Pascal Knew Men and Triangles

Thursday, 23 January 2014

Blaise Pascal

Blaise Pascal (1623–1662).  The Art of Persuasion, Minor Works.

(Pascal publishes "Provincial Letters," Jan. 23, 1656.)
Pascal, the keen-minded philosopher and mathematician, fathomed the human traits of man's nature with the same accurate measurements which made him famous in the realm of geometry. Read his searching analysis of man's conceit.

THE ART of persuasion has a necessary relation to the manner in which men are led to consent to that which is proposed to them, and to the conditions of things which it is sought to make them believe.

  No one is ignorant that there are two avenues by which opinions are received into the soul, which are its two principal powers: the understanding and the will. The more natural is that of the understanding, for we should never consent to any but demonstrated truths; but the more common, though the one contrary to nature, is that of the will; for all men are almost led to believe not of proof, but by attraction. This way is base, ignoble, and irrelevant: every one therefore disavows it. Each one professes to believe and even to love nothing but what he knows to be worthy of belief and love.

  I do not speak here of divine truths, which I shall take care not to comprise under the art of persuasion, because they are infinitely superior to nature: God alone can place them in the soul and in such a way as it pleases him. I know that he has desired that they should enter from the heart into the mind, and not from the mind into the heart, to humiliate that proud power of reasoning that pretends to the right to be the judge of the things that the will chooses; and to cure this infirm will which is wholly corrupted by its filthy attachments. And thence it comes that whilst in speaking of human things, we say that it is necessary to know them before we can love them, which has passed into a proverb, (1) the saints on the contrary say in speaking of divine things that it is necessary to love them in order to know them, and that we only enter truth through charity, from which they have made one of their most useful maxims.

  From which it appears that God has established this super-natural order, which is directly contrary to the order that should be natural to men in natural things. They have nevertheless corrupted this order by making of profane things what they should make of holy things, because in fact we believe scarcely any thing except that which pleases us. And thence comes the aversion which we have to consenting to the truths of the Christian religion that are opposed to our pleasures. “Tell us of pleasant things and we will hearken to you,” said the Jews to Moses; as if the agreeableness of a thing should regulate belief! And it is to punish this disorder by an order which is conformed to him, that God only pours out his light into the mind after having subdued the rebellion of the will by an altogether heavenly gentleness which charms and wins it.

  I speak therefore only to the truths within our reach; and it is of them that I say that the mind and the heart are as doors by which they are received into the soul, but that very few enter by the mind, whilst they are brought in in crowds by the rash caprices of the will, without the counsel of the reason.

  These powers have each their principles and their main-springs of action.

  Those of the mind are truths which are natural and known to all the world, as that the whole is greater than its part, besides several particular maxims that are received by some and not by others, but which as soon as they are admitted are as powerful, although false, in carrying away belief, as those the most true.

  Those of the will are certain desires natural and common to all mankind, as the desire of being happy, which no one can avoid having, besides several particular objects which each one follows in order to attain, and which having the power to please us are as powerful, although pernicious in fact, in causing the will to act, as though they made its veritable happiness.

  So much for that which regards the powers that lead us to consent.

  But as for the qualities of things which should persuade us, they are very different.

  Some are drawn, by a necessary consequence, from com-mon principles and admitted truths. These may be infallibly persuasive; for in showing the harmony which they have with acknowledged principles there is an inevitable necessity of conviction, and it is impossible that they shall not be received into the soul as soon as it has been enabled to class them among the principles which it has already admitted.

  There are some which have a close connection with the objects of our satisfaction; and these again are received with certainty, for as soon as the soul has been made to perceive that a thing can conduct it to that which it loves supremely, it must inevitably embrace it with joy.

  But those which have this double union both with admitted truths and with the desires of the heart, are so sure of their effect that there is nothing that can be more so in nature.

  As, on the contrary, that which does not accord either with our belief or with our pleasures is importunate, false, and absolutely alien to us.

  In all these positions, there is no room for doubt. But there are some wherein the things which it is sought to make us believe are well established upon truths which are known, but which are at the same time contrary to the pleasures that interest us most. And these are in great danger of showing, by an experience which is only too common, what I said at the beginning—that this imperious soul, which boasted of acting only by reason, follows by a rash and shameful choice the desires of a corrupt will, whatever resistance may be opposed to it by the too enlightened mind.

  Then it is that a doubtful balance is made between truth and pleasure, and that the knowledge of the one and the feeling of the other stir up a combat the success of which is very uncertain, since, in order to judge of it, it would be necessary to know all that passes in the innermost spirit of the man, of which the man himself is scarcely ever conscious.

  It appears from this, that whatever it may be of which we wish to persuade men, it is necessary to have regard to the person whom we wish to persuade, of whom we must know the mind and the heart, what principles he acknowledges, what things he loves; and then observe in the thing in question what affinity it has with the acknowledged principles, or with the objects so delightful by the pleasure which they give him.

  So that the art of persuasion consists as much in that of pleasing as in that of convincing, so much more are men governed by caprice than by reason!

  Now, of these two methods, the one of convincing, the other of pleasing, I shall only give here the rules of the first; and this in case we have granted the principles, and remain firm in avowing them: otherwise I do not know whether there could be an art for adapting proofs to the inconstancy of our caprices.

  But the manner of pleasing is incomparably more difficult, more subtle, more useful, and more admirable; therefore, if I do not treat of it, it is because I am not capable of it; and I feel myself so far disproportionate to the task, that I believe the thing absolutely impossible.

  Not that I do not believe that there may be as sure rules for pleasing as for demonstrating, and that he who knows perfectly how to comprehend and to practice them will as surely succeed in making himself beloved by princes and by people of all conditions, as in demonstrating the elements of geometry to those who have enough imagination to comprehend its hypotheses. But I consider, and it is, perhaps, my weakness that makes me believe it, that it is impossible to reach this. At least I know that if any are capable of it, they are certain persons whom I know, and that no others have such clear and such abundant light on this matter.

  The reason of this extreme difficulty comes from the fact that the principles of pleasure are not firm and stable. They are different in all mankind, and variable in every particular with such a diversity that there is no man more different from another than from himself at different times. A man has other pleasures than a woman; a rich man and a poor man have different enjoyments; a prince, a warrior, a merchant, a citizen, a peasant, the old, the young, the well, the sick, all vary; the least accidents change them.

  Now there is an art, and it is that which I give, for showing the connection of truths with their principles, whether of truth or of pleasure, provided that the prin-ciples which have once been avowed remain firm, and without being ever contradicted.

  But as there are few principles of this kind, and as, a part from geometry, which deals only with very simple figures, there are hardly any truths upon which we always remain agreed, and still fewer objects of pleasure which we do not change every hour, I do not know whether there is a means of giving fixed rules for adapting discourse to the inconstancy of our caprices.

  This art, which I call the art of persuading, and which, properly speaking, is simply the process of perfect methodical proofs, consists of three essential parts: of defining the terms of which we should avail ourselves by clear definitions; of proposing principles or evident axioms to prove the thing in question; and of always mentally substituting in the demonstrations the definition in the place of the thing defined.

  The reason of this method is evident, since it would be useless to propose what it is sought to prove, and to undertake the demonstration of it, if all the terms which are not intelligible had not first been clearly defined; and since it is necessary in the same manner that the demonstration should be preceded by the demand for the evident principles that are necessary to it, for if we do not secure the foundation we cannot secure the edifice; and since, in fine, it is necessary in demonstrating mentally, to substitute the definitions in the place of the things defined, as otherwise there might be an abuse of the different meanings that are encountered in the terms. It is easy to see that, by observing this method, we are sure of convincing, since the terms all being understood, and perfectly exempt from ambiguity by the definitions, and the principles being granted, if in the demonstration we always mentally substitute the definitions for the things defined, the invincible force of the conclusions cannot fail of having its whole effect.

  Thus, never can a demonstration in which these conditions have been observed be subject to the slightest doubt; and never can those have force in which they are wanting.

  It is, therefore, of great importance to comprehend and to possess them; and hence, to render the thing easier and more practicable, I shall give them all in a few rules which include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the art of persuading.

Rules for Definitions

  I. Not to undertake to define any of the things so well known of themselves that clearer terms cannot be had to explain them.

  II. Not to leave any terms that are at all obscure or ambiguous without definition.

  III. Not to employ in the definition of terms any words but such as are perfectly known or already explained.

Rules for Axioms

  I. Not to omit any necessary principle without asking whether it is admitted, however clear and evident it may be.

  II. Not to demand, in axioms, any but things that are perfectly evident of themselves.

Rules for Demonstrations

  I. Not to undertake to demonstrate any thing that is so evident of itself that nothing can be given that is clearer to prove it.

  II. To prove all propositions at all obscure, and to employ in their proof only very evident maxims or propositions already admitted or demonstrated.

  III. To always mentally substitute definitions in the place of things defined, in order not to be misled by the ambiguity of terms which have been restricted by definitions.

  These eight rules contain all the precepts for solid and immutable proofs, three of which are not absolutely necessary and may be neglected without error; while it is difficult and almost impossible to observe them always exactly, although it is more accurate to do so as far as possible; these are the three first of each of the divisions.

  For definitions. Not to define any terms that are perfectly known.

  For axioms. Not to omit to require any axioms perfectly evident and simple.

  For demonstrations. Not to demonstrate any things well-known of themselves.

  For it is unquestionable that it is no great error to define and clearly explain things, although very clear of themselves, nor to omit to require in advance axioms which cannot be refused in the place where they are necessary; nor lastly to prove propositions that would be admitted without proof.

  But the five other rules are of absolute necessity, and cannot be dispensed with without essential defect and often without error; and for this reason I shall recapitulate them here in detail.

  Rules necessary for definitions. Not to leave any terms at all obscure or ambiguous without definition;

  Not to employ in definitions any but terms perfectly known or already explained.

  Rule necessary for axioms. Not to demand in axioms any but things perfectly evident.

  Rules necessary for demonstrations. To prove all propositions, and to employ nothing for their proof but axioms fully evident of themselves, or propositions already demonstrated or admitted;

  Never to take advantage of the ambiguity of terms by failing mentally to substitute definitions that restrict and explain them.

  These five rules form all that is necessary to render proofs convincing, immutable, and to say all, geometrical; and the eight rules together render them still more perfect.

  I pass now to that of the order in which the propositions should be arranged, to be in a complete geometrical series.

  After having established (2) …

  This is in what consists the art of persuading, which is comprised in these two principles: to define all the terms of which we make use; to prove them all by mentally substituting definitions in the place of things defined.

  And here it seems to me proper to anticipate three principal objections which may be made:

  1st, that this method has nothing new; 2d, that it is very easy to learn, it being unnecessary for this to study the elements of geometry, since it consists in these two words that are known at the first reading; and, 3d, that it is of little utility, since its use is almost confined to geometrical subjects alone.

  It is necessary therefore to show that there is nothing so little known, nothing more difficult to practise, and nothing more useful or more universal.

  As to the first objection, that these rules are common in the world, that it is necessary to define every thing and to prove every thing, and that logicians themselves have placed them among the principles of their art, I would that the thing were true and that it were so well known that I should not have the trouble of tracing with so much care the source of all the defects of reasonings which are truly so common. But so little is this the case, that, geometricians alone excepted, who are so few in number that they are single in a whole nation and long periods of time, we see no others who know it. It will be easy to make this understood by those who have perfectly comprehended the little that I have said; but if they have not fully comprehended this, I confess that they will learn nothing from it.

  But if they have entered into the spirit of these rules, and if the rules have made sufficient impression on them to become rooted and established in their minds, they will feel how much difference there is between what is said here and what a few logicians may perhaps have written by chance approximating to it in a few passages of their works.

  Those who have the spirit of discernment know how much difference there is between two similar words, according to their position, and the circumstances that accompany them. Will it be maintained, indeed, that two persons who have read the same book, and learned it by heart, have a like acquaintance with it, if the one comprehends it in such a manner that he knows all its principles, the force of its conclusions, the answers to the objections that may be made to it, and the whole economy of the work; while to the other these are but dead letters and seeds, which, although like those which have produced such fruitful trees, remain dry and unproductive in the sterile mind that has received them in vain.

  All who say the same things do not possess them in the same manner; and hence the incomparable author of the Art of Conversation (3) pauses with so much care to make it understood that we must not judge of the capacity of a man by the excellence of a happy remark that we have heard him make; but instead of extending our admiration of a good speech to the speaker, let us penetrate, says he, the mind from which it proceeds; let us try whether he owes it to his memory, or to a happy chance; let us receive it with coldness and contempt, in order to see whether he will feel that we do not give to what he says the esteem which its value deserves: it will oftenest be seen that he will be made to disavow it on the spot, and will be drawn very far from this better thought in which he does not believe, to plunge himself into another quite base and ridiculous. We must, therefore, sound in what manner this thought is lodged in its author; (4) how, whence, to what extent he possesses it; otherwise, the hasty judgment will be a rash judge.

  I would inquire of reasonable persons whether this principle: Matter is naturally wholly incapable of thought, and this other: I think, therefore I am, are in fact the same in the mind of Descartes, and in that of St. Augustine,, who said the same thing twelve hundred years before. (5)

  In truth, I am far from affirming that Descartes is not the real author of it, even though he may have learned it only in reading this distinguished saint; for I know how much difference there is between writing a word by chance without making a longer and more extended reflection on it, and perceiving in this word an admirable series of conclusions, which prove the distinction between material and spiritual natures, and making of it a firm and sustained principle of a complete metaphysical system, as Descartes has pretended to do. For without examining whether he has effectively succeeded in his pretension, I assume that he has done so, and it is on this supposition that I say that this expression is as different in his writings from the same saying in others who have said it by chance, as is a man full of life and strength from a corpse.

  One man will say a thing of himself without comprehending its excellence, in which another will discern a marvellous series of conclusions, which make us affirm boldly that it is no longer the same expression, and that he is no more indebted for it to the one from whom he has learned it, than a beautiful tree belongs to the one who cast the seed, without thinking of it, or knowing it, into the fruitful soil which caused its growth by its own fertility.

  The same thoughts sometimes put forth quite differently in the mind of another than in that of their author: unfruitful in their natural soil, abundant when transplanted. But it much oftener happens that a good mind itself makes its own thoughts produce all the fruit of which they are capable, and that afterwards others, having heard them admired, borrow them, and adorn themselves with them, but without knowing their excellence; and it is then that the difference of the same word in different mouths is the most apparent.

  It is in this manner that logic has borrowed, perhaps, the rules of geometry, without comprehending their force; and thus, in placing them by chance among those that belong to it, it does not thence follow that they (6) have entered into the spirit of geometry, and I should be greatly averse if they gave no other evidence of it than that of having mentioned it by chance, to placing them on a level with that science that teaches the true method of directing the reason.

  But I should be, on the contrary, strongly disposed to exclude them from it, and almost irrevocably. For to have said it by chance, without having taken care that every thing was included within it, and instead of following this light to wander blindly in useless researches, pursuing what they promise but never can give, is truly showing that they are not very clear-sighted, and much more than if they had failed to follow the light, because they had not perceived it.

  The method of not erring is sought by all the world. The logicians profess to guide to it, the geometricians alone attain it, and apart from their science, and the imitations of it, there are no true demonstrations. The whole art is included in the simple precepts that we have given; they alone are sufficient, they alone afford proofs; all other rules are useless or injurious. This I know by long experience of all kinds of books and persons.

  And on this point I pass the same judgment as those who say that geometricians give them nothing new by these rules, because they possessed them in reality, but confounded with a multitude of others, either useless or false, from which they could not discriminate them, as those who, seeking a diamond of great price amidst a number of false ones, but from which they know not how to distinguish it, should boast, in holding them all together, of possessing the true one equally with him who without pausing at this mass of rubbish lays his hand upon the costly stone which they are seeking and for which they do not throw away the rest.

  The defect of false reasoning is a malady which is cured by these two remedies. Another has been compounded of an infinity of useless herbs in which the good are enveloped and in which they remain without effect through the ill qualities of the compound.

  To discover all the sophistries and equivocations of captious reasonings, they have invented barbarous names that astonish those who hear them; and whilst we can only unravel all the tangles of this perplexing knot by drawing out one of the ends in the way proposed by geometricians, they have indicated a strange number of others in which the former are found included without knowing which is the best.

  And thus, in showing us a number of paths which they say conduct us whither we tend, although there are but two that lead to it, it is necessary to know how to mark them in particular. It will be pretended that geometry which indicates them with certainty gives only what had already been given by others, because they gave in fact the same thing and more, without heeding that this boon lost its value by abundance, and was diminished by adding to it.

  Nothing is more common than good things: the point in question is only to discriminate them; and it is certain that they are all natural and within our reach and even known to all mankind. But they know not how to distinguish them. This is universal. It is not among extraordinary and fantastic things that excellence is to be found, of whatever kind it may be. We rise to attain it and become removed from it: it is oftenest necessary to stoop for it. The best books are those, which those who read them believe they themselves could have written. Nature, which alone is good, is wholly familiar and common.

  I make no doubt therefore that these rules, being the true ones, are simple, artless, and natural, as in fact they are. It is not Barbara and Baralipton that constitute reasoning. The mind must not be forced; artificial and constrained manners fill it with foolish presumption, through unnatural elevation and vain and ridiculous inflation, instead of solid and vigorous nutriment. And one of the principal reasons that diverts those who are entering upon this knowledge so much from the true path which they should follow, is the fancy that they take at the outset that good things are inaccessible, giving them the name of great, lofty, elevated, sublime. This destroys every thing. I would call them low, common, familiar:these names suit them better; I hate such inflated expressions.

Note 1. Ignoti nulla cupido—”We do not desire what we do not know.”
Note 2. The rest of the phrase is wanting; and all this second part of the composition, either because it was not redacted by Pascal, or because it has been lost, is found neither in our MS. nor in Father Desmolets.—Faugère.
Note 3. Montaigne, Essais, liv. III, chap. viii.—Faugère.
Note 4. Montaigne’s expression is: “Feel on all sides how it is lodged in its author.” Essais,same chapter.—Ibid.
Note 5. Civ. Dei, l. XI, c. xxvi.
Note 6. Doubtless the logicians.—Faugère.

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