86

adjungat his multiplicare et dividere, non abnuam, cum multiplicatio idem sit quod æqualium additio, divisio quod æqua"lium quoties fieri potest subtractio. Recidit itaque ratioci"natio omnis ad duas operationes animi, additionem et subtrac"tionem." How wonderfully does this jargon agree with the assertion of Condillac, that all equations are propositions, and all propositions equations!

These speculations, however, of Condillac and of Hobbes relate to reasoning in general; and it is with mathematical reasoning alone, that we are immediately concerned at present. That the peculiar evidence with which this is accompanied is not resolvable into the perception of identity, has, I flatter myself, been sufficiently proved in the beginning of this article; and the plausible extension by Condillac of the very same theory to our reasonings in all the different branches of moral science, affords a strong additional presumption in favour of our conclusion.

From this long digression, into which. I have been insensibly led by the errors of some illustrious foreigners concerning the

* The Logica of Hobbes has been lately translated into French, under the title of Calcul ou Logique, by M. Destutt-Tracy. It is annexed to the third volume of his Elémens d'Idéologie, where it is honoured with the highest eulogies by the ingenious translator. 66 L'ouvrage en masse (he observes in one passage) mérite d'être regardé comme un produit precieux des méditations de Bacon et de Descartes sur le sys"tême d'Aristote, et comme le germe des progrès ultérieures de la science." (Disc. Prel. p. 117.)

nature of mathematical demonstration, I now return to a further examination of the distinction between sciences which rest ultimately on facts, and those in which definitions or hypotheses are the sole principles of our reasonings.

III.

Continuation of the Subject.-Evidence of the Mechanical Philosophy, not to be confounded with that which is properly called Demonstrative or Mathematical.-Opposite Error of some late Writers.

NEXT to geometry and arithmetic, in point of evidence and certainty, is that branch of general physics which is now called mechanical philosophy;-a science in which the progress of discovery has been astonishingly rapid, during the course of the last century; and which, in the systematical concatenation and filiation of its elementary principles, exhibits every day more and more of that logical simplicity and elegance which we admire in the works of the Greek mathematicians. It may, I think, be fairly questioned, whether, in this department of knowledge, the affectation of mathematical method has not been already carried to an excess; the essential distinction between mechanical and mathematical truths being, in many of the physical systems which have lately appeared on the Continent, studiously kept out of the reader's view, by exhibiting both, as nearly as possible, in the same form. A variety of circumstances, indeed, conspire to iden

tify in the imagination, and, of consequence, to assimilate in the mode of their statement, these two very different classes of propositions; but as this assimilation (beside its obvious tendency to involve experimental facts in metaphysical mystery) is apt occasionally to lead to very erroneous logical conclusions, it becomes the more necessary, in proportion as it arises from a natural bias, to point out the causes in which it has originated, and the limitations with which it ought to be understood.

The following slight remarks will sufficiently explain my general ideas on this important article of logic.

1. As the study of the mechanical philosophy is, in a great measure, inaccessible to those who have not received a regular mathematical education, it commonly happens, that a taste for it is, in the first instance, grafted on a previous attachment to the researches of pure or abstract mathematics. Hence a natural and insensible transference to physical pursuits, of mathematical habits of thinking; and hence an almost unavoid able propensity to give to the former science, that systematical connection in all its various conclusions, which, from the nature of its first principles, is essential to the latter, but which can never belong to any science which has its foundations laid in facts collected from experience and observation.

2. Another circumstance, which has co-operated powerfully with the former in producing the same effect, is that proneness to simplification which has misled the mind, more or less, in all its researches ; and which, in natural philosophy, is peculiarly

encouraged by those beautiful analogies which are observable among different physical phenomena;-analogies, at the same time, which, however pleasing to the fancy, cannot always be resolved by our reason into one general law. In a remarkable analogy, for example, which presents itself between the equality of action and re-action in the collision of bodies, and what obtains in their mutual attractions, the coincidence is so perfect, as to enable us to comprehend all the various facts in the same theorem; and it is difficult to resist the temptation which it seems to offer to our ingenuity, of attempting to trace it, in both cases, to some common principle. Such trials of theoretical skill I would not be understood to censure indiscriminately; but, in the present instance, I am fully persuaded, that it is at once more unexceptionable in point of sound logic, and more satisfactory to the learner to establish the fact, in particular cases, by an appeal to experiment; and to state the law of action and re-action in the collision of bodies, as well as that which regulates the mutual tendencies of bodies towards each other, merely as general rules which have been obtained by induction, and which are found to hold invariably as far as our knowledge of nature extends *.

It is observed by Mr Robison, in his Elements of Mechanical Philosophy, that "Sir Isaac Newton, in the general scholium on the laws of motion, seems to consider "the equality of action and reaction, as an axiom deduced from the relations of ideas. "But this (says Mr Robison) seems doubtful. Because a magnet causes the iron to approach towards it, it does not appear that we necessarily suppose that iron also at"tracts the magnet." In confirmation of this he remarks, that notwithstanding the previous conclusions of Wallis, Wren, and Huyghens, about the mutual, equal, and contrary action of solid bodies in their collisions, " Newton himself only presumed that, be"cause the sun attracted the planets, these also attracted the sun; and that he is at

An additional example may be useful for the illustration of the same subject. It is well known to be a general principle in mechanics, that when, by means of any machine, two heavy bodies counterpoise each other, and are then made to move together, the quantities of motion with which one descends, and the other ascends perpendicularly, are equal. This equilibrium bears such a resemblance to the case of two moving

"much pains to point out phenomena to astronomers, by which this may be proved, "when the art of observation shall be sufficiently perfected." Accordingly, Mr Robison, with great propriety, contents himself with stating this, third law of motion, as a fact" with respect to all bodies on which we can make experiment or observation fit "for deciding the question."

In the very next paragraph, however, he proceeds thus: "As it is an universal law, we "cannot rid ourselves of the persuasion that it depends on some general principle which "influences all the matter in the universe;"-to which observation he subjoins a conjecture or hypothesis concerning the nature of this principle or cause.

For an outline of his theory I must refer to his own statement. (See Elements of Mechanical Philosophy, Vol. I. pp. 124, 125, 126.)

Of the fallaciousness of synthetical reasonings concerning physical phenomena, there cannot be a stronger proof, than the diversity of opinion among the most eminent philo, sophers with respect to the species of evidence on which the third law of motion rests, On this point, a direct opposition may be remarked in the views of Sir Isaac Newton, and of his illustrious friend and commentator, Mr Maclaurin; the former seeming to lean to the supposition, that it is a corollary deducible a priori from abstract principles; while the latter (manifestly considering it as the effect of an arbitrary arrangement) strongly recommends it to the attention of those who delight in the investigation of final causes*. My own idea is, that, in the present state of our knowledge, it is at once more safe and more logical, to consider it merely as an experimental truth; without venturing to decide positively on either side of the question. As to the doctrine of final causes, it fortunately stands in need of no aid from such dubious speculations.

• Account of Newton's Philosophical Discoveries. Book II. Chap. 2. § 28.