The difference between the mathematical and the intuitive mind.[1]—In the one the principles are palpable, but removed from ordinary use; so that for want of habit it is difficult to turn one's mind in that direction: but if one turns it thither ever so little, one sees the principles fully, and one must have a quite inaccurate mind who reasons wrongly from principles so plain that it is almost impossible they should escape notice.
But in the intuitive mind the principles are found in common use, and are before the eyes of everybody. One has only to look, and no effort is necessary; it is only a question of good eyesight, but it must be good, for the principles are so subtle and so numerous, that it is almost impossible but that some escape notice. Now the omission of one principle leads to error; thus one must have very clear sight to see all the principles, and in the next place an accurate mind not to draw false deductions from known principles.
All mathematicians would then be intuitive if they had clear sight, for they do not reason incorrectly from principles known to them; and intuitive minds would be mathematical if they could turn their eyes to the principles of mathematics to which they are unused.
The reason, therefore, that some intuitive minds are not mathematical is that they cannot at all turn their attention to the principles of mathematics. But the reason that mathematicians are not intuitive is that they do not see what is before them, and that, accustomed to the exact and plain principles of mathematics, and not reasoning till they have well inspected and arranged their principles, they are lost in matters of intuition where the principles do not allow of such arrangement. They are scarcely seen; they are felt rather than seen; there is the greatest difficulty in making them felt by those who do not of themselves perceive them. These principles are so fine and so numerous that a very delicate and very clear sense is needed to perceive them, and to judge rightly and justly when they are perceived, without for the most part being able to demonstrate them in order as in mathematics; because the principles are not known to us in the same way, and because it would be an endless matter to undertake it. We must see the matter at once, at one glance, and not by a process of reasoning, at least to a certain degree. And thus it is rare that mathematicians are intuitive, and that men of intuition are mathematicians, because mathematicians wish to treat matters of intuition mathematically, and make themselves ridiculous, wishing to begin with definitions and then with axioms, which is not the way to proceed in this kind of reasoning. Not that the mind does not do so, but it does it tacitly, naturally, and without technical rules; for the expression of it is beyond all men, and only a few can feel it.
Intuitive minds, on the contrary, being thus accustomed to judge at a single glance, are so astonished when they are presented with propositions of which they understand nothing, and the way to which is through definitions and axioms so sterile, and which they are not accustomed to see thus in detail, that they are repelled and disheartened.
But dull minds are never either intuitive or mathematical.
Mathematicians who are only mathematicians have exact minds, provided all things are explained to them by means of definitions and axioms; otherwise they are inaccurate and insufferable, for they are only right when the principles are quite clear.
And men of intuition who are only intuitive cannot have the patience to reach to first principles of things speculative and conceptual, which they have never seen in the world, and which are altogether out of the common.
2
There are different kinds of right understanding;[2] some have right understanding in a certain order of things, and not in others, where they go astray. Some draw conclusions well from a few premises, and this displays an acute judgment.
Others draw conclusions well where there are many premises.
For example, the former easily learn hydrostatics, where the premises are few, but the conclusions are so fine that only the greatest acuteness can reach them.
And in spite of that these persons would perhaps not be great mathematicians, because mathematics contain a great number of premises, and there is perhaps a kind of intellect that can search with ease a few premises to the bottom, and cannot in the least penetrate those matters in which there are many premises.
There are then two kinds of intellect: the one able to penetrate acutely and deeply into the conclusions of given premises, and this is the precise intellect; the other able to comprehend a great number of premises without confusing them, and this is the mathematical intellect. The one has force and exactness, the other comprehension. Now the one quality can exist without the other; the intellect can be strong and narrow, and can also be comprehensive and weak.
3
Those who are accustomed to judge by feeling do not understand the process of reasoning, for they would understand at first sight, and are not used to seek for principles. And others, on the contrary, who are accustomed to reason from principles, do not at all understand matters of feeling, seeking principles, and being unable to see at a glance.
4
Mathematics, intuition.—True eloquence makes light of eloquence, true morality makes light of morality; that is to say, the morality of the judgment, which has no rules, makes light of the morality of the intellect.
For it is to judgment that perception belongs, as science belongs to intellect. Intuition is the part of judgment, mathematics of intellect.
To make light of philosophy is to be a true philosopher.
5
Those who judge of a work by rule[3] are in regard to others as those who have a watch are in regard to others. One says, "It is two hours ago"; the other says, "It is only three-quarters of an hour." I look at my watch, and say to the one, "You are weary," and to the other, "Time gallops with you"; for it is only an hour and a half ago, and I laugh at those who tell me that time goes slowly with me, and that I judge by imagination. They do not know that I judge by my watch.[4]
6
Just as we harm the understanding, we harm the feelings also.
The understanding and the feelings are moulded by intercourse; the understanding and feelings are corrupted by intercourse. Thus good or bad society improves or corrupts them. It is, then, all-important to know how to choose in order to improve and not to corrupt them; and we cannot make this choice, if they be not already improved and not corrupted. Thus a circle is formed, and those are fortunate who escape it.
7
The greater intellect one has, the more originality one finds in men. Ordinary persons find no difference between men.
8
There are many people who listen to a sermon in the same way as they listen to vespers.
9
When we wish to correct with advantage, and to show another that he errs, we must notice from what side he views the matter, for on that side it is usually true, and admit that truth to him, but reveal to him the side on which it is false. He is satisfied with that, for he sees that he was not mistaken, and that he only failed to see all sides. Now, no one is offended at not seeing everything; but one does not like to be mistaken, and that perhaps arises from the fact that man naturally cannot see everything, and that naturally he cannot err in the side he looks at, since the perceptions of our senses are always true.
10
People are generally better persuaded by the reasons which they have themselves discovered than by those which have come into the mind of others.
11
All great amusements are dangerous to the Christian life; but among all those which the world has invented there is none more to be feared than the theatre. It is a representation of the passions so natural and so delicate that it excites them and gives birth to them in our hearts, and, above all, to that of love, principally when it is represented as very chaste and virtuous. For the more innocent it appears to innocent souls, the more they are likely to be touched by it. Its violence pleases our self-love, which immediately forms a desire to produce the same effects which are seen so well represented; and, at the same time, we make ourselves a conscience founded on the propriety of the feelings which we see there, by which the fear of pure souls is removed, since they imagine that it cannot hurt their purity to love with a love which seems to them so reasonable.
So we depart from the theatre with our heart so filled with all the beauty and tenderness of love, the soul and the mind so persuaded of its innocence, that we are quite ready to receive its first impressions, or rather to seek an opportunity of awakening them in the heart of another, in order that we may receive the same pleasures and the same sacrifices which we have seen so well represented in the theatre.
12
Scaramouch,[5] who only thinks of one thing.
The doctor,[6] who speaks for a quarter of an hour after he has said everything, so full is he of the desire of talking.
13
One likes to see the error, the passion of Cleobuline,[7] because she is unconscious of it. She would be displeasing, if she were not deceived.
14
When a natural discourse paints a passion or an effect, one feels within oneself the truth of what one reads, which was there before, although one did not know it. Hence one is inclined to love him who makes us feel it, for he has not shown us his own riches, but ours. And thus this benefit renders him pleasing to us, besides that such community of intellect as we have with him necessarily inclines the heart to love.
15
Eloquence, which persuades by sweetness, not by authority; as a tyrant, not as a king.
16
Eloquence is an art of saying things in such a way—(1) that those to whom we speak may listen to them without pain and with pleasure; (2) that they feel themselves interested, so that self-love leads them more willingly to reflection upon it.
It consists, then, in a correspondence which we seek to establish between the head and the heart of those to whom we speak on the one hand, and, on the other, between the thoughts and the expressions which we employ. This assumes that we have studied well the heart of man so as to know all its powers, and then to find the just proportions of the discourse which we wish to adapt to them. We must put ourselves in the place of those who are to hear us, and make trial on our own heart of the turn which we give to our discourse in order to see whether one is made for the other, and whether we can assure ourselves that the hearer will be, as it were, forced to surrender. We ought to restrict ourselves, so far as possible, to the simple and natural, and not to magnify that which is little, or belittle that which is great. It is not enough that a thing be beautiful; it must be suitable to the subject, and there must be in it nothing of excess or defect.
17
Rivers are roads which move,[8] and which carry us whither we desire to go.
18
When we do not know the truth of a thing, it is of advantage that there should exist a common error which determines the mind of man, as, for example, the moon, to which is attributed the change of seasons, the progress of diseases, etc. For the chief malady of man is restless curiosity about things which he cannot understand; and it is not so bad for him to be in error as to be curious to no purpose.
The manner in which Epictetus, Montaigne, and Salomon de Tultie[9] wrote, is the most usual, the most suggestive, the most remembered, and the oftenest quoted; because it is entirely composed of thoughts born from the common talk of life. As when we speak of the common error which exists among men that the moon is the cause of everything, we never fail to say that Salomon de Tultie says that when we do not know the truth of a thing, it is of advantage that there should exist a common error, etc.; which is the thought above.
19
The last thing one settles in writing a book is what one should put in first.
20
Order.—Why should I undertake to divide my virtues into four rather than into six? Why should I rather establish virtue in four, in two, in one? Why into Abstine et sustine[10] rather than into "Follow Nature,"[11] or, "Conduct your private affairs without injustice," as Plato,[12] or anything else? But there, you will say, everything is contained in one word. Yes, but it is useless without explanation, and when we come to explain it, as soon as we unfold this maxim which contains all the rest, they emerge in that first confusion which you desired to avoid. So, when they are all included in one, they are hidden and useless, as in a chest, and never appear save in their natural confusion. Nature has established them all without including one in the other.
21
Nature has made all her truths independent of one another. Our art makes one dependent on the other. But this is not natural. Each keeps its own place.
22
Let no one say that I have said nothing new; the arrangement of the subject is new. When we play tennis, we both play with the same ball, but one of us places it better.
I had as soon it said that I used words employed before. And in the same way if the same thoughts in a different arrangement do not form a different discourse, no more do the same words in their different arrangement form different thoughts!
23
Words differently arranged have a different meaning, and meanings differently arranged have different effects.
24
Language.—We should not turn the mind from one thing to another, except for relaxation, and that when it is necessary and the time suitable, and not otherwise. For he that relaxes out of season wearies, and he who wearies us out of season makes us languid, since we turn quite away. So much does our perverse lust like to do the contrary of what those wish to obtain from us without giving us pleasure, the coin for which we will do whatever is wanted.
25
Eloquence.—It requires the pleasant and the real; but the pleasant must itself be drawn from the true.
26
Eloquence is a painting of thought; and thus those who, after having painted it, add something more, make a picture instead of a portrait.
27
Miscellaneous. Language.—Those who make antitheses by forcing words are like those who make false windows for symmetry. Their rule is not to speak accurately, but to make apt figures of speech.
28
Symmetry is what we see at a glance; based on the fact that there is no reason for any difference, and based also on the face of man; whence it happens that symmetry is only wanted in breadth, not in height or depth.
29
When we see a natural style, we are astonished and delighted; for we expected to see an author, and we find a man. Whereas those who have good taste, and who seeing a book expect to find a man, are quite surprised to find an author. Plus poetice quam humane locutus es. Those honour Nature well, who teach that she can speak on everything, even on theology.
30
We only consult the ear because the heart is wanting. The rule is uprightness.
Beauty of omission, of judgment.
31
All the false beauties which we blame in Cicero have their admirers, and in great number.
32
There is a certain standard of grace and beauty which consists in a certain relation between our nature, such as it is, weak or strong, and the thing which pleases us.
Whatever is formed according to this standard pleases us, be it house, song, discourse, verse, prose, woman, birds, rivers, trees, rooms, dress, etc. Whatever is not made according to this standard displeases those who have good taste.
And as there is a perfect relation between a song and a house which are made after a good model, because they are like this good model, though each after its kind; even so there is a perfect relation between things made after a bad model. Not that the bad model is unique, for there are many; but each bad sonnet, for example, on whatever false model it is formed, is just like a woman dressed after that model.
Nothing makes us understand better the ridiculousness of a false sonnet than to consider nature and the standard, and then to imagine a woman or a house made according to that standard.
33
Poetical beauty.—As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and the reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry. We do not know the natural model which we ought to imitate; and through lack of this knowledge, we have coined fantastic terms, "The golden age," "The wonder of our times," "Fatal," etc., and call this jargon poetical beauty.[13]
But whoever imagines a woman after this model, which consists in saying little things in big words, will see a pretty girl adorned with mirrors and chains, at whom he will smile; because we know better wherein consists the charm of woman than the charm of verse. But those who are ignorant would admire her in this dress, and there are many villages in which she would be taken for the queen; hence we call sonnets made after this model "Village Queens."
34
No one passes in the world as skilled in verse unless he has put up the sign of a poet, a mathematician, etc. But educated people do not want a sign, and draw little distinction between the trade of a poet and that of an embroiderer.
People of education are not called poets or mathematicians, etc.; but they are all these, and judges of all these. No one guesses what they are. When they come into society, they talk on matters about which the rest are talking. We do not observe in them one quality rather than another, save when they have to make use of it. But then we remember it, for it is characteristic of such persons that we do not say of them that they are fine speakers, when it is not a question of oratory, and that we say of them that they are fine speakers, when it is such a question.
It is therefore false praise to give a man when we say of him, on his entry, that he is a very clever poet; and it is a bad sign when a man is not asked to give his judgment on some verses.
35
We should not be able to say of a man, "He is a mathematician," or "a preacher," or "eloquent"; but that he is "a gentleman." That universal quality alone pleases me. It is a bad sign when, on seeing a person, you remember his book. I would prefer you to see no quality till you meet it and have occasion to use it (Ne quid nimis[14]), for fear some one quality prevail and designate the man. Let none think him a fine speaker, unless oratory be in question, and then let them think it.
36
Man is full of wants: he loves only those who can satisfy them all. "This one is a good mathematician," one will say. But I have nothing to do with mathematics; he would take me for a proposition. "That one is a good soldier." He would take me for a besieged town. I need, then, an upright man who can accommodate himself generally to all my wants.
37
[Since we cannot be universal and know all that is to be known of everything, we ought to know a little about everything. For it is far better to know something about everything than to know all about one thing. This universality is the best. If we can have both, still better; but if we must choose, we ought to choose the former. And the world feels this and does so; for the world is often a good judge.]
38
A poet and not an honest man.
39
If lightning fell on low places, etc., poets, and those who can only reason about things of that kind, would lack proofs.
40
If we wished to prove the examples which we take to prove other things, we should have to take those other things to be examples; for, as we always believe the difficulty is in what we wish to prove, we find the examples clearer and a help to demonstration.
Thus when we wish to demonstrate a general theorem, we must give the rule as applied to a particular case; but if we wish to demonstrate a particular case, we must begin with the general rule. For we always find the thing obscure which we wish to prove, and that clear which we use for the proof; for, when a thing is put forward to be proved, we first fill ourselves with the imagination that it is therefore obscure, and on the contrary that what is to prove it is clear, and so we understand it easily.
41
Epigrams of Martial.—Man loves malice, but not against one-eyed men nor the unfortunate, but against the fortunate and proud. People are mistaken in thinking otherwise.
For lust is the source of all our actions, and humanity, etc. We must please those who have humane and tender feelings. That epigram about two one-eyed people is worthless,[15] for it does not console them, and only gives a point to the author's glory. All that is only for the sake of the author is worthless. Ambitiosa recident ornamenta.[16]
42
To call a king "Prince" is pleasing, because it diminishes his rank.
43
Certain authors, speaking of their works, say, "My book," "My commentary," "My history," etc. They resemble middle-class people who have a house of their own, and always have "My house" on their tongue. They would do better to say, "Our book," "Our commentary," "Our history," etc., because there is in them usually more of other people's than their own.
44
Do you wish people to believe good of you? Don't speak.
45
Languages are ciphers, wherein letters are not changed into letters, but words into words, so that an unknown language is decipherable.
46
A maker of witticisms, a bad character.
47
There are some who speak well and write badly. For the place and the audience warm them, and draw from their minds more than they think of without that warmth.
48
When we find words repeated in a discourse, and, in trying to correct them, discover that they are so appropriate that we would spoil the discourse, we must leave them alone. This is the test; and our attempt is the work of envy, which is blind, and does not see that repetition is not in this place a fault; for there is no general rule.
49
To mask nature and disguise her. No more king, pope, bishop—but august monarch, etc.; not Paris—the capital of the kingdom. There are places in which we ought to call Paris, Paris, and others in which we ought to call it the capital of the kingdom.
50
The same meaning changes with the words which express it. Meanings receive their dignity from words instead of giving it to them. Examples should be sought....
51
Sceptic, for obstinate.
52
No one calls another a Cartesian[17] but he who is one himself, a pedant but a pedant, a provincial but a provincial; and I would wager it was the printer who put it on the title of Letters to a Provincial.
53
A carriage upset or overturned, according to the meaning To spread abroad or upset, according to the meaning. (The argument by force of M. le MaÎtre[18] over the friar.)
54
Miscellaneous.—A form of speech, "I should have liked to apply myself to that."
55
The aperitive virtue of a key, the attractive virtue of a hook.
56
To guess: "The part that I take in your trouble." The Cardinal[19] did not want to be guessed.
"My mind is disquieted." I am disquieted is better.
57
I always feel uncomfortable under such compliments as these: "I have given you a great deal of trouble," "I am afraid I am boring you," "I fear this is too long." We either carry our audience with us, or irritate them.
58
You are ungraceful: "Excuse me, pray." Without that excuse I would not have known there was anything amiss. "With reverence be it spoken...." The only thing bad is their excuse.
59
"To extinguish the torch of sedition"; too luxuriant. "The restlessness of his genius"; two superfluous grand words.
