of our reason dwells originally only in the dim twilight of the sense-world until, trained by exercise, it is able to enter and participate in the bright daylight of the realm of pure thought. But there is an essential difference between the Platonic and the Aristotelian doctrines when the two methods are defined more distinctly. Plato rather requires an ascent to the general notion by means of abstraction, and a descent to the more special notion by means of division; while Aristotle finds this to be a particular instance of the double method of forming inferences-the inductive, which conducts to a knowledge of the universal, and the syllogistic, which, by means of its middle notion, derives the particular from the universal with apodictic certainty. The (Platonic) method of division is only an insignificant part of syllogistic procedure: ὅτι δ' ἡ διὰ τῶν γενῶν διαίρεσις μικρόν τι μόριόν ἐστι τῆς εἰρημένης μεθόδου, ῥᾴδιον ἰδεῖν· ἐστὶ γὰρ ἡ διαίρεσις οἷον ἀσθενὴς συλλογισμός· ὃ μὲν γὰρ δεῖ δεῖξαι, αἰτεῖται, συλλογίζεται δ' ἀεί τι τῶν ἄνωθεν.—εὐδαμοῦ γὰρ ἀνάγκη γίνεται τὸ πρᾶγμα ἐκεῖνο εἶναι τωνδὶ ὄντων. This charge against the Platonic method of division holds good only in so far as this method is synthetic. But division cannot be subordinated as a μxpòv μópiov under syllogistic procedure; it must take its place beside syllogism as an equally valid form of thought and knowledge of independent value.

Aristotle calls the reduction of given concrete products to their principal elements a solution or analysis, ávaλúv, and he was accustomed to cite his logical work itself, because it was a scientific reduction of thinking, and especially of the different modes of inference, under the title of Analytic.

5

Alexander of Aphrodisias says, in harmony with this use of Aristotle: ἀναλυτικὰ δὲ, ὅτι ἡ παντὸς συνθέτου εἰς τὰ ἐξ ὧν ἡ σύνθεσις αὐτοῦ ἀναγωγὴ ἀνάλυσις καλεῖται·—ἡ μὲν γὰρ σύνθεσις ἀπὸ τῶν ἀρχῶν ὁδός ἐστὶν ἐπὶ τὰ ἐκ τῶν ἀρχῶν, ἡ δὲ ἀνάλυσις ἐπανοδός ἐστιν ἐπὶ τὰς ἀρχὰς ἀπὸ τοῦ τέλους.

6

Philoponus directs attention to the use of the terms analysis

1 Anal. Pri. i. 31.

3 Eth. Nic. iii. 5; Anal. Pri. i. 32. 5 Ad Anal. Pri. f. 4 a.

2 Anal. Post. ii. 5.

4 Cf. above, pp. 6, 25.

6 Ad Anal. Post. f. 35 B.

and synthesis in Geometry. Analysis means finding reasons for a given theorem; Synthesis is the opposite procedure.1 Melanchthon says: "Geometris usitata nomina sunt et notissima: compositio Synthesis, quae à priori procedit; e contra resolutio seu Analysis, quae à posteriori ad principia regreditur.'

The terms Analysis and Synthesis have been used in Logic since the time of Des Cartes 2 to denote reduction to principles and derivation from principles.

Newton says (at the conclusion of his Optics) the analytical must always precede the synthetical in mathematical and physical investigation. Methodus analytica est: experimenta capere, phenomena observare, indeque conclusiones generales inductione inferre, nec ex adverso ullas objectiones admittere, nisi quae vel ab experimentis vel ab aliis certis veritatibus desumantur. Hac analysi licebit ex rebus compositis ratiocinatione colligere simplices, ex motibus vires moventes et in universum ex effectis causas ex causis particularibus generales, donec ad generalissimas tandem sit deventum. Synthetica methodus est causas investigatas et comprobatas assumere pro principiis eorumque ope explicare phenomena ex iisdem orta, istasque explicationes comprobare.

3

Wolff, following the Cartesian definitions, says: ordo, quo utimur in tradendis dogmatis, dicitur methodus; appellatur autem methodus analytica, qua veritates ita proponuntur, prout vel inventae fuerunt, vel minimum inveniri potuerunt; methodus e contrario synthetica appellatur, qua veritates ita proponuntur, prout una ex altera facilius intelligi et demonstrari potest; methodus mixta est, quae ex utriusque combinatione resultat. This distinction of the methods is not good as a definition, because it gives the derivative and not the fundamentally essential characteristics.

1 Galen also speaks of geometrical Analytic, probably in the sense of Logic expounded according to geometrical methods. He mentions in his De Propr. Libr. xvi. a treatise of his entitled: öryεwμεTPIKN ἀναλυτικὴ ἀμείνων τῆς τῶν Στωϊκῶν ὑπόμνημα ἕν.

Kant distinguishes analytic from synthetic Judgments,' but prefers to apply to Method the terms regressive and progressive (methodus regrediens a principiatis ad principia, methodus progrediens a principiis ad principiata).2

Hegel' assumes that both methods are true in the positive sciences only because the knowledge conveyed in them relates only to the understanding,' and is only finite knowledge. The method of philosophical speculation is Dialectic, the form of the Absolute Idea,' of the 'pure reason.' But this Dialectic is only the supposititious attempt at a synthesis, which does not yield the results of Analysis.

Schleiermacher requires that the process of deduction' should rest upon a 'process of induction' (and Synthesis upon Analysis).

Trendelenburg, avoiding both an exclusive empiricism and the Hegelian theory of pure thinking,' sees synthesis to be the glory of the sciences, but recognises that the condition of the scientific character of synthesis is its subjection to the strict discipline of the analytic methods.

Beneke proves how synthesis in all the sciences, mathematics not excepted, is conditioned by previous analysis, and warns us against betaking ourselves to syntheses à priori, which, because they are knowledge without foundation, are no better than caprice and fancy.

The following remark will suffice upon the present mathematical use of the expressions Analysis and Synthesis. Constructive Geometry usually takes the synthetic course of proof, and leaves the analytic methods to find proofs in solutions of problems. However, Geometry, which reckons on the basis of the systems of co-ordinates, proceeds, by way of preference, analytically, when it regressively seeks the conditions under which certain equivalents are satisfied. It proceeds by means of algebraical analysis which rests also on this regressive procedure, and is therefore called Analytical Geometry.

1 Cf. above, § 83.

3 Encycl. § 226 ff.

5 Log. Unters. 2nd ed. ii. 294.

2 Logik, § 117.

4 Dial. § 283.

6 Log. ii. pp. 159-188.

§ 140. The empirical data, from which all scientific investigation in its regressive or analytical part (or inductive investigation in the wider use of the expression) must start, are given immediately by external and internal Perception (perceptio), and mediately by Testimony (testimonium).

Perception when animated by a conscious aim becomes Observation (observatio), and when the object admits of the investigation, Experiment (experimentum). In experiment we ourselves change the conditions of what happens; we seek to know what conditions are influential and the kind of influence they possess expressly for the sake of the observation, and the answer to the question stated is given by Nature herself.

The trustworthiness (fides) of testimony is settled by the general logical rules which govern the inference from the conditioned to the condition, and, more particularly, the construction and verification of hypotheses (§ 134), for this is only a special case of that more general class. The fact to be concluded is the real prius of the testimony. The content of the testimony may have for its ground, either that the event has happened and has been observed exactly in the same way, or that the observation has been influenced by a false apprehension, an untrue recollection, preference of some fancy to strict accuracy, or the confusion of subjective judgment with objective fact. But the witness of an immediate or eyewitness (testis primitivus, proximus, oculatus), who is an immediate witness notoriously or according to the assured concurrence of historical criticism, is

trustworthy, provided that he has been able to apprehend the fact strictly and truly, according to his intellectual and moral condition, and to represent it truly, and has taken care to do so. The agreement of several immediate witnesses with each gives to their assertion a very high probability, if it is proved that they are independent, that they have not been deceived by the same deception, nor have been affected and psychologically influenced by the same one-sidedness in apprehension and statement; for a purely accidental agreement in an accidental circumstance has, according to the laws of the calculation of probability (cf. § 132), a very high degree of probability in all complicated relations. The trustworthiness of mediate witnesses (testes secundarii, ex aliis testibus pendentes) is determined partly by their sense and critical capacity, partly and chiefly by their relation to immediate witnesses. It is an essential problem, but seldom absolutely soluble, to discover the genealogy of testimony. The testimony of later witnesses is suspicious, especially when there is anything in it to serve a distinct (poetical, national, philosophical, dogmatic, or practical) tendency, and the further it stands from the actual occurrences. The verification of the subjective trustworthiness of different witnesses is reciprocally related to the verification of the objective probability, which what is attested has in itself and in connection with undoubted facts. Criticism is positive, so far as it has to construct a complete picture of the real previous occurrence, by combining the true elements and excluding the false.

The regressive or analytical investigation seeks to

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