On the Philosophy of Discovery, Chapters Historical and Critical

But it may be asked, Is it not then true, and an important scientific truth, that the quantity of matter is measured by the inertia? Is it not true, and proved by experiment, that the weight is proportional to the inertia? If this be not the result of Newton's experiments mentioned above, what, it may be demanded, do they prove?

To these questions I reply: It is true that quantity of matter is measured by the inertia, for it is true that inertia is as the quantity of matter. This truth is indeed one of the laws of motion. That weight is proportional to inertia is proved by experiment, as far as the laws of motion are so proved: and Newton's experiments prove one of the laws of motion, so far as any experiments can prove them, or are needed to prove them.

That inertia is proportional to weight, is a law equivalent to that law which asserts, that when pressure produces motion in a given body, the velocity produced in a given time is as the pressure. For if the velocity be as the pressure, when the body is given, the velocity will be constant if the inertia also be as the pressure. For the inertia is understood to be that property of bodies to which, ceteris paribus, the velocity impressed is inversely proportional. One body has twice as much inertia as another, if, when the same force acts upon it for the same time, it acquires but half the velocity. This is the fundamental conception of inertia.

In Newton's pendulum experiments, the pressure producing motion was a certain resolved part of the weight, and was proportional to the weight. It appeared by the experiments, that whatever were the material of which the pendulum was formed, the rate of oscillation was the same; that is, the velocity acquired was the same. Hence the inertia of the different bodies must have been in each case as the weight: and thus this assertion is true of all different kinds of bodies.

Thus it appears that the assertion, that inertia is universally proportional to weight, is equivalent to the law of motion, that the velocity is as the pressure. The conception of inertia (of which, as we have said, the fundamental conception is, that the velocity impressed is inversely proportional to the inertia,) connects the two propositions so as to make them identical.

Hence our argument with regard to the universal gravity of matter brings us to the above law of motion, and is proved by Newton's experiments in the same sense in which that law of motion is so proved.

Perhaps some persons might conceive that the identity of weight and inertia is obvious at once; for both are merely resistance to motion;—inertia, resistance to all motion (or change of motion)—weight, resistance to motion upwards.

But there is a difference in these two kinds of resistance to motion. Inertia is instantaneous, weight is continuous resistance. Any momentary impulse which acts upon a free body overcomes its inertia, for it changes its motion; and this change once effected, the inertia opposes any return to the former condition, as well as any additional change. The inertia is thus overcome by a momentary force. But the weight can only be overcome by a continuous force like itself. If an impulse act in opposition to the weight, it may for a moment neutralize or overcome the weight; but if it be not continued, the weight resumes its effect, and restores the condition which existed before the impulse acted.

But weight not only produces rest, when it is resisted, but motion, when it is not resisted. Weight is measured by the reaction which would balance it; but when unbalanced, it produces motion, and the velocity of this motion increases constantly. Now what determines the velocity thus produced in a given time, or its rate of increase? What determines it to have one magnitude rather than another? To this we must evidently reply, the inertia. When weight produces motion, the inertia is the reaction which makes the motion determinate. The accumulated motion produced by the action of unbalanced weight is as determinate a condition as the equilibrium produced by balanced weight. In both cases the condition of the body acted on is determined by the opposition of the action and reaction.

Hence inertia is the reaction which opposes the weight, when unbalanced. But by the conception of action and reaction, (as mutually determining and determined,) they are measured by each other: and hence the inertia is necessarily proportional to the weight.

But when we have reached this conclusion, the original objection may be again urged against it. It may be said, that there must be some fallacy in this reasoning, for it proves a state of things to be necessary when we can so easily conceive a contrary state of things. Is it denied, the opponent may ask, that we can readily imagine a state of things in which bodies have no weight? Is not the uniform tendency of all bodies in the same direction not only not necessary, but not even true? For they do in reality tend, not with equal forces in parallel lines, but to a center with unequal forces, according to their position: and we can conceive these differences of intensity and direction in the force to be greater than they really are; and can with equal ease suppose the force to disappear altogether.

To this I reply, that certainly we may conceive the weight of bodies to vary in intensity and direction, and by an additional effort of imagination, may conceive the weight to vanish: but that in all these suppositions, even in the extreme one, we must suppose the rule to be universal. If any bodies have weight, all bodies must have weight. If the direction of weight be different in different points, this direction must still vary according to the law of continuity; and the same is true of the intensity of the weight. For if this were not so, the rest and motion, the velocity and direction, the permanence and change of bodies, as to their mechanical condition, would be arbitrary and incoherent: they would not be subject to mechanical ideas; that is, not to ideas at all: and hence these conditions of objects would in fact be inconceivable. In order that the universe may be possible, that is, may fall under the conditions of intelligible conceptions, we must be able to conceive a body at rest. But the rest of bodies (except in the absolute negation of all force) implies the equilibrium of opposite forces. And one of these opposite forces must be a general force, as weight, in order that the universe may be governed by general conditions. And this general force, by the conception of force, may produce motion, as well as equilibrium; and this motion again must be determined, and determined by general conditions; which cannot be, except the communication of motion be regulated by an inertia proportional to the weight.

But it will be asked, Is it then pretended that Newton's experiment, by which it was intended to prove inertia proportional to weight, does really prove nothing but what may be demonstrated à priori? Could we know, without experiment, that all bodies,—gold, iron, wood, cork,—have inertia proportional to their weight? And to this we reply, that experiment holds the same place in the establishment of this, as of the other fundamental doctrines of mechanics. Intercourse with the external world is requisite for developing our ideas; measurement of phenomena is needed to fix our conceptions and to render them precise: but the result of our experimental studies is, that we reach a position in which our convictions do not rest upon experiment. We learn by observation truths of which we afterwards see the necessity. This is the case with the laws of motion, as I have repeatedly endeavoured to show. The same will appear to be the case with the proposition, that bodies of different kinds have their inertia proportional to their weight.

For bodies of the same kind have their inertia proportional to their weight, both quantities being proportional to the quantity of matter. And if we compress the same quantity of matter into half the space, neither the weight nor the inertia is altered, because these depend on the quantity of matter alone. But in this way we obtain a body of twice the density; and in the same manner we obtain a body of any other density. Therefore whatever be the density, the inertia is proportional to the quantity of matter. But the mechanical relations of bodies cannot depend upon any difference of kind, except a difference of density. For if we suppose any fundamental difference of mechanical nature in the particles or component elements of bodies, we are led to the same conclusion, of arbitrary, and therefore impossible, results, which we deduced from this supposition with regard to weight. Therefore all bodies of different density, and hence, all bodies whatever, must have their inertia proportional to their weight.

Hence we see, that the propositions, that all bodies are heavy, and that inertia is proportional to weight, necessarily follow from those fundamental ideas which we unavoidably employ in all attempts to reason concerning the mechanical relations of bodies. This conclusion may perhaps appear the more startling to many, because they have been accustomed to expect that fundamental ideas and their relations should be self-evident at our first contemplation of them. This, however, is far from being the case, as I have already shown. It is not the first, but the most complete and developed condition of our conceptions which enables us to see what are axiomatic truths in each province of human speculation. Our fundamental ideas are necessary conditions of knowledge, universal forms of intuition, inherent types of mental development; they may even be termed, if any one chooses, results of connate intellectual tendencies; but we cannot term them innate ideas, without calling up a large array of false opinions. For innate ideas were considered as capable of composition, but by no means of simplification: as most perfect in their original condition; as to be found, if any where, in the most uneducated and most uncultivated minds; as the same in all ages, nations, and stages of intellectual culture; as capable of being referred to at once, and made the basis of our reasonings, without any special acuteness or effort: in all which circumstances the Fundamental Ideas of which we have spoken, are opposed to Innate Ideas so understood.

I shall not, however, here prosecute this subject. I will only remark, that Fundamental Ideas, as we view them, are not only not innate, in any usual or useful sense, but they are not necessarily ultimate elements of our knowledge. They are the results of our analysis so far as we have yet prosecuted it; but they may themselves subsequently be analysed. It may hereafter appear, that what we have treated as different Fundamental Ideas have, in fact, a connexion, at some point below the structure which we erect upon them. For instance, we treat of the mechanical ideas of force, matter, and the like, as distinct from the idea of substance. Yet the principle of measuring the quantity of matter by its weight, which we have deduced from mechanical ideas, is applied to determine the substances which enter into the composition of bodies. The idea of substance supplies the axiom, that the whole quantity of matter of a compound body is equal to the sum of the quantities of matter of its elements. The mechanical ideas of force and matter lead us to infer that the quantity both of the whole and its parts must be measured by their weights. Substance may, for some purposes, be described as that to which properties belong; matter in like manner may be described as that which resists force. The former involves the Idea of permanent Being; the latter, the Idea of Causation. There may be some elevated point of view from which these ideas may be seen to run together. But even if this be so, it will by no means affect the validity of reasonings founded upon these notions, when duly determined and developed. If we once adopt a view of the nature of knowledge which makes necessary truth possible at all, we need be little embarrassed by finding how closely connected different necessary truths are; and how often, in exploring towards their roots, different branches appear to spring from the same stem.

END OF THE APPENDIX

1

Metaph. xii. 4.

2

Diog. Laert. Vit. Plat.

3

T. ii. p. 16, c, d. ed. Bekker, t. v. p. 437.

4

See the remarks on this phrase in the next chapter.

5

Hist. Ind. Sc. b. iii. c. ii.

6

This matter is further discussed in the Appendix, Essay A.

7

These matters are further discussed in the Appendix, Essay B.

8

See Appendix, Essay B.

9

Hist. Ind. Sc. b. ii. Additions to 3rd Ed.

10

See these views further discussed in the Appendix, Essay C.

11

Metaph. xii. 4.

12

Hist. Ind. Sc. b. i. c. iii. sect. 2.

13

Analyt. Prior. i. 30.

14

Analyt. Post. i. 18.

15

Analyt. Prior. ii. 23, περι της επαγωγης.

16

Analyt. Post. ii. 19.

17

But the best reading seems to be not ἔν τι but ἔτι: and the clause must be rendered "both to perceive and to retain the perception in the mind." This correction does not disturb the general sense of the passage, that the first principles of science are obtained by finding the One in the Many.

18

Analyt. Post. i. 34.

19

Ibid. ii. 19.

20

Analyt. Prior. ii. 25.

21

See on this subject Appendix, Essay D.

22

See the chapter on Certain Characteristics of Scientific Induction in the Phil. Ind. Sc. or in the Nov. Org. Renov.

23

Phil. Ind. Sc. b. viii. c. i. art. 11, or Hist. Sc. Id. b. viii.

24

B. i. c. xi. sect. 2.

25

B. iii. c. i. sect. 9.

26

De Cælo, ii. 13.

27

Ibid. ii. 10.

28

xii. 8.

29

B. xvi. c. vi.

30

On the Classification of Mammalia, &c.: a Lecture delivered at Cambridge, May 10, 1859, p. 3.

31

B. i. c. xi.

32

History of Scientific Ideas, and Novum Organum Renovatum.

33

The remainder of this chapter is new in the present edition.

34

Hist. of Greece, Part ii. chap. 68.

35

De Antiqua Medicina, c. 20.

36

Lib. i. c. 9.

37

De Elem. i. 6.

38

In former editions I have not done justice to this passage.

39

Hist. Ind. Sc. Addition to Introduction in Third Edition.

40

Lib. i. Fast.

41

Hist. Nat. i. 75.

42

Quæst. Nat. vii. 25.

43

Quæst. Nat. vii. 30, 31.

44

Ibid. iii. 7.

45

Hist. Ind. Sc. b. iii. c. iv. sect. 8.

46

Ibid. b. ix. c. ii.

47

See Hist. Ind. Sc. b. iv. c. i.

48

See the opinion of Aquinas, in Degerando, Hist. Com. des Syst. iv. 499; of Duns Scotus, ibid. iv. 523.

49

Liber Excerptionum, Lib. i. c. i.

50

Tr. Ex. Lib. i. c. vii.

51

Tenneman, viii. 461.

52

Mores Catholici, or Ages of Faith, viii. p. 247.

53

Tenneman, viii. 460.

54

If there were any doubt on this subject, we might refer to the writers who afterwards questioned the supremacy of Aristotle, and who with one voice assert that an infallible authority had been claimed for him. Thus Laurentius Valla: "Quo minus ferendi sunt recentes Peripatetici, qui nullius sectæ hominibus interdicunt libertate ab Aristotele dissentiendi, quasi sophos hic, non philosophus." Pref. in Dial. (Tenneman, ix. 29.) So Ludovicus Vives: "Sunt ex philosophis et ex theologis qui non solum quo Aristoteles pervenit extremum esse aiunt naturæ, sed quâ pervenit eam rectissimam esse omnium et certissimam in natura viam." (Tenneman, ix. 43.) We might urge too, the evasions practised by philosophical Reformers, through fear of the dogmatism to which they had to submit; for example, the protestation of Telesius at the end of the Proem to his work, De Rerum Natura: "Nec tamen, si quid eorum quæ nobis posita sunt, sacris literis, Catholicæve ecclesiæ decretis non cohæreat, tenendum id, quin penitus rejiciendum asseveramus contendimusque. Neque enim humana modo ratio quævis, sed ipse etiam sensus illis posthabendus, et si illis non congruat, abnegandus omnino et ipse etiam est sensus."

55

Ages of Faith, viii. 247: to the author of which I am obliged for this quotation.

56

Algazel. See Hist. Ind. Sc. b. iv. c. i.

57

Tenneman, viii. 830.

58

Degerando, iv. 535.

59

Leibnitz's expressions are, (Op. t. vi. p. 16): "Quand j'étais jeune, je prenois quelque a l'Art de Lulle, mais je crus y entrevoir bien des défectuosités, dont j'ai dit quelque chose dans un petit Essai d'écolier intitulé De Arte Combinatoria, publié en 1666, et qui a été réimprimé après malgré moi. Mais comme je ne méprise rien facilement, excepté les arts divinatoires que ne sont que des tromperies toutes pures, j'ai trouvé quelque chose d'estimable encore dans l'Art de Lulle."

60

Works, vii. 296.

61

Fratris Rogeri Bacon, Ordinis Minorum, Opus Majus, ad Clementem Quartum, Pontificem Romanum, ex MS. Codice Dubliniensi cum aliis quibusdam collato, nunc primum edidit S. Jebb, M.D. Londini, 1733.

62

Opus Majus, Præf.

63

Contents of Roger Bacon's Opus Majus.

Part I. On the four causes of human ignorance:—Authority, Custom, Popular Opinion, and the Pride of supposed Knowledge.

Part II. On the source of perfect wisdom in the Sacred Scripture.

Part III. On the Usefulness of Grammar.

Part IV. On the Usefulness of Mathematics.

(1) The necessity of Mathematics in Human Things (published separately as the Specula Mathematica).

(2) The necessity of Mathematics in Divine Things.—1o. This study has occupied holy men: 2o. Geography: 3o. Chronology: 4o. Cycles; the Golden Number, &c.: 5o. Natural Phenomena, as the Rainbow: 6o. Arithmetic: 7o. Music.

(3) The necessity of Mathematics in Ecclesiastical Things. 1o. The Certification of Faith: 2o. The Correction of the Calendar.

(4) The necessity of Mathematics in the State.—1o. Of Climates: 2o. Hydrography: 3o. Geography: 4o. Astrology.

Part V. On Perspective (published separately as Perspectiva).

(1) The organs of vision.

(2) Vision in straight lines.

(3) Vision reflected and refracted.

(4) De multiplicatione specierum (on the propagation of the impressions of light, heat, &c.)

Part VI. On Experimental Science.

64

Op. Maj. p. 1.

65

Ibid. p. 2.

66

Ibid. p. 10.

67

I will give a specimen. Opus Majus, c. viii. p. 35: "These two kinds of philosophers, the Ionic and Italic, ramified through many sects and various successors, till they came to the doctrine of Aristotle, who corrected and changed the propositions of all his predecessors, and attempted to perfect philosophy. In the [Italic] succession, Pythagoras, Archytas Tarentinus and Timæus are most prominently mentioned. But the principal philosophers, as Socrates, Plato, and Aristotle, did not descend from this line, but were Ionics and true Greeks, of whom the first was Thales Milesius.... Socrates, according to Augustine in his 8th book, is related to have been a disciple of Archelaus. This Socrates is called the father of the great philosophers, since he was the master of Plato and Aristotle, from whom all the sects of philosophers descended.... Plato, first learning what Socrates and Greece could teach, made a laborious voyage to Egypt, to Archytas of Tarentum and Timæus, as says Jerome to Paulinus. And this Plato is, according to holy men, preferred to all philosophers, because he has written many excellent things concerning God, and morality, and a future life, which agree with the divine wisdom of God. And Aristotle was born before the death of Socrates, since he was his hearer for three years, as we read in the life of Aristotle.... This Aristotle, being made the master of Alexander the Great, sent two thousand men into all regions of the earth, to search out the nature of things, as Pliny relates in the 8th book of his Naturalia, and composed a thousand books, as we read in his life."

68

Ibid. p. 36.

69

Autonomaticè.

70

Op. Maj. p. 46.

71

See Pref. to Jebb's edition. The passages, there quoted, however, are not extracts from the Opus Majus, but (apparently) from the Opus Minus (MS. Cott. Tib. c. 5.) "Si haberem potestatem supra libros Aristotelis, ego facerem omnes cremari; quia non est nisi temporis amissio studere in illis, et causa erroris, et multiplicatio ignorantiæ ultra id quod valeat explicari.... Vulgus studentum cum capitibus suis non habet unde excitetur ad aliquid dignum, et ideo languet et asininat circa male translata, et tempus et studium amittit in omnibus et expensas."

72

Part ii.

73

Parts iv. v. and vi.

74

Op. Maj. p. 476.

75

Op. Maj. p. 15.

76

Ibid. p. 445, see also p. 448. "Scientiæ aliæ sciunt sua principia invenire per experimenta, sed conclusiones per argumenta facta ex principiis inventis. Si vero debeant habere experientiam conclusionum suarum particularem et completam, tunc oportet quod habeant per adjutorium istius scientiæ nobilis (experimentalis)."

77

Op. Maj. p. 60.

78

Ibid. p. 64.

79

"Veritates magnificas in terminis aliarum scientiarum in quas per nullam viam possunt illæ scientiæ, hæc sola scientiarum domina speculativarum, potest dare." Op. Maj. p. 465.