mind. Secondly, that upon them the other parts of our knowledge depends."

It is evident, therefore, that Mr. Locke does not deny but expressly admit, that first or intuitive truths, are the foundation of all our knowledge; but only that these general maxims, whatever is, is, and the like, are the præcognita or præconcessa upon which our knowledge is built. He maintains, and with a force of evidence which no philosopher can resist, that these general maxims are not first known to the mind, but rather the particular propositions included under them. For instance, the child would know that the two apples which it had, if both equal to a third, would be equal to each other, long before it knew or felt the force of the general proposition, things equal to the same thing are equal to one another. No one can deny the truth of such a doctrine, who has the slightest acquaintance with the structure and operations of the human mind. This is a branch of Mr. Locke's opinions, which were opposed to those who maintained, that man had originally innate ideas and innate maxims, both of which doctrines he has most successfully exploded.

The next objection of Dr. Reid to Mr. Locke's doctrine on this point is; "that he maintains, no science is or hath been built upon maxims." The Dr. here also does not correctly state the opinion of Mr. Locke. That writer does not maintain, that no science is or hath been built upon maxims or first truths of some kind, but upon such maxims or general truths as those before mentioned; whatever is, is; and it is impossible for the same thing to be and not to be, and the like. "Surely Mr. Locke," continues the Dr., "was not ignorant of geometry, which hath been built upon maxims prefixed to the elements, as far back as we are able to trace it. But though they had not been prefixed, which was a matter of utility rather than necessity, yet it must be granted, that every demonstration in geometry is grounded either upon propositions formerly demonstrated, or upon self-evident prin

eiples." The Dr. seems to labour under a very great misconception of Mr. Locke's views, or he must have discerned that this writer would have acknowledged with him, the last part of his assertions, "that every demonstration in geometry is grounded either upon propositions formerly demonstrated, or upon self-evident principles," and yet have denied the truth of his first position," that geometry is built upon those maxims or general propositions prefixed to the Elements of Euclid." It is one thing to maintain, that all the propositions in Euclid are founded upon self-evident truths, which is undeniable; and it is quite a different one to assert, that they are all founded in the postulates and axioms, which he states in the commencement of his treatise, which would not be true. Upon the principles of Mr. Locke, and the more they are understood the more conclusive will they be found, lay aside all the postulates and axioms of Euclid, and the propositions which he demonstrated would be no less clear and satisfactory to the understanding. Nothing can be more certain than this statement of the matter, when rightly apprehended. For example, take any two arbitrary points, as A. and B. at some distance from each other. Now is it not as certain that these two points may be joined together by a right line, as that the first postulate is true, which requires it to be granted, that a straight line may be drawn from any one point to any other point? Does a recurrence to the postulate render the matter any more clear or incontrovertible? The same remark will apply to all the other postulates as well as axioms. Take the first axiom also by way of illustration. When I have shown that two triangles, whose properties I am examining, are each equal to the same square or parallelogram, am I not as sure that they are equal to each other, as when I have recurred to the general maxim in confirmation of this truth, that things equal to the same thing are equal to one another? In a word, is not the certainty, which is found in a particular proposition which is

self-evident, as great as that which accompanies the general? And is not the general proposition, maxim, or axiom, derived from the particular, and not the particular from the general? Of this philosophers at the present day ought scarcely to entertain a doubt. For, as Mr. Locke justly remarks," in particulars our knowledge begins, and so spreads itself by degrees to generals; though afterwards the mind takes quite a contrary course, and having drawn its knowledge into as general propositions as it can, makes those familiar to its thoughts, and accustoms itself to have recourse to them, as to the standards of truth and falsehood." And here too we may perceive distinctly pointed out the use and advantage of postulates and axioms in mathematical science. If they cannot assist the mind in attaining to the truths of that science, and do not form the basis upon which it rests any more than many other propositions equally evident with themselves, they may be of very great service when rendered familiar to the learner, to be appealed to as the standards of truth and falsehood, and as Mr. Locke observes, to stop the mouths of wranglers, and put an end to controversy. Should any one, for instance, become sceptical and captious enough to deny what is clearly self-evident, an appeal to a general maxim, whose justness and force he had been accustomed to recognise, might bring him to a right perception of the matter, and expose to him the fallacy and absurdity of his objections.

Let it then, be distinctly understood, that Mr. Locke, with all good philosophers admits, that all science must rest upon first principles, or self-evident propositions, or propositions which must be taken for granted, and for which we have no proof, except the light of that evidence, which shines around them.

The first principles, however, upon which he considers all knowledge as founded, are not those general maxims so much spoken of in the schools, but those particular and simple

truths that enter into every subject which we attempt to investigate; and which, instead of being limited to the small number attempted to be enumerated in books are almost numberless. For example, the truths contained in Euclid's Elements of Geometry, although they rest upon intuitive certainty, have no more immediate connection with the axioms and postulates with which he commences his treatise, than with many other propositions equally intuitive with themselves. "Farther, it is evident," says Mr. Locke, book 4, ch. 12," that it was not the influence of those maxims, which are taken for principles in mathematics, that hath led the masters of that science, into those wonderful discoveries, they have made. Let a man of good parts know all the maxims generally made use of in mathematics never so perfectly, and contemplate their extent and consequences as much as he pleased, he will, by their assistance, I suppose, scarce ever come to know, that the square of the hypothenuse in a right angled triangle, is equal to the squares of the other sides. The knowledge that the whole is equal to all its parts, and if you take equals from equals, the remainder will be equal, &c. helped him not, I presume, to this demonstration. And a man may, I think, pore long enough on these axioms, without ever seeing one jot the more of mathematical truth. They have been discovered by the thoughts otherwise applied; the mind had other objects, other views before it, far different from those maxims, when it first got the knowledge of such kind of truths in mathematics." That is to say, the mind in tracing the agreement and disagreement of its ideas in order to the making of discoveries in mathematics, as for instance, in discovering that the square of the hypothenuse in a right angled triangle is equal to the squares of the other two sides, did not have recourse to any of the axioms or postulates so formally laid down, but followed its natural train of thoughts suited to lead it on to that kind of conclusion, or commencing in those particular propositions suited

to the subject, passed from those which were intuitively cer tain to those that resulted from them by irresistible inference, until at length it was conducted to the desired result. Thus all the propositions of Euclid may have been proved, as well as the Pythagorean, without the philosopher having once thought of those general propositions, called maxims or axioms. Of consequence these axioms cannot be considered as the foundation of mathematical science. The same remarks would apply to all the other branches of science. Are, then, it may be asked, these postulates and axioms in mathematics, and first truths in all the sciences, of no importance? And are they so formally prescribed by philosophers only in empty ostentation?

Mr. Locke distinctly understood, acknowledged, and explained their uses. "They are of use," says he, in his Treatise on Maxims," in the ordinary method of teaching the sciences as far as they are advanced, but of little or no use in advancing them farther. When schools were erected, and sciences had their professors to teach what others had found out, they often made use of maxims: i. e. laid down certain propositions which were self-evident, or to be received for true, which being settled in the minds of their scholars, as unquestionable verities, they on occasion made use of, to convince them of truths in particular instances, that were not so familiar to their minds as those general axioms which had before been inculcated to them, and carefully settled in their mind."

2dly. "They are of use in disputes, for the silencing of obstinate wranglers, and bringing those contests to some conclusions. Whether a need of them to that end, came not in, in the following manner, I crave leave to inquire. The schools having made disputation the touchstone of men's abilities, and the criterion of knowledge, adjusted victor to him that kept the field, and he that had the last word, was concluded to have the better of the argument, if not of the cause.