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Of First Principles, Axioms, and Maxims of Science.
NOTHING would seem more certain, than that every branch of sound science must rest ultimately upon first principles, or propositions, whose truth is either intuitively discerned or previously admitted. This is equally undeniable, whether we prosecute our inquiries, by means of the analytical or synthetical method. If we pursue the synthetical method, in order to give satisfaction to the understanding, we must commence with those simple propositions, whose truth is intuitively perceived or previously allowed, and from these advance by just gradations, until we arrive at the most complex and recondite maxims; if the analytical, we must resolve complicated maxims into those simple propositions, whose truth is self-evident or admitted. In each case, therefore, the effort of our understandings, in order to attain satisfaction, is to arrive at intuitive or undeniable truth. This is a doctrine in which all the best philosophers, from the days of Aristotle, to those of Newton and Locke, with one consent, agree. All the difficulty and doubtfulness, which have been introduced into a subject so extremely simple by the Scottish metaphysicians, has arisen, I am inclined to think, from mere misconception of the principles of Newton and Locke. In explaining the principles of these philosophers, then, on this subject, we think we shall contribute sufficiently to its elucidation.
The term axiom, as it is used in mathematical works, and from these the same meaning of it has been transferred to the other branches of science, implies a theoretical proposi. tion, whose truth is intuitively discerned, or in other words, is so clear and undeniable, that it flashes irresistible conviction upon the understanding. This is the present signification of the term, but I apprehend not the original meaning of the one from which it is derived. The latin word axioma, taken from the Greek, and translated axiom or maxim, denotes any truth or principle, which is either intuitive or demonstrable, or founded upon experience, and exactly corres. ponds to our term maxim as now generally used. Lord Bacon frequently makes use of the terms axioma and axiomata in his latin treatises; and we are not aware that he could have selected a better term in that language with which to convey his meaning. He always understands by it, some maxim or principle of science established by induction, as in the passages before quoted from him. That the heavenly bodies gravitate towards each other according to settled laws of attraction, and that the rising and falling of the tides in our rivers are caused by the united influence of the sun and moon, are, what lord Bacon would denominate axiomata generalia or general maxims of science, and they are derived solely from an induction of facts. The reader will readily perceive, therefore, that there are two different meanings annexed to the term axioms in scientific works; the one in which it is made equivalent to self-evident truths, as in mathematical works; the other in which it is synonimous to maxims or principles of science, in which sense it may or may not be regarded as implying self-evidence, as in the tracts of lord Bacon. Considering this circumstance, the criticisms of professor Stewart upon the use of this term by Sir Isaac Newton, in his principia and optics, might have been spared. They evidently arose out of a want of a just comprehension of the meaning annexed to it by that philosopher. When Newton, for instance, gives the name of axioms to his laws of motion, or in the beginning of his optics, prescribes as axioms the following propositions: “ that the angles of reflection and refraction lie in the same plane with the angle of incidence; that the angle of reflection is equal to the angle of incidence; that refraction out of a rarer medium is made towards the perpendicular, and such like, it is evident that he could not have considered such propositions as axioms, in the technical meaning of the word in books of mathematics; but merely as equivalent to the term maxims, or principles of science which are undeniable. In this signification of the word, he seems strictly to follow the authority of lord Bacon, whose works he evidently understood, and whose method of philosophizing called induction, it was his province to carry into natural philosophy.
After this explication of the term, we proceed to controversies drawing after them more important consequences.
It has been made a question, whether axioms, self-evident maxims, or first principles, as they are called, lie at the foundation of the sciences. The doctrines of Mr. Locke, on this subject, in our estimation, have been controverted and denied only from being misapprehended. We shall first state them, and then endeavour to show that they are not to be overthrown.
Mr. Locke maintains, that those maxims which are usually received as axioms, as, for example, that whatsoever is, is; it is impossible for the same thing to be and not to be; if equals be taken from equals, the remainder will be equal; which because of the self-evidence that accompanies them, are considered innate, are not innate, but like all our other ideas acquired by experience and reflection.
2dly. He maintains, that these axioms or maxims, which terms he takes as equivalent, have no more self-evidence in them, than many other propositions, not so frequently considered as such.
3dly. He asserts, that these general maxims are not so soon known to the mind, as the particular propositions comprehended under them.
4thly. He maintains, that no science has been built upon such maxims as those above mentioned.
In all these propositions, we contend, that when rightly understood, he has advanced nothing but the truth.
In the first three of these propositions, Dr. Reid agrees with Mr. Locke; but imagines, that he has found an inconsistency in the following passages, In book 4, ch. 2, of his treatise, Mr. Locke says, “ There is a part of our knowledge which we call intuitive-In this the mind is at no pains in proving or examining, but perceives the truth as the eye does light, only by being directed towards it. And this kind of knowledge is the clearest and most certain that human nature is capable of. This part of knowledge is irresistible, and like bright sunshine, forces itself immediately to be perceived, as soon as ever the mind turns its view that way.” He further observes, “ that this intuitive knowledge is necessary to connect all the steps of a demonstration.” Upon these two passages, Dr. Reid makes the following observations—“ From this I think, it necessarily follows, that in every branch of knowledge we must make use of truths that are intuitively known, in order to deduce from them such as require proof.” But I cannot reconcile this with what he says Sect. 8th, of the same chapter. “The necessity of this intuitive knowledge, in every step of scientifical or demonstrative reasoning, gave occasion, I imagine, to that mistaken axiom, that all reasoning was ex præcognitis et præconcessis, which, how far it is mistaken, I shall have occasion to show more at large, when I come to consider propositions, and particularly those propositions which are called maxims; and to show that it is by a mistake that they are supposed to be the foundation of all our knowledge and reasonings." Dr. Reid imagines, that he has detected an inconsistency between these two positions of Mr. Locke's work; inasmuch as in the one he asserts, that all our abstract knowledge commences in intuitive certainty, and that intuitive certainty, which like bright sunshine forces itself upon the mind with irresistible light, and moreover that this intuitive certainty must accompany us through all the steps of a demonstration; and in the other, that the maxim is mistaken which supposes all reasoning to be ex præcognitis et præconcessis. There is, it is certain, an apparent inconsistency in this representation; but it is merely apparent. Had Dr. Reid attended a little more closely to the meaning of Mr. Locke, as explained by himself in different parts of his works, he would easily have seen this slight difficulty solved, and this apparent inconsistency reconciled. Mr. Locke does not mean to assert, that all our reasonings must not commence in first principles, for this truth he expressly recognises in several parts of his work; but that they do not rest upon what were generally deemed the præcognita and præconcessa of the schools, and the philosophers with whom he is contending; that is, the maxims, which we have before enumerated, and which, by some, were made the foundations of all science. Hear his very expressions—“The necessity of this intuitive knowledge in every step of scientific or demonstrative reasoning gave occasion, I imagine, to that mistaken axiom, that all reasoning was ex præcognitis et præconcessis, which, how far it is mistaken, I shall have occasion to show more at large, when I come to consider propositions and particularly those propositions which are called maxims.” Now, look at what he says in his chapter upon maxims, and his drift becomes as clear as day-light.“ The rules established in the schools," says he, “ in that chapter, that all reasons are ex præcognitis et præconcessis, seem to lay the fourdation 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