XII.

Logica, quae in usu est, ad errores (qui in notionibus vulgaribus fundantur) stabiliendos et figendos valet, potius quam ad inquisitionem veritatis; ut magis damnosa sit, quam utilis.

XIII.

Syllogismus ad principia scientiarum 13 non adhibetur, ad

required, then, not in order to replace, but in order to supplement, the old logic, is a logic which shall guarantee the premisses as well as the conclusions, which shall probe the validity of our elementary notions and first principles, as well as develope their ulterior consequences. Such a logic Bacon proposed to supply, or at least to inaugurate.

That Bacon recognised the function of the Syllogism as supplementary to Induction, is evident from several passages of the Novum Organum itself. But perhaps his most explicit statement on this subject is to be found in a letter to Father Baranzan (published in Spedding's Letters and Life of Bacon, vol. vii. pp. 375-7). This letter, which is also interesting on other accounts, contains the following passages :—

'Non est meum abdicare in totum syllogismum. Res est syllogismus magis inhabilis ad praecipua, quam inutilis ad plurima.

'Ad Mathematica quidni adhibeatur? Cum fluxus materiae et inconstantia corporis physici illud sit, quod inductionem desideret; ut per eam veluti figatur, atque inde eruantur notiones bene terminatae.

'De Metaphysica ne sis sollicitus. Nulla enim erit post veram Physicam inventam; ultra quam nihil praeter divina.

'In Physica prudenter notas, et idem tecum sentio, post notiones primae classis, et axiomata super ipsas, per inductionem bene eruta et terminata, tuto adhiberi syllogismum, modo inhibeatur saltus ad generalissima, et fiat progressus per scalam convenientem.'

On the place of Induction in Aristotle's system of logic, we have spoken in the Introduction.

13 The apxai of Aristotle. That the apxai, being the ultimate major premisses from which syllogism proceeds, do not themselves admit of syllogistic proof, is constantly insisted on by Aristotle. See, for instance, An. Post. i. 2 (72 a. 7), ἀρχὴ δ ̓ ἐστὶν ἀποδείξεως πρότασις ἄμεσος, ἄμεσος δὲ ἧς μή ἐστιν ἄλλη προτέρα. He also constantly insists on the fact that these ultimate principles must be gained by induction. See, for instance, Ethics, vi. 3. (3), Εκ προγινωσκομένων δὲ πᾶσα διδασκαλία, ὥσπερ καὶ ἐν τοῖς ἀναλυτικοῖς λέγομεν· ἡ μὲν γὰρ δι ̓ ἐπαγωγῆς, ἡ δὲ συλλογισμῷ. Ἡ μὲν δὴ ἐπαγωγὴ ἀρχή ἐστι καὶ τοῦ καθόλου, ὁ δὲ συλλογισμὸς ἐκ τῶν καθόλου. Εἰσὶν ἄρα ἀρχαὶ ἐξ ὧν ὁ συλλογισμὸς, ὧν οὐκ ἔστι συλλογισμός· ἐπαγωγὴ ἄρα. Amongst other decisive passages to the same effect may be specially cited An. Post. ii. 19, and Metaph. i. I.

media axiomata frustra adhibetur 1, cum sit 15 subtilitati naturae longe impar. Assensum itaque constringit, non res.

XIV.

Syllogismus ex propositionibus constat, propositiones ex verbis, verba notionum tesserae sunt 16. Itaque si notiones ipsae (id quod basis rei est) confusae sint, et temere a rebus abstractae; nihil in iis, quae superstruuntur, est firmitudinis. Itaque spes est una in inductione vera 17.

XV.

In notionibus nil sani est, nec in logicis, nec in physicis : non substantia, non qualitas, agere, pati, ipsum esse, bonae notiones sunt; multo minus grave, leve, densum, tenue, humidum, siccum, generatio, corruptio, attrahere, fugare, elementum,

For if the principia scientiarum be uncertain, the axiomata media, which are deduced from them, must, of course, be uncertain as well. We cannot rely on the truth of the conclusion, till we have placed beyond doubt the truth of the premisses.

15 The reason here assigned applies to both the preceding clauses.

16 The spoken or written word, it is true, is only the symbol of the notion in the mind of the speaker or writer, but could the notion itself be formed or retained without the use of language? This or that particular word is, of course, separable from the corresponding idea (as is shewn by the mere fact of translation from one language into another), but, without the use of signs of some kind or other, we could hardly think at all. These considerations, however, do not affect the truth of Bacon's criticism. Whether we speak of the ultimate constituents of the syllogism as words or notions, it is essential to all reasoning that we should have a clear understanding of them.

17 Cp. ii. 19, with the notes on that Aphorism. At first sight, it may not seem plain why it should be the office of Induction to remedy the defect of obscure, false, or inadequate notions. But all notions; we must recollect, involve judgments. In forming or attempting to realise a notion, we really assert a number of propositions. Thus if I put before my mind the notion of gold, I think of it as yellow, malleable, heavy, capable of being exchanged, etc., and, without forming these judgments, I should not realise the notion. Now, when we are dealing with Nature, sound judgments, and, therefore, sound notions can only be gained by observation of facts and a legitimate generalisation from those facts. We may see from what has been said that the Definition of natural objects or qualities (as distinct from merely technical terms) ought always to rest on previous inductions.

materia, forma, et id genus; sed omnes phantasticae et male terminatae 18.

XVI.

Notiones infimarum specierum, hominis, canis, columbae, et prehensionum immediatarum sensus, calidi, frigidi, albi, nigri, non fallunt magnopere; quae tamen ipsae a fluxu materiae et commissione rerum quandoque confunduntur 19; reliquae omnes (quibus homines hactenus usi sunt) aberrationes sunt, nec debitis modis a rebus abstractae et excitatae.

XVII.

Nec minor est libido et aberratio in constituendis axiomatibus, quam in notionibus abstrahendis; idque in ipsis principiis, quae ab inductione vulgari 20 pendent. At multo major 21 est in axiomatibus, et propositionibus inferioribus, quae educit syllogismus.

XVIII.

Quae adhuc inventa sunt in scientiis, ea hujusmodi sunt, ut notionibus vulgaribus fere subjaceant: ut vero ad interiora et remotiora naturae penetretur, necesse est ut tam notiones quam axiomata magis certa et munita via a rebus abstrahantur, atque omnino melior et certior intellectus adoperatio in usum veniat.

XIX.

Duae viae 22 sunt, atque esse possunt, ad inquirendam et

18 Ill-defined.

19 It must be recollected that there is no breach of continuity in Nature as there is in our distinctions. Hence, our terms or notions are never exhaustive or adequately representative of the endless varieties of Nature. Mr. Ellis proposes to read commistione for commissione. From the context it is clear that Bacon means that the union of bodies of different kinds, by giving rise to new qualities and species intermediate to those for which we have recognised names, tends to confuse our ideas of the latter. I think therefore we ought to read "commistione" for "commissione."'

20 He is alluding to the Inductio per enumerationem simplicem as distinguished from the Scientific Induction by which he proposes to replace it. 21 For, by deducing error from error, we recede further and further from the truth.

22 It should be noticed that even the falsest and flimsiest generalisations about Nature rest upon some slight basis of fact. After observing a few

inveniendam veritatem. Altera a sensu et particularibus advolat ad axiomata maxime generalia, atque ex iis prin

particulars, Bacon complains, men usually fly off to the widest generalisations, and then acquiesce in these, as if they were so many indubitable truths. But, in considering this frequent source of error, he does not perceive that rapid generalisation is often indispensable to the scientific enquirer. The fault does not consist so much in making rapid generalisations as in acquiescing too readily and confidently in them, when made. The method of gradual and continuous ascent from particulars to the highest axioms, through all the intermediate steps, which is here commended by Bacon, is not the method which, for the most part, has been actually pursued by the most successful investigators of Nature, nor would its general adoption contribute to the advancement of science. Provided a hypothesis be regarded simply as a hypothesis, and not assumed as true without a rigorous investigation, the mere fact of its generality ought to be no objection to it. Indeed, by stimulating enquiry and directing its course, it is plain that a very general hypothesis, such as the theory of universal gravitation, or Laplace's nebular hypothesis, or the wave-theory of light and sound, or the theory of evolution, or the theory of final causes, even in its cruder forms, may, whether ultimately proved to be true or false, be of the utmost service in the investigation even of small groups of facts. The all-important proviso, of course, is that, till proved, such a hypothesis must be taken simply quantum valeat, as a hypothesis and no more. It would be far from an advantage to science, to restrain the flights of scientific imagination, but the products of imagination must never be confounded with the results of proof. The fantastic character of the Ancient Physics was due far less to an exuberant imagination than to a defective sense of evidence. And the true remedy was to insist on the necessity of verification rather than on the suppression of hypothesis.

There is, therefore, a third way of investigation which is not open to Bacon's animadversions and which is peculiarly the way of genius. It begins, like the other two, with the observation of particulars, for this always is and must be the first step, and then, by an effort of imagination, frames for itself some explanation which has a far wider range of application than the special class of phenomena which has been observed. This axioma maxime generale is regarded as a hypothesis, to be hereafter proved or disproved, but, meanwhile, it serves as a provisional explanation of the facts, and stimulates to further investigations. From it may be deduced a number of axiomata media which admit of being constantly compared with facts, and thus an ever-increasing experience tends to prove or disprove the axiom in question. If facts do not agree with the deductions from the hypothesis, it must be thrown aside as useless or modified to meet the exceptions; but if it agree with the facts, there is a strong presumption in its favour. Even still, however, it must not be finally admitted as an ascertained truth, till it has been shewn to conform to the rigorous requirements of the inductive methods, or con

cipiis eorumque immota veritate judicat et invenit axiomata media; atque haec via in usu est. Altera a sensu et particu

nected deductively with some still higher generalisations which have been established on independent grounds. When this final step has been taken, the axiomata media deduced from it may be accepted with implicit confidence.

Generally speaking, the axioma maxime generale, even when conceived before the axiomata media, will rest on an induction from these, as its final proof; as these themselves will probably rest on lower axioms, and so on till we reach the axioms which rest on an induction from individual facts. But, in the order of conception, though not in the order of proof, the axioma maxime generale or one of the highest of the intermediate axioms usually comes first, and this circumstance it is which distinguishes the method we are describing from that commended by Bacon.

The history of the Theory of Gravitation supplies an example of a scientific doctrine, the steps of which were established almost in the exact order which Bacon recommends. This may be seen by consulting the Inductive Table of Astronomy given in Dr. Whewell's Novum Organum Renovatum. Moreover, in all sciences this order is the most convenient mode of representing the laws, when once established, though, as we have seen, it is by no means that in which they are always actually established, as a matter of fact. Bearing in mind this qualification, we may adopt the words of Dr. Whewell :

'We have, indeed, already explained that science consists of Propositions which include the Facts from which they were collected; and other wider Propositions, collected in like manner from the former, and including them. Thus, that the stars, the moon, the sun, rise, culminate, and set, are facts included in the proposition that the heavens, carrying with them all the celestial bodies, have a diurnal revolution about the axis of the earth. Again, the observed monthly motions of the moon, and the annual motions of the sun, are included in certain propositions concerning the movements of those luminaries with respect to the stars. But all these propositions are really included in the doctrine that the earth, revolving on its axis, moves round the sun, and the moon round the earth. These movements, again, considered as facts, are explained and included in the statement of the forces which the earth exerts upon the moon, and the sun upon the earth. Again, this doctrine of the forces of these three bodies is included in the assertion, that all the bodies of the solar system, and all parts of matter, exert forces, each upon each. And we might easily shew that all the leading facts in astronomy are comprehended in the same generalisation. In like manner with regard to any other science, so far as its truths have been well established and fully developed, we might shew that it consists of a gradation of propositions, proceeding from the most special facts to the most general theoretical assertions.' (Novum Organum Renovatum, ch. vi. § 1.)

Even in Astronomy, however, the heliocentric hypothesis had occurred to the ancients long before the state of their knowledge was sufficient