therefore to be upon in this place) does not appear; but this appears by the words wherewith you introduce this examen, that it is to avoid doing me wrong.

Your lordship, as if you had been sensible that your former discourse had led you towards doing me wrong, breaks it off of a sudden, and begins this new one of demonstration, by telling me, "you will do me no wrong." Can it be thought now, that you forget this promise, before you get half through your examen? or is a misciting my words, and misrepresenting my sense, no wrong? Your lordship, in this very examen, sets down a long quotation out of my Essay, and in the close you tell me:"these are my own words which your lordship has set down at large, that I may not complain that you misrepresent my sense:" this one would think guaranty enough in a less man than your lordship and yet, my lord, I must crave leave to complain, that not only my sense, but my very words, are in that quotation misrepresented.

To show that my complaint is not groundless, give me leave, my lord, to set down my words, as I read them in that place of my book which your lordship quotes for them, and as I find them here in your second letter.

If we add all the self-evident propositions may be made about all our distinct ideas, principles will be almost infinite, at least innumerable, which men arrive to the knowledge of at different ages; and a great many of these innate principles they never come to know all their lives. But whether they come in view of the mind earlier or later, this is true of them, that they are all known by their native evidence, are wholly independent, receive no light, nor are capable of any proof, one from another,' &c.

Essay, b. iv. c. 7. § 10.

"That it is true of our particular distinct ideas, that they are all known by their native evidence, are wholly independent, receive no light, nor are capable of any proof, from an

one

other, &c.

By their standing thus together, the reader will without any pains see whether those your lordship has set down in your letter are my own words; and whether in that place, which speaks only of self-evident propositions or principles, I have any thing in words or in sense like this, "that our particular distinct ideas are known by their native evidence," &c. Though your lordship closes the quotation with that solemn declaration above-mentioned, " that they are my own words, which you have set down at large, that I may not complain you misrepresent my sense." And yet nothing can more misrepresent my sense than they do, applying all that to particular ideas, which I speak there only of self-evident propositions or principles; and that so plainly, that I think I may venture any one's mistaking it in my own words: and upon this misrepresentation of my sense your lordship raises a discourse, and manages a dispute for, I think, a dozen pages following, against my placing demonstration on self-evident ideas; though self-evident ideas are things wholly unknown to me; and are nowhere in my book, nor were in my thoughts.

But let us come to your exceptions against my way of demonstration, which your lordship is pleased to call demonstration without principles. Answ. If you mean by principles self-evident propositions, then you know my demonstration is not without principles, in that sense of the term principles: for your lordship in the next page blames my way, because I suppose every intermediate idea in demonstration to have a self-evident connexion with the other idea; for two such ideas as have a self-evident connexion, joined together in a proposition, make a self-evident proposition. If your lordship means by principles those which in the place there quoted by your lordship I mean, viz. " whatever is, is; and it is impossible for the same thing to be, and not to be *;" and such other general propositions, as are received under the name of maxims; I grant, that I do say, that they are not absolutely requisite in every demonstration; and I think I have shown, that there be demonstrations * Essay, b. iv. c. 2. § 8.

VOL. IV.

DD

which may be made without them: though I do not, that I remember, say, that they are excluded, and cannot be made use of in demonstration.

Your lordship's first argument against my way of demonstration is, "that it must suppose self-evidence must be in the ideas of my mind; and that every intermediate idea, which I take to demonstrate any thing by, must have a self-evident connexion with the others." Answ. Taking self-evidence in the ideas of the mind to mean in the perceived agreement or disagreement of ideas in the mind; I grant, I do not only suppose, but say so.

Το prove it not to be so in demonstration, your lordship says, "that it is such a way of demonstration as the old philosophers never thought of." Answ. Nobody, I think, will question, that your lordship is very well read in the old philosophers: but he that will answer for what the old philosophers ever did, or did not think of, must not only understand their extant writings better than any man ever did; but must have ways to know their thoughts, that other men have not. For all of them thought more than they writ; some of them writ not at all, and others writ a great deal more than ever came to us. But if it should happen, that any of them placed the proof of any proposition in the agreement of two things in a third, as I think some of them did; then it will, I humbly conceive, appear, that they did think of my demonstration; unless your lordship can show, that they could see that two things agreed in a third, without perceiving their agreement with that third and if they did in every syllogism of a demonstration perceive that agreement, then there was a selfevident connexion; which is that which your lordship says they never thought of.

But supposing they never thought of it, must we put out our eyes, and not see whatever they overlooked? Are all the discoveries made by Galileo, my lord Bacon, Mr. Boyle, and Mr. Newton, &c. to be rejected as false, because they teach us what the old philosophers never thought of? Mistake me not, my lord, in thinking that I have the vanity here to rank myself, on this occasion,

with these great discoverers of truth, and advancers of knowledge. On the contrary, I contend, that my way of certainty, my way of demonstration, which your lordship so often condemns for its newness, is not new; but is the very same that has always been used, both by ancients and moderns. I am only considering here your lordship's argument, of never having been thought of by the old philosophers; which is an argument that will make nothing for or against the truth of any proposition advanced by a modern writer, till your lordship has proved, that those old philosophers (let the happy age of old philosophers determine where your lordship pleases) did discover all truth, or that they had the sole privilege to search after it, and besides them nobody was to study nature, nobody was to think or reason for himself; but every one was to be barely a reading philosopher, with an implicit faith.

Your objection in the next words, that then every demonstration carries its own light with it, shows that your way by reason is what I do not understand. For this I thought heretofore was the property of demonstration, and not a proof that it was not a demonstration, that it carried its own light with it: but yet though in every demonstration there is a self-evident connexion of the ideas, by which it is made; yet that it does not follow from thence, as your lordship here objects, that then every demonstration would be as clear and unquestionable as that two and two make four, your lordship may see in the same chapter, and the reason of it *.

You seem in the following words to allow, that there is such a connexion of the intermediate ideas in mathematical demonstration; but say, "you should be glad to see any demonstration (not about figures and numbers) of this kind." And if that be a good argument against it, I crave leave to use it too on my side; and to say, "that I would be glad to see any demonstration (not about figures and numbers) not of this kind;" i. e. wherein there is not a self-evident connexion of all the intermediate ideas. If you have any such, I earnestly beg your lordship to favour me with * Essay, b. iv. c. 2. § 4, 5, 6.

it; for I crave liberty to say, that the reason, and form, and way of evidence in demonstration, wherever there is demonstration, is always the same.

But you say, "THIS is a quite different case from mine;" I suppose your lordship means by THIS, mathematical demonstration, the thing mentioned in the preceding period; and then your sense will run thus: mathematical demonstrations, wherein certainty is to be had by the intuition of the self-evident connexion of all the intermediate ideas, are different from that demonstration which I am there treating of. If you mean not so, I must own, I know not what you mean by saying, "THIS is a quite different case from mine." And if your lordship does mean so, I do not see how it can be so as you say: your words taken all together run thus: "my principal ground is from mathematical demonstrations, and my examples are brought from them. But this is quite a different case from mine:" i. e. I am speaking in that chapter of my Essay concerning demonstration in general, and the certainty we have by it. The examples I use are brought from mathematics, and yet you say, " mathematical demonstrations are quite a different case from mine." If I here misunderstand your lordship's THIS, I must beg your pardon for it; it is one of your privileged particles, and I am not master of it. Misrepresent your sense I cannot; for your very words are set down, and let the reader judge.

But your lordship gives a reason for what you had said in these words subjoined, where you say, "I grant that those ideas, on which mathematical demonstrations proceed, are wholly in the mind, and do not relate to the existence of things; but our debate goes upon a certainty of knowledge of things as really existing." In which words there are these things remarkable:

1. That your lordship's exception here, is against what I have said concerning demonstration in my Essay, and not against any thing I have said in either of my letters to your lordship. If therefore your lordship and I have since, in our letters, had any debate about the