recognise real principles on the basis of admissible facts. Its knowledge is either given to it in perception as such, or is innate in the subject in such a way that it is brought into consciousness by progressive development -not that it is ascertained by an immediate intuition of reason, but that it is obtained from the given content of perception by a thinking objectively conditioned. This thinking fashions the material of perception, not (as an artist does a block of marble) according to forms, which are in themselves foreign to it, but (as nature does the living germ) according to the relations given in itself and conditioned by the forms of the objective reality. In reference to this material element, the proposition is true: nihil est in intellectu, quod non fuerit in sensu;' but the fashioning of the material of (external and internal) perception in thinking is not an operation of less value, it is the more essential side of the process of knowledge.

Abstraction leads to the most general notions of principle significance. Abstraction, in conjunction with the idealising activity passing beyond what is given, fashions what is the higher in science according to scientific laws (as in art according to aesthetic laws), into the Idea (idea in the subjective sense) or into the regulative (typical) notions.

Judgments which contain scientific axioms of value as principles (axiomata) are framed partly analytically, partly synthetically. The former (e.g. the arithmetical axioms) originate by the resolution (analysis) of intuitions or notions present before the mind, and have immediate evidence independent of experience. The

latter (e.g. axioms of geometry and the postulates, which are only another form of axioms, and which assert the possibility of doing what is required) depend partly on Induction and Analogy, partly on idealisation and hypothetical assertion, accompanied by the verification of the truth of the hypothesis in its consequences, which leads to a successive exclusion of the false (by means of indirect proof) and the confirmation of what is true. In complicated problems the first attempts at hypotheses must not include the whole problem. As many fixed starting points as possible must first be gained inductively and by means of special hypotheses and their verification, in order thereby to settle the principal question. Every principle, if it contains hypothetical elements, must be verified in its consequences, and hence it is possible to decide between contradictory elements in this way, that each shows its true character in its theoretical and practical consequences. The axiom: 'contra negantem principia non est disputandum,' is false and inhuman. In a normal development in knowledge, as in life, the lower element is overcome by the higher, and contradictory principles equally justifiable find their true place of union in a common higher principle.

There is no need for a special ars inveniendi' or Topic,' co-ordinate Logic as the ars judicandi,' such as Christian Wolff and other logicians, following the view of Leibniz, have desired. The analytical method which employs the modes of knowledge explained above in detail, the product of perceptions, intuitions, notions, judgments, inductions, &c. is the true art of invention, and so is the synthetic method from its own side. Topic can only be divorced from Logic when used in the service of Rhe

1

toric. Trendelenburg says very truly:' Disputation or Logic should abolish the chapter De Inventione. When the laws of Logic are once founded on the basis of the individual sciences, they will become much better able to guide one in discovery than could have been the case by means of the previous abstract treatment, whether conducted in the interest of rhetoric or of science.

The true apprehension of facts, free from any individual and subjective confusion, is a work of education. The teacher, physician, historian and judge, have daily occasion to observe how little men are accustomed to describe the simple facts, and how very much they mix up in the statement (unconsciously and unintentionally) their own opinions and interests. It is inconceivably hard, I had almost said impossible, to describe what has been seen or heard wholly and exactly as it has been seen and heard. We often introduce our own feelings without anticipating it, and although we have the strongest and purest love of truth.' 2 We see in the descriptions not the things themselves, but only the impressions which they have made upon the soul of our author, and we know that the account of the impression never fully corresponds to the things. It is the business of the historical critic to infer back from the narrative to the first form of the impression, and from this to the actual fact, to remove the additions and changes due to subjective influence, and to restore the objective occurrence.'3

The task of the regressive (à potiori inductive) investigation consists in starting from ascertained individuals, and in explaining everything that follows, where premises are gained sufficient to prove the truth as accurately as possible. The result again serves as a premise for further argumentation, so that, so far as this arrangement goes, all other points of view are noticed only in so far as the final purpose, which consists

1 Erläut. zu den Elem. der Arist. Log. p. viii.

2 Schiller in Caroline von Wolzogen, Schiller's Leben, ii. 206, 1830.

3 Heinr. von Sybel, Ueber die Gesetze der Historischen Wissens, p. 12 f.: Bonn, 1864.

in the attainment of the greatest certainty possible, allows free play to each. After that a series of individuals has been thoroughly established in this way, the first thing to be done is to settle what the principles are. When full certainty cannot be attained, the degrees of probability are to be discovered and denoted with as much accuracy as possible.' These postulates are equally true for the sciences of Nature and of mental life. K. O. Müller, looking upon them as elements of method common to history and the natural sciences, designates them: a quick observation of the events of what is given in experience, the collection of as many individual points as it is possible to find, the enquiry into their regular concatenation according to the laws of probability, and their reference to the given fundamental elements of the universe of nature.

The investigation of individuals gains in significance as it can insert itself as a moment in the sum total of the scientific labour. Advance in the higher grades of knowledge is not to be made by means of a crude independence, which, trusting to common sense or guided by the idle fancy of personal genius, for the sake of a supposititious 'freedom from prejudice'—which is often only an unscientific persistence in superficial opinions, and full of unripe conceits-despises the study of the investigations of others, or contents itself with half and half apprehension without thorough-going reflection and critical accuracy. Nor is it attained by a compulsory soulless resignation, which, proceeding wholly upon acquired knowledge, and devoted to the safe appropriation and faithful reproduction of treasures produced by creative spirits, leaves unemployed its own power of production. It is attained by reaching an independent insight from the basis of the most accurate acquaintance with the whole development of the science up to this time. In science man, starting from the natural condition of freedom from restraint, must reach true freedom by submission.

The speculative instinct aims at the most general principles, and anticipates them in poetical or half-poetical forms before

1 Cf. the remarks on method in my Platonischen Untersuchungen, pp. 99, 112, and 268: Wien, 1861.

Exact investigation

strict science is able to recognise them. contents itself with the inductive discovery and verification of merely empirical laws, while the first principles cannot be established on the basis of facts with strict accuracy, but is too ready to sacrifice depth to certainty. The highest problem is to attain the end, pointed out by speculation, by the methods of exact investigation. Bunsen calls this, more immediately with reference to the Philosophy of History, the union of the spirit of the Baconian system with the categories of the German speculative mental Philosophy.'1

What may be said upon the history of the doctrines of Empiricism, Rationalism, Critical Philosophy, &c., because it must confine itself to the general stand-point of a theory of knowledge, belongs to the whole history of Logic as the doctrine of knowledge. We must therefore here refer to our

historical survey.2

§ 141. The means which method has at command for the constructive or synthetic construction of knowledge are: Definition, Division, and Deduction.

Definition ensures the permanence of the result of the process of abstraction, and serves as a foundation for Division and Deduction; and these processes again lead to new definitions.

Division separates the sum total of the scientific material, according to the relations of superordination, subordination, and co-ordination, in the belief that their regular arrangement ensures a true copy of the real relations. They are not reduced to a ready-made scheme, but the schematism, down to its last sub

1 Hippol. i. 276; cf. my article Ueber Idealismus, Realismus und Ideal-Realismus in Fichte's Zeitschrift, vol. xxxiv. 63-82, 1859.

2 Cf. above, §§ 10-35; cf. also expressions in §§ 37; 40; 44; 46 f.; 51; 56 f.; 67; 73; 74 ff.; 83; 127; 129; 131; 134 ff.; 138 f.