it must be extream Abfurdity for any Man to pretend to write.

But what fall we fay to the Confequence of an Hypothetical Syllogifm; is not that a Confequence from one fingle Principle? No fuch Matter. Such a Confequence is no Confequence at all, but only a Propofition, declaring that fuch a thing would follow if fuch a Condition were put: But then till it be put, that is, till another Propofition be added, there is actually no Confequence, but only an Affirmation that if it were put; fuch would be the Confequence of it. So that what is here called a Confequence, is indeed only a Hypothetical Propofition, or an Affirmation of a Conditional, the connexion not lying between the fubject and the fimple Attribute, but between the subject and the complex Attribute, or intire Conditional, as I fhew at large in my former Part. And this appears from the denial of, or contradiction to fuch a Confequence. For what is it that we then deny or contradict ? Not the Part following, upon the Condition, but the intire Conditional itself. We say, indeed, Negatur Confequentia, but we must be fuppofed to deny the fame that we contradict, and the Contradiction, as every Logician knows affects the whole Conditional. For we contradict here, with a Non fi, which plainly fhews that there the Affirmation must properly be understood to lie. And fo alfo, when fuch a Confequence is proved, the Enthymematical way of proving it fhews the fame: For 'tis not any actual Confequence, or the Part following upon the Condition, that is pretended to be proved,

b 2

but

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but the intire Conditional itself. What we then prove is not any Confequence that actually is, but a Propofition, declaring a Confequence that would be upon fuch a Condition. As to return to our Geometrick Inftance: If A B be opposed to the leaft Angle, then A B is the leaft fide. Suppofe any one to deny this Confequence (as we usually Speak, tho' indeed we should more properly fay, this Propofition) what is it that I am to prove? Not furely that A B is the leaft fide, but the intire Conditional, that if it be oppofed to the leaft Angle, that then it is the leaft fide. What I am to prove is the whole Conditional, the part following, or that would follow upon the Condition, being still left in fufpenfe. For thus my proof proceeds: The leaft fide is oppofed to the leaft Angle; therefore if A B be oppofed to the leaft Angle, then AB is the leaft fide: If it be, but whether it be or no, is the business of another Propofition to fhew, and till that be done, nothing actually follows; but things hang in the fame fufpenfe as before: By which it clearly appears, that the Confequence (as 'tis called) of an Hypothetical Syllogifm is not properly an actual Confequence, that is a Propofition actually following from fomething premifed, but only a fingle Propofition declarative of a Confequence that would follow upon fuch a Pofition. Which, by the way, I take to be the Reafon (or else I am not Logician enough to affign any) why, tho' the Conclufion of a Syllogifm may not be denied, yet the Confequence of it may. But, I pray, why so? Is not a Confequence and a Conclufion of the fame?

Yes,

Yes, an actual Confequence is, for what is a Conclufion but a Propofition following upon Premifes And therefore if the Confequence of fuch a Syllogifm were an actual Confequence, it ought no more to be denied than the Conclufion, but rather the Premises upon which it depends: But then this fhews plainly that it is not. And indeed the true Reafon that juftifies the denial of fuch a Confequence, I take to be this, That the confequence of a Hypothetical Syllogifm is confidered not as an actual Confequence, but as a bare Propofition,tho' of a particular Kind or Form: And 'tis no ftrange thing for a Propofition to be denied. From all which it is clear, that the Confequence of an HypotheticalSyllogifm,is indeed no actual Confequence as aConclufion is (for then it would be no more to be denied than aConclufion)but only a bare Enuntiation, till the Hypothefis be put; and when it is put, then indeed there will be an actual Confequence: But not from one Propofition, for then there will be another added to it, and a Confequence from two Propofitions premifed, is the very thing which we call a Syllogifm, out of which therefore there is no actual Confequence to be found (for the true Confequence of an Hypothetick Syllogifm, that is, that which actually and really follows, is no other than the Conclufion) nor confequently any effectual Arguing or Reafoning; and therefore for any Man to pretend to imploy his Reafon to the dif paragement of that wherein, and whereby all true Reafoning proceeds, muft needs be an odd and a bold Extravagance.

Now as to the usefulness of Syllogism, Imight fay a great deal, but touching upon it here only enpaffant, ball but just glance at a few Confiderations. As ift. That it shortens and draws together our view of things, and brings a large Field of Truth under a narrow compass. This we look upon as the great advantage of Algebra, that it teaches us the way to abridge our Ideas, whereby the Capacity of the Mind is inlarged for the dif covery of fuch compounded Truths, as at first view appear incomprehenfible. For indeed the leaving out fuch things as would needlefly fill and diftract the Attention of the Mind, is equivalent to the inlarging of its Capacity; it being to all intents of Vifion the fame thing, whether the fight be carried further, and Spread wider, or the prospect be brought nearer home and made more contracted. But then this, in its proportion, is as true of Syllogifm. Then again, as it contracts the subject of our Contemplation, fo it ferves 2dly, as a measure to us in the management and difpofal of our Thoughts in our Reasonings and Difcourfes to others, wherein we cannot otherwife avoid Confufion and Diforder, than by confidering what the Conclufion is which we would prove, by what mediums we would prove it, and to which part of the Argument, whether Major or Minor, or Conclufion, this or that particular part of our Difcourfe relates; fo that tho' our Difcourfe be not laid out in the exact formality of Syllogifm (which ordinarily to affect, would perhaps favour a little too much of School-Pedantry)

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yet we should have a kind of a fyllogiftical Plan before us, that fo. in every Stage of our Difcourfe we may know where about we are, and what we are doing. But then Laftly, as it regulates our own, So it will ferve as a measure whereby to judge of the Difcourfes of others. For paffing a right Judgment upon which, we must confider what the Conclufion is which they offer to prove, what the Premifes are whereby they prove it, and whether fuch Premifes do indeed prove fuch a Conclufion. And indeed I know no better way to form a right Judgment of any Difcourfe; or, to prevent our being impofed upon by the plaufible flourish of a long Harangue, than to reduce it to Syllogifm. For then you will fee all the parts of the Argument in Miniature, what truly belongs to it, and what is put in only for Shew, Pomp, Amusement, and every part in its proper Place and Order; and withal what Connexion one part has with another, which is the best way that I know of whereby to judge of the whole. Whereby it may appear that there is fome other use of Syllogifm than what the Author is pleafed to mention, viz. That the chief and main Use of it is in the Schools, where Men are allow'd without Shame to deny the Agreement of Ideas which do manifeftly agree, Which Reffection perhaps is neither fo True, nor yet fo Pertinent as it should be, Not fo true, fince by the Laws of Argumenta tion, the Refpondent is not fo at liberty to deny whatever comes in his way; but that in certain Cafes (whereof the denial of a manifeft Truth is one) he may be justly required to affign a Reafon for it, Nor b 4

yet