The philosophy of Jacobi is essentially unsystematic. A certain fundamental view which underlies all his thinking is brought to bear in succession upon those systematic doctrines which appear to stand most sharply in contradiction to it, and any positive philosophic results are given only occasionally. The leading idea of the whole is that of the complete separation between understanding and apprehension of real fact. For Jacobi understanding, or the logical faculty, is purely formal or elaborative, and its results never transcend the given material supplied to it. From the basis of immediate experience or perception thought proceeds by comparison and abstraction, establishing connexions among facts, but remaining in its nature mediate and finite. The principle of reason and consequent, the necessity of thinking each given fact of perception as conditioned, impels understanding towards an endless series of identical propositions, the records of successive comparisons and abstractions. The province of the understanding is therefore strictly the region of the conditioned; to it the world must present itself as a mechanism. If, then, there is objective truth at all, the existence of real facts must be made known to us otherwise than through the logical faculty of thought; and, as the regress from conclusion to premises must depend upon something not itself capable of logical grounding, mediate thought implies the consciousness of immediate truth. Philosophy therefore must resign the hopeless ideal of a systematic (i.e. intelligible) explanation of things, and must content itself with the examination of the facts of consciousness. It is a mere prejudice of philosophic thinkers, a prejudice which has descended from Aristotle, that mediate or demonstrated cognition is superior in cogency and value to the immediate perception of truths or facts.
As Jacobi starts with the doctrine that thought is partial and limited, applicable only to connect facts, but incapable of explaining their existence, it is evident that for him any demonstrative system of metaphysic which should attempt to subject all existence to the principle of logical ground must be repulsive. Now in modern philosophy the first and greatest demonstrative system of metaphysic is that of Spinoza, and it lay in the nature of things that upon Spinoza’s system Jacobi should first direct his criticism. A summary of the results of his examination is thus presented (Werke, i. 216-223): (1) Spinozism is atheism; (2) the Kabbalistic philosophy, in so far as it is philosophy, is nothing but undeveloped or confused Spinozism; (3) the philosophy of Leibnitz and Wolff is not less fatalistic than that of Spinoza, and carries a resolute thinker to the very principles of Spinoza; (4) every demonstrative method ends in fatalism; (5) we can demonstrate only similarities (agreements, truths conditionally necessary), proceeding always in identical propositions; every proof presupposes something already proved, the principle of which is immediately given (Offenbarung, revelation, is the term here employed by Jacobi, as by many later writers, e.g. Lotze, to denote the peculiar character of an immediate, 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 demonstrative 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 comprehensible, would be disturbed, and we should have an unintelligible 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.
The best introduction to Jacobi’s philosophy is the preface to the second volume of the Works, and Appendix 7 to the Letters on Spinoza’s Theory. See also J. Kuhn, Jacobi und die Philosophie seiner Zeit (1834); F. Deycks, F. H. Jacobi im Verhältnis zu seinen Zeitgenossen (1848); H. Düntzer, Freundesbilder aus Goethes Leben (1853); E. Zirngiebl, F. H. Jacobis Leben, Dichten, und Denken, 1867; F. Harms, Über die Lehre von F. H. Jacobi (1876). Jacobi’s Auserlesener Briefwechsel has been edited by F. Roth in 2 vols. (1825-1827).
JACOBI, JOHANN GEORG (1740-1814), German poet, elder brother of the philosopher, F. H. Jacobi (1743-1819), was born at Düsseldorf on the 2nd of September 1740. He studied theology at Göttingen and jurisprudence at Helmstedt, and was appointed, in 1766, professor of philosophy in Halle. In this year he made the acquaintance of J. W. L. (“Vater”) Gleim, who, attracted by the young poet’s Poetische Versuche (1764), became his warm friend, and a lively literary correspondence ensued between Gleim in Halberstadt and Jacobi in Halle. In order to have Jacobi near him, Gleim succeeded in procuring for him a prebendal stall at the cathedral of Halberstadt in 1769, and here Jacobi issued a number of anacreontic lyrics and sonnets. He tired, however, of the lighter muse, and in 1774, to Gleim’s grief, left Halberstadt, and for two years (1774-1776) edited at Düsseldorf the Iris, a quarterly for women readers. Meanwhile, he wrote many charming lyrics, distinguished by exquisite taste and true poetical feeling. In 1784 he became professor of literature at the university of Freiburg im Breisgau, a post which he held until his death there on the 4th of January 1814. In addition to the earlier Iris, to which Goethe, his brother F. H. Jacobi, Gleim and other poets contributed, he published, from 1803-1813, another periodical, also called Iris, in which Klopstock, Herder, Jean Paul, Voss and the brothers Stollberg also collaborated.
Jacobi’s Sämmtliche Werke were published in 1774 (Halberstadt, 3 vols.). Other editions appeared at Zürich in 1807-1813 and 1825. See Ungedruckte Briefe von und an Johann Georg Jacobi (Strassburg, 1874); biographical notice by Daniel Jacoby in Allg. Deutsche Biographie; Longo, Laurence Sterne und Johann Georg Jacobi (Vienna, 1898); and Leben J. G. Jacobis, von einem seiner Freunde (1822).
JACOBI, KARL GUSTAV JACOB (1804-1851), German mathematician, was born at Potsdam, of Jewish parentage, on the 10th of December 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 extraordinary and in 1829 ordinary professor of mathematics at Königsberg, 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, which occurred on the 18th of February 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 theoriae functionum ellipticarum (Königsberg, 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 über Dynamik, edited by R. F. A. Clebsch (Berlin, 1866). It was in analytical development that Jacobi’s peculiar power mainly lay, and he 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 and elsewhere from 1826 onwards will sufficiently indicate. He was one of the early founders of the theory of determinants; in particular, he invented the functional determinant formed of the n² differential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations (see [Algebraic Forms]). 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 K. F. Gauss. 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. His other works include Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem (1832), Canon arithmeticus (1839), and Opuscula mathematica (1846-1857). His Gesammelte Werke (1881-1891) were published by the Berlin Academy.
See Lejeune-Dirichlet, “Gedächtnisrede auf Jacobi” in the Abhandlungen der Berliner Akademie (1852).