its sensible effects, exactly analogous to those which, in the instance of the universe, Philo would reject as illusions of the fancy.*

But leaving for future consideration these abstract topics, let us, for a moment, attend to the scope and amount of Philo's reasoning.-To those who examine it with attention, it must appear obvious, that, if it proves any thing, it leads to this general conclusion, That it would be perfectly impossible for the Deity if he did exist, to exhibit to Man any satisfactory evidence of design by the order and perfection of his works. That every thing we see is consistent with the supposition of its being produced by an intelligent author, Philo himself has explicitly acknowledged in these remarkable words: "Supposing there were a God, who did not discover himself immediately to our senses; would it be possible for him to give stronger proofs of his existence, than what appear on the whole face of nature? What, indeed, could such a Divine Being do, but copy the present economy of things;-render many of his artifices so plain, that no stupidity could mistake them;-afford glimpses of still greater artifices, which demonstrate his prodigious superiority above our narrow apprehensions; and conceal altogether a great many from such imperfect creatures?" The sceptical reasonings of Philo, therefore, do not, like those of the ancient Epicureans, hinge, in the least, on alleged disorders and imperfections in the universe, but entirely on the impossibility, in a case to which experience furnishes nothing parallel or analogous, of rendering intelligence and design manifest to our faculties by their sensible effects. In thus shifting his ground from that occupied by his predecessors, Philo seems to me to have abandoned the only post from which it was of much importance for his adversaries to dislodge him. The logical subtilties, formerly quoted about experience and belief, (even supposing them to remain unanswered,) are but little calculated to shake the authority of principles, on which we are every moment forced to judge and to act, by the exigencies of life. For this change in the tactics of modern sceptics, we are evidently, in a great measure, if not wholly, indebted to the lustre thrown on the order of nature, by the physical researches of the two last centuries.

Another concession extorted from Philo by the discoveries of modern science is still more important. I need not point out its coincidence with some remarks in the first part of this section, on the unconscious deference often paid to final causes by those inquirers who reject them in theory;—a coincidence which had totally escaped my recollection when these remarks were written. I quote it here, chiefly as a pleasing and encouraging confirmation of the memorable prediction with which Newton concludes his Optical Queries; that, "if Natural Philosophy, in all its parts, by pursuing the inductive method, shall at length be perfected, the bounds of Moral Philosophy will be enlarged also."

"A purpose, an intention, a design," says Philo, "strikes every where the most careless, the most stupid thinker; and no man can be so hardened in absurd systems as at all times to reject it. That Nature does nothing in vain, is a maxim, established in all the schools, merely from the contemplation of the works of Nature, without any religious purpose; and from a firm conviction of its truth, an anatomist, who had observed a new organ or canal, would never be satisfied till he had also discovered its use and intention. One great foundation of the COPERNICAN system is the maxim, That Nature acts by the simplest methods, and chooses the most proper means to any end; and astronomers often, without thinking of it, lay this strong foundation of piety and religion. The same thing is observable in other parts of philosophy: And thus all the sciences lead us almost insensibly to acknowledge a first intelligent author; and their authority is often so much the greater, as they do not directly profess that intention."

*This last consideration is ably stated by Dr. Reid. (See Essays on the Intellectual Powers, pp. 631, 632, 4to. Ed.) The result of his argument is, that "according to Philo's reasoning we can have no evidence of mind or design in any of our fellow-men."-At a considerably earlier period, Buffier had fallen into the same train of thinking. Among the judgments which he refers to common sense, he assigns the first place to the two following: "1. Il y a d'autres etres, et d'autres hommes que moi au monde. 2. Il ya dans eux quelque chose qui s'appelle verite, sagesse prudence," &c. &c. (Cours de Sciences, p. 566. Paris, 1732.) I have already objected to the application of the phrase common sense, to such judgments as these; but this defect, in point of expression, does not detract from the sagacity of the author in perceiving, that in the conclusions we form concerning the minds and characters of our fellow creatures, (as well as in the inferences drawn concerning the invisible things of God from the things which are made,) there is a perception of the understanding implied, for which neither reasoning nor experience is sufficient to account.

* P. 73.

Since this sheet was cast off, I have been informed from the best authority, that the conversation here alluded to, which I had understood to have taken place between Lord Chief Justice Mansfield, and the late Sir Basil Keith, really passed between his Lordship and another very distinguished officer, the late gallant and accomplished Sir Archibald Campbell. I have not, however, thought it worth while, in consequence of a mistake which does not affect the substance of the anecdote, to cancel the leaf;-more especially, as there is at least a possibility that the same advice may have been given on more than one occasion.

APPENDIX.

ARTICLE I. (See page 117.)

THE following article relates entirely to the question,-" How far it is true, that all mathematical evidence is resolvable into identical propositions." The discussion may, in one point of view, be regarded as chiefly verbal; but that it is not, on that account, of so trifling importance as might at first be "imagined, appears from the humiliating inference to which it has been supposed to lead concerning the narrow limits of human knowledge. "Put the question," says Diderot," to any candid mathematician, and he will acknowledge, that all mathematical propositions are merely identical; and that the numberless volumes written (for example) on the circle, only repeat over in a hundred thousand forms, that it is a figure in which all the straight lines drawn from the centre to the circumference are equal. The whole amount of our knowledge, therefore, is next to nothing."-That Diderot has, in this very paradoxical conclusion, stated his own real opinion will not be easily believed by those who reflect on his extensive acquaintance with mathematical and physical science; but I have little doubt, that he has expressed the amount of the doctrine in question, agreeably to the interpretation put on it by the great majority of readers.

As the view of this subject which I have taken in the text, has not been thought satisfactory by my friend M. Prévost, I have thought it a duty, both to him and to myself, to annex to the foregoing pages, in his own words, the remarks subjoined to the excellent and faithful translation with which he has honored this part of iny work, in the Bibliothèque Britannique. Among these remarks, there is scarcely a proposition to which I do not give my complete assent. The only difference between us turns on the propriety of the language in which some of them are expressed; and on this point it is not surprising, if our judgments should be somewhat biassed by the phraseology to which we have been accustomed in our earlier years. The few sentences to which I am inclined to object, I have distinguished from the rest, by printing them in small capitals.-Such explanations of my own argument as appear to be necessary, I have thrown into the form of notes, at the foot of the page. In the course of M. Prévost's observations on the point in question, he has introduced various original and happy illustrations of the important distinction between conditional and absolute truths;—a subject on which I have the pleasure to find, that all our views coincide exactly.

"A la fin de l'article que l'on vient de lire, l'ingénieux auteur renvoie à ce qu'il a dit au commencement. Il pense y avoir suffisamment prouvé que l'évidence particulière qui accompagne le raisonnement mathématique ne peut pas se résoudre dans la perception de l'identité. Recourons donc à cette preuve. Elle se trouve consister toute entière en réfutation.

"I. L'auteur commence par remarquer, que quelques personnes fondent l'opinion qu'il rejette sur celle qui prend les axiomes pour premiers principes. Et comme il a combattu celle-ci, il en conclut que sa conséquence doit être fausse. Un tel argument a en effet beaucoup de force pour ceux qui sont partis d'une certaine théorie sur les axiomes pour en conclure l'assertion contestée; mais il n'en a point pour les autres. Le rédacteur de cet article se range parmi ces derniers. Il a dit et i

VOL. II.

Chap. II. Sect. 3. Art. II. of this volume.

49

pense encore, que le mathématicien avance de supposition en supposition; que c'est en retournant sa pensée sous diverses formes, qu'il arrive à d'utiles résultats; QUE C'EST LA RECONNOISSANCE DE QUELQUE IDENTITÉ QUI AUTORISE CHACUNE DE SES CONCLUSIONS; et toutefois il a dit et il persiste à croire, que les axiomes mathématiques ne font que tenir la place ou de définitions ou de théorèmes; et que les définitions sont les seuls principes des sciences de la nature de la géométrie. Voici ces propres expressions.* 'J'observe que de bonnes définitions initiales sont les seuls principes rigoureusement suffisans dans les sciences de raisonnement pur .......... C'est dans les définitions que sont véritablement contenues les hypothèses dont ces sciences partent...........On pourroit concevoir, [toujours dans ces mêmes sciences,] que les principes fussent si nettement posés, que l'on n'y trouvât autre chose que de bonnes définitions. De ces définitions retournées, résulteroient toutes les propositions subséquentes. LES DIVERSES PROPRIÉTÉS DU CERCLE QUE SONTELLES AUTRE CHOSE, QUE DIVERSES FACES DE LA PROPOSITION QUI DÉFINIT CETTE COURBE?-C'est donc l'imperfection (peut-être inévitable) de nos conceptions, qui a engagé à faire entrer les axiomes pour quelque chose dans les principes des sciences de raisonnement pur. Et ils y font un double office. Les uns remplacent des définitions. Les autres remplacent des propositions susceptibles d'être démontrées.' "Il est manifeste que celui qui a tenu de tout temps ce langage n'a pas fondé son opinion, vraie ou fausse, relativement à l'évidence mathématique, sur une opinion fausse relativement aux axiomes; ou du moins, qu'étant si parfaitement d'accord avec Mr. Dugald Stewart en ce qui concerne les premiers principes des mathématiques, ce n'est point de là que dérive l'apparente discordance de ses expressions et de celles de son ami, sur ce qui concerne le principe de l'évidence mathématique dans la déduction démonstrative. Dès lors il est évident que ce premier argument de l'auteur reste pour lui comme nul.

"II. Fassons au second. Celui-ci est encore purement négatif et personnel. Il s'addresse à ceux qui dérivent, d'un principe propre à la géométrie, l'assertion que l'auteur combat. De ce que l'égalité en géométrie se démontre par la congruence, ces philosophes se pressent de conclure, que, dans toutes les mathématiques, les vérités reposent sur l'identité. Ceux donc qui n'ont jamais songé à donner un tel appui à l'assertion contestée ne peuvent absolument pas se rendre à l'attaque dirigée contre cet appui. Il est probable qu'un très-grand nombre de partisans du principe de l'identité, considéré comme base de la démonstration, se trouvent (comme le rédacteur peut ici le dire de lui-même) tout à fait étrangers à la manière de raisonner que l'auteur réfute; et n'ont point formé leur opinion relativement à l'évidence mathématique d'après la congruence (réelle ou potentielle) de deux espaces. C'est ce que le rédacteur affirme ici, quant à lui, de la manière la plus positive; et de là résulte que l'argument personnel,† dirigé contre ceux qui ont été menés d'une de ces opinions à l'autre, ne l'atteint point.

"Il est un peu plus difficile de prouver cette affirmation, que quand il étoit question des axiomes, parce que ceux-ci ne peuvent pas manquer de s'offrir aux recherches du logicien, au lieu qu'il n'est pas appellé à prévoir l'application inconsidérée du principe de superposition à toute espèce de démonstration. Si cependant il fait voir que son opinion sur la démonstration dérive de principes universels et tout différens de celui qu'on a en vue, il aura fait, je pense, tout ce qu'il est possible d'attendre de lui. "Qu'il soit maintenant permis au rédacteur de quitter la tierce personne, et pour éviter quelques longueurs et quelques expressions indirectes, d'établir nettement son opinion et la marche qu'il a tenue en l'exposant.

"Dès les premières pages de ma logique, je pars de la distinction à faire entre les deux genres de vérité; la conditionelle et l'absolue. Puis j'ajoute :

"LE MOYEN UNIQUE, PAR LEQUEL NOUS CONNOISSONS SI UNE PROPOSITION CƠNDITIONNELLE EST VRAIE, OU LE CARACTERE D'UNE TELLE VÉRITÉ, EST L'IDENTITÉ BIEN ÉTABLIE ENTRE LE PRINCIPE ET LA CONSÉQUENCE. CETTE IDENTITÉ n'est PAS COMPLETE SANS DOUTE; MAIS ELLE EST TELLE A QUELQUE ÉGARD, QUE LA CONSÉQUENCE DOIT ETRE TOUTE ENTIERE COMPRISE DANS LE PRINCIPE." ‡

* Essais de Philos. Tom. II. p. 29, à Genève, chez Paschoud, 1804. † Ad hominem.

Essais de Phil. Tom. II. p. 2. "Le lecteur équitable voudra bien se rappeler que l'ouvrage, dont ce passage est tiré, n'est que l'esquisse d'un cours fort étendu, dans lequel se trouvent développés, par des exemples et de toute manière, les simples énoncés du texte. A peine est-il nécessaire de dire ici en explication ce que