abstractions are, as it were, ready-made by nature, gravitation being the sole quality that it is necessary to take into view. Friction, the rigidity of materials, and a resisting mediumthough of this last there may be some doubt - are eliminated by the nature of the case; the problem is complicated only by the gravitating effect of different bodies on each other. Our conclusions are very general, then, but also very limited, as they relate exclusively to position and motion. Astronomy, it was remarked many years ago, is a perfect science; and so it is, the theory of it, though the improvement of instruments is daily bringing to light new facts.

Thus it appears, that we approximate the sphere of metaphysical evidence and demonstrative reasoning just in proportion as we leave the world of realities and facts, and abandon the consideration of objects in their entireness, or in all their relations.*

must be understood, in order to find the point of the strain, as well as the true proportion between depth and breadth. And, lastly, the peculiar properties of the several species of timber must be precisely known, and known by experiment; . . . and it is not the mathematician, but the naturalist, who must inform the practical man on these points."

"Now, let it, in these cases, be supposed that the mathematician, dogmatically confident of his demonstrations, (and this is in fact the fault of the earlier mathematicians, and not seldom of Leibnitz,) to determine the problem above mentioned, as if it were a pure abstraction; or, if he referred loosely to certain vulgar facts concerning the strength of timber, were neither to make experiments of this physical kind, nor to swerve at all from his mathematical processes in regard to them: - in this case, all his products must be erroneous. Or, though correct mathematically, they would be inapplicable to the real world, and useless, or worse than useless, in practice." Isaac Taylor's Introduction to Edwards on the Will, p. cxxxiii.

*Every one would wish to speak of Dr. Whewell with the respect which is required by his encyclopædic learning, his indefatigable activity of mind, and the zealous devotion of all his powers to the best interests of science and education. But it has been wittily said of him, that "his forte is science, and his foible is omniscience." It is to be wished that he had let metaphysics alone, and had contented himself with the glory of mastering, and doing something to improve, every one of the Inductive Sciences. His great work on these sciences contains, along with many ingenious disquisitions and a prodigious amount of learning, a great deal of bad phi

losophy. He seriously undertakes to prove, that Astronomy and Mechanics are not Mixed, but Pure Sciences; that the data on which they rest, as well as the steps of reasoning by which they proceed, are intuitions of pure reason, independent of all experience; that gravity, for instance, is a necessary and inherent quality of matter, like extension and figure, a doctrine which Newton himself emphatically disavows; and that the three primary laws of motion, in like manner, are not general facts, made known by induction, but are original and necessary truths, not evolved out of experience, but first revealed by careful study and reflection upon the train of our ideas. He thus binds himself to prove, (to adopt Sir J. Herschel's illustration,) that a clever man, shut up alone, might work out for himself, by dint of hard thinking, the whole Principia of Newton, without any aid from experiment and observation. These heresies have been sufficiently and sharply reproved by Sir William Hamilton, Mr. Mansel, (the author of Prolegomena Logica,) and, in advance, by Dugald Stewart. (Hamilton argues thus:

"Dr. Whewell asserts, that such propositions do not depend at all upon experience.' On the contrary, I maintain that all propositions which involve the notion of gravitation, weight, pressure, presuppose experience; for by experience alone do we become aware, that there is such a quale and quantum in the universe. To think it existent, there is no necessity of thought; for we can easily in thought conceive the particles of matter, (whatever these may be) indifferent to each other,―nay, endowed with a mutually repulsive, instead of a mutually attractive force. We can even, in thought, annihilate matter itself. So far, the asserted axiom is merely a derived, and that too merely an empirical, proposition. But, moreover, not only are we dependent on experience for the fact of the existence of gravitation, etc., we are also indebted to observation for the further facts of the uniform and continuous operation of that force; and thus, in a second (and even third) potence, are all such propositions dependent upon experience."

But Dr. Whewell remarks, if it be said that we cannot have the idea of pressure without the use of the senses, and this is experience, the same may be said of our ideas of relation in space; and thus Geometry, no less than Mechanics, depends upon experience in this sense.

Hamilton replies, “This is only another instance of confusion of thought and ignorance of the subject. The ideas of relation in space and the ideas of pressure differ obtrusively in this:- that we can, in thought, easily annul pressure, all the properties of matter, and even matter itself; but are wholly unable to think away from space and its relations. The latter are conditions of, the former are educts from, experience; and it is this difference of their object-matters, which constitutes Geometry and Arithmetic pure or a priori sciences, and Mechanics a science empirical, or a posteriori”

Mr. Stewart, in animadverting upon the error into which Dr. Whewell

has since fallen, has pointed out very clearly the bias of mind in which it has its origin. "As the study of the mechanical philosophy," he observes, "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 unavoidable 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."

"In pure geometry, no reference to the senses can be admitted, but in the way of illustration; and any such reference, in the most trifling step of a demonstration, vitiates the whole. But in Natural Philosophy, all our reasonings must be grounded on principles for which no evidence but that of sense can be obtained; and the propositions which we establish, differ from each other only as they are deduced from such principles immediately, or by the intervention of a mathematical demonstration. An experimental proof, therefore, of any particular physical truth, when it can be conveniently obtained, although it may not always be the most elegant or the most expedient way of introducing it to the knowledge of the student, is as rigorous and as satisfactory as any other; for the intervention of a process of mathematical reasoning can never bestow on our conclusions a greater degree of certainty than our principles possessed.

"I have been led to enlarge on these topics by that unqualified application of mathematical method to physics, which has been fashionable for many years past among foreign writers, and which seems to have originated chiefly in the commanding influence which the genius and learning of Leibnitz has so long maintained over the scientific taste of most European nations. I have [elsewhere] taken notice of some other inconveniences resulting from it, still more important than the introduction of an unsound logic into the elements of Natural Philosophy; in particular, of the obvious tendency which it has to withdraw the attention from that unity of design, which it is the noblest employment of philosophy to illustrate, by disguising it under the semblance of an eternal and necessary order, similar to what the mathematician delights to trace among the mutual relations of quantities and figures. The consequence has been, (in too many physical systems,) to level the study of nature, in point of moral interest, with the investigations of the algebraist ; -an effect, too, which has taken place most remarkably, where, from the sublimity of the subject, it was least to be expected,—in the application of the mechanical philosophy to the phenomena of the heavens."

CHAPTER II.

THIS DISTINCTION APPLIED TO PHILOSOPHY AND THEOLOGY.

Summary of the last Chapter. In the last chapter, I endeavored to define and distinguish the nature and scope of physical and metaphysical inquiry, to show that the one was properly confined to matters of fact, and the other to relations of ideas. Demonstrative reasoning, I attempted to prove, belongs exclusively to the latter, and its conclusions are always abstract; the truths of physical science are obtained only by the inductive method, by observation and experiment, and by generalizations extending from individuals to a class. Yet the former method has no superiority over the latter, when considered simply as a foundation of belief. Both alike command our assent on indisputable grounds, though the media of proof are radically unlike. Sensible evidence and inductive reasoning, it is true, admit of degrees, and lead to all shades of belief, from the faintest probability up to what is called moral certainty. Demonstrative reasoning, on the other hand, has no degrees; a proposition is established by it either conclusively, or not at all. If successful, it would be contradictory and absurd to deny the conclusion, the proof being then equivalent, but not superior, to that which in the former case renders a fact morally certain. To adopt Locke's distinction between insanity and idiocy, we might say that only a madman can reject a mathematical proof after it has been once explained to him, while to be incapable of governing one's conduct by that sensible evidence which controls the actions of our fellows, is simply idiocy. Such a person is usually said to be incapable of keeping out of fire and water, because he is not able to learn from induction, or repeated experiment, that the former will burn and the latter will drown him. A very brief glance at the history of science was

intended to show, that most of the mistakes, retrogressions, and absurdities which have hindered the progress of it, may be traced to ignorance or forgetfulness of the distinction here pointed out, to an attempt to deduce facts from abstract conceptions, or to draw down pure ideas to sensible observation and material tests,—to calling for demonstration in physics, or following the guidance of the senses only in metaphysical investigations. Illustrations of this error might easily be multiplied from the whole domain of science and speculation, not less numerous and apt in our own day, perhaps, than they were among the ancients or in the times of the schoolmen; but less conspicuous, affecting a smaller class of minds, and therefore less likely, we may hope, to be chronicled for the mingled amusement and pity of future generations. They are now the follies of a sect, a party, or a clique,— usually a small one; while in former days, they were the indications of a universal evil, proceeding from ill-formed habits of thought, and offering a far-extended and almost insuperable barrier to the progress of knowledge.

Nature and Object of Philosophy, or Metaphysical Science.Leaving the task of mere illustration, then, I proceed to inquire how far the distinction now pointed out may be made available for one great purpose of this work, to determine clearly the respective limits of Religion and Philosophy. It is obvious that the latter term, which is often applied very generally to the pursuit of all knowledge, must here be used in a restricted sense, and be made synonymous, in fact, with metaphysics. It cannot be defined more clearly, without a tedious enumeration of all the questions and problems which it comprehends. It is concerned with the origin and explication of our ideas of cause, power, infinity, knowledge, freewill, identity, substance, and the like, all of which are pure abstractions, so that we must reason about them demonstratively, or not at all. Philosophy, in this narrow meaning of the word, includes precisely that class of subjects which Milton assigned for contemplation to one band. of the spirits fallen from heaven, who, in their place of punishment,