tradictions can be forced upon it as absolutely demonstrated. It is to us a wonderful phenomenon that a mind of such force and penetration should have accepted fallacies which to common view are so palpable. They seem in each case to have proceeded from an inaccurate a priori idea of infinity, to which he adhered, though contradicted at every step by conceptions of a more definite character drawn froin elementary notions of quantity. Sir W. Hamilton had a contempt for mathematical studies, which he regarded as intolerably wearisome to a genius of the sublimer order, from their great facility. opinions on this point may suggest a doubt whether he had any very profound acquaintance with a science which, according to Comte, is the product of "a vast concatenated series of prolonged intellectual exertions, offering inexhaustible aliment to the mind;” 7 and of which Sir J. Ilerschel, referring

1 to certain analytical researches, says that “the contention of mind for which they call is enormous.” However that

# may be, we have sometimes thought that if the great Scotch metaphysician had been more thoroughly on his guard against the undefined and fluctuating conceptions so often veiled by the generalities of abstract terms, he would have avoided some errors into which he has unfortunately fallen; and we believe the more difficult mathematical investigations, requiring, as they often do, highly subtle and exact discriminations, founded on real differences which cannot be neglected without error in the result, are mental exercises well suited to teach that cautionary lesson.

* "To minds of any talent, mathematics are only difficult because they are ton easy.”—“Mathematics are found more peculiarly intolerable by minds endowed with the most varied and vigorous faculties. ... The continued and monotonous attention they necessitate to a long concatenated deduction, each step in the lucid series calling forth, on the same external relation, and to the same moderate amount, the same simple deduction of reason. This, added to the inertion to which they condemn all the noble and more pleasurable energies of thought, is what renders mathematics—in themselves the easiest of rational studies--the most arduous for those very minds to which studies in themselves most arduous, are easiest. In mathematics, dulness is thus elevated into talent, and talent degraded into incapacity.”-Discourse on the Study of Mathematics. + Phil. Pos., vol. i., p. 91.

Outlines of Astronomy $ 10.

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But, to return to the Duke of Argyle. He begins with the question: What is the supernatural ?-adding, "M. Guizot tells us that belief in it is the special difficulty of our timethat denial of it is the form taken by all modern assaults on Christian faith ; and again, that acceptance of it lies at the

1 root, not only of Christianity, but of all positive religion whaterer,” His

grace then proceeds to inquire in what this difficulty consists, and thinks it must in part be ascribed to a vague use of the word supernatural. There


be some men,” “ who disbelieve in the supernatural, only because they are absolute atheists; but it is certain that there are others who have great difficulty in believing in the supernatural who are not atheists. What they doubt or deny is, not that God exists, but that he enacts, or perhaps can act, unless in and through what they call the laws of Nature.” The conclusion he comes to at length is, that they find it so hard to believe in supernatural power, because by it they mean “power independent of the use of means, as distinguished from power depending on knowledge—even infinite knowledge—of the means proper to be employed.” But this difficulty, in his opinion, is unnecessarily encountered. The action of the Deity, in creation, providence, or revelation, he believes, suspends or violates no law of nature; and, therefore, is not with strict propriety termed supernatural. The properties of dead matter, the physiological laws of organized beings, and the spontaneous forces by which the volitions of brutes and of man can modify the effects of other causes; all those are within the domain of nature. And, if a great immaterial Being exists, capable, by the mysterious relation he bears to matter, of exerting infinite physical force, and possessing knowledge in equal degree to make the laws of nature subserve his purposed ends, he might employ powers which, though superhuman, would so far resemble those exercised by man, as to justify equally the application of the term natural. By such means, he could alter the course of natural sequences without suspending natural laws, and thus subject the world to special providential reg. ulation. If it pleased him to send a revelation to man, he could, by similar displays of superhuman power, authenticate the message by miracles; and, in that way, raise it above the posVOL. XLII.—NO. I.


sibility of human contrivance. He could also, by the same means, grant special answers to prayer, and thus establish that immediate personal dependence on himself, without which, religion, as a living practical principle, cannot exist. All this is not only natural, but becomes more credible a priori, because it is the result of means exactly analogous to those employed by man in accomplishing his own ends, the difference covsisting mainly in the infinite superiority of resources possessed by the Deity. The relation which this great Being bears to the laws of nature themselves is left undetermined, as unnecessary to the argument: but certain expressions used by the author have fallen a little unpleasantly on our ear, because they might perhaps raise a doubt whether he did not think it possible that some of those laws—such as flow directly from the essential properties of matter, for example-were uncontrollable even by the Divine will. “It may be,” he says, “that all natural forces are resolvable into some one force.

It may also be that this one force.

is itself but a mode of action of the Divine will. But we have no instruments whereby to reach this last analysis. Whatever the ultimate relation may be between mental and material force, we can at least see clearly that, in nature, there is the most elaborate machinery to accomplish purpose through the instrumentality of means.

It seems as if all that is done in nature, as well as all that is done in art, were done by knowing how to do it. It is curious how the language of the great seers of the Old Testament corresponds with this idea.

Exactly the same language is applied to the rarest exertions of power, and to the gentlest and most constant of all natural operations. Thus, the saying that “The Lord by wisdom hath founded the earth : by understanding, hath he established the heavens,'-—is coupled in the same breath with this other say. ing, “By his knowledge, the depths are broken up, and the

, clouds drop down the dew.'”—Pp. 129–131.

It seems that our author would lessen the difficulty Guizct thought the present age had, in believing the supernatural, by discarding that word, and by comprising within the bounds of the natural whatever is essential to the being of a personal, moral, wise, powerful, and all-controlling God. To this exten

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sion of the latter term, and to the positions it includes, he seeks to conciliate favor by pointing out the analogies between the powers exercised by man, and those he ascribes to the Supreme Being. The objectors, indeed, deny that God “ever acts, or perhaps can act, unless in and through what they call the laws of nature;" yet, since the power man exerts modifies their operation and produces specific results, so the infinite power of God, acting through similar means, may produce results infinitely greater, and, therefore, sufficient for all his designs, whether in nature, in providence, or in the miraculous attestation of his will. From the same analogy, he concludes that "the mind of man has within it something of a truly creative energy and force—that we are in a sense “fellow-workers with God,' and have been in a measure “made partakers of the Divine nature.' "--P. 10.

We trust the exacter classification of ideas offered by his grace's definitions may relieve some honest minds perplexed by doubts and groping through darkness to find the truth; but, we confess, we are not very sanguine as to the result. The views he presents may give consistence and clearness to some speculative opinions in regard to the connection of a special providence with the immutability of natural laws; but we fear it will not meet the objections of the class to whom M. Guizot referred. The only powers they recognize as acting in nature, appear to be that series of physical causes which embraces the material universe, with so much power of spontaneous action in addition as is placed within the control of brutes and men. They allow no immaterial agents, neither God, angel, spirit, nor devil, to interfere in any way with this great chain of causation, since any force acting upon it from without, whether analogous to that exerted by man or not, they regard as quite inconsistent with the observed order of nature.

Nor do we very clearly perceive how any substantial difficulty in admitting the truth of miracles would be removed by the author's scheme. Let us take, as an example, Christ's feeding the multitude with the loaves and fishes. By his grace's hypothesis, the miracle was wrought by superhuman power, which acted in strict accordance with natural laws. But in what way are we to suppose the effect was produced ?

Shall we assume that spirits, moving with inconceivable celerity, collected the constituent elements of the food, and, by aid of chemical laws, coinbined them together in the proportions and relative positions necessary to produce both the qualities and appearance of the substance required? This might respect those laws which issue directly from the primary properties of matter; but, another law requiring that all products of organization should grow from germs deriving life from a parent stock, appears to be violated. Or shall we suppose some invisible agent collected the food, ready prepared, from distant localities, and with it supplied the waste caused by the distribution ? This avoids the former difficulty, but leaves another unanswered,—that by this world's constitution, as we know it, spirits never act on matter, except through the medium of an organized living body. But whatever hypothesis, consistent with the recorded facts, is adopted, we think it will hardly take the faith of most readers, less than the simple supposition that the Saviour, by Divine power, called into existence the additional food with which the multitude were fed.

It is very probable bis grace would not accept either of our suppositions as fairly representing his theory; and, indeed, we offer them but as suggestions, because we are really at some loss how to give his abstract principle a particular application in the case of miracles. His distinction between the superhuman and the supernatural, between power which may be infinite, but acts only through law, and power which for the occasion suspends the

operation of some law, though sufficiently clear in many cases, seems undefined and shadowy as applied to this.

In the chapter on “Creation by Law,” he considers the development theory, quoting from Darwin the admission that it structural modifications subserving beauty merely, apart from utility, could be shown to exist, his hypothesis must fall. For answer, he brings forward many curious facts in regard to the colors and ornaments of the numerous species of humming-birds, and argues that there is sufficient proof that differences abound among them which cannot be referred to the principle of utility, which do not better adapt the birds

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