§212What is deceptive in this subject, as I have already observed, is that one feels an inclination to believe that what is the best in the whole is also the best possible in each part. One reasons thus in geometry, when it is a question de maximis et minimis. If the road from A to B that one proposes to take is the shortest possible, and if this road passes by C, then the road from A to C, part of the first, must also be the shortest possible. But the inference from quantity to quality is not always[261] right, any more than that which is drawn from equals to similars. For equals are those whose quantity is the same, and similars are those not differing according to qualities. The late Herr Sturm, a famous mathematician in Altorf, while in Holland in his youth published there a small book under the title of Euclides Catholicus. Here he endeavoured to give exact and general rules in subjects not mathematical, being encouraged in the task by the late Herr Erhard Weigel, who had been his tutor. In this book he transfers to similars what Euclid had said of equals, and he formulates this axiom: Si similibus addas similia, tota sunt similia. But so many limitations were necessary to justify this new rule, that it would have been better, in my opinion, to enounce it at the outset with a reservation, by saying, Si similibus similia addas similiter, tota sunt similia. Moreover, geometricians often require non tantum similia, sed et similiter posita.

§213This difference between quantity and quality appears also in our case. The part of the shortest way between two extreme points is also the shortest way between the extreme points of this part; but the part of the best Whole is not of necessity the best that one could have made of this part. For the part of a beautiful thing is not always beautiful, since it can be extracted from the whole, or marked out within the whole, in an irregular manner. If goodness and beauty always lay in something absolute and uniform, such as extension, matter, gold, water, and other bodies assumed to be homogeneous or similar, one must say that the part of the good and the beautiful would be beautiful and good like the whole, since it would always have resemblance to the whole: but this is not the case in things that have mutual relations. An example taken from geometry will be appropriate to explain my idea.

§214There is a kind of geometry which Herr Jung of Hamburg, one of the most admirable men of his time, called 'empiric'. It makes use of conclusive experiments and proves various propositions of Euclid, but especially those which concern the equality of two figures, by cutting the one in pieces, and putting the pieces together again to make the other. In this manner, by cutting carefully in parts the squares on the two sides of the right-angled triangle, and arranging these parts carefully, one makes from them the square on the hypotenuse; that is demonstrating empirically the 47th proposition of the first book of Euclid. Now supposing that some of these pieces taken from the two smaller squares are lost, something[262] will be lacking in the large square that is to be formed from them; and this defective combination, far from pleasing, will be disagreeably ugly. If then the pieces that remained, composing the faulty combination, were taken separately without any regard to the large square to whose formation they ought to contribute, one would group them together quite differently to make a tolerably good combination. But as soon as the lost pieces are retrieved and the gap in the faulty combination is filled, there will ensue a beautiful and regular thing, the complete large square: this perfect combination will be far more beautiful than the tolerably good combination which had been made from the pieces one had not mislaid alone. The perfect combination corresponds to the universe in its entirety, and the faulty combination that is a part of the perfect one corresponds to some part of the universe, where we find defects which the Author of things has allowed, because otherwise, if he had wished to re-shape this faulty part and make thereof a tolerably good combination, the whole would not then have been so beautiful. For the parts of the faulty combination, grouped better to make a tolerably good combination, could not have been used properly to form the whole and perfect combination. Thomas Aquinas had an inkling of these things when he said: ad prudentem gubernatorem pertinet, negligere aliquem defectum bonitatis in parte, ut faciat augmentum bonitatis in toto (Thom., Contra Gentiles, lib. 2, c. 71). Thomas Gatacre, in his Notes on the book of Marcus Aurelius (lib. 5, cap. 8, with M. Bayle), cites also passages from authors who say that the evil of the parts is often the good of the whole.

§215Let us return to M. Bayle's illustrations. He imagines a prince (p. 963) who is having a city built, and who, in bad taste, aims rather at airs of magnificence therein, and a bold and unusual style of architecture, than at the provision of conveniences of all kinds for the inhabitants. But if this prince has true magnanimity he will prefer the convenient to the magnificent architecture. That is M. Bayle's judgement. I consider, however, that there are cases where one will justifiably prefer beauty of construction in a palace to the convenience of a few domestics. But I admit that the construction would be bad, however beautiful it might be, if it were a cause of diseases to the inhabitants; provided it was possible to make one that would be better, taking into account beauty, convenience and health all together. It may be, indeed, that one cannot have all these[263] advantages at once. Thus, supposing one wished to build on the northern and more bracing side of the mountain, if the castle were then bound to be of an unendurable construction, one would prefer to make it face southward.

§216M. Bayle raises the further objection, that it is true that our legislators can never invent regulations such as are convenient for all individuals, 'Nulla lex satis commoda omnibus est; id modo quaeritur, si majori parti et in summam prodest. (Cato apud Livium, L. 34, circa init.)' But the reason is that the limited condition of their knowledge compels them to cling to laws which, when all is taken into account, are more advantageous than harmful. Nothing of all that can apply to God, who is as infinite in power and understanding as in goodness and true greatness. I answer that since God chooses the best possible, one cannot tax him with any limitation of his perfections; and in the universe not only does the good exceed the evil, but also the evil serves to augment the good.

§217He observes also that the Stoics derived a blasphemy from this principle, saying that evils must be endured with patience, or that they were necessary, not only to the well-being and completeness of the universe, but also to the felicity, perfection and conservation of God, who directs it. The Emperor Marcus Aurelius gave expression to that in the eighth chapter of the fifth book of his Meditations. 'Duplici ratione', he says, 'diligas oportet, quidquid evenerit tibi; altera quod tibi natum et tibi coordinatum et ad te quodammodo affectum est; altera quod universi gubernatori prosperitatis et consummationis atque adeo permansionis ipsius procurandae ([Greek: tes euodias kai tes synteleias kai tes symmones autes]) ex parte causa est.' This precept is not the most reasonable of those stated by that great emperor. A diligas oportet ([Greek: stergein chre]) is of no avail; a thing does not become pleasing just because it is necessary, and because it is destined for or attached to someone: and what for me would be an evil would not cease to be such because it would be my master's good, unless this good reflected back on me. One good thing among others in the universe is that the general good becomes in reality the individual good of those who love the Author of all good. But the principal error of this emperor and of the Stoics was their assumption that the good of the universe must please God himself, because they imagined God as the soul of the world. This error has nothing in common with my dogma, [264] according to which God is Intelligentia extramundana, as Martianus Capella calls him, or rather supramundana. Further, he acts to do good, and not to receive it. Melius est dare quam accipere; his bliss is ever perfect and can receive no increase, either from within or from without.

§218I come now to the principal objection M. Bayle, after M. Arnauld, brings up against me. It is complicated: they maintain that God would be under compulsion, that he would act of necessity, if he were bound to create the best; or at least that he would have been lacking in power if he could not have found a better expedient for excluding sins and other evils. That is in effect denying that this universe is the best, and that God is bound to insist upon the best. I have met this objection adequately in more than one passage: I have proved that God cannot fail to produce the best; and from that assumption it follows that the evils we experience could not have been reasonably excluded from the universe, since they are there. Let us see, however, what these two excellent men bring up, or rather let us see what M. Bayle's objection is, for he professes to have profited by the arguments of M. Arnauld.

219. 'Would it be possible', he says, Reply to the Questions of a Provincial, vol. III, ch. 158, p. 890, 'that a nature whose goodness, holiness, wisdom, knowledge and power are infinite, who loves virtue supremely, and hates vice supremely, as our clear and distinct idea of him shows us, and as well-nigh every page of Scripture assures us, could have found in virtue no means fitting and suited for his ends? Would it be possible that vice alone had offered him this means? One would have thought on the contrary that nothing beseemed this nature more than to establish virtue in his work to the exclusion of all vice.' M. Bayle here exaggerates things. I agree that some vice was connected with the best plan of the universe, but I do not agree with him that God could not find in virtue any means suited for his ends. This objection would have been valid if there were no virtue, if vice took its place everywhere. He will say it suffices that vice prevails and that virtue is trifling in comparison. But I am far from agreeing with him there, and I think that in reality, properly speaking, there is incomparably more moral good than moral evil in rational creatures; and of these we have knowledge of but few.