Books of Logick with a Variety of Inventions about Moods and Figures, wherein by the artificial Contexture of the Letters A, E, I, and O, Men have endeavoured to transform Logick, or the Art of Reasoning, into a fort of Mechanifm, and to teach Boys to fyllogize, or frame Arguments and refute them, without any real inward Knowledge of the Question. This is almost in the fame Manner as School-boys have been taught perhaps in their trifling Years to compofe Latin Verfes; i. e. by certain Tables and Squares, with a Variety of Letters in them, wherein by counting every fixth, seventh, or eighth Letter, certain Latin Words fhould be framed in the Form of Hexameters or Pentameters; and this may be done by those who know nothing of Latin or of Verses.

I confefs fome of thefe logical Subtilties have much more Ufe than thofe verfifying Tables, and there is much Ingenuity difcovered in determining the precife Number of Syllogifms that may be formed in every Figure, and giving the Reafons of them; yet the Light of Nature, a good Judgment, and due Confideration of Things tend more to true Reasoning than all the Trappings of Moods and Figures.

But left this Book be charged with too great Defects and Imperfections, it may be proper to give fhort Hints of that which fome Logicians have spent so much Time and Paper upon.

All the possible Combinations of three of the Letters A, E, I, O, to make three Propositions amount to fixty four ; but fifty four of them are

' excluded from forming true Syllogisms by the seven Rules in the foregoing Section: The remaining Ten are variously diversified by Figures and Moods into fourteen Syllogisms.

The Figure of a Syllogism is the proper Disposition of the middle Term with the parts of the Question.

A Mood is the regular Determination of Propositions according to their Quantity and Quality, 1. e, their universal or particular Affirmation or Negation; which are signified by certain artificial Words wherein the Consonants are neglected, and these four Vowels A, E, I, O, are only regarded.

There are generally counted three Figures.

In the first of them the middle Term is the Subject of the major Proposition, and the Predicate of the minor. This contains four Moods (viz.) Barbara, Celarent, Darii, Ferio. And it is the Excellency of this Figure that all Sorts of Questions or Conclusions may be proved by it, whether A, E, I, or O, i. e. universal or particular, affirmative or negative, as,

Bar- Every wicked Man is truly miserable.

ba- All Tyrants are wicked Men;
ra. Therefore all Tyrants are truly miserable.

Ce- He that's always in Fear is not happy ;

la- Covetous Men are always in Fear ; rent, Therefore covetous Men are not happy.

Dan