Page:Encyclopædia Britannica, Ninth Edition, v. 13.djvu/562

 538 J A C J A C (agreements, truths conditionally necessary), proceeding always in identical propositions ; every proof presupposes something already proved, the principle of which is immediately given (0/enbarung, revelation, is the term here employed by Jacobi, as by many later writers, e.g., Lotze, to denote the peculiar character of an immedi ate, unproved truth) ; (6) the keystone (Element) of all human knowledge and activity is belief (Glaube). Of these propositions only the first and fourth require further notice. Jacobi, accepting the law of reason and consequent as the fundamental rule of demon strative reasoning, and as the rule explicitly followed by Spinoza, points out that, if we proceed by applying this principle so as to recede from particular and qualified facts to the more general and abstract conditions, we land ourselves, not in the notion of an active, intelligent creator of the system of things, but in the notion of an all-comprehensive, indeterminate Nature, devoid of will or intelligence. Our unconditioned is either a pure abstraction, or else the impossible notion of a completed system of conditions. In either case the result is atheism, and this result is necessary if the demonstrative method, the method of understanding, is regarded as the only possible means of knowledge. Moreover, the same method inevitably lands in fatalism. For, if the action of the human will is to be made intelligible to understanding, it must be thought as a conditioned phenomenon, having its sufficient ground in preceding circumstances, and, in ultimate abstraction, as the outflow from nature which is the sum of conditions. But this is the fatalist conception, and any philosophy which accepts the law of reason and consequent as the essence of understanding is fatalistic. Thus for the scientific understanding there can be no God and no liberty. It is impossible that there should be a God, for if so he would of necessity be finite. But a finite God, a God that is known, is no God. It is impossible that there should be liberty, for if so the mechanical order of phenomena, by means of which they are com prehensible, would be disturbed, and we should have an unintelli gible world, coupled with the requirement that it shall be understood. Cognition, then, in the strict sense, occupies the middle place between sense perception, which is belief in matters of sense, and reason, which is belief in supersensuous fact. (Jacobi wavered much in his terminology, especially with respect to the word reason ; but even at this stage of his thinking the distinctions just named are sufficiently apparent.) Such a view, and especially the fundamental peculiarity that the categories of the understanding are to be regarded as mere forms of the conditioned, from their very nature limited and relative, presented a certain analogy to the critical philosophy, and accordingly, in the second period of Jacobi s speculative development, he is driven to a comparison of his doc trines with those of Kant. His adverse criticism of the Kantian doctrines was directed on three points mainly, and, though in itself but ill-founded, it deserves the careful consideration of all Kantian students. (1) The categories of the understanding and the forms of intuition supply a blank scheme for the given element of sense. But if the given element be merely sensation, and not actually the external thing, we are still, Jacobi thinks, within the position of subjective idealism. At no point in the whole process do we ever get beyond empty form, bare identity. The synthetical unity of consciousness, if no reality be supplied in regard to which it may operate, is mere repetition of the form of conjunction, mere possibility of cognition. Whence do we obtain the reality, the objectivity, of knowledge ? To Jacobi it seemed that Kant, in the second edition of the Kritik, made an effort to demonstrate the external reality of phenomena of experi ence, and he views the change in Kant s doctrine as the effect of his own critical comments. Nevertheless such demonstration still seems to him unsatisfactory ; it yields only the thought-form of externality, not externality in fact. (2) Jacobi agrees with Kant so far as the critical view of the incapacity of understanding to encompass the ideas is concerned, but lie thinks Kant in error in supposing that such incapacity results from the subjective limitation of our power of thinking and not from the nature of the categories of understanding in themselves. At the same time he holds that Kant treats the ideas unjustly, and that in his view of reason he tends to make that faculty inferior to understanding. (3) Kant s moral theory is as little satisfactory as his theory of perception. Here, too, in the demand for universally valid law as the law of a will that is its own content, Jacobi can find but the form and not the reality of a universal rule. The universal will is void of con tent, and the sharp opposition which in the Kantian ethics appears between the ethical motive and all modes of feeling is the natural result of mere formalism. When Jacobi endeavours to supply the place of the Kantian theorems which lie rejects, the inherent weak ness of his own principle becomes apparent. External things arc known to us by immediate perception, a combination of intuition and belief. The principle of inference to realities is that of cause and effect, the significance of which we learn from observing the relation between our will and changes in the objective world, and this principle by a natural necessity we extend to all existence. The infinite progress from consequents, to grounds, which is the form of procedure of understanding, yields no conclusion as regards the being of a God. But when we regard the whole system of real things, we are compelled to infer a real cause, which, from the significance of the causal principle, is seen to be of necessity an active intelligent will, a God who foresees events. This apprehen sion of God is faith, reason, or feeling, as Jacobi, following Fries, is willing to call it. Not even in his latest work of importance ( Von den gottlichcn Dingcn), which is specifically on religion, docs Jacobi manage to make clear the step, which he has himself characterized as the salto mortale of the human intellect, from the finite to the infinite ; still less the further difficulty as to the possibility of holding that the God who for cognition is the unknown God must be held to possess providence, personality, life. He acknowledges that this is anthropomorphic, bitterly assails Schelling for identifying divine and human reason, but leaves the problem standing. The truth is that what Jacobi called feeling, and regarded as immediate knowledge, is not a simple act of mind, capable of yielding simple results, but the very essence of complex thinking. We cannot separate know ledge of things from apprehension of them in the way he has adopted. Nor can the human reason rest satisfied with a system devoid of inner coherence and harmony. The best introductions to Jacobi s philosophy are the preface to the second vol. of the Worts, and Appendix 7 to the Letters on Spinoza s Theory. There are two monographs of some extent upon him : Kuhn, Jacobi und die Philosophic seiner Zeit, 1834; and Zirngiehl, F. II. Jacobi s Leben, Dichten, vnd Denken, 1867. See also F. II Jacobi s Auserlesener Brief wechsel, 2d ed., by Roth, 2 vols., 1825-27 : and Gildemeister s edition of Ilamann s Schriften, vol. v. (It. A IX) JACOBI, KARL GUSTAV JACOB (1804-1851), one of the great mathematicians of the present century, was born at Potsdam, of Jewish parentage, December 10, 1804. He studied at Berlin university, where he obtained the degree of doctor of philosophy in 1825, his thesis being an analytical discussion of the theory of fractions. In 1827 he became &quot;extraordinary&quot; and in 1829 &quot;ordinary&quot; professor of mathematics at Konigsberg ; and this chair he filled till 1842, when he visited Italy for a few months to recruit his health. On his return he removed to Berlin, where he lived as a royal pensioner till his death, February 18, 1851. His investigations in elliptic functions, the theory of which he established upon quite a new basis, and more particularly his development of the Theta-function, as given in his great treatise Fundamenta Nova Theorise Functionum Ellipticarum (Konigsberg, 1829), and in later papers in Crelle s Journal, constitute his grandest analytical discoveries. Second in importance only to these are his researches in differential equations, notably the theory of the last multiplier, which is fully treated in his Vorlesungen iiber Dynamik, edited by Clebsch (Berlin, 1866). It was in analytical development that Jacobi s peculiar power mainly lay, and lie made many important contributions of this kind to other departments of mathematics, as a glance at the long list of papers that were published by him in Crelle s Journal from 1826 onwards will sufficiently indi cate. Thus he was one of the early founders of the theory of determinants ; in particular, he invented the functional determinant formed of the 2 differential coefficients of n given functions of n independent variables, which now bears his name (Jacobi an), and which has played an im portant part in many analytical investigations. Valuable also are his papers on Abelian transcendents, and his investigations in the theory of numbers, in which latter department he mainly supplements the labours of Gauss, with whom as with the other great Continental mathe maticians of the day, Legendre, Bessel, Abel, &c., he was on terms of the closest intimacy. The planetary theory and other particular dynamical problems likewise occupied his attention from time to time. He left a vast store of manuscript, portions of which have been published at intervals in Crelle s Journal. See INFINITESIMAL CAL CULUS. JACOBITE CHURCH, an ecclesiastical organization thinly spread over Syria, Mesopotamia, and Babylonia, having for its distinctive doctrinal principle theMonophysite thesis with regard to the person of Christ ; it consequently accepts the decrees of the second (&quot;Robber&quot;) synod cf