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While metaphysical studies, however, contract in this way the sphere of our enjoyment, they enlarge it in another, by the pleasures arising from the exercise of the understanding, and from the gratification of the curiosity. Whether the compensation be complete or not, I shall not at present inquire ;* as my object is, not to compare the advantages and disadvantages of different literary pursuits, but to remark their general effect in modifying the principles of our nature, as intellectual, active, and sensitive beings. Whatever opinion we may form on this speculative question, one thing seems to be equally indisputable, that if the pleasures of Imagioation, when uncontrolled by the exercise of the reasoning faculty, affect the mind with the most exquisite delight, it is only by combining the pleasures arising from both parts of our frame, that the duration of the former can be prolonged beyond the short period of youth'; or that they can be enjoyed even then, for any length of time, without ending in languor and satiety. The activity which always accompanies the exercise of our reasoning powers, seems, in truth, to be essentially necessary to enliven the comparatively indolent state of mind which the pleasures of Imagination and of Taste have a tendency to encourage.
Such a combination, too, will be found the most effectual, perhaps the only expedient, for preserving the powers of Imagination and Fancy in full vigour to the close of life; while, on the other hand, without the stimulus which these powers apply to our active propensities, Reasoning and Invention would have scarcely any motive to animate their exertions, after the period when the stronger passions have spent their force.
"bon Métaphysicien. Celui-ci est un homme interieur qui ne voit qu' en lui
même, qui a, si j'ose ainsi parler, les yeux tournés en dedans ; l'artiste et l'ama“teur sont, au contraire, tout yeux, et tout oreilles, leur âme se repand au dehors; " les couleurs, les formes, les situations, voilà ce qui les frappe sans cesse, tandis
que le philosophe n’est occupé que de rapports, de différences, de généralités, " d'abstractions.
“Que cette opposition de l'esprit et du goût des beaux arts avec l'esprit méta
physique et philosophique soit générale ou non, je déclare qu' au moins elle est " en moi jusqu'à un certain degré. Les tableaux m'ont fait peu de plaisir.” Mémoires de l'Abbé Morellet, Tom I. pp. 56, 57.
* What was Sterne's opinion upon this point may be guessed from the following passage : “ I would ge fifty miles on foot to kiss the hand of that man whose ge
nerous heart will give up the reins of his imagination into his author's hands, “ be pleased he knows not why, and cares not wherefore.”—Mr. Burke has expressed the same opinion in stronger and less equivocal terms. - The pleasures
of imagination” (he observes) * are much higher than any which are derived " from a rectitude of the judgment: the judgment is, for the greater part, em"ployed in throwing stumbling-blocks in the way of the imagination, in dissipa
ting the scenes of its enchantment, and in tying us down to the disagreeable
yoke of our reason.”-See the Essay on Taste, prefixed to his Inquiry into the Sublime and Beautiful.
The field in which the powers of the Metaphysician appear to greatest advantage, is in general and comprehensive views of Science, and of human atiairs ; such views as Leibnitz ascribes to Bacon and Campanella in the following passage:* “ Some men, in conducting operations where an attention to “ minutiæ is requisite, discover a mind vigorous, subtile, and “ versatile, and seem to be equal to any undertaking how ar66 duous soever. But when they are called upon to act on a “ greater scale, they hesitate, and are lost in their own medi“tations ; distrustful of their judgment, and conscious of their 6 incompetency to the scene in which they are placed ; men, “ in a word, possessed of a genius rather acute than compre6 hensive. A similar difference inay be traced among authors. “ What can be more acute ihan Descartes in physics, or than 6 Hobbes in morals! And yet, if the one be compared with « Bacon, and the other with Campanella, the former writers “ seems to grovel upon the earth,—the latter to soar to the
heavens, by the vastness of their conceptions, their plans, “ and their enterprises ; and to aim at objects beyond the reach “ of the human powers. The former, accordingly, are best “ filted for delivering the first elements of knowledge, the lat6 ter for establishing conclusions of important and general ap" plication."
This tendency to abstraction and generalization commonly grows upon us as we advance in life ; partly from our own growing impatience in the study of particulars, and partly from the inaptitude of our declining faculties to embrace with accuracy a multiplicity of minute details. Hence, the mind is led to experience an increasing delight in those vantage-grounds which afford it an enlarged survey of its favourite objects. The flattened eye which can no longer examine the microscopical beauties of an insect's wing, may yet enjoy the variegated tiuts of an autumnal wood, or wander over the magnificence of an Alpine prospect.
İs it not owing to this, among other causes, that time appears to pass more swiftly the longer we live ? As the events we contemplate swell in magnitude and importance, (the attention being daily less engrossed with individuals, and more with communities and nations,) the scene must, of course, shift more slowly, and the plot advance more leisurely to its accomplishment. Hence, that small portion of our thread which remains unspun, appears to bear a less and less proportion to the space likely to be occupied by the transactions in which we are inte
* How Leibnitz was led to unite these two names, it is not easy to imagine..
rested. Franklin, towards the close of life, complained repeatedly in my hearing, that time passed much more rapidly in his old age than when he was young. “ The year” (he said) “ is no sooner begun than it is ended ;''-adding with his usual good humour, “ I am sometimes tempted to think they do “not give us so good measure now as formerly.” Whoever compares the latter part of this great man's history with his first outset, will not think this change in his estimate of time very wonderful.
The feelings which Franklin experienced when an old man, in consequence of the accidental circumstances of his history, are the natural effects of the habits of thinking which the philosopher loves to indulge. In consequence of these habits, he feels every day more and more as a citizen of the world ; and, associating himself with the inhabitants of the most remote regions, takes a deeper interest in the universal drama of human affairs. And if, in consequence of this, his years should appear to pass over his head more swiftly, it must be remembered that, after a certain period of life, this ceases to be a misfortune. Franklin himself, while he affected to hold a different language, plainly considered the matter in this light; and, 'indeed, could not have given a stronger proof of the happiness of his old age, than by the complaints he made of the rapid flight of time. It is only when our prospects accord with our wishes, that we are liable to the influence of this illusion.
The intellectual habits of the Mathematician aré, in some respects, the same with those we have been now considering ; but, in other respects, they differ widely. Both are favourable to the improvement of the power of attention; but not in the same manner, nor in the same degree.
Those of the metaphysician give a capacity of fixing the attention on the subjects of our consciousness, without being distracted by things external ; but they afford little or no exercise to that species of attention which enables us to follow long processes of reasoning, and to keep in view all the various steps of an investigation till we arrive at the conclusion. In mathematics, such processes are much longer than in any other sci. ence; and hence the study of it is peculiarly calculated to strengthen the power of steady and concatenated thinking ; a power which, in all the pursuits of life, whether speculative or active, is one of the most valuable endowments we can possess. This command of attention, however, it may be proper to add, is to be acquired, not by the practice of the modern methods, but by the study of the Greek geometry ; more particularly, by accustoming ourselves to pursue long trains of demonstration, without availing ourselves of the aid of any sensible diagrams; the thoughts being directed solely to those ideal delineations which the powers of conception and of memory enable us to form.*
* The following remark of Descartes on a peculiarity in the intellectual character of mathematicians, has, at first view, very much the air of a paradox; and yet, from the great eminence of the author, both in mathematics and metaphysics,' every thing that falls from his pen on such a subject is well entitled to a careful examination. His words, literally interpreted, seem to imply, that Imagination is a faculty which mathematical studies tend, in an extraordinary degree, to exercise and cultivate ; and that it is owing to this, that mathematicians seldom succeed in metaphysical reasonings ; whereas the obvious and indisputable fact is, that of all the departments of human knowledge, mathematics is that in which imagination is least concerned. “ Admodum difficile est, uti scribis, Analystarum vestrorum “ opiniones de existentia Dei, deque honore illi exhibendo, corrigere, non quod “ desint satis validæ rationes quibus convincantur, sed quia ejusmodi homines cum “ putent se pollere ingenio, sæpe sunt minus quam alii, rationi obsequentes ; ea “ enim ingenii pars, imaginatio nempe, quæ ad Mathesin maxime juvat, plus “nocet quam prodest ad metaphysicas speculationes.”—(Cartesii Epist Pars. II. Ep. xxxiii.)
On a moi attentive consideration, however, of this passage, it oceurs to me, that the word imagination is to be here understood, not in its ordinary sense, but as synonymous with conception, as defined and used in these EEMENTS ; on which supposition the remark of Descartes amounts to no more than this,—that the habit of geometers of contemplating diagrams while carrying on their reasonings, is adverse to the cultivation of those powers of abstracted reflection, on which the success of our metaphysical researches depends. I am confirmed in the justness of this interpretation by a passage in a letter addressed to Earl Stanhope, (22d of March, 1751,) by the late Ďr. Robert Simpson of Glasgow, in which that very distinguished mathematician plainly understands the word Imagination in the same sense in which I have supposed it to be employed by Descartes. This passage is on other accounts an object of curiosity; as the slightest relic from the hand of such a writer always is, when he records any phenomena connected with the history of his own mind.
“ Persons of my age (now past sixty-three) generally lose the ability they had " when younger, of a quick and ready imagination, and their memory (which, “ in my opinion, is either the imagination of sensations past, or the recalling the “ imaginations we had formerly,) manifestly decays; and so far with me, that I “ have oftentimes difficulty to recall those I had the last hour, or even a few mi“ nutes before. And in long investigations, where it is necessary to look back a “ good way, this inability is most easily observed, especially where most of the
steps are not wrote down; for I remember when I could go through a longer “ series of steps without writing than I can now well do with the help of it. This, “ my Lord, makes me afraid that I shall not be able to engage in the undertaking " you are pleased to recommend to me, and which, indeed, would be very agree " able to me; the applying the method of the ancients to the modern inventions, “ so as they might be demonstrated in such a way as would (to use your Lord. * ship's just and elegant description of accuracy and strictness,) convince a Eu. " clid, an Archimedes, or an Appollonius, risen from the grave to examine them." See the very interesting Memoir of Dr. Simpson by Dr. Traill.
It is not, however, on such efforts alone that the success of our researches depends in many of our most important inquiries. How accurate soever the logical process may be,-if our first principles be rashly assumed,—or, if our terms be indefinite and ambiguous, there is no absurdity so great that we may not be brought to adopt it, and it unfortunately happens, that, while mathematical studies exercise the faculty of reasoning or deduction, they give no employment to the other powers of the understanding concerned in the investigation of truth. On the contrary, they are apt to produce a facility in the admission of data ; and the circumscription of the field of speculation by partial and arbitrary definitions. Of this many examples might be quoted from the works of those geométricians and algebraists, who, without the advantages of a very liberal education, or of an extensive commerce with the world, have ventured to speculate on questions beyond the limits of their ordinary pursuits. A very respectable mathematician of the Roman Catholic persuasion seems to have felt somewhat of this bias in himself, when he excused himself from intermeddling with theological disputes, by saying, “ That it was the business of “the Sorbonne to discuss ; of the Pope to decide ; and of the “ Mathematician to go to Heaven in a perpendicular line."* The atheism and materialism professed by some late mathematicians on the continent, is, I suspect, in many cases, to be as cribed to the very same cause ; a credulity yielding itself up as blindly to the fashionable disbelief of the day, as that of their predecessors submitted itself to the creed of the infallible church,t
The bias now mentioned is strengthened by another circumstance ;-the confidence which the mere mathematician natur, ally acquires in his powers of reasoning and judgment ;-in consequence of which, though he may be prevented, in his own pursuits, from going far astray, by the absurdities to which his errors lead him, he is seldom apt to be revolted by absurd
*“ Il disoit en propres termes (M. Ozanam) qu'il appartient aux docteurs de “Sorbonne de disputer, au Pape de prononcer, et au mathematicien d'aller au Pa“ radis en ligne perpendiculaire.” – Eloge de M. Ozanam par Fontenelle..
† Mr. Locke speaks somewhat vaguely on the subject of mathematical studies.“ Would you have a man reason well, you must use him to it betimes, exercise “his mind in observing the connexion of ideas, and follow them in train. No" thing does this better than mathematics, which, therefore, I think should be “ taught all those who have the time and opportunity, not so much to make them “ mathematicians, as to make them reasonable creatures.”—(Conduct of the Understanding.) Lord Bacon is much more precise on this head. " If a man's wit “ be wandering, let him study the mathematics ; for in demonstrations, if his wit “ be called away ever so little, he must begin again."--Essays.