tion about real Beings in the way of Intuition of Ideas. For this you told me was P. 134. your fecond Realon to prove this Propofition. This Confequence your Lordfhip, it feems, looks upon as fo clear, that it needs no Proot; I can find none P. 141. here where you take it up again. To prove fomething, you fay, Suppofe an Idea happen to be thought by fome to be clear and diftinct, and others should think the contrary to be fo: In obedience to your Lordship, I do Juppofe it. But, when it is fuppos'd, will that make good the above-mention'd Confequence? You your feif, my Lord, do not fo much as pretend it; but in this Queftion fubjoin'd; Ibid. (What hopes of Demonftration by clear and diftinct Ideas then?) infer a quite different Propofition. For, It is impoffible to come to a Demonstration about real Beings in the way of Intuition of Ideas; and, There is no hopes of Demonftration by clear and dif. tinct Ideas; appear to me two very different Propofitions.

There appears fomething to me yet more incomprehenfible in your way of managing this Argument here. Your Reafon is, as we have feen, in these words, There may be contradictory Opinions about fome Ideas, that I account mest clear and diftinct: And your Inftance of it is in thefe words, Suppose an Idea happen to be thought by fome to be clear and diftinct, and others should think the contrary to be fo. Anfw. So they may, without having any contradictory Opinions ábout any Idea, that I account most clear and diftinct. A Man may think his Idea of Heat to be clear and diftinct, and another may think his Idea of Cold (which I take to be the contrary Idea to that of Heat) to be clear and distinct, and bé both in the right, without the leaft appearance of any contradictory Opinions. All therefore that your Lordfhip fays, in the remaining part of this Paragraph, having nothing in it of contradictory Opinions about Ideas that I think meft clear, ferves not at all to make good your fecond Reafon. The truth is, all that you fay here concerning Des Cartes's Idea of Space, and another Man's Idea of Space, amounts to no more but this; That different Men may fignify different Ideas by the fame Name, and will never fix on me what your Lordfhip would perfuade the World I fay, that both Parts of a Contradiction may be true. Tho' I do fay, that in fuch a loose use of the Terms Body and Vacuum, it may be demonftrated both that there is, and is not a Vacuum: Which is a Contradiction in words, and is apt to impofe, as if it were fo in Senfe, on those who miftake Words for Things; who are a kind of Reafoners, whereof I perceive there is a greater Number than I thought there had been. All that I have faid in that place Effay, B. 4. quoted by your Lordfhip, is nothing but to flew the Danger of relying upon Maxims, without a careful Guard upon the ufe of words, without which they will ferve to make Demonftrations on both fides. That this is fo, I dare appeal to any Reader, fhould your Lordship prefs me again, as you do here, with P. 143. all the force of thefe Words, Say you fo? What! Demonftrations on both fides? And in the way of Ideas too? This is extraordinary indeed!

C. 7. §. 12.

That all the Oppofition between Des Cartes and thofe others, is only about the naming of Ideas, I think may be made appear from thefe words of your Lordship P. 143. in the next Paragraph; In the Ideas of Space and Body, the Question Suppos'd, is, whether they be the fame or no. That this is a Question only about Names, and not about Ideas themselves, is evident from hence, that no body can doubt whether the fingle Idea of pure Distance, and the two Ideas of Distance and Solidity, are one and the fame Idea, or different Ideas, any more than he can doubt whether one and two are different. The Queftion then in the Cafe, is not whether Extenfion confider'd feparately by it felf, or Extenfion and Solidity together, be the fame Idea or no; but whether the fimple Idea of Extenfion alone fhail be call'd Body, or the complex Idea of Solidity and Extenfion together fhall be call'd Body. For that thefe Ideas themfelves are different, I think I need not go about to prove to any one, who ever thought of Emptiness or Fulness: for whether in Fact the Bottle in a Man's Hand be empty or no, or can by him be empty'd or no; this, I think, is plain, That his Idea of Fulnefs, and his Idea of Emptiness, are not the fame. This the very Difpute concerning a Vacuum fuppofes; for if Mens Idea of pure Space were not different from their Idea of Solidity and Space together, they could never fo far feparate them in their Thoughts, as to make a Queftion, whether they did always exift together, any more than they could queftion, whether the fame thing exifted with it felf. Motion cannot be feparated in Exiftence from Space; and yet no body ever took

the

the Idea of Space and the Idea of Motion to be the fame., Solidity likewife cannot exist without Space; but will any one from thence fay, the Idea of Solidity and the Idea of Space are one and the fame?

Your Lordship's third Reason, to prove that it is impoffible to come to a Demon- P. 134. ftration about real Beings in this way of Intuition of Ideas, is, That granting the Ideas to be true, there is no Self-evidence of the Connection of them, which is necessary to made a Demonftration. This, I muft own, is to me as incomprehenfible a Confequence as the former as alfo is that which your Lordship fays to make it P. 143. out, which I fhall fet down in your own words, that its Force may be left entire to the Reader: Put granting the Ideas to be true, yet when their Connection is not self-evident, then an intermediate Idea muft compleat the Demonftration. But how doth it appear, that this middle Idea is felf-evidently connected with them? For 'tis faid, if that intermediate Idea be not known by Intuition, that must need a proof; and fo there can be no Demonftration: which your Lordship is very apt to believe in this way of Ideas; unless these Ideas get more light by being put between two others. Whatever there be in these words to prove the Propofition in question, I leave the Reader to find out: but that he may not be led into a Mistake, that there is any thing in my words that may be serviceable to it, I must crave leave to acquaint him, That these words fet down by your Lordship, as out of my Elay, are not to be found in that place, nor any where in my Book, or any B. 4. C. 2. thing to this purpose, That the intermediate Idea is to be known by Intuition; but §.7. this, That there must be an intuitive Knowledg or Perception of the Agreement or Difagreement of the intermediate Idea with thofe, whose Agreement or Difagreement by its intervention it domonftrates.

Leaving therefore all that your Lordship brings out of Gaffendus, the Cartefuns, Morinus, and Bernier, in their Argument from Motion, for or against a Vacuum, as not being at all concern'd in it; I fhall only crave leave to obferve, that you feem to make ufe here of the fame way of Argumentation, which I think I may call your main, if not only one, it occurs fo often, viz. That when I have faid any thing to fhew wherein Certainty or Demonftration, &c. confifts, you think it fufficiently overthrown, if you can produce any Inftance out of my Book, of any thing advanc'd by me, which comes fhort of Certainty or Demonstration: Whereas, my Lord, I humbly conceive, it is no proof against my Notion of Certainty, or my way of Demonftration, that I cannot attain to them in all Cafes. I only tell wherein they confift, wherever they are ; but if I mifs of either of them, either by reafon of the Nature of the Subject, or by Inadvertency in my way of Proof, that is no Objection to the Truth of my Notions of them: For I never undertook that my way of Certainty or Demonftration, if it ought to be call'd my way, fhould make me or any one Omniscient or Infallible.

That which makes it neceffary for me here again to take notice of this your way of Reasoning, is the Queftion wherewith you wind up the account you have given of the Dispute of the Parties above-named about a Vacuum; And is P. 145. it poffible to imagine, that there should be a self-evident Connection in the Cafe? Anfw. It concerns not me to examine, whether, or on which fide, in that Difpute, fuch a felf-evident Connection is, or is not poffible. But this I take the liberty to fay, That wherever it is not, there is no Demonftration, whether it be the Cartefians or the Gaffendifts this fail'd in this Point. And I humbly conceive, that to conclude from any one's failing in this, or any other Cafe, of a felf-evident Connection in each step of his Proof, that therefore it is not neceffary in Demonstration, is a Conclufion without Grounds, and a way of arguing that proves nothing.

In the next Paragraph you come to wind up the Argument, which you have P. 145. been fo long upon, viz. to make good what you undertook; i. e. To fhew the P. 105. difference of my Method of Certainty by Ideas, and the Method of Certainty by Reafon; in anfwer to my faying, I can find no Oppofition between them: which Oppofition, according to the account you give of it, after forty Pages spent in it, amounts at laft to this;

(1) That I affirm, That general Principles and Maxims of Reason are of little P. 146. or no ufe; and your Lordship fays, they are of very great use, and the only proper Foundation of Certainty. To which I crave leave to fay, That if by Principles

Vol. I.

Zzz 2

and

P. 146.

P. 146.

and Maxims your Lordship means all felf evident Propofitions, our ways are even in this part the fame; for as you know, my Lord, I make my felf-evident Propofitions neceffary to Certainty, and found all Certainty only in them. If by Principles and Maxims you mean a fele& number of felf evident Propofitions, diftinguifh'd from the reft by the name Maxims, which is the fense in which I ufe the term Maxims in my Effay; then to bring it to a Decifion, which of us two, in this point, is in the right, it will be neceffary for your Lordship to give a Lift of thofe Maxims; and then to fhew, That a Man can be certain of no Truth, without the help of thofe Maxims. For to affirm Maxims to be the only Foundation of Certainty, and yet not to tell which are thofe Maxims, or how they may be known; is, I humbly conceive, so far from laying any fure Grounds of Certainty, that it leaves even the very Foundations of it uncertain. When your Lordship has thus fettled the Grounds of your way of Certainty by Reafon, one may be able to examine, whether it be truly the way of Reafon, and how far my way of Certainty by Ideas differs from it.

Pa 114.

The fecond Difference that you affign, between my way of Certainty by Ideas, and your's by Reafon, is, That I fay, that Demonftration is by way of Intuition of Ideas, and that Reafon is only the Faculty employ'd in difcovering and comparing Ideas with themselves, or with others intervening; and that this is the only way of Certainty. Whereas your Lordship affirms, and, as you fay, have prov'd, That there can be no Demonftration by Intuition of Ideas; but that all the Certainty we can attain to, is from general Principles of Reafon, and neceffary Deductions made from them. Anfw. I have faid, that Demonftration confifts in the Perception of the Agreement or Difagreement of the intermediate Idea, with thole whofe Agreement or Difagreement it is to fhew, in each step of the Demonftration: And if you will fay this is different from the way of Demonftration by Reason, it will then be to the point above-mention'd, which you have been fo long upon. If this be your Meaning here, it seems pretty ftrangely exprefs'd, and remains to be prov'd: But if any thing elle be your Meaning, that Meaning not being the Propofition to be prov'd, it matters not whether you have prov'd it or no.

Your Lordship farther fays here, That all the Certainty we can attain to, is from general Principles of Reason, and neceffary Deductions made from them. This, you fay, you have prov'd. What has been prov'd, is to be feen in what has been already confider'd. But if your Proof, That all the Certainty we can attain to, is from general Principles of Reason, and necessary Deductions made from them, were as clear and cogent, as it feems to me the contrary; this will not reach to the point in debate, till your Lordship has prov'd, that this is oppofite to my way of Certainty by Ideas. 'Tis ftrange (and perhaps to fome may be matter of thought) that in an Argument wherein you lay fo much stress on Maxims, geneneral Principles of Reason, and neceffary Deductions from them, you should never once tell us, what, in your account, a Maxim or general Principle of Reason is, nor the Marks it is to be known by; nor offer to fhew what a neceffary Deduction is, nor how it is to be made, or may be known. For I have feen Men please themfelves with Deductions apon Deductions, and fpin Confequences, it matter'd not whether out of their own or other Mens Thoughts; which, when look'd into, were visibly nothing but mere Ropes of Sand.

'Tis true, your Lordship fays, you now come to Certainty of Reason by Deductions. But when all that truly learned Difcourfe which follows, is read over and over again, I would be glad to be told, what it is your Lordship calls a necessary Deduction; and by what Criterion you diftinguifh it from fuch Deductions, as come fhort of Certainty, or even of Truth it felf. I confefs I have read over those Pages more than once, and can find no fuch Criterion laid down in them by your Lordship, tho' a Criterion be there much talk'd of. But whether it be my want of Capacity for your way of writing, that makes me not find any light given by your Lordship into this matter; or whether in truth you have not fhew'd, wherein what you call a neceffary Deduction confifts, and how it may be known from what is not fo, the Reader must judg. This I crave leave to lay, That when you have fhewn what general Principles of Reafon and necessary DeduEtiens are, the world will then fee, and not till then, whether this your way of Certainty by Reason, from general Principles and necessary Deductions made from

them,

them, be oppofite to, or fo much as different from, my way of Certainty by Ideas, which was the thing to be fhewn.

In the Paragraph under Confideration, you blame me, that in my Chapter P, 145. concerning Reafon I have treated it only as a Faculty, and not in the other Senfes which I there give of that Word. This Exception to my Book, is, I fuppofe, only from your Lordship's general Care of letting nothing pafs in my Eay, which you think needs an amendment. For any particular Reafon, that brings it in here, or ties it on to this part of your Difcourfe, I confefs I do not fee. However, to this I answer,

1. The Understanding as a Faculty, being the Subject of my Essay, it carry'd me to treat directly of Reafon no otherwife than as a Faculty. But yet Reason as ftanding for true and clear Principles, and alfo as ftanding for clear and fair Deductions from thofe Principles, I have not wholly omitted; as is manifeft from what I have faid of felf-evident Propofitions, intuitive Knowledg, and Demonftration, in other parts of my Effay. So that your Queftion, Why in a Chap- P. 145. ter of Reafon are the two other Senfes of the word neglected? blaming me for no other fault that I am really guilty of, but want of Order, and not putting every thing in its proper place; does not appear to be of fo mighty weight, but that I fhould have thought it might have been left to the little Nibblers in Controverfy, without being made ufe of by fo great a Man as your Lordship. But the putting things out of their proper place, being that which your Lordship thinks fit to except against in my Writings, it fo falls out, that to this too I can plead not guilty. For in that very Chapter of Reason, I have not omitted to treat §. 2, 3, 4, 14, of Principles and Deductions; and what I have faid there, I prefume is enough 15,16,17,18, to let others fee, that I have not neglected to declare my poor Sense about selfevident Propofitions, and the Cogency and Evidence of demonstrative or probable Deductions of Reafon : Tho' what I have faid there, not being back'd with Authorities, nor warranted by the Names of ancient Philofophers, was not worth your Lordship's taking notice of.

I have, I confefs, been fo unwary to write out of my own Thoughts, which your Lordship has, more than once, with fome fort of Reprimand taken notice of. I own it, your Lordship is much in the right: the fafer way is, never to declare one's own Senfe in any material point. If I had fill'd my Book with Quotations and Collections of other Mens Opinions, it had fhewn much more Learning, and had much more fecurity in it; and I my felf had been safe from the Attacks of the Men of Arms, in the Commonwealth of Letters: But in writing my Book, I had no Thoughts of War, my Eye was fix'd only on Truth, and that with fo fincere and unbiafs'd an Endeavour, that I thought I fhould not have incur'd much blame, even where I had mifs'd it. This I perceive, too late, was the wrong way I fhould have kept my felf still fafe upon the referve. Had I learnt this Wifdom of Thrafo in Terence, and refolv'd with my felf, Hic ego ero post principia; perhaps I might have deferv'd the Commendation was given him, Illuc eft fapere ut hos inftruxit ipfus fibi cavit loco. But I deferv'd to be foundly corrected, for not having profited by Reading, so much as this comes to.

But to return to your Accufation here, which all together stands thus: Why in P. 145. a Chapter of Reafon are the other two Senfes neglected? We might have expected here full Satisfaction as to the Principles of Reafon, as diftinct from the Faculty, but the Author of the Essay wholly avoids it. What I guess these words accuse me to have avoided, I think I have fhewn already that I did not avoid.

Before you conclude, you say, you must obferve that I prove, That Demonftration P. 146. must be by Intuition, in an extraordinary manner from the fenfe of the word. He that will be at the pains to read that Paragraph which you quote for it, will Effay, B. 4. fee that I do not prove that it must be by Intuition, because it is call'd Demonftra- C. 2. §. 3. tion; but that it is call'd Demonftration, because it is by Intuition. And as to the Propriety of it, what your Lordship fays in the following words, It would be P. 147. moft proper for occular Demonftration or by the Finger, will not hinder it from being proper alfo in mental Demonftration, as long as the Perception of the Mind is properly exprefs'd by feeing.

Against my obferving, that the Notation of the word imported fhewing or making to fee, your Lordfhip farther fays, Demonftration among fome Philofophers P. 152.

fignify'd

fignify'd only the Conclufion of an Argument, whereby we are brought from Something we did perceive, to fomething we did not; which feems to me to agree with what I fay in the cafe, viz. That by the Agreement of Ideas which we do perceive, we are brought to perceive the Agreement of Ideas which before we did P. 152. not perceive. To which no doubt will be anfwer'd, as in a like cafe, Not by a way of Intuition, but by a Deduction of Reafon; i. e. we perceive not in a way that affords us Intuition or a Sight, but by Deductions of Reason, wherein we fee nothing. Whereas, my Lord, I humbly conceive, that the Force of a Dedu&ion of Reason confifts in this, That in each step of it we see what a Connection it has, i. e. have an Intuition of the certain Agreement or Difagreement of the Ideas, as in Demonftration; or an Intuition or Perception, that they have a probable, or not so much as a probable Connection, as in other Deductions of Reason.

P. 147.

B. 4. C. 7.

S. 10, 19. and elfewhere.

B.4. C. 2.

P. 148--150.

P. 148.

You farther overthrow the neceffity of intuitive Knowledg, in every step of a Demonftration, by the Authority of Ariftotle, who fays, Things that are felfevident cannot be demonftrated. And fo I fay too, in feveral places of my Essay. When your Lordship can fhew any Inconfiftency between these two Propolitions, viz. That intuitive Knowledg is neceffary in each step of a Demonftration, and Things that are felf-evident cannot be demonftrated; then I hall own you have overthrown the neceffity of Intuition in every step of a Demonftration by Reason, as well as by Ariftotle's Authority.

In the remainder of this Paragraph, I meet with nothing but your Lordship finding fault with fome, who, in this Age, have made ufe of Mathematical Demonftrations in Natural Philofophy. Your Lordship's two Reasons against this way of advancing Knowledg upon the fure Grounds of Mathematical Demonftration, are thele:

(1.) That Des Cartes, a Mathematical Man, has been guilty of Miftakes in his Syftem. Anfw. When Mathematical Men will build Syftems upon Fancy, and not upon Demonftration, they are as liable to Mistakes as others. And that Des Cartes was not led into his Mistakes by Mathematical Demonstrations, but *Mr. Newton for want of them, I think has been demonftrated by * fome of thofe MathemaPhil. Natur. ticians who feem to be meant here.

Princip. Mathemat. l. 2. $.9.

(2.) Your fecond Argument against accommodating Mathematicks to the nature of material things, is, That Mathematicians cannot be certain of the manner and deP. 149. grees of Force given to Bodies, so far diftant as the fix'd Stars; nor of the Laws of Motion in other Syftems. A very good Argument why they fhould not proceed demonstratively in this our Syftem upon Laws of Motion, obferv'd to be eftablifh'd here: A Reason that may perfuade us to put out our Eyes, for fear they should mislead us in what we do fee, because there be things out of our fight. 'Tis great pity Ariftotle had not understood Mathematicks as well as Mr. Newton, and made use of it in Natural Philofophy with as good fuccefs: His Example had then authoriz'd the accommodating of it to material things. But 'tis not to be ventur'd, by a Man of this Age, to go out of the Method which Ariftotle has prefcrib'd, and which your Lordship, out of him, has fet down in the folP. 150--153. lowing Pages, as that which fhould be kept to: For it is a dangerous Prefumption to go out of a track chalk'd out by that fuppos'd Dictator in the Commonwealth of Letters, tho' it led him to the Eternity of the World. I fay not this, that I do not think him a very great Man; he made himself fo, by not keeping precifely to beaten Tracks: which fervile Subjection of the Mind, if we may take my Lord Bacon's word for it, kept the little Knowledg the World had from growing greater, for more than a few Ages. That the breaking loofe from it in this Age, is a Fault, is not directly faid; but there is enough faid, to fhew there is no great Approbation of fuch a Liberty. Mathematicks in grofs, 'tis plain, are a Grievance in Natural Philofophy, and with reafon : For Mathematical Proofs, like Diamonds, are hard as well as clear, and will be touch'd with nothing but ftri& Reasoning. Mathematical Proofs are out of the reach of topical Arguments, and are not to be attack'd by the equivocal ufe of Words or Declamation, that make fo great a part of other Difcourfes; nay, even of Controverfies. How well you have prov'd my way by Ideas guilty of any Tendency to Scepticifm, the Reader will fee; but this I will crave leave to fay, That the fecluding Mathematical Reasoning from Philofophy, and instead

thereof