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But because by this means there was like to be no decision between skilful combatants, whilst one never failed of a me. dius terminus to prove any proposition, and the other could as constantly, without or with a distinction, deny the major or minor. To prevent as much as could be the running out of disputes into an endless train of syllogisms, certain general propositions, most of them, indeed, self-evident, were introduced into the schools; which, being such as all men allowed and agreed in, were looked on as general measures of truth, and served instead of principles (where the disputants had not laid down any other between them) beyond which there was no going, and which must not be receded from by either side. And thus these maxims getting the name of principles, beyond which men in dispute could not retreat, were by mistake taken to be the originals and sources from whence all knowledge began, and the foundations whereon the sciences were built.” This view of the matter recommends itself by its own intrinsic evidence, to the minds of all persons who have studied and understood this subject. How idle after all this, appear the strictures of Dr. Reid upon this part of Mr. Locke's principles? In essay 7, ch. 6, of his Intellectual and Active Powers, he says—“Mr. Locke farther says, that maxims are not of use to help men forward in the advancement of the sciences, or new discoveries of yet unknown truth; that Newton, in the discoveries he made in his never enough to be admired book, has not been assisted by the general maxims, whatever is, is; or the whole is greater than a part, or the like. I answer, the first of these is, as was before observed, an identical, trifling proposition of no use in mathematics or any other science. The second is often used by Newton and by all mathematicians, and many demonstrations rest upon it. In general, Newton, as well as all other mathematicians, grounds his demonstrations of mathematical propositions upon the axioms laid down by Euclid, or upon propositions which have before been demonstrated by help of those axioms. But it deserves to be particularly observed, that Newton, intending in the third book of his Principia, to give a more scientific form to the physical part of astronomy, which he had at first composed in a popular form, thought proper to follow the example of Euclid, and to lay down first, in what he calls regulæ philosophandi, and in his phenomena, the first principles which he assumes in his reasoning. Nothing, therefore, could have been more unluckily adduced by Mr. Locke to support his aversion to first principles than the example of Sir Isaac Newton, who by laying down first principles upon which he reasons, in those parts of nataral philosophy which he cultivated, has given a stability to that science which it never had before, and which it will retain to the end of the world.” We see in this passage a striking proof, how easy it is to animadvert upon the principles of an author without having taken the pains to understand him, or the subject of which he was treating. We have before shown, that Mr. Locke had not, as here represented, an aversion to first principles, in the true meaning of the term first principles, by which is implied those particular self-evident propositions in which all good reason. ing must have its foundation. We have now barely to remark, that, so far from Dr. Reid's stricture being just in this respect, Mr. Locke could not have produced a case more in point than that of the discoveries of Newton. Who that has the slightest acquaintance with the subject could confound his regulæ philosophandi, with self-evident propositions, or suppose that his reasonings in the principia depend upon them? They are not even self-evident. No more causes of things are to be admitted than are both true and sufficient to explain the phenomena. This is one of his rules of philosophizing, and a very just and profound one it is; but has this any connection with the solution of the phenomena, except that it might facilitate our advance in philosophy, by directing us to proceed in the best and most expeditious method? Long enough might Newton have received this rule, which he drew immediately from Bacon's precepts, before he would have been led by it to broach his theory of gravitation, and still longer before he would have been supplied with arguments to substantiate it. His rules of philosophizing, instead of being self-evident truths upon which his subsequent demonstrations are grounded, are merely excellent philosophical precepts, by which to regulate his inquiries, deduced from a profound observation of nature, and the clearest views of her structure and operations. They are no more the basis upon which his philosophical speculations are built, than the rules of architecture, by which the artist constructs his edifice, are the foundation of the structure he has reared. The same or similar remarks would apply to the axioms laid down by Newton, of which we have spoken before. By this time, I think, we must perceive that the error in this statement does not lie at the door of Mr. Locke, but upon him who has undertaken to cavil at his principles without going through the trouble of understanding them.
From the foregoing view of the subject, it will be perceived that professor Stewart also, although he seems to think that his opinions on this point, while they depart from those of Dr. Reid, correspond to Mr. Locke's, is entirely mistaken. He has not entered into Mr. Locke's views, and has adopted and held doctrines not only incompatible with them, but in a high degree frivolous and unfounded. His opinion divides itself into two parts. First, although he says with Mr. Locke, that axioms or general self-evident propositions are not the foundations of mathematical science, yet with strange oscitancy of understanding, he maintains that definitions form the foundation of it.
2dly. He says, that “axioms form the vincula which give coherence to our chains of reasoning. A process of logical reasoning has often been likened to a chain supporting a
weight. If this similitude be adopted, the axioms or elemental truths now mentioned, may be compared to the successive concatenations which connect the different links immediately with each other; the principles of our reasoning resemble the hook, or rather the beam from which the whole is suspended." This may be regarded as very flourishing rhetoric, but it is very unsound philosophy. It is strange, that Mr. Stewart should have imagined that in these opinions he coincided, or very nearly coincided with Mr. Locke.
In the first place, as to definitions being the foundation of mathematical science, no conception could be more idle and frivolous. If Mr. Locke denied that axioms as they are generally understood, are the basis of this branch of science, what would he have thought of those who make definitions such? Definitions are livided into two kinds in the treatises of logic, and very justly; into definitions of words, and definitions of things. In the first sense, they are the mere explications of terms, and of course under this view could no more be considered as the basis of our reasoning, than the names of the carpenter's tools form the foundation of his structure,
They are very proper and useful to ascertain our ideas in the commencement of any kind of disquisition, and serve greatly to keep up that clearness of conception and accuracy of thinking, which are so necessary to the successful prosecution of science, and which are so remarkably preserved in mathematics. But what has the definition of a term to do with the discovery of truth, or in tracing the agreement or disagreement of our ideas, except as a method of facilitating our progress in the acquisition of it? And in cases in which we attempt the definitions of things, or giving a description of the properties of things, to enable us to discriminate them from all others, so far from being the foundation of our knowledge, or the propositions upon which our conclusions are built, that it is a very just observation of Mr. Burke, that instead of
eommencing our inquiries with definitions, we should rather conclude with them. Thus, Aristotle would, conformably to the principles of his philosophy, have defined the sun to be a luminous body, moving round the earth, which was stationed in the centre. The Copernican system has shown how false a description of the sun such a definition would be, and would more accurately define it to be that luminous body placed in the centre, or nearly in the centre, around which the planets revolve. Here we must understand the true system of philosophy, before we are able to give a good definition of the sun, and of course our defini, tion instead of commencing should terminate our inquiries. Take any mathematical definition, and see whether it can be considered as the ground of important inferences to be deduced from it. Will our definition of a triangle, that it is the space included between three straight lines that cut each, ever lead us on to the conclusion, that the three angles of every triangle, are equal to two right angles? Does it at all enter into the inquiry? Does it form any part of the argument? A man might long enough study all definitions of triangles, circles and squares in mathematics, and ponder over them again and again, before he would arrive at the conclusion, that the square of the hypothenuse in a rectangular triangle, is equal to the sum of the squares of the two sides.
In the second place, when the professor maintains, that axioms form the vincula, or connecting links between the different parts of a chain of reasoning, he is equally mistaken. He seems to think that Mr. Locke is aiming at a similar doctrine, but from this circumstance it appears that he has not understood that writer. According to Mr. Locke, these general maxims or axioms, neither lie at the foundation of truth and knowledge, nor considering a train of reasoning as a chain can they form the links that connect the parts together. They are not at all essential to the structure of scie