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means qualified to reafon with Advantage, until we have per fectly mastered the Science to which they belong; it being hence chiefly, that we are furnished with tho fe intermediate Ideas, which lead to a juft and fuccefsful Solution.

Why Matbefmaticians

ometimes

fwer not the Expectation their great

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VIII. AND here as it comes fo naturally in my Way, I cannot avoid taking notice of an Obfervation, that is frequently to be met with, and feems to carry in it at firft, fomething very ftrange and unaccountable. It is in fhort this; that Mathematicians, even fuch as are univerfally allowed to excel in their own Profeffion, and to have difcovered themselves perfect Mafters in the Art of Reasoning, have not yet been always happy in treating upon other Subjects; but rather fallen fhort, not only of what might naturally have been expected from them, but of many Writers much lefs exercifed in the Rules of Argumentation. This will not appear fo very extraordinary, if we reflect on what has been hinted above. Mathematics is an engaging Study, and Men who apply themfelves that Way, fo wholly plunge into it, that they are for the moft part but little acquainted with other Branches of Knowledge. When therefore they quit their favourite Subject, and enter upon others that are in a manner new and ftrange to them, no wonder if they find their Invention at a ftand. Because however perfect they may be in the Art of Reafoning, yet wanting here thofe intermediate Ideas, which are neceffary to furnifh out a due Train of Propofitions, all their Skill and Ability fails them. For bare Knowledge of the Rules is not fufficient. muft farther have Materials whereunto to apply them. And when thefe are once obtained, then it is that an able Reafoner difcovers his Superiority, by the juft Choice he makes, and a certain mafterly Difpofition, that in every Step of the Procedure, carries Evidence and Conviction along with it. And hence it is, that fuch Mathematicians as have of late Years applied themfelves to other Sciences, and not contented with a fuperficial Knowledge, endeavoured to reach their inmost Receffes; fuch Mathematicians, I fay, have by mere Strength of Mind, and a happy Application of Geomet ical Reasoning, carried their Difcoveries far beyond, what was heretofore judged the utmoft Limits of human Knowledge. This is a Truth abundantly known, to all who are acquainted with the late wonderful Improvements in Natural Philofophy.

Secondly, the Skill of apflying inter

VIII. I COME now to the fecond thing required, in order to a fuccefsful Progrefs in Reafoning, namely; the Skill and Talent of applying inter

mediate

mediate Ideas happily, in all particular Inftances mediate Ideas that come under Confideration. And here I fhall happily in not take up much time in laying down Rules and particular InPrecepts, because I am apt to think they would fances. do. but little Service. Ufe and Experience are the best Instructors in the present Cafe: and whatever Logicians may boast, of being able to form perfect Reafoners by Book and Rule, yet we find by Experience, that the Study of their Precepts, does not always add any great Degree of Strength to the Underftanding. In fhort, 'tis the Habit alone of Reasoning, that makes a Reafoner. And therefore the true Way to acquire this Talent is, by being much converfant in thofe Sciences, where the Art of Reasoning is allowed to reign in the greatest Perfection. Hence it was that the Ancients, who fo well underftood the Manner of forming the Mind, always began with Mathematics, as the Foundation of their Philofophical Studies. Here the Understanding is by Degrees habituated to Truth, contracts infenfibly a certain Fondness for it, and learns never to yield its Affent to any Propofition, but where the Evidence is fufficient to produce full Conviction. For this Reafon Plato has called Mathematical Demonftrations the Cathartics or Purgatives of the Soul, as being the proper Means to cleanfe it from Error, and restore that natural Exercife of its Faculties, in which juft Thinking confifts. And indeed I believe it will be readily allowed, that no Science furnishes so many Inftances, of a happy Choice of intermediate Ideas, and a dexterous Application of them, for the Discovery of Truth, and Enlargement of Knowledge.

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The Study of Mathematical Demonftrations of great Avail in this

Refpe.

IX. IF therefore we would form our Minds to a Habit of Reasoning clofely and in train, we cannot take any more certain Method, than the exercifing ourselves in Mathematical Demonftrations, fo as to contract a kind of Familiarity with them. "Not that we look upon it as neceflary, "(to use the Words of the great Mr. Locke) that all Men "thould be deep Mathematicians, but that, having got the "Way of Reafoning which that Study neceffarily brings the "Mind to, they may be able to transfer it to other Parts of Knowledge, as they fhall have Occafion. For in all forts "of Reasoning, every fingle Argument fhould be managed as "a Mathematical Demonftration, the Connection and Depen"dence of Ideas fhould be followed, till the Mind is brought to the Source on which it bottoms, and can trace the Co"herence through the whole Train of Proofs. It is in the general obfervable, that the Faculties of our Souls are improved

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"and made useful to ns, juft after the fame manner, as our "Bodies are. Would you have a Man write or paint, dance "or fence well, or perform any other manual Operation, dex"teroufly and with Eafe? Let him have ever fo much Vigour "and Activity, Suppleness and Addrefs naturally, yet nobody expects this from him unless he has been used to it, and "has employed Time and Pains in fafhioning and forming "his Hand, or outward Parts, to thefe Motions. Juft fo it is in the Mind; would you have a Man reafon well, you muft ufe him to it betimes, exercife his Mind in obferving "the Connection of Ideas, and following them in train. "Nothing does this better than Mathematics, which there"fore I think fhould be taught all thofe, who have the Time "and Opportunity, not fo much to make them Mathema"ticians, as to make them reasonable Creatures; for though we "all call ourselves fo, becaufe we are born to it, if we please; yet we may truly fay, Nature gives us but the Seeds of it. "We are born to be, if we please, rational Creatures; but 'tis "Ufe and Exercife only that makes us fo, and we are indeed "fo, no farther than Industry and Application has carried us." Conduct of the Understanding.

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As alfo of fuch Authors on other Sub jects, as are diftinguifbed for Strength and Fuftness of Reafoning.

X. BUT although the Study of Mathematics, be of all others the moft ufeful, to form the Mind, and give it an early relifh of Truth, yet ought not other Parts of Philofophy to be neglected. For there also we meet with many Opportunities of exercifing the Powers of the Understanding; and the Variety of Subjects naturally leads us, to ob

ferve all thofe different Turns of Thinking, that are peculiarly adapted to the feveral Ideas we examine, and the Truths we fearch after. A Mind thus trained, acquires a certain Maftery over its own Thoughts, infomuch that it can range and model them at pleasure, and call fuch into view, as beft fuit its prefent Defigns. Now in this the whole Art of Reafoning confifts, from among a great Variety of different Ideas, to fingle out thofe that are most proper for the Business in hand, and to lay them together in fuch Order, that from plain and eafy Beginnings, by gentle Degrees, and a continued Train of evident Truths, we may be infenfibly led on to fuch Difcoveries, as at our first fetting out appeared beyond the Reach of human Understanding. For this Purpose, befides the Study of Mathematics before recommended, we ought to apply ourfelves diligently to the reading of fuch Authors, as have diftinguished themselves for Strength of Reafoning, and a juft and accurate Manner of Thinking. For it is obfervable, that a

Mind exercifed and feafoned to Truth, feldom refts fatisfied in a bare Contemplation of the Arguments offered by others, but will be frequently affaying its own Strength, and purfuing its Difcoveries upon the Plan it is moft accustomed to. Thus

we infenfibly contract a Habit, of tracing Truth from one Stage to another, and of inveftigating those general Relations and Properties, which we afterwards afcribe to particular Things, according as we find them comprehended under the abstract Ideas, to which the Properties belong. And thus having particularly fhewn, how we are to diftribute the feveral Objects of Nature under general Ideas, what Properties we are to afcribe to them in confequence of that Diftribution, and how to trace and inveftigate the Properties themfelves; I think I have fufficiently explained all that is neceflary towards a due Conception of Reasoning, and fhall therefore here conclude this Chapter.

Σ.

H'

CHA P. IV.

Of the Forms of Syllogifms.

The Figures

ITHERTO we have contented ourfelves with a general Notion of Syllo- of Syllogifms. gifms, and of the Parts of which they confift. It is now time to enter a little more particularly into the Subject, to examine their various Forms, and lay open the Rules of Argumentation proper to each. In the Syllogifms mentioned in the foregoing Chapters, we may obferve, that the middle Term is the Subject of the Major Propofition, and the Predicate of the Minor. This Difpofition, though the most natural and obvious, is not however neceffary; it frequently happening, that the middle Term is the Subject in both the Premiffes, or the Predicate in both; and fometimes, directly contrary to its Difpofition in the foregoing Chapters, the Predicate in the Ma jor, and the Subject in the Miner. Hence the Diftinction of Syllogifms into various Kinds, called Figures by Logicians. For Figure, according to their Ufe of the Word, is nothing elfe, but the Order and Difpofition of the middie Term in any Syllogifm. And as this Difpofition, is we fee fourfold, fo the Figures of Syllogifms thence arifing, are four in Number. When the middle Term is the Subject of the Major Propofi tion, and the Predicate of the Minor, we have what is called the first Figure. If on the other hand, it is the Predicate of

both

Book III. both the Premiffes, the Syllogifm is faid to be in the fecond Figure. Again in the third Figure, the middle Term is the Subject of the two Premiffes. And laftly, by making it the Predicate of the Major, and Subject of the Minor, we obtain Syllogifms in the fourth Figure.

II. BUT befides this fourfold Diftinction of The Moods of Syllogifms, Syllogifms, there is alfo a farther Subdivifion of them in every Figure, arifing from the Quantity and Quality as they are called of the Propofitions. By Quantity we mean the Confideration of Propofitions as univerfal or particular, by Quality as affirmative or negative. Now as in all the feveral Difpofitions of the middle Term, the Propofitions of which a Syllogifm confifts, may be either univerfal or particular, affirmative or negative; the due Determination of thefe, and fo putting them together, as the Laws of Argumentation require, conftitute what Logicians call the Moods of Syllogifm. Of these Moods there are a determinate Number to every Figure, including all the poffible Ways, in which Propofitions differing in Quantity or Quality can be combined, according to any Difpofition of the middle Term, in order to arrive at a juft Conclufion. The Shortness of the present Work, will not allow of my entering into a more particular Defcription, of thefe feveral Diftinctions and Divifions. I fhall therefore content myself, with referring the Reader to the Port-Royal Art of Thinking, where he will find the Moods and Figures of Syllogifms diftinctly explained, and the Rules proper to each very neatly demonftrated.

Foundation of

the other Di

vifion of Syllogijms.

III. THE Divifion of Syllogifms, according to Mood and Figure, refpects thofe efpecially, which are known by the Name of plain fimple Syllogifms; that is, which are bounded to three Propofitions, all fimple, and where the Extremes and middle Term are connected, according to the Rules laid down above. But as the Mind is not tied down to any one precife Form of Reasoning, but fometimes makes ufe of more, fometimes of fewer Premiffes, and often takes in compound and conditional Propofitions, it may not be amifs to take notice of the different Forms derived from this Source, and explain the Rules by which the Mind conducts itself in the Use of them.

Conditional

Syllogifms.

IV. WHEN in any Syllogifm, the Major is a conditional Propofition, the Syllogifm itself is termed Conditional. Thus :

If there is a God, he ought to be worshiped.
But there is a God:

There

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