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ed or denied one of the other, to be the same or different; it is presently and infallibly certain of the truth of such a proposition, and this equally, whether these propositions be in terms standing for more general ideas, or such as are less so, v. g. whether the general idea of being be affirined of itself, as in this propofition, whatsoever is, is ; or a more particular idea be affirmed of itself, as a man is a man, or what. foever is white, is white ; or whether the idea of bee ing in general be denied of not being, which is the only (if I may so call it) idea different from it, as in this other proposition, it is imposible for the same thing to be, and not to be ; or any idea of any particular being be denied of another different from it, as a man is not a borfe, red is not blue. The difference of the i leas, as soon as the terms are understood, makes the truth of the proposition presently visible, and that with an equal certainty and easiness in the less, as well as the more general propositions, and all for the same reason, viz. because the mind perceives in any ideas, that it has the same idea to the same with itself; and two different ideas to be different, and not the same; and this it is equally certain of, whether these ideas be more or less general, abstract and comprehensive. It is not therefore alone to these two general propoficions, whatsoever is, is ; and, it is imposible for the fame thing to be, and not to be ; that this self-evidence belongs by any peculiar right. The perception of being, or not being, belongs no more to these vague ideas, fignified by the terms whatsoever and thing, than it does to any other ideas; these two general maxims amounting to no more, in short, but this, that the same is the fame, and fame is not different, are truths known in more particular instances, as well as in these ge. neral maxims, and known also in particular instances, before these general maxims are ever thought on, and draw all their force from the discernment of the mind employed about particular ideas. There is nothing inore visible than that the mind, without the help of any proof, or reflection on either of these general propositions, perceives so clearly, and knows so certainly, that the idea of white is the idea of white, and not the ilca of blue ; and that the idea of white, when it is in the mind, is there, and is not absent ; that the consideration of these axioms can add nothing to the evidence or certainty of its knowledge. Just so it is (as every one may experiment in himself) in all the ideas a man has in his mind : He knows each to be itself, and not to be another; and to be in his mind, and not away when it is there, with a certainty that cannot be greater; and therefore the truth of no ge. neral proposition can be known with a greater certain. ty, nor add any thing to this. So that in respect of i. dentity, our intuitive knowledge reaches as far as our ideas ; and we are capable of making as many selfevident propositions, as we have names for distinct ideas. And I appeal to every one's own mind, whether this proposition, a circle is a circle, be not as selfevident a proposition, as that consisting of more general terms, what foever is, is : And again, whether this proposition, blue is not red, be not a propofition that the mind can no more doubt of, as soon as it unstands the words, than it does of that axiom, it is impoffible for the same thing 20 be, and not to be ; and so of all the like. § 5. 2. In Co-existence we have few self-evident
Propofitions. SECONDLY, As to co-existence, or such necessary connection between two ideas, that in the subject where one of them is supposed, there the other must necel. sarily be allo : Of such agreement or disagreement as this, the mind has an imediate perception but in very few of them, and therefore in this fort we have but very little intuitive knowledge; nor are there to be found' very many propositions that are felf-evident, though some there are, v. g. the idea of filling a place equal to the contents of its superficies, being annexed to our idea of body, I think it is a self evident propofition, that two bodies cannot be in the same place.
$ 6. 3. In other Relations we may have. THIRDLY, As to the relations of modes, mathematicians have framed many axioms concerning that one relation of equality ; as, equals taken from equals, the remainder will be equals ; which, with the rest of that kind, however, they are received for maxims by the mathematicians, and are unquestionable truths ; yet, I think, that any one who considers them, will not find that they have a clearer self-evidence than these, that one and one are equal to two; that if you take froin the five fingers of one banl two, and from the five fingers of the other hand two, the remaining num. bers will be equal. These and a thousand other such propofitions may be found in numbers, which at the very first hearing, force the allent, and carry with them an equal, if not greater clearness, than those ma. thematical axio:n3.
§ 7. 4. Concerning real Existence we have none. FOURTHLY, As to real existence, since that has no connection with any other ideas, but that of ourselves, and of a first being, we have in that, concerning the real existence of all other beings, not so much as de. monttrative, much less a self-evident knowledge; and therefore concerning those there are no maxims. $ 8. Those Axioms do not much influence our other
Knowledge. In the next place, let us contider what influence these received maxims have upon the other parts of our knowledge. The rules established in the schools, that all reasonings are ex præcognitis et præconcefhs, seem to lay the foundation of all other knowledge in these maxims, and to suppose them to be præcognita ; whereby, I think, are meant these two things : First, That these axioms are those truths that are first known to the mind ; and, Secondly, That upon them the other parts of our knowledge depend.
§ 9. Because they are not the Truths we first knew. FIRST, That they are not the truths first known to the mind is evident to experience, as we have shown in another place, Book I. Chap. 2. Who perceives not that a child certainly knows that a stranger is not its mo. ther; that its fucking-bottle is not the rod, long be. fore he knows that it is impossible for the same thing to be, and not to be? And how many truths are there about numbers, which it is obvious to observe that the mind is perfectly acquainted with, and fully convinced of, before it ever thought on these general maxims, to which mathematicians, in their arguings, do sometimes refer them? Whereof the reason is very plain : For that which makes the mind assent to such propositions, being nothing else but the perception it has of the agreement or disagreement of its ideas, according as it finds them affirmed or denied one of another in words it understands, and every idea being known to be what it is, and every two distinct ideas being koown not to be the same ; it must necessarily follow, that such self-evident truths must be first known, which consist of ideas that are first in the mind : and the ideas first in the mind, it is evident, are those of particular things, from whence, by low degrees, the understanding proceeds to fome few general ones ; which being taken from the ordinary and familiar objects of sense, are settled in the mind, with general names to them. Thus, particular ideas are first received and distinguished, and so knowledge got about them; and next to them, the less general or specific, which are next to particular; for abftract ideas are not so obvious or easy to children, or the yet unexercised inind, as particular ones. If they seem so to grown men, it is only because by constant and familiar use they are made fo ; for when we nicely reflect upon them, we fhall find, that general ideas are fictions and contrivances of the mind, that carry difficulty with them, and do not so easily offer themselves, as we are apt to imagine. For example, does it not require some pains and skill to form the general idea of a triangle.? (which is yet none of the most abstract, comprehensive, and difficult), for it muft be neither oblique, nor rectangle, neither equilateral, equicrural, nor scalenon; but all and none of these at once. In effect, it
is something imperfe&, that cannot exis ; an idea wherein soine parts of several different and inconfiftent ideas are put together. It is true, the mind, in this imperfect state, has need of such ideas, and makes all the halte to them it can, for the conveniency of communication and enlargement of knowledge; to both which it is naturally very much inclined. But yet one has reason to suspect such ideas are marks of our imperfection ; at least this is egough to show, that the most abstract and general ideas are not those that the mind is first and most easily acquainted with, nor such as its earliest knowledge is conversant about. $ 10. Because on them the other parts of our Know
ledge do not depend. SECONDLY, From what has been said, it plainly follows, that these magnified maxims are not the princi. ples and foundations of all our other knowledge ; for if there be a great many other truths, which have as inuch self-evidence as they, and a great many that we know before them, it is impossible they should be the principles from which we deduce all other truths. Is it imposible to know that one and two are equal to tbree, but by virtue of this, or some such axioin, viz. the whole is equal to all its parts taken together? Many a one knows that one and two are equal to three, with. out having heard or thought on that or any other axiom by which it might be proved; and knows it as certainly, as any other man knows, that the whole is equal to all its parts, or any other maxim, and all from the same reason of self-evidence; the equality of those ideas being as visible and certain to him with. out that, or any other axiom, as with it, it needing no proof to make it perceived ; nor after the knowledge, that the whole is equal to all its parts, does he know that one and i wo are equal to three, better or more certainly, than he did before ; for if there be any odds in those ideas, the whole and parts are more obscure, or at least more difficult to be settled in the mind, than those of one, two, and three. And indeed, I think, I may ask these men, who will needs have all know