Obrázky na stránke
PDF
ePub

which he governs the world. It is evident by their writings, that they meant it in no sense which interferes with the liberty of human actions." Of the truth of this remark the most satisfactory evidence is afforded by the very first sentence of the Enchiridion of Epictetus, in which it is explicitly stated, "That opinion, pursuit, desire, and aversion, and, in one word, whatever are our own actions are in our own power."*

Such, too, is the philosophy of Virgil:

"Stat sua cuique dies, breve et irreparabile tempus

Omnibus est vitæ ; sed famam extendere factis
Hoc virtutis opus."†

The doctrine, however, of fatalism, and of an inevitable destiny, must not be confounded with that of the Divine prescience, between which and the freedom of human actions some of our profoundest philosophers, as I have already observed, (particularly Clarke and Reid,) have labored to show that there is no inconsistency,‡ while other writers, of no less eminence, have apprehended that there is no absurdity in supposing that the Deity may, for wise purposes, have chosen to open a source of contingency in the voluntary actions of his creatures, to which no prescience can possibly extend.

Whatever opinion we may adopt on this point, the conclusions formerly stated concerning man's free agency remain unshaken. Our own free will we know by our consciousness; and we can have no evidence for any other truth so irresistible as this. On the other hand, it would unquestionably be rash and impious in us, from the fact of our own free will, to deny that our actions may be foreseen by the Deity, or to measure the Divine attributes by a standard borrowed from our imperfect faculties. The conclusion of St. Augustine on this subject is equally pious and philosophical. "Wherefore we are nowise reduced to the necessity, either by admitting the prescience of God, to deny the freedom of the human will, or by admitting the freedom of the will, to hazard the impious assertion, that the prescience of God does not extend to all future contingencies: But, on the contrary, we are disposed to embrace both doctrines, and with sincerity to bear testimony to their truth, the one that our faith may be sound, the other that our lives may be good.” §

That the doctrine of fatalism, however, led some of the Stoics to very impious and alarming consequences, appears from the following words, which Lucan puts into the mouth of Cato.

"Summum, Brute, nefas civilia bella fatemur,
Sed quo fata trahunt, virtus secura sequetur.
Crimen erit superis et me fecisse nocentem."
Phar. ii. 254.

See also the Seventh Book of the Pharsalia, line 657.-Copleston, Prælect. Acad. p. 277.

†The notions of Virgil, however, on this point, as is well observed by Servius, do not seem to have been quite consistent. How are the following lines, which he applies to Dido, to be reconciled with the above passage?

"Nam quia nec fato, meritâ nec morte peribat;
Sed misera ante diem."-Æn. Lib. iv. l. 695.

So also Milton:

§ Note (B.)

"If I foreknew, Foreknowledge had no influence on their fault, Which had no less prov'd certain unforeseen."

APPENDIX II.

(See p. 325.)

AMONG the later philosophers on the continent, the advocates for atheism seem to me to lay the chief stress on the old Epicurean argument, as stated by Lucretius. The sceptical suggestions on the same subject which occur in Mr. Hume's Essay on the idea of Necessary Connexion, and which have given occasion to so much discussion in this country, do not seem to have ever produced any considerable impression on the French philosophers. Very few of the number, I am inclined to think, have thoroughly comprehended their impott and tendency.*

"Nam certè neque consilio primordia rerum

Ordine se quæque, atque sagaci mente locârunt;
Nec quos quæque darent motus pepigêre profectò ;
Sed quia multimodis, multis, mutata, per omne
Ex infinito vexantur percita plagis,
Omne genus motûs et cœtûs experiundo,
Tandem deveniunt in taleis disposituras,
Qualibus hæc rebus consistit summa creata." †

And still more explicitly in the following lines :

"Nam cum respicias immensi temporis omne
Præteritum spatium; tum motus materiaï
Multimodi quam sint; facile hoc accredere possis,

Semina sæpe in eodem, ut nunc sunt, ordine pôsta." ‡

To this argument Diderot repeatedly refers in his voluminous writings; and even sometimes steps out of his way to introduce it; a remarkable instance of which occurs in his Traité du Beau, and also in the article Beau in the Encyclopédie.

"Le beau n'est pas toujours l'ouvrage d'une cause intelligente; le mouvement établit souvent, soit dans un être considéré solitairement, soit entre plusieurs êtres comparés entr'eux, une multitude prodigieuse de rapports surprenans. Les cabinets d'histoire naturelle en offrent un grand nombre d'exemples. Les rapports sont alors des résultats de combinaisons fortuites, du moins par rapport à nous. La nature imite, en se jouant, dans cent occasions, les productions d'art; et l'on pourroit demander, je ne dis pas si ce philosophe qui fut jeté par une tempête sur les bords d'une île inconnue, avoit raison de s'écrier, à la vue de quelques figures de géométrie; Courage, mes amis, voici des pas d'hommes; mais combien il faudroit marquer de rapports dans un être, pour avoir une certitude complète qu'il est l'ouvrage d'un artiste § (en quelle occasion, un seul défaut de symmétrie prouveroit plus que toute somme donnée de rapports); comment sont entr'eux le tems de

According to De Gérando, (Hist. Comparée, Tome II. pp. 151, 152,) Mendelsohn was the first who thought of opposing Hume's Scepticism about Cause and Effect, by considerations drawn from the calculus of probabilities. This statement is confirmed by Lacroix, who refers for further information to Mendelsohn's Treatise on Evidence, which obtained the prize from the Academy of Berlin in 1763. De Gérando himself, in his Traité des Signes et de l'Art de Penser, (published l'an viii.) has adopted the same view of the subject, without being then aware (as he assures us himself) that he had been anticipated in this speculation by Mendelsohn. (Ibid. p. 155.) Lacroix remarks the coincidence of opinion of these different authors, with some hints suggested by Helvetius, in a note on the first chapter of the first discourse, in his work entitled l'Esprit.-(Traité Elémentaire du Calcul des Probabilités.)

† Lucret. Lib. i. 1. 1020.

Lucret. Lib. iii. 1. 867.

Is not this precisely the sophistical mode of questioning known among logicians by the name of Sorites or Acervus? "Vitiosum sane," says Cicero, "et captiosum genus."-Acad. Quæst. Lib. iv. xvi.

l'action de la cause fortuite et les rapports observés dans les effets produits; et si (á l'exception des œuvres du Tout-puissant) il y a des cas où le nombre des rapports ne puisse jamais être compensé par celui des jets." This passage forms the conclusion of the article Beau in the French Encyclopédie, and, notwithstanding the parenthetical salvo in the last clause, the drift of the argument is sufficiently obvious. In one of the articles, however, of his Pensées Philosophiques, Diderot has explained his meaning on this subject much more fully.

"J'ouvre les cahiers d'un philosophe célèbre, et je lis: 'Athées, je vous accorde que le mouvement est essentiel à la matière; qu'en concluez-vous? que le monde résulte du jet fortuit des atômes? j'aimerois autant que vous me dissiez que l'Iliade d'Homère ou la Henriade de Voltaire est un résultat de jets fortuits de caractères.'" -"Je me garderai bien de faire ce raisonnement à un Athée. Cette comparaison lui donneroit beau jeu. Selon les lois de l'analyse des sorts, me diroit-il, je ne dois point être surpris qu'une chose arrive, lorsqu'elle est possible, et que la difficulté de l'événement est compensée par la quantité des jets. Il y a tel nombre de coups dans lesquels je gagerois avec avantage d'amener cent mille six à-la-fois avec cent mille dez. Quelle que fût la somme finie de caractères avec laquelle on me proposeroit d'engendrer fortuitement l'Iliade, il y a telle somme finie de jets qui me rendroit la proposition avantageuse; mon avantage seroit même infinie, si la quantité de jets accordée étoit infinie."*

The very same reasoning, in substance, has been since brought forward by different French mathematicians; among others, by the justly celebrated Laplace, in his Philosophical Essay on Probabilities. I shall quote at length one of his most remarkable reasonings.

“Au milieu des causes variables et inconnues que nous comprenons sous le nom de hazard, et qui rendent incertaine et irrégulière la marche des événemens; on voit naître à mesure qu'ils se multiplient, une régularité frappante qui semble tenir à un dessein, et que l'on a considérée comme une preuve de la Providence qui gouverne le monde. Mais en y réfléchissant, on reconnoît bientôt que cette régularité n'est que le developpement des possibilités respectives des événemens simples qui doivent se présenter plus souvent lorsqu'ils sont plus probables. Concevons, par exemple, une urne qui renferme des boules blanches et des boules noires; et supposons qu'à chaque fois que l'on en tire une boule, on la remette dans l'urne pour proceder à un nouveau tirage. Le rapport du nombre des boules blanches extraites, au nombre des boules noires extraites, sera le plus souvent très irrégulier dans les premiers tirages; mais les causes variables de cette irrégularité, produisent des effets alternativement favorables et contraires à la marche régulière des événemens, et qui se détruisant mutuellement dans l'ensemble d'un grand nombre de tirages, laissent de plus en plus apperçevoir le rapport des boules blanches aux boules noires contenues dans l'urne, ou les possibilités respectives d'en extraire une boule blanche ou une boule noire à chaque tirage. De la résulte le théoréme suivant.

"La probabilité que le rapport du nombre des boules blanches extraites, au nombre total des boules sorties, ne s'écarte pas au delà d'un intervalle donné, du rapport du nombre des boules blanches, au nombre total des boules contenues dans l'urne, approche indefiniment de la certitude, par la multiplication indéfinie des événemens, quelque petit que l'on suppose cet intervalle.

"On peut tirer du théorème précédent, cette conséquence qui doit être regardée comme une loi générale, savoir, que les rapports des effets de la nature, sont à fort

Pensées Philosophiques, xxi. See first volume of his work. Naigeon's edition. With respect to the passages here extracted from Diderot, it is worthy of observation, that, if the atheistical argument from chances be conclusive in its application to that order of things which we behold, it is not less conclusive when applied to every other possible combination of atoms which imagination can conceive; and affords a mathematical proof, that the fables of Grecian mythology, the tales of the Genii, and the dreams of the Rosicrucians, may, or rather must, all of them be somewhere realized in the infinite extent of the universe; a proposition which, if true, would destroy every argument for or against any given system of opinions founded on the reasonableness or the unreasonableness of the tenets involved in it; and would, of consequence, lead to the subversion of the whole frame of the human understanding.

I have pursued this argument further in the Dissertation prefixed to the Encyclopædia Britannica, Part ii. pp. 241, 242, 243.

peu près constans, quand ces effets sont considérés en grand nombre. Ainsi malgré la variété des années, la somme des productions pendant un nombre d'années considérable, est sensiblement la même; en sorte que l'homme, par une utile prévoyance, peut se mettre à l'abri de l'irrégularité des saisons, en répandant également sur tous les temps, les biens que la nature distribue d'une manière inégale. Je n'excepte pas de la loi précédente, les effets dus aux causes morales. Le rapport des naissances annuelles à la population, et celui des mariages aux naissances, n'éprouvent que de très-petites variations: à Paris, le nombre des naissances annuelles a toujours été le même à peu près; et j'ai ouï dire qu'à la poste, dans les temps ordinaires, le nombre des lettres mises au rebut par les défauts des adresses, change peu, chaque année; ce qui a été pareillement observé à Londres.

"Il suit encore de ce théorème, que dans une série d'événemens, indéfiniment prolongée, l'action des causes régulières et constantes doit l'emporter à la longue, sur celle des causes irrégulières.

"Si l'on applique ce théorème au rapport des naissances des garçons, à celles des filles, observé dans les diverses parties de l'Europe; on trouve que ce rapport, partout à peu près égal à celui de 22 à 21, indique avec une extrême probabilité, une plus grande facilité dans les naissances des garçons. En considérant ensuite qu'il est le même à Naples qu'à Pétersbourg, on verra qu'à cet égard, l'influence du climat est insensible. On pouvoit donc soupçonner contre l'opinion commune, que cette supériorité des naissances masculines subsiste dans l'Orient même. J'avais en conséquence invité les savans Français envoyés en Egypte, à s'occuper de cette question intéressante; mais la difficulté d'obtenir des renseignemens précis sur les naissances ne leur a pas permis de la résoudre. Heureusement, Humboldt n'a point négligé cet objet dans l'immensité des choses nouvelles qu'il a observées et recueillies en Amérique, avec tant de sagacité, de constance et de courage. Il a retrouvé entre les tropiques le même rapport des naissances des garçons à celles des filles, que l'on observe à Paris; ce qui doit faire regarder la superiorité des naissances masculines comme une loi générale de l'espèce humaine. Les lois que suivent à cet égard les divers espèces d'animaux, me paraissent dignes de l'attention des naturalistes."*

From these quotations, it appears that the constancy in the proportion of births to the whole population of a country, in that of births to marriages, and in that of male children to females, are considered by Laplace as facts of the same kind, and to be accounted for in the same way with the very narrow limits within which the number of misdirected letters in the General Post-Office of Paris varies from year to year. The same thing, he tells us, has been observed in the Dead-Letter Office at London. But as he mentions both these last facts merely on the authority of a hearsay, I do not know to what degree of credit they are entitled, and I shall therefore leave them entirely out of our consideration in the present argument. The meaning which Laplace wished to convey by this comparison cannot be mistaken.

Among the different facts in political arithmetic here alluded to by Laplace, that of the constancy in the proportion of male to female births (which he himself pronounces to be a general law of our species) is the most analogous to the example of the urn containing a mixture of white and of black balls, from which he deduces his general theorem. I shall accordingly select this in preference to the others. The intelligent reader will at once perceive that the same reasoning is equally applicable to all of them.

Let us suppose, then, that the white balls in Laplace's urn represent male infants, and the black balls female infants, upon which supposition, the longer that the operation (described by Laplace) of drawing and returning the balls is continued, the nearer will the proportion of white to black balls approach to that of 22 to 21. What inference (according to Laplace's own theorem) ought we to deduce from this, but that the whole number of white balls in the urn is to the whole number of black balls in the same proportion of 22 to 21; or, in other words, that this is the proportion of the whole number of unborn males to the whole number of unborn females in the womb of futurity? And yet this inference is regarded by Laplace as a proof that the approximation to equality in the number of the two sexes affords no evidence of foresight or design.

* Essai Philosophique sur les Probabilités, par M, le Comte Laplace. 3me Ed. pp. 73, 74, 75, 76. See Note (C.)

[blocks in formation]

"La constance de la supériorité des naissances des garçons sur celles des filles, à Paris et à Londres, depuis qu'on les observe, a paru à quelques savans, être une preuve de la Providence sans laquelle ils ont pensé que les causes irrégulières qui troublent sans cesse la marche des événemens, auroit du plusieurs fois rendre les naissances annuelles des filles, supérieures à celle des garçons.

"Mais cette preuve est un nouvel exemple de l'abus que l'on a fait si souvent des causes finales qui disparaissent toujours par un examen approfondi des questions, lorsqu'on a les données nécessaires pour les résoudre. La constance dont il s'agit, est un résultat des CAUSES REGULIERES qui donnent la supériorité aux naissances des garçons, et qui l'emportent sur les anomalies dues au hazard, lorsque le nombre des naissances annuelles est considérables."*

With the proposition announced in the last sentence I perfectly agree. That the constancy of the results in the instance now in question depends on regular causes, (which in this case is merely a synonymous expression with general laws,) the most zealous advocates for a designing cause will be the most forward to admit; and if Laplace means nothing more than to say, that the uniformity of the effect, when observed on a large scale, may be sufficiently explained without supposing the miraculous interference of Providence in each individual birth, the question does not seem worthy of a controversy. If the person who put the white and black balls into the urn had wished to secure the actual result of the drawing, what other means could he have employed for the purpose, than to adjust to each other the relative proportions of these balls in the whole number of both? Could any proof more demonstrative be given, that this was the very end he had in view?

Nor do I think that the authors whom Laplace opposes ever meant to dispute the operation of these regular causes. Dr. Arbuthnot, certainly, one of the earliest writers in this country, who brought forward the regular proportion between male and female births as an argument in favor of wise design, not only agrees in this point with Laplace, but has proposed a physical theory to account for this regularity. The theory is indeed too ludicrous to deserve a moment's consideration: but it at least shows that Laplace has advanced nothing in favor of his conclusions, which had not been previously granted by his adversaries.

APPENDIX III.

THE following strictures on the Philosophical Essay of Laplace have all a reference, more or less direct, to the argument stated in the foregoing Appendix.

Under the general title of the doctrine of Probabilities, two very different things are confounded together by Laplace, as well as by many other writers of an earlier date. The one is the purely mathematical theory of chances; the other, the inductive anticipations of future events deduced from observations on the past course of nature. The calculations about dice furnish the simplest of all examples of the first sort of theory. The conclusions to which they lead are as rigorously exact as any other arithmetical propositions; amounting to nothing more than a numerical statement of the ways in which a given event may happen, compared with those in which it may not happen. Thus, in the case of a single die, the chance that ace shall turn up at the first throw, is to the chances against that event as one to five. The more complicated cases of the problem all depend on the application of the same fundamental principle. "This principle," as Condorcet has well remarked, "is only a definition (une verité de définition;) and consequently the calculations founded on it are all rigorously true."†

To this theory of chances Laplace labors, through the whole of his work, to assimilate all the other cases in which mathematics are applied to the calculus of

* Essai Philosophique sur les Probabilités, par M. le Comte Laplace. 3me Ed. pp. 84, 85.

† Essai sur l'Application de l'Analyse à la Probabilité des Décisions rendues à la pluralité des voix. Disc. Prélim. p. 11.

« PredošláPokračovať »