till they terminate in those which are universal'.

Axioms thus investigated and established, are applicable to all parts of learning, and are the indispensable', and the truly admirable expedients by which reason pushes on her inquiries in the particular pursuit of truth, in every branch of knowledge. The method of reasoning by which they are

and disagreement of ideas, of which he has said so much as the sole criteria of truth.

In the twelfth chapter of this book indeed he exposes the absurdity of taking axioms upon credit; but shows how little he understood of their use. His conception of the improvement of learning was very imperfect; for though he might understand the nature of physics, he was unacquainted with the philosophy of ethics and mathematics.

* Duæ viæ sunt atque esse possunt ad inquirendam veritatem. Altera a sensu et particularibus advolat ad axiomata maximè generalia, atque ex his principiis eorumque immotâ veritate judicat et invenit axiomata media: atque hæc via in usu est. Altera a sensu et particularibus excitat axiomata ascendendo continenter et gradatim, ut ultimo loco perveniatur ad maxime generalia; quæ via vera est et intentata.— Bacon. Nov. Org. lib. i. aph. 19. See also lib. i. aph.

102-107.

7

Τῶν ἀρχῶν δὲ αἱ μὲν ἐπαγωγῇ θεωρῶνται, αἱ δὲ αἰσθήσει, αἱ δὲ ἐθισμῷ τινὶ, καὶ ἄλλαι δὲ ἄλλως. Μετιέναι δὲ πειρατέον ἑκάσας ᾗ πεφύκασι, σπυδατέον δὲ ὅπως ὁρισθῶσι καλῶς. Μεγάλην γὰρ ἔχεσι ῥοπὴν πρὸς τὰ ἑπόμενα. Δοκεῖ ἦν πλεῖον ἢ τὸ ἥμισυ τῶ παντὸς εἶναι ἡ ἀρχὴ, καὶ πολλὰ ἐμφανῆ γίνεσθαι δι' αὐτῆς τῶν nTeμévwv.-Aristot. Ethic. Nicom. lib. i. cap. 7.

formed is that of true and legitimate induction, which is therefore called by the best and soundest of logicians, the key of interpretation'.

If instead of taking his axioms out of the great families of the categories by an immediate and indolent extraction, and erecting them by his own sophistical invention into the principles upon which his disputation was to be employed", the analytical genius of Aristotle had presented us with the laws of the true inductive logic by which axioms are philosophically formed, and given us an example of it with his usual sagacity

• Inductionem censemus eam esse demonstrandi formam quæ sensum tuetur et naturam premit, et operibus imminet ac fere immiscetur.-Bacon. Distrib. Operis.

9 Ibid. Nov. Org. lib. ii. aph. 10.

10 Ex experientia arripiunt varia et vulgaria, eaque neque certo comperta, nec diligenter examinata et pensitata; reliqua in meditatione atque ingenii agitatione ponunt.Hujus generis exemplum in Aristotele maxime conspicuum est, qui philosophiam dialecticâ suâ corrupit, quum mundum ex categoriis effecerit, et innumera pro arbitrio suo naturæ rerum imposuerit, magis ubique sollicitus quomodo quis respondendo se explicet, et aliquid reddatur in verbis positivum, quam de interna rerum veritate.--Ille enim prius decreverat; neque experientiam ad constituenda axiomata rite consuluit; sed, postquam pro arbitrio suo decrevisset, experientiam ad sua placita tortam circumducit et captivam. -Ibid, lib. i. aph. 62, 63.

in a single branch of science"; he would have brought an offering more valuable and acceptable to the temple of truth, than he effected by the aggregate of all his logical and philosophical productions.

It is after the inductive process has been industriously pursued and successfully per

"Though in different parts of his works he gives a general idea of induction (Ομοίως δὲ καὶ περὶ τοὺς λόγος, οἵ τε διὰ συλλογισμῶν, καὶ οἱ δι' ἐπαγωγῆς· ἀμφότεροι γὰρ διὰ προγινωσ κομένων ποιῦνται τὴν διδασκαλίαν· οἱ μὲν, λαμβάνοντες ὡς παρὰ ξυνιέντων· οἱ δὲ, δεικνύντες τὸ καθόλε, διὰ τῶ δῆλον εἶναι τὸ καθέκατον.Analyt. Post. lib. i. cap. i. Ἐκ προγινωσκομένων δὲ πᾶσα διδασκαλία. Ἡ μὲν δι' ἐπαγωγῆς, ἡ δὲ συλλογισμῷ. Ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐτι καὶ τῷ καθόλο. Ο δὲ συλλογισμὸς ἐκ τῶν καθόλο. Εἰσὶν ἄρα ἀρχαὶ, ἐξ ὧν ὁ συλλογισμός, ὧν ἐκ ἔτι συλλογισμός.-Ethic. Nicom. lib. vi. cap. 3.) from the whole of them, analytical, topical, and physical, it is clear he was very imperfectly acquainted with the particular philosophy of the inductive organon: and it is apparent from a passage in his Ethics (μὴ λανθανέτω δ ̓ ἡμᾶς, ὅτι διαφέρεσιν οἱ ἀπὸ τῶν ἀρχῶν λόγοι, καὶ οἱ ἐπὶ τὰς ἀρχάς. Εὖ γὰρ καὶ Πλάτων ἠπόρει τῦτο καὶ ἐζήτει, πότερον ἀπὸ τῶν ἀρχῶν, ἢ ἐπὶ τὰς ἀρχάς ἐτιν ἡ ὁδός, ὥσπερ ἐν τῷ ταδίῳ, ἀπὸ τῶν ἀθλοθετῶν ἐπὶ τὸ πέρας, ἢ ἀνάπαλιν. Αρκτέον μὲν γὰρ ἀπὸ τῶν γνωρίμων. Ταῦτα δὲ διττῶς. Τὰ μὲν γὰρ ἡμῖν, τὰ δε ἁπλῶς. Ἴσως ὖν ἡμῖν γε ἀρκτέον ἀπὸ τῶν ἡμῖν γνωρίμων.—ἀρχὴ γὰρ τὸ ὅτι· καὶ εἰ τόσο φαίνοιτο ἀρκόντως, ἐδὲν προσδεήσει τῷ διότι.-Ethic. Nicom. lib. i. cap. 4.) that he never put it in practice in the formation of his axioms and principles, which he chose rather to assume gratuitously, or to fabricate by his own invention. See Analyt. Post. lib. i. cap. 24.

formed, that definition1 so pompously but prematurely, so formally but gratuitously affected by the old logicians and their disciples of the schools, may be logically and usefully introduced, by beginning with the genus, passing through all the graduate and subordinate stages, and marking the specific difference as it descends, till it arrive at the individual which is the subject of the question. By adding an affirmation or negation of the attribute of the genus, to the species or individual, or that of a general accident, to the particular substance so defined, and thus making the definition a proposition, the truth of the question will be logically solved, without any farther process. So that instead of being the first, as employed by the logic in common use, definition should form the last act of reason in the search of all truth, except that which is strictly mathematical.

But we are now anticipating the subject of the following section.

12 Δεῖ γὰρ ἐξ ὧν ὁ ὁρισμὸς, προειδέναι καὶ εἶναι γνώριμα. Aristot. Metaph. lib. i. cap. 7.

13 Aristot. Analyt. Post. lib. i. cap. 10.

SECT. VI.

Of Reasoning by Syllogism.

THESE HESE axioms or general propositions thus inductively established, become another species of principles which may be properly called secondary, and which lay the foundation of another and different method of reasoning.

When these are formed, and not before, we may safely admit the maxim with which the old logicians set out in the exercise of their art, as the great hinge on which their reasoning and disputation turn,-from truths that are already known', to derive others which are not known. Or to state it more comprehensively, so as to apply to probable, as well as to demonstrative reasoning-from truths which are better known', to derive others which are less known.

1

Ἐξ ἀληθῶν καὶ πρώτων καὶ ἀμέσων καὶ γνωριμοτέρων καὶ πporépwv kai airɩwv тõ ovμπépaoμaros.—Aristot. Analyt. Post. lib. i.

Ex præcognitis et præconcessis.