181 



I.I IH.MTZ. 



prevented him from entirely rejecting the schoUtic 

 philosophy. There are in philos|.l.\ . a- in maihr. 

 tics, necessary truths, which cannot be learned 

 from experience, but must be grounded in tin- -,>ul 

 itwlf, M they rest on principles, the proof of which 

 i independent of the evidence ot tlie MIITS. Tin's 

 forms the basis of tin- Leihniuum ralionalism, the 

 principal characteristics of which urc a peculiar 

 theory of knowledge, the doctrine of Monadolog-y, 

 and l! . i. or doctrine of optimism. With 



regard to knowledge, according to this system 1. 

 The necessary truths are innate in the soul, not, 

 indeed, actually forming objects of knowledge, but 

 capable of being called forth by circumstances. 

 Whatever is derived from the senses is confused, 

 and distinct knowledge is possessed only by the 

 -landing. These views are opposed to the 

 eni|>irici-in of Locke. In order to attain truth, it is 

 necessary to use the rules of logic, as mathematicians 

 also use them, by unfolding, analytically, the simple 

 truths contained in a subject, until the fundamental 

 truth is attained. The Cartesian criterion clear- 

 ness and distinctness is not sufficient. " Our con- 

 clusions," says Leibnitz (Op. ii, 24), " rest on two 

 great principles the principle of contradiction (ac- 

 cording to which we deem that false which involves 

 a contradiction, and that true which is opposed to 

 falsehood), and the principle of the sufficient reason 

 (which teaches that no assertion is true, if no sufficient 

 reason can be given why it is true, rather than false), 

 which leads to an absolute final reason, independent 

 of accidental circumstances. But the final reason of 

 the certainty of innate necessary truths is in God, as 

 the source of all necessary and eternal truth. 2. Mo- 

 nadology forms the central point of the system, and 

 Leibnitz believed that, in this, he had discovered 

 the fundamental basis of actual knowledge. All 

 experience teaches us that there are compound sub. 

 stances; consequently there must be simple ones. 

 The senses give us only confused, the understanding 

 distinct, knowledge; and the simple, which cannot 

 be recognised by the senses, is the ground of the 

 compound. These simple substances, from which 

 the compound are formed, and each of which differs, 

 in its qualities, from all others, since there are no 

 two things exactly alike, Leibnitz calls monads, of 

 which he assumes four sorts pure monads (or living- 

 beings), the souls of beasts, the souls of men, and 

 God, who, as the origin of all knowledge, of reality, 

 and of the existence of things, the eternal, original 

 Monad, he calls the Monas monadum. All created 

 monads are united with bodies, or, rather, all finite 

 beings are aggregates of monads, some having a 

 central and governing monad. The different classes 

 of monads conceive of the universe with different 

 degrees of distinctness: God alone conceives it per- 

 fectly. There is no actual influence (influxus physi- 

 cut) of one thing on another, but only an ideal con- 

 nexion ; i. e. the internal changes of each monad 

 are so arranged as to agree with the changes in the 

 monads immediately connected with it. The cause 

 of this agreement is the infinite wisdom and almighty 

 power of the Deity. The divine understanding is 

 the prototype of all truth, beauty, and absolute good, 

 iind by it all the interior changes in the monads were 

 so predetermined, that there is a perfect harmony in 

 their succession. This predetermination or estab- 

 lished harmony was arranged by the Godhead when 

 the plan of the world was formed. 3. The Theo- 

 dicea is the defence of the supreme wisdom of the 

 Cmitor of the world, which had been impugned, on 

 account of the existence of evil. Such a Theodicea 

 Lcihniu attempted, particularly on account of the 

 contrary views brought forward by Bayle. Accord- 

 ing to the Leibnitzian system, an infinite number of 



worlds arc possible in the divine understanding; but, 

 of all possible ones, God has chosen and formed the 

 best. Kven thing which really is, is best in con- 

 nexion, evni if, by itself, it is imperfect. This 

 system i< therefore denominated optimism. Each 

 briiii; is intended to attain the highest degree of 

 happiness of which it is capable, and is to contribute, 

 as a part, to the perfection of the whole. The exis- 

 tence of evil is no argument against this system, 

 because metaphysical evil is merely a necessary im- 

 perfection in the nature of finite things, from which 

 imperfection, physical evil, (suffering) and moral evil 

 (sin) necessarily proceed. Moral evil is founded in 

 the freedom of finite spirits, which consists in choos- 

 ing, according to grounds of preference, one among 

 many physically possible actions; for, although every 

 thing in the world is necessarily determined, still 

 man, being ignorant of the future, must act from the 

 convictions of his reason. Leibnitz nowhere makes a 

 complete connected exposition of this philosophical 

 system, but has only proposed it in his writings, by 

 piecemeal, and it is therefore difficult to follow his 

 course of thought. 



This is not the place to enter into a more critical 

 examination of the value of these hypotheses ; it is 

 sufficient to observe, that they have been of the 

 greatest service in promoting the progress of reason, 

 as they have given that impulse to the philosophical 

 world, which his mathematical discoveries, to an 

 account of which we now proceed, gave to the 

 mathematicians of his time. His attention was early 

 directed to mathematical researches ; and, in a letter 

 to the countess of Kielmannsegge (1716), he relates, 

 that, even in his sixteenth year, he was occupied in 

 considering the differences of those numbers whose 

 succession forms a regular series. He thus arrived 

 at the law of constant magnitudes, which is always 

 found exactly, or by approximation, if the members 

 of the series, and then their first, second, &c., dif- 

 ferences are subtracted from each other; but, when 

 he was in England, wishing to publish his supposed 

 discovery, he found himself anticipated by a French 

 mathematician, Regnault. A second similar affair 

 induced him to study Mercator's Logarithmotechnica, 

 which he carried with him to France, where he sur- 

 prised Huygens by communicating to him his dis- 

 covery of an infinite series for the surface of the 

 circle, similar to that of Mercator for the hyperbola. 

 This was made known by Oldenburg to Newton, 

 who congratulated Leibnitz on his discovery. Ani- 

 mated by this result, Leibnitz resumed his researches 

 into the difference of numbers, and, in this way, he 

 was led to the discovery of the differential calculus. 

 In a letter of June 21, 1677, he communicated this 

 discovery to Oldenburg, for Newton's examination. 

 In comparing the whole course of reasoning which 

 he pursues in his calculations, with the views which 

 lie at the foundation of Newton's method of fluxions, 

 not the least similarity can be discovered between 

 the two methods ; which is the best proof that each 

 of these great men, in reality, attained the same 

 result for himself, entirely independent of the other. 

 Leibnitz, however, received no answer from Newton 

 to this remarkable letter, and things remained in 

 this state till 1(582, when the Acta Eruditorum was 

 commenced. Leibnitz was, from the beginning, one 

 of its most active contributors, and, in the October 

 number of 1684, he published a complete account of 

 his differential calculus, exactly as he had communi- 

 cated it to Newton. It is worthy of remark, that, at 

 this time, no one questioned the claims of Leibnitz to 

 tin: discovery of this new mode of calculation. On 

 the contrary, Newton publicly acknowledged the 

 merit of the German, and made the most honourable 

 mention of him in his Principia. Leibnitz continued, 



