will be equal, &c. which, however received for axioms, yet I think have not a clearer self-evidence than these, that One and one are equal to two: that If from the five fingers of one hand you take two, and from the five fingers of the other hand two, the remaining numbers will be equal. These and a thousand other such propositions may be found in numbers, which carry with them an equal, if not greater clearness than those mathematical axioms.

As to real existence, since that has no connexion with any other of our ideas, but that of ourselves, and of a first Being; we have not so much as a demonstrative, much less a self-evident knowlege, concerning the real existence of other beings.

In the next place, let us consider what influence these maxims have on the other parts of our knowlege. The rules established in the schools, that all reasonings are ex præcognitis et præconcessis, seem to lay the foundation of all other knowlege in these maxims, and to suppose them to be præcognita ; whereby I think is meant two things: 1. that these axioms are those truths that are first known to the mind; 2. that on them the other parts of our knowlege depend.

1. That these axioms are not the truths first known to the mind, is evident from experience for who knows not that a child perceives that a stranger is not its mother, long before 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 the mind is perfectly acquainted with, and fully convinced of, before it ever thought on these general maxims? Of this the reason is plain; for that which makes the mind assent to such propositions, being nothing but the perception it has of the agreement or disagreement of its ideas, according as it finds them affirmed or denied in words one of another; and every idea being known to be what it is, and every two distinct ideas not to be

the same, it must necessarily follow, that such selfevident 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 slow degrees, the understanding proceeds to some 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 knowlege got about them; and next to them the less general or specific, which are next to particular ones.

For abstract ideas are not so obvious or easy to children, or the yet unexercised mind, as particular ones. If they seem so to grown men, it is only because by constant and familiar use they are made so. For when we nicely reflect on them, we shall find, that general ideas carry difficulty with them, and do not so easily offer themselves as we are apt to imagine. It is true, the mind, in this imperfect state, has need of such ideas, and makes all the haste to them it can, for the conveniency of communication and enlargement of knowlege; to both which it is naturally very much inclined.

2. From what has been said, it plainly follows, that these magnified maxims are not the principles and foundations of all our other knowlege: for if there be a great many other truths, as self-evident as they, and a great many that we know before them, it is impossible that they should be the principles from which we deduce all other truths. Thus, that One and two are equal to three, is as evident, and easier known, than that the Whole is equal to all its parts. Nor after the knowlege of this maxim, do we know that One and two are equal to three, better, or more certainly than we did before; for if there be any odds in these ideas, the ideas of whole, and parts, are more obscure, or at least more difficult to be settled in the

mind, than those of one, two, and three. Either, therefore, all knowlege does not depend on certain præcognita, or general maxims, called principles; or else, such as these, (that one and one are two, that two and two are four, &c.) and a great part of numeration will be so. To which, if we add all the selfevident propositions that may be made about all our distinct ideas, principles will be almost infinite, at least innumerable, which men arrive to the knowlege of at different ages; and a great many of those innate principles they never come to know all their lives. But whether they come in view early or later, they are all known by their native evidence, and receive no light, nor are capable of any proof one from another much less the more particular from the more general; or the more simple from the more compounded: the more simple and less abstract being the most familiar, and the easier and earlier apprehended.

;

These general maxims, then, are only of use in disputes, to stop the mouths of wranglers; but not of much use to the discovery of unknown truths; or to help the mind forwards in its search after knowlege. Several general maxims are no more than bare verbal propositions; and teach us nothing but the respect and import of names, one to another; as, The whole is equal to all its parts,-what real truth does it teach us more, than what the signification of the word totum, or whole, does of itself import?

But yet, mathematicians do not without reason place this, and some other such, amongst their maxims; that their scholars having in the entrance perfectly acquainted their thoughts with these propositions made in such general terms, may have them ready to apply to all particular cases: not that if they be equally weighed, they are more clear and evident, than the particular instances they are brought to confirm; but that being more familiar to the mind, the very naming them is enough to satisfy the understanding. But this,

I

say, is more from our custom of using them, than the different evidence of the things.

One thing farther, I think, it may not be amiss to observe, concerning those general maxims, that they do not prove the existence of things without us; neither of these two self-evident principles,-viz. What is is, and The same thing cannot be, and be,-will serve to prove to us, that any, or what bodies do exist : for that we are left to our senses, to discover to us as far as they can. Those universal and self-evident principles can assure us of nothing that passes without the mind; they cannot discover or prove to us the least knowlege of the nature of substances, as they are found and exist without us, any farther than grounded on experience.

So that, if rightly considered, I think we may say, that where our ideas are clear and distinct, there is little or no use at all of these maxims, to prove the agreement or disagreement of any of them. He that cannot discern the truth or falsehood of such propositions, without the help of these and the like maxims, will not be helped by these maxims to do it. that needs any proof to make him certain, and give his assent to this proposition, that Two are equal to two, or that White is not black, will also have need of a proof to make him admit that What is is, or that It is impossible for the same thing to be and not to be.

He

And as these maxims are of little use, where we have clear and distinct ideas; so they are of dangerous use, where our ideas are confused, and where we use words that are not annexed to clear and distinct ideas; but to such as are of a loose and wandering signification, sometimes standing for one, and sometimes for another idea, from which follows mistake and error, which these maxims (brought as proofs to establish propositions wherein the terms stand for

confused and uncertain ideas) do by their authority confirm and rivet.

CHAPTER VIII.

Of trifling Propositions.

There are universal propositions, which, though they be certainly true, yet add no light to our understandings, bring no increase to our knowlege: such

are,

1. All purely identical propositions. These, at first blush, appear to contain no instruction in them ; for when we affirm the same term of itself, it shows us nothing but what we must certainly know before, whether such a proposition be either made by, or proposed to us.

2. Another sort of trifling propositions is, when a part of the complex idea is predicated of the name of the whole; a part of the definition, of the word defined, as, Lead is a metal-man an animal. These carry no information at all, to those who know the complex ideas, the names lead and man stand for indeed to a man that knows the signification of the word metal, and not of the word lead, it is a shorter way to explain the signification of the word lead, by saying it is a metal, than by enumerating the simple ideas one by one, which make up the complex idea of metal.

Alike trifling it is to predicate any one of the simple ideas of a complex one of the name of the whole complex idea; as, All gold is fusible; for fusibility being one of the simple ideas, that goes to the making up the complex one, the sound gold stands for; what can it be but playing with sounds, to affirm that of the name gold, which is comprehended in its received signification? What instruction can it carry, to tell one that which he is supposed to know before? for I am supposed to know the signification of the word another uses to me, or else he is to tell me.