Εικόνες σελίδας
Ηλεκτρ. έκδοση
[ocr errors]

he employs the word forms, in speaking of natural philosophy, he is always to be understood as meaning the laws of nature.* Whether so accurate a reasoner as Locke would have admitted Bacon's general apology for so glaring an abuse of words, may perhaps be doubted: but, after comparing the two foregoing sentences, would Locke (notwithstanding his ignorance of the syllogistic art) have inferred, that Bacon's opinion of the proper object of science was the same with that of Plato? The attempt to identify Bacon's induction with the induction of Aristotle, is (as I trust will immediately appear) infinitely more extravagant. It is like confounding the Christian Graces with the Graces of Heathen Mythology.

The passages in which Bacon has been at pains to guard against the possibility of such a mistake are so numerous, that it is surprising how any person, who had ever turned over the pages of the Novum Organon, should have been so unlucky as not to have lighted upon some one of them. The two following will suffice for my present purpose.

"(1) In constituendo autem axiomate, forma inductionis alia quam "adhuc in usu fuit, excogitanda est. Inductio enim quae procedit 66 per enumerationem simplicem res puerilis est, et precario concludit. "At inductio, quae ad inventionem et demonstrationem scientiarum "et artium erit utilis, naturam separare debet, per rejectiones et "exclusiones debitas; ac deinde post negativas tot quot sufficiunt,

non in materia determinatas contemplando et prensando. Quod si diligenter, serio, et sincere, ad actionem, et usum, et oculos convertamus; non difficile erit disquirere, et noti tiam assequi, quae sint illae formae, quarum cognitio res humanas miris modis locupletare et beare possit. De Augment. Scient. Lib iii. Cap. iv.

[It is clear, that Plato, a man of sublime genius and who saw every thing around him as from a lofty eminence, in his doctrine of images, saw that forms are the true object of science; though he lost the advantage of this most true opinion, by arresting and contempla ting forms as wholly abstracted from matter, and not as existing in matter. Whereas, if we diligently, carefully, and sincerely turn to practice, and use, and the perception of our senses, it will not be difficult for us to enquire, or to learn, what are those forms, an acquaintance with which will so wonderfully extend the boundaries of human knowledge.]

*Nos quum de formis loquimur, nil aliud intelligimus, quam leges illas, quae naturam aliquam simplicem ordinant et constituunt ; ut calorem, lumen, pondus, in omnimoda ma. teria et subjecto susceptibili. Itaque eadem res est forma calidi, aut forma luminis, et lex calidi, sive lex luminis."-- Nov. Org. Lib. ii. Aph xvii.

[When we speak of forms, we understand nothing more, than those laws which regulate and constitute any simple disposition of nature; as heat, light, weight, in matter, and every subject susceptible of them; therefore the form of heat, the form of light, is the same as the law of heat, the law of light, &c.]

(1) [In the formation of an Axiom, a form of induction different from that in common use must be struck out. For that induction which proceeds by simple enumeration is a childish thing and concludes unsatisfactorily. But an induction which will be useful to the discovery and demonstration of the arts and sciences, ought to separate those proper ties which are original, by proper rejections and exclusions; and then, after as many negatives as are sufficient, to decide upon the affirmatives. This as yet hath not been done, nor indeed attempted, except in some degree by Plato, who has indeed in some measure made use of this form of induction for the purpose of thoroughly examining definitions and ideas. But to a good and proper use of this kind of induction, very many things are necessary which no man has hitherto thought of: so that more labour must be bestowed upon it, than has been spent upon syllogism. And in this species of induction is our greatest hope.]

"super affirmativas concludere; quod adhuc factum non est, nec "tentatum certe, nisi tantummodo a Platone, qui ad excutiendas de"finitiones et ideas, hac certe forma inductionis aliquatenus utitur. "Verum ad hujus inductionis, sive demonstrationis, instructionem "bonam et legitimam, quamplurima adhibenda sunt, quae adhuc "nullius mortalium cogitationem subiere; adeo ut in ea major sit "consumenda opera, quam adhuc consumpta est in syllogismo. At"que in hac certe inductione, spes maxima sita est."*

"(1) Cogitavit et illud Restare inductionem, tanquam ulti"mum et unicum rebus subsidium et perfugium. Verum et hujus nomen "tantummodo notum esse; vim et usum homines hactenus latuisse."†

That I may not, however, be accused of resting my judgment entirely upon evidence derived from Bacon's writings, it may be proper to consider, more particularly, to what the induction of Aristotle really amounted, and in what respects it coincided with that to which Bacon has extended the same name.

[ocr errors]

"Our belief (says Aristotle in one passage) is, in every instance, "founded either on syllogism or induction." To which observation he adds, in the course of the same chapter, that "induction is an "inference drawn from all the particulars which it comprehends." It is manifest, that, upon this occasion, Aristotle speaks of that induction which Bacon, in one of the extracts quoted above, describes as proceeding by simple enumeration; and which he, therefore, pronounces to be "a puerile employment of the mind, and a mode "of reasoning leading to uncertain conclusions."

In confirmation of Bacon's remark, it is sufficient to mention, by way of illustration, a single example; which example, to prevent cavils, I shall borrow from one of the highest logical authorities,Dr. Wallis of Oxford.

"In an inference from induction, (says this learned writer) if the "enumeration be complete, the evidence will be equal to that of a "perfect syllogism; as if a person should argue, that all the planets "(the Sun excepted) borrow their light from the Sun, by proving "this separately of Saturn, Jupiter, Mars, Venus, Mercury, and the "Moon. It is, in fact, a syllogism in Darapti, of which this is the ❝ form.

Nov. Org. Lib. i. Aph. cv.

+ Cogitata et Visa. The short tract to which Bacon has prefixed this title contains a summary of what he seems to have considered as the leading tenets of his philosophical works. It is one of the most highly finished of all his pieces, and is marked throughout with an impressive brevity and solemnity, which commands and concentrates the attention. Nor does it affect to disguise that consciousness of intellectual force, which might be expected from a man destined to fix a new era in the history of human reason.-Franciscus Baconus sic cogitavit, &c. &c.

First Analytics, Chap. xxiii. Vol. I. p. 126. Edit. Du Val.

(1) [It hath been his opinion, that there yet remains an induction, our sole and last refuge. As yet, however, this is known by name only; its power and use have been hitherto con. cealed from mankind.]

"Saturn, Jupiter, Mars, Venus, Mercury, and the Moon, each "borrow their light from the Sun:

"But this enumeration comprehends all the Planets, the Sun excepted:

"Therefore all the Planets, (the Sun excepted) borrow their light from the Sun.”*

If the object of Wallis had been to expose the puerility and the precariousness of such an argument, he could not possibly have selected a happier illustration. The induction of Aristotle, when considered in this light, is indeed a fit companion for his syllogism; in as much, as neither can possibly advance us a single step in the acquisition of new knowledge. How different from both is the induction of Bacon, which, instead of carrying the mind round in the same circle of words, leads it from the past to the future, from the known to the unknown?†

Institutio Logica, Lib. iii. cap. 15. The reasoning employed by Wallis to shew that the above is a legitimate syllogism in Darapli, affords a specimen of the facility with which a logical conjuror can transform the same argument into the most different shapes. "Siquis objiciat, hunc non esse legitimum in Darapti syllogismum, eo quod conclusionem habeat universalem; dicendum erit hanc universalem (qualis qualis est) esse universalem collectivam; quae singularis est. Estque vox omnis hic loci (quae dici solet) pars Categorematica; utpote pars termini minoris (ut ex minori propositione liquet) qui hic est (non Planetae sed) omnes Planetae (excepto sole,) seu tota collectio reliquorum (excepto sole) Planetarum, quae collectio unica est; adeoque conclusio singularis. Quae quidem (ut singulares aliae) quamvis sit propositio Universalis, vi materiae; non tamen talis est ut non possit esse conclusio in tertia figura. Quippe in tertia figura quoties rinor terminus, seu praedicatum minoris propositionis (adeoque subjectum conclusionis) est quid singulare, necesse est ut conclusio ea sit (vi materiae, non formae) ejusmodi universalis."

lu justice to Dr. Wallis, it is proper to subjoin to these quotations, a short extract from the dedication prefixed to this treatise." Exempla retineo, quae apud logicos trita sunt; ex philosophia quam vocant Veterem et Peripateticam petita: quia logicam bie trado, et quidem Peripateticam; non naturalem philosophiam. Adeoque, de quatuor elementis; de telluris quiete in universi medio, de gravium motu deorsum, leviumque sursum; de septenario planetarum numero, aliisque; sic loquor, ut loqui solent Peripatetici."{

"In arte judicandi (ut etiam vulgo receptum est) aut per Inductionem, aut per Syllogismum concluditur. At quatenus ad judicium, quod fit per inductionem, nihil est, quod nos detinere debeat: uno siquidem eodemque mentis opere illud quod quaeritur, et inveni

[If any one object that this is not a legitimate syllogism in Darapti, because it has a universal conclusion; I shall reply, that this universal, whatever it be, is a universal collec tive; which is singular. And the word all, here really forms part of the predicate; as part of the minor term, (as being in a minor proposition) which here is (not the pla nets, but) all the planets (the sun excepted) or the collective enumeration of all the planets, (the sun excepted) which collection is one, and the conclusion therefore singular. Which indeed (as other singular propositions) although it be a universal proposition on account of the matter of which it is formed; yet it is not such that it cannot be a conclusion in the third figure. For in the third figure, as often as the minor term, or the predicate of the minor proposition, (and therefore the subject of the conclusion,) is any thing singular, of necessity the conclusion (in virtue of the matter, not the form) is a universal of the same kind.]

[I retain as examples those which are common with logicians; drawn from the philosophy which they call the ancient or Peripatetic; because I here treat of logic and the Peripatetic art, not of natural philosophy. And so, of the four elements, of the rest of the earth in absolute space, of the motion downwards of heavy bodies, and of light bodies upwards, of the septenary number of the planets, and of other matters; I speak as the Pe ripatetics are wont to do.]

use in

Dr. Wallis afterwards very justly .remarks, "that inductions of Induction "this sort are of frequent use in mathematical demonstrations; in on on y mod “which, after enumerating all the possible cases, it is proved, that of histotle "the proposition in question is true of each of these considered seof use "parately; and the general conclusion is thence drawn, that the mathematics "theorem holds universally. Thus, if it were shewn, that, in all "right-angled triangles, the three triangles are equal to two right "angies, and that the same thing is true in all acute-angled, and also "in all obtuse angled triangles; it would necessarily follow, that in every triangle the three angles are equal to two right angles; "these three cases manifestly exhausting all the possible varieties "of which the hypothesis is susceptible."


My chief motive for introducing this last passage, was to correct an idea, which, it is not impossible, may have contributed to mislead some of Wallis's readers. As the professed design of the treatise in question, was to expound the logic of Aristotle, agreeably to the views of its original author; and as all its examples and illustrations assume as truths the Peripatetic tenets, it was not unnatural to refer to the same venerated source. the few incidental reflections with which Wallis has enriched his work. Of this number is the foregoing remark, which differs so very widely from Aristotle's account of mathematical induction, that I was anxious to bring the two opinions into immediate contrast. The following is a faithful translation from Aristotle's own words:

"If any person were to show, by particular demonstrations, that "every triangle, separately considered, the equilateral, the scalene, "and the isosceles, has its three angles equal to two right angles, "he would not, therefore, know that the three angles of a triangle "are equal to two right angles, except after a sophistical manner. "Nor would he know this as an universal property of a triangle, "although, beside these, no other triangle can be conceived to ex"ist; for he does not know that it belongs to it quâ triangle: Nor "that it belongs to every triangle, excepting in regard to number; "his knowledge not extending to it as a property of the genus, al"though it is impossible that there should be an individual which "that genus does not include."*

tur et judicatur—At inductionis formam vitiosam prorsus valere jubemus; legitimam ad Novum Organum remittimus."-De Aug. Scient. Lib. v. Cap. iv,

[lo the art of reasoning (at least as commonly received,) the conclusion is drawn either by induction or by syllogism. As to the judgment which is drawn from induction, there is nothing which need detain us, for whatever is sought is both discovered and judged of by one and the same effort of the mind. We neglect, therefore, the form of induction which we consider useless, and refer for the true to the Novum Organum.]


ТО σκαλώνων, X치 То ισοσκελές"

Δια τουτο ουδ' αν τις δειξη καθ' έκαστον το τρίγωνον αποδείξει η μια η έτερα, ότι δυο ορθας έχει έκαστον. το ισοπλευρον χωρίς, και ουπω οιδε το τριγωνον ότι δυο ορθαίς ίσον, ει μη τον σοφιστικον τρόπον ουδε καθόλου τρίγωνον, οὐδ' εἰ μηδεν εστι παρά ταύτα τρίγωνον ἑτερον ου γαρ, ή τρίγωνν οἶδεν· ουδε σαν τριγων, αλλ' ή κατ ́ αριθμόν· κατ' είδος δὲ οὗ τσαν, και ει μηδὲν ἔστιν ὁ ουκ od.-Analyt. Poster. Lib. i. Cap. v.

For what reason Aristotle should have thought of applying to such an induction as this the epithet sophistical, it is difficult to conjecture. That it is more tedious, and therefore less elegant than a general demonstration of the same theorem, is undoubtedly true; but it is not on that account the less logical, nor, in point of form, the less rigorously geometrical. It is, indeed, precisely on the same footing with the proof of every mathematical proposition which has not yet been pushed to the utmost possible limit of generalization.

It is somewhat curious, that this hypothetical example of Aristotle is recorded as a historical fact by Proclus, in his commentary on Euclid. "One person, we are told (I quote the words of Mr. Mac"laurin) discovered, that the three angles of an equilateral triangle "are equal to two right angles; another went farther, and shewed "the same thing of those that have two sides equal, and are called "isosceles triangles: and it was a third that found that the theorem "was general, and extended to triangles of all sorts. In like man66 ner, when the science was farther advanced, and they came to "treat of the conic sections, the plane of the section was always "supposed perpendicular to the side of the cone; the parabola was "the only section that was considered in the right-angled cone, the "ellipse in the acute-angled cone, and the hyperbola in the obtuse"angled. From these three sorts of cones, the figures of the sec❝tions had their names for a considerable time; till, at length, Apol"lonius shewed that they might all be cut out of any one cone, and, "by this discovery, merited in those days the appellation of the "Great Geometrician."*

It would appear, therefore, that in mathematics, an inductive inference may not only be demonstratively certain, but that it is a natural, and sometimes perhaps a necessary step in the generalization of our knowledge. And yet it is of one of the most unexceptionable inductive conclusions in this science, (the only science in which it is easy to conceive an enumeration which excludes the possibility of any addition) that Aristotle has spoken,-as a conclusion resting on sophistical evidence.

So much with respect to Aristotle's induction, on the supposition that the enumeration is complete.

In cases where the enumeration is imperfect, Dr. Wallis afterwards observes, "That our conclusion can only amount to a pro


bability or to a conjecture; and is always liable to be overturn


ed by an instance to the contrary." He observes also, "That this "sort of reasoning is the principal instrument of investigation in "what is now called experimental philosophy; in which, by observ"ing and examining particulars, we arrive at the knowledge of

I have rendered the last clause according to the best of my judgment; but in case of any misapprehension on my part. I have transcribed the author's words. It may be proper to mention, that this illustration is not produced by Aristotle as an instance of induc tion; but it obviously falls under his own definition of it, and is accordingly considered in that light by Dr. Wallis.

* Account of Sir 1. Newton's Phil. Discoveries, Book i. Chap. v.

« ΠροηγούμενηΣυνέχεια »