« PoprzedniaDalej »
few, but the results of which are so extremely delicate, that none but a peculiarly acute intellect can trace them; and most probably, these men never would have been great geometricians, because geometry involves a great many principles; and that the nature of a mind may be such, that it can trace a few principles up to their extreme results ; yet not adequately comprehend those things in which a multitude of principles are combined.
There are then two sorts of minds, the one fathoms rapidly and deeply the principles of things, and this is the spirit of accurate discrimination ; the other comprehends a great many principles without confusing them, and this is the spirit of mathematics. The one is energy and clearness of mind; the other is expansion of mind. Now, the one may exist without the other. The mind may be powerful, but narrow; or it may be expanded and feeble.
There is much difference between the geometrical mind, and the acute mind. The principles of the one are clear and palpable, but removed from common usages; so that, for want of the habit, it is difficult to bring the attention down to such things; but as far as the attention is given to them, the principles of those things are plainly seen, and would need a mind altogether in error, to reason falsely on such commonplace matters ; so that, it is almost impossible that the principles of such things should not be ascertained.
But in the case of the acute mind, the principles in which it is conversant are found in common usage, and before the eyes of all men. You have but to turn your head without effort, and they are before you. The only essential point is a right perception ; for the principles are so inter woven and so numerous, that it is almost impossible but that some should be lost sight of. Now, the omission of one principle leads to error; hence it needs a very accurate perception to ascertain all the principles, and then a sound judgment not to reason falsely on known principles.
All the geometricians would be acute men, if they
possessed this keenness of perception, for they cannot reason falsely on the principles which they perceive; and the men of acute mind would be geometricians, if they couid not turn their attention to the less prominent principles of geometry.
The reason then why some men of acute intellect are not geometers is, that they cannot turn their atiention to the principles of geometry; but the reason why geometers have not this acuteness is, that they do not perceive what is before their eyes, and that being accustomed to the plain and palpable principles of geometry, and never reasoning till they have well ascertained, and handled their principles, they are lost in these matters of more acute perception, where the principles cannot be so easily ascertained. They are seen with difficulty,—they are felt rather than
It is scarcely possible to make them evident to those who do not feel them of themselves. They are so delicate and so multitudinous, that it requires a very keen and ready intellect to feel them; and that generally, without being at all able to demonstrate them in order, as in geometry ; because these principles cannot be so gathered, and it were an endless labor to undertake it. The thing must be seen at once, at a glance, and not by a process of reasoning; at least, to a certain degree. And hence it is rarely the case, that geometers are acute men, or acute men geometers; because geometers will treat these nicer matters geometrically, and thus make themselves ridiculous; they will begin with definitions, and then go to principles-a mode that will not answer in this sort of reasoning. It is not that the mind does not take this method, bnt it does so silently, naturally, without the forms of art—for all men are capable of the expressson of it; but this feeling of it is the talent of few.
And the acute mind, on the contrary, accustomed to judge at a glance, is so astonished when they present to it a series of propositions, where it understands but little, and when to enter into them, it is necessary to go previously through a host of definitions and dry principles, that not having been accustomed thus to examine in detail, it turns away in disgust. There are, however, many weaker, minds, which are neither acute nor geometrical.
Geometers, then, who are exclusively geometers, possess a sound judgment, provided only that the matter_be properly explained to them by detinitions and principles; otherwise they go wrong altogether, for they only judge rightly upon principles wbich are clearly laid down for them; and your acute men, who are exclusively so, have no patience to go down into first principles in matters of speculation and imagination, which they have never seen in use in the world.
3. It often happens, that to prove certain things, men adduce such examples, that they might actually take the things themselves to prove the examples ; which does not fail of producing an effect; for as they believe always that the difficulty lies in the thing to be proved, the example, of course, appears more intelligible. Thus, when they wish to illustrate a general principle, they exhibit the rule of a particular case. But if they wish to illustrate a particular case, they begin with the general rule. They always find the thing to be proved obscure, but the mediurn of proof clear and intelligible; for when it is purposed to prove a point, the mind pre-occupies itself with the thought, that it is obscure and difficult. Whilst, on the contrary, it assumes that the mode by which it is to be proved will be clear, and consequently, under that impression, comprehends it easily.
4. All our reasonings, are compelled to yield to feeling. A mere imagination, however, is both similar and contrary to feeling.—Similar, because it does not reason,-contrary, because it is false : so that it is difficult to distinguish between these contrarieties. One man says that my feeling is a mere fancy, and that his fancy is a real feeling; and I say the same of him. We need then a criterion : reason offers itself;, but it may be biassed to either side, and hence there is no fixed rule.
5. They who judge of a work by rule, are, with respect to those who do not, as those who possess a watch, with respect to those who do not. We have been here now two hours. Another says, It is but three qarters of an hour. I look at my watch, and say to one, You grow weary; and to the other, Time flies fast with you, for it is just an hour and a half; and I smile at those who tell me, that time lingers with me, and that I judge by imagination. They know not that I judge by my watch.
6. There are men who speak well, but do not write well. The place, the circumstances, &c. excite them, and elicit from their mind, more than they would find in it without that extraordinary stimulus.
7. That which is good in Montaigne, can only be acquired with difficulty: that which is evil, (I except his morals,) might be corrected in a moment, if we consider that he tells too many stories, and speaks too much of himself.
8. It is a serious fault, to follow the exception instead of the rule. We ought to be rigidly opposed to the exception. Yet since it is certain that there are exceptions to the rule, we should judge rigidly,
9. There are men who would have an author never speak of the things of which others have spoken; and if he does, they accuse him of saying nothing new. But if the subjects are not new, the dispositions of them
may be. When we play at tennis, both play with the same ball, but one may play it better than the other. They might just as well accuse us of using old words, as if the same thoughts differently arranged, would not form a different discourse; just as the same words differently arranged would express different thoughts.
10. We are more forcibly persuaded, in general by the reasons which we ourselves search out, than by those which are suggestions of the minds of others. 11. The mind makes progress naturally, and the
will naturally clings to objects; so that in default of right objects, it will attach itself to wrong ones.
12. Those great efforts of mind to which the soul occasionally reaches are such as it cannot habitually maintain. It reaches them by a sudden bound, but only to fall again.
13. Man is neither an angel nor a brute ; and the mischief is, they who would play the angel, often play the brute.
14. Only discover a man's ruling passion, and you are sure of pleasing him ; and yet each one has in the very notion that he has formed of good, some phantasies which are opposed to his real interest; and this is a strange incongruity, which often disconcerts those who would gain his affection.
15. A horse does not seek to be admired by its companion. There is to be sure, a sort of emulation in the course, but this leads to nothing; for in the stable the clumsiest and worst made, will not on that account give up his corn to the others. It is not so among
Their virtue is not satisfied with itself; and they are not satisfied, unless they obtain by it some advantage over others. 16. We injure the mind and the moral sentiments in
The mind and the moral sentiments are formed by conversation. The good or the evil improve or injure them respectively. It is of importance, then, to know how to choose well, so as to benefit, and not injure them. But we are unable to make this choice, unless the mind is already formed and not injured. There, then, is a circle, from which happy are they who escape!
17. When among those things in nature, the knowledge of which is not absolutely necessary, there are some, the truth of which we do not know, it is perhaps not to be lamented, that frequently one common error obtains, which fixes most minds. As for example, the moon, to which we attribute the change of weather, and the fluctuations of disease, &c. For one of man's greatest evils is a restless curiosity after the
the same way.