APPENDIX: SOME BASIC IDEAS IN

NEWTON'S PHYSICS

Newton's theory of motion is based on his discovery that "ultimately" the chord, arc and tangent become equal. "Ultimately" means, to remind us, at the moment the end points defining the arc become united, not before and not after it. As long as they differ from each other, nothing in Newton's Principia can even start, which is indeed what happened until Newton wrote it.

The solution of the Kepler problem starts by a proof, which opens the Principia, that motion according to Kepler's first law is sufficient for deriving the existence of a force directed to the vertex of the areas described by the planet's radius-vector in equal times, and then in the following (second) theorem of the book the inverse proposition is proved. The proof of the logical equivalence between Kepler's first law and the action of a central force then becomes a basis for the derivation of similar logical equivalence between Kepler's second and third laws, and the exact value of this central force as a function of distance. Each of these theorems involves the first two theorems, as well as another independent use of the ultimate quality of the arc-chord-tangent, which thus becomes the corner-stone of the whole edifice of the Principia. Its importance is not technical only (even though as technical it is of crucial importance) but rather as an indication that the metaphysical basis of the Principia is inseparably interlocked with its technical-mathematical apparatus. In fact, as I urged in a previous chapter, the metaphysics of the Principia is the metaphysics of its infinitesimal mathematics, and this in its turn is concentrated in the ultimate equality of the arc-chord­tangent, namely, in the idea that at the moment of disappearance in a single point, this point contains within its point-like unity a plurality of three different entities which hold a definite length ratio between them.

The technical side of Newton's discovery of the solution to Kepler's problem is wholly contained in his discovery of the fact that the magni­tude of the central force is proportional to the length of the ultimate versine of the angle between the tangent and the chord. This means simply the length of BC, where aAb is the actual path of the planet, OA the radius of the osculating (tangent) circle at the point A, and

513

514 APPENDIX

a

Fig. 1.

AB, AC, and AC, the tangent, chord and arc, respectively. C is some arbitrary point on the circle taken for demonstration purposes only, because the problem is to calculate the length of the versine BC not of some arbitrary angle, such as drawn here, but of the ultimate angle which exists at the moment ("not before and not after", as Newton made clear) the points A, B, C coalesce as C approaches A. The calculation of this ultimate versine at the moment the chord AC, the arc AC and the tangent AB coalesce and become equal, is the central discovery of the Principia.

Once this is grasped, the sequence of argumentation in the Principia becomes very clear and simple, and can be described exhaustively in few words. It begins with four statement about the nature of matter and its motion under the action of forces. These are the definition of "vis insita", or the force of inertia, and the three laws of motion. The definition of the force of inertia intends to argue that matter has an innate force which is proportional to its quantity of matter, and which acts so as to keep the body moving if it moves and to keep it stationary if it is not moving. There is a difference between these two actions of the force, since there is an absolute - even though not practical -difference between the two states. The difference stems from the fact that motion is absolute, in the sense that it is an instantaneous property of the body and is independent of the existence of any material frame of reference. Hence a body at rest in space and a body moving in

SOME BASIC IDEAS IN NEWTON'S PHYSICS 515

space are in different states and such difference may be illustrated by comparing the effects which an external push have on the two bodies. The body at rest would start moving in the direction of the force, but the body in motion would only change its motion to some degree but would not start moving in the direction of the force.

Hence the force of inertia is not in general vectorial, since it opposes the external force equally whatever the direction of this external force. Yet it has a vectorial character in the case of a moving body, for it then acts in the direction of the motion. Another important characteristic is the fact that it does not cause acceleration, and hence it cannot start a motion. This action of the force of inertia may, therefore, be described as causing the constant velocity in a body set in motion by an external force which had caused its previous change of velocity.

The externality of the accelerating force is characterised by saying that it is always external to the body, and so never stays in the body after it ceases acting, and as long as it acts it changes the body's velocity.

In particular, an external force may be impressed on the body for exactly one instant of time, during which the body's velocity changes. This change of velocity, therefore, does not take any time-interval, and the body does not change its velocity, strictly speaking, for at any chosen time-interval which does not include the instant at which the force acts, it moves at a constant velocity. This is the import of the second law which says that the "change in the motion" is proportional to the force impressed. "Motion" is the factor mv and its change is mLlv proportional to the change in velocity. For a body at rest, Llv is equal to the new velocity v after the action of the impressed force, and so also the distance covered in the direction of the forces during a given, fixed time. And so, in sum, we have

(1) foes

for a force impressed on a body at rest. Care should be taken to appreciate the fact that such a body is in uniform motion all the time during which it covers the distance s, for the force acts on it only during an instant, not an interval.

Now the laws of motion are followed by a set of eleven mathematical lemmas, which aim to establish a measure of the versed sine of the angle of contact between the tangent and a curve. This versed sine is the distance s which the travelling body is deflected from its tangential path at the point into its actually ensuing curve. And since this distance

516 APPENDIX

A

o Fig. 2.

s is proportional to the deflecting force, according to the second law, it follows that in order to estimate the force all that is needed is a measure of the versed sine. The versed sine of a is the line AC, where OC = cos a so that AC = versinea = 1-cosa.

Now, suppose aAb to be the actual curve along which the body travels, and at A to be touched by the osculating circle centered at 0, with AE the tangent at A. Then EB = AC is the distance s which some force must deflect the body if it is to be at B and not at E. To calculate this force, we must calculate EB, the versed sine of the angle 2 BAE = 2 ABC. Now, since in the similar triangles ABD and ACB we have

a

o Fig. 3.

SOME BASIC IDEAS IN NEWTON'S PHYSICS 517

AB2 = AC x AD, and since AD = 2r = constant for this point of con­tact A, it follows that

AB2=KxAC

Now, since ultimately, when the angle of contact vanishes and B touches A,

Ab = AB = AB = AE

we may put

(2) versinea = AC = K'AB2 (Principia I, Lemma XI, Cor. II)

which is the measure needed. Since all the variables here are infinitesi­mal, that is "ultimate", the length of the infinitesimal arc AB is pro­portional to the velocity of the body at A, and so to the time t taken to cover it. Hence,

(3) versinea = K"t? (ibid. Cor. III, and cf. Whiteside's MWN, 6:538-49)

Proposition I of the Principia now proves that a body obeying Kepler's first law obeys it because it is deflected from its tangential path by a force directed to the vertex of the equal areas the body describes in equal times. And here a basic technique is introduced. The curved path is first represented by its chords AB, BD, DF, each of which is resolved into two components: Thus BD is resolved into an inertial component BC which is the inertial prolongation of the previous chord, and an impulse component CD. The direction of the impulse is actually towards S, but it is approximated by CD which is only parallel to BS.

Since it is given by Kepler's law of areas that if the chords AB, BD, are covered in equal times then the triangle areas .6.ABS and .6.BDS are equal it follows that .6.ABS = .6.BCS (since AB = BC because they are both covered in the same velocity during equal times), and so .6.BCS = .6.BDS and hence CD is parallel to BS and points approxi­mately towards S. In the limit, when D melts into B, CD will point "ultimately" towards S exactly.

This is interpreted as follows. BC is the path along which the body would move under its force of inertia alone in time equal to that which it took to cover AB. BD' is the path the body would travel after being impulsed at B by the central force "tending to S". The motion along

518 APPENDIX

s Fig. 4.

BD' = CD is strictly inertial because, in accordance with the explana­tion given to the notion of "impressed force" in Definition IV, the impressed force is an "action exerted upon the body" and "remains no longer in the body when the action is over". This is intended as a clear mark differentiating the "impressed force" from the old "impetus" which did remain in the body after "the action exerted on the body" was over. The point of the new concept of force is almost wholly exhausted in this pure externality, for this is what enabled Newton now to compose a strictly continuously acting force from its ultimate instantaneous components, the instant-after-instant "exerted actions". At each instant of time during which the continuous force acts, it is both impressed and is over at once. Now, after its action is over the motion it caused is conserved, but this conservation is due to the action of the force of inertia, "for the body maintains every new state it acquires by its inertia only", as Definition IV emphasises. That is why the first corollary which Newton immediately deduces from his laws of motion is the law of parallelogram. On it he builds all the next corollaries.

In fact we may regard the first and second law, together with their correlated Definitions (III and IV) as especially geared to imply im­mediately the parallelogram. Now this is not a parallelogram of forces, but only of their resulting changed motions which are, as a result of the instantaneous nature of the impressed force, strictly inertial. Hence the new "motions" may be represented by the distances covered during

SOME BASIC IDEAS IN NEWTON'S PHYSICS 519

some time. Once distances deputize for motions (because these are of uniform velocities) it is possible to compose the force of inertia (result­ing in a uniform velocity) with the impressed force (resulting in another uniform velocity) in order to get the composed new inertial motion along the resultant.

In this way every continuously curved path is resolved into its compo­nent straight lines, which represent the resultant inertial motion com­posed in its turn from the component inertial motions one of which is caused by the force of inertia and maintained by it, and the other caused by an impressed force but again maintained by the force of inertia. The only difference between these two components is that the one describes the path and velocity the body would have starting from the same velocity it had before, while the other component describes the velocity it would have starting from rest.

NOTES

NOTES TO THE INTRODUCTION

1 See note 5 to chapter 1 below. 2 This is now Appendix 2 to Bechler (1989a). Sambursky's texts are analysed in section 3 of this Appendix. The main villain of the story was, it turned out, Duhem. 3 See Bechler (1987). I must mention here the important impact of Feyerabend's early philosophical work on the concept of realism. The notion that circularity is inherent in realism is more than implicit in his (1958), (1962), (1963), (1964) and mainly (1970). What later became his main interest, i.e., the question of the "right" methodology for progress, is to me, however, an idle and boring issue. 4 The "platonist" is a device already used by Lear (1982):188 and Annas (1976):3 passim. I have not yet met "aristotelian". A recent paper of E. Grant deals with a related problem - who is to be classed as Aristotelian during the middle ages. His solution takes as a model the method of David Hull in defining "Darwinism" (Grant 1987). Hull arrived at the conclusion that "a scientist can be a Darwinian without accepting all or even a large proportion of the elements of Darwinism. Conversely, a scientist can by and large accept the tenets of Darwinism without being a Darwinian" (Hull 1985:809). This is not much better than my consequence: Darwin may turn out to be not a Darwinian at all. It might be even worse, for it all depends on what are "the elements of Darwinism", which are definitely not everything Darwin argued for in his Origin or the Descent. A compound difficulty arises on trying to examine whether Darwinism is aristotelian. My answer is that it is, see my (1989):ch. 2. As to Aristotle himself, my answer is my (1989a).

NOTES TO CHAPTER ONE

1 See the first argument in De Caelo 308b19, 27, 309b13-15. Less crucial are 301a21-b18, or 290al. The second argument is in Phys. 216a18. 2 E.g., see Grant (1962), (1964), (1965) and his recent (1981):3-67. 3 The first to point out this incongruity was, I believe, Weisheipl (1965). 4 To take only a select sample, see Sambursky (1956):92-97, Lloyd (1970):114-115, Crombie (1961)II:48-9. See a detailed analysis in Bechler (1989a): Appendix 2. 5 Most representative is Sambursky (1962):77 who writes:

Natural motion according to Aristotle's doctrine was bound up with the teleological conception of the striving of a body to reach its natural place. It was quite logical for him to make the assertion that the heavier the body is the greater its desire to reach that place, and therefore to make the incorrect assumption, that the velocity of a falling body is proportional to its weight.

520

NOTES 521

None of the five references he gives to Aristotle bears his interpretation even remotely. These are 273b30, 277b4, 290a1, 309bl3, 311b5-13, see Sambursky (1962): notes 24, 25, 26, to p. 77. 6 There are two main causes for inducing this interpretation. First, Aristotle's cosmological proof for the existence of God. Second, Aristotle's correction of the Eudoxos-Callipus astronomy. Since the first unmoved mover moves the first sphere directly (Phys. 258b12) this motion "is imparted to the whole system of concentric spheres since they are in contact with one another" (Joachim 1922:255). Joachim also refers to "the eternal life which is God" which "radiates through the whole system. It communicates itself immedi­ately ... to the 1TPW-rOV KLVOVJ.L€VOV in the form of eternal uniform revolution" (Joachim ibid:256, and xviii). But none of Joachim's references mentions or hints at any radiation effect. His references are: Met. 1072a19-1073a13; Phys. 250b11; De Caelo 279a16; 288a13; 292a18-b25. Aristotle uses only the metaphor of the lover yearning for his loved one: Met. 1072b5. See a summary view of the situation in Aristotle in 2.13 down, and Bechler (1989a): chapter 1, and in particular 1.9, 2.1. This Platonization (or maybe Stoicization) of Aristotle is still alive today, see Rist (1965). The roots of this trend among modern commentators may be found in Ross (1925) which rejects both Plato's "Separation" terminology as "ill advised" (ibid:147) and Aristotle's refutation of it as an "error in the sense of having fallen for it". Basically, Ross in (1925) obliterated any ontological distinction between Plato and Aristotle by being himself an Aristotelian interpreter of Plato. 7 See Ellis (1962), (1963), (1965):43, Koslow (1969): 552-4. 8 Looking for continuity in scientific thought invariably leads to the suppression of its ontological foundations, and to the view that revolutions in science are merely formal, instrumental affairs. This view was established by Mach and Duhem's (1892), (1893), (1906), (1908), (1913). This ends in viewing Einstein as a technical extension of Newton (to higher velocities etc.). Feyerabend's recent reinterpretation of Mach in his (1984a) does not convince me. g Since my view presupposes a realistic, platonic view of theories, it is only verbally similar to Kuhn's notion of incommensurability, which is merely a psychological-sociological­biological notion. Consistently interpreted, his view is irrelevant to mine, which contrad­icts the main theses of his (1962). I am much closer to Feyerabend, in his golden-realistic days, e.g., his (1963), before the sociological orgy hit him. 10 Pace Grant (1981):266 n.18. No one has explained as yet Aristotle's declaration about the absurdity of the equi-velocity fall of different weights in the void. The law serves, therefore, no purpose in Aristotle's argumentation in Phys. IV, 8. 11 The concept of informativity I use is strictly ontological, depending only on the denotations of the terms used. Consequently it is essentially qualitative and so refers only to the internal, logical structure of theories. It has no bearing on matters of test­ability, preference, acceptability, which are in my view misconceived issues of philosophy. My view is entirely non-normative and deals only with theories, and not at all with scientists. Consequently it cannot be reduced to such current views of informativity as Popper's (1961):112-126 or even Hintikka and Suppes eds. (1970):3-27, 263-297, and (1973a):ch. 7. Most importantly, my notion of informativity highlights the inherent irrationality and the ineliminable, nay, inalterable uncertainty necessarily involved in any informative proposition. I think that Putnam uses a similar notion of "philosophical informativity" about reductive statements. Popper, though, came close to it but finally

522 NOTES

failed in his propensity theory which is strictly a variety of Aristotle's potentiality and so inherently non-informative. For fully detailed analysis see Bechler (1989):ch. 2. 12 The close link between French late 19th century positivism and a strict Parmenidean ideal of rationality can be seen in the prime mover of French conventionalism Emile Boutroux, setting in motion Le Roy's and Duhem's revolutionary series of papers. 13 Thus Newton's Opticks:262, McGuire and Heimann (1971), McGuire (1966), (1970). Though Locke, for instance, believed in the visibility-in-principle of the "inner consti­tution" of bodies, he was explicit about the invisibility-in-principle of their modus op­erandi. On the link between the century's platonism and skepticism see Popkin's (1951), (1952), (1967), and van Leeuwen (1963). 14 One of Duhem's "principal aims" in his (1913-1959) was to show that "modern science was born, so to speak, on March, 7, 1277, from the decree issued by Msgr. Etienne, bishop of Paris", VI:66 (published in 1954, and see also his 1906a, 11:411-19, published 1909, III:246-9, published in 1913). The nominalist origins of modern science led him somehow to the conclusion that the scientific revolution was nominalistic in essence too. He was, however, brave enough to hold this even though he knew that all its main figures failed to see this (see his 1908:63 on Copernicus' "illusion", p. 104 on Kepler's "strange reveries" and "childish fancies", pp. 109-112 on the logical blindness of Galileo). The bearers ofthe true notion of what was going on were, therefore, such figures as Osiander, Ryemer Baer(p. 68), Gemma Frisius (p. 69), Erasmus Reinhold (p. 70), and their pupils, Ariel Bicard, Kaspar Pencer (pp. 74-77) and others such as Schreckenfuchs, Wursteisen (p. 78), Piccolomini, Cesalpino, Giuntini (pp. 78-86), and Barberini (p. 111). Copernicus, Kepler and Galileo, on the other hand, were thickheaded (p. 99), childish (p. 106) obstructions to a long scientific tradition which made constant "advances in astronomy" only because of its instrumentalist and nominalist view of science (p. 87). 15 See, however, the revistionist view of these two kinds of God's power in Oberman (1974) and Courtenay (1974). The crucial role of the Platonic elements in Aquinas is analysed in Fakhry (1958):166-193, whose conclusions apply to corpusculists such as Descartes. See also Moody (1958). On the basic incompatibility of Aristotle's ontology with Christianity and on the preference of the Church Fathers for Plato, see More (1925). He links this with Plato's inherent irrationalism in his epistemology stemming from the separateness of the Ideas from the world which implies a separate God. See also Ross' dispute with him in Ross (1925) which fails to see the separateness of universals "as being of such serious import as Aristotle would have us believe" (ibid: 146). One is puzzled. 16 The centrality of divine voluntarism and the Christian doctrine of creation was first argued for in Forster's admirable series (1934), (1935), (1936). Its first important appli­cation was made by Oakley (1961). For the link of voluntarism and mystical movements, see Ozment (1974). The subject of voluntarism and its mystical implications will be central to my argument about inertia both in Descartes (ch. 7.9-19 below) and in Newton (ch. 11 below). 17 Duhem's influence can be seen in action in Moody's (1958) which views the new science as an anti-metaphysical movement and so is unable to explain its incorporation of such entities as force, space and absolute motion. Similarly, Oberman (1975) argues that Copernicus was "formally a step backwards in comparison to nominalistic research stan­dards" (p. 413). Even McGuire, who is the most important discoverer of the rich ontologi­cal basis of Newton, surrendered once to the Duhemian myth in his (1972). 18 See Hankins (1970):151-195. The same aristotelian view pervades d'Alembert's mathe­matics, Boyer (1959):247-250.

NOTES 523

19 The problem exploded in the Newtonian tradition of the 18th century around the issue of Locke's notion of thinking matter. James Harris, criticizing it, wrote:

At another time we hear of bodies so exceedingly fine that their very exility makes them susceptible of sensation and knowledge: as if they shrunk into intellect by their exquisite subtility, which rendered them too delicate to be bodies any longer. It is to this notion we owe many curious inventions such as subtle ether, animal spirits, nervous ducts, vibrations, etc., terms which modern philosophy, upon parting with occult qualities, has found expedient to provide itself to supply their place.

Quoted in Priestley's Examination of Reid's Inquiry into the Human Mind on the Principles of Common Sense, (London, 1775):336. 20 This is, in my perspective, the ultimate consequence which McGuire's work has pointed out in the series of his trailblazing studies (1966), (1967), (1969), (1978). 21 Newton's lifelong flirtation with the notion that mass is inverse to force and so finally may dissolve in force need be mentioned in this context, see Bechler (1974a). Priestley, who rejected the historical veracity of Harris' account (n.19 above), conveniently forgets that most influential Newtonian throughout the 18th century and well into the 19th century, David Hartley, even though he issued Hartley's principal work in a digested edition. Hartley wrote that

If we suppose an infinitesimal elementary body to be intermediate between the soul and gross body, which appears to be no improbable supposition then the ethereal vibrations may be assumed to act directly on these "elementary bodies" and by their means on the soul. (Hartley, Observations on Man, his Frame, his Duty and his Expectations 1:34, London, 1749)

No surprise that Priestley suppressed in his edition this vibratory mechanism. See the important review of the conception of materialism in the 18th century in Yolton (1983a), (1983b).

NOTES TO CHAPTER TWO

1 This chapter is a condensed statement of some chapters of my (1989a), which should be consulted for the full arguments and literature. 2 For a very persistent and convincing argument that Aristotle held the principle of plenitude, see the papers collected in Hintikka (1973) dating from 1959. The Hintikka thesis was attacked by M. Kneale (1974) and Mulhern (1969). Hintikka's thesis and arguments determined much of my views. However, 1 cannot see how to avoid the centrality of consistency-potentials in Aristotle, but Hintikka sees this as negligible (1977:26). More important yet, 1 conclude that the notion of potentiality as striving and force has no place in Aristotle but Hintikka states the contrary (ibid:25-{j). Without consistency-potentials 1 see no explanation of such difficult passages as De Gen. et Corr. 316a23, Met. l003a2, 1071bl3, De Int. 19a12, and most problematic An.Post. 74b37-75a35. 3 That non-genuine potentiality is always a potentiality for contradictories entails that it is a non-genuine attribute, and so this serves for Aristotle as a refutation of Protagorean relativism:

524 NOTES

Now since contradictories cannot be truly predicated of the same subject at the same time, it follows that the same subject cannot at the same time possess contrary attributes. (Met. 1011b17)

4 See Hintikka (1977):45 on the way Aristotle manages to accept the Megarians' view which he criticizes, and see the parallel case of his critique of Plato in Cherniss (1962):441, 453,458-9. 5 However, the accepted view of Aristotle's teleology ignores this; see, e.g., Gotthelf (1976). 6 See Waterlow (1982a):109-110. Asking what kind of thing is potentiality, the answer supplied is that it is the potentiality to be something in actuality, and so is not something "indefinite". Waterlow defends Aristotle against "circularity-spotters" (ibid: 114) , but it is not clear how. 7 See also Charlton's extended argument that Aristotle's form is identical with the thing, to be designated by a concrete noun ("bed"), rather than by the abstract noun ("bedness") (Charlton 1970:70-76). See, however, also Hartman (1976). 8 The relativity of the consistency potentiality is captured by a central usage of Aristotle's "qua"-locution, concerning which see Barnes (1975):112-121 on An.Post. I, 4. 9 Thus Charlton argues that the transition from potentiality to actuality is not a change. See his commentary on Phys. II, 1, in his (1970):92, confirming this by De An. 417b1-16 on the actualisation of knowledge. See also explicit words in De An. 431a4, and Hamlyn (1974):145. Also see Waterlow (1982a) as a good defence of the contrary view, but see ibid: 113. 10 On the sea-battle in De Int. 9 see Anscombe (1956), Hintikka (1973):ch. viii, Waterlow (1982):ch. v and the bibliographies in Hintikka ibid:176-8. 11 There seems to be a basic incongruity in Aristotle's doctrine of substance and form as a consequence of his denial that a non-particular thing can be substance, coupled to his view that form must be universal (for only thus can scientific knowledge exist), which together exclude form from being substance. Yet he also insists that the form is what most truly is substance. See Woods (1967), Albritton (1957), Lacey (1965), and Lesher (1971). 12 An important attempt to exhibit the informativity of Aristotle's physics may be found in Mourelatos (1967). On p. 100 he refers to Met. 1048a17 but fails to see that it is logical and not physical necessity that causes actualisation there. On p. 102 he attacks attempts to see Aristotle as building on tautology, but can save Aristotle's qua-healable gambit in De Caelo 31Ob16 only by introducing the arch-obscurant "constitutive". 13 Witness Ross: "In Aristotle's system, taken strictly, matter does not desire form nor strives towards it" (1924:cxxxvii). I take Aristotle's system strictly. 14 See Wolfson (1961), Pines (1961), Rescher and Marmura (1965). 15 See, on Aristotle's syllogism, Patzig (1968) and Lear (1980), as well as Veatch (1972). 16 Aristotle implies this demand elsewhere: Top. 158a33, b4, b39, De An. 402bl6-26, Met. 998b5, Et.Nic. 1142a26, 1143a26, b2. 17 On Aristotle's infinity see Edel (1934) and Hintikka (1966). But the problematic existence of mathematical entity is due not only to its link with infinity. A consequence of the priority of the actual is that number exists only as the enumerative actuality of mind, and so time, i.e., the number of motion, exists only where and when mind exists (Phys. 233a22-28).

NOTES 525

18 Since the point is in a line only as a consistency potentiality for a dividing mind, it does not exist apart from mind (Phys. 208b22, Joachim 1922:116 and p. xix) even if it could be actualised by a finite number of divisions. Since it cannot, it is not even a consistency potential. The same holds for lines and planes. Aristotle refers to their existence mode as "abstraction" (Met. 1061a28) or as a "special sense" of existence (Met. 998alO). See Lear (1979), (1982), Mueller (1970), Hussey (1983):176-184, Feyerabend (1983a). Also van Fraassen (1980). 19 I have argued for this interpretation in detail, as well as for its implications concerning the possibility of symbolic thought in Greek philosophy against J. Klein's thesis in my (1989a):ch. 5 and appendix 3. My view is strengthened by Charlton's commentary in his (1970):96, which refers to De An. 429a18-20.

NOTES TO CHAPTER THREE

1 The non-teleological character of the Socratic and the Platonic cosmology is argued in detail in 3.1.4, and see Cherniss (1962):381. 2 See Cornford's edition (1961):222-230. 3 Compare, however, Hackforth (1955):131 for the standard view about the issue. I could not find any hard evidence for this view, and Socrates certainly never mentions any "final cause" (ibid:131) either here or elsewhere in the dialogue. 4 I find in the Socrates story a direct evidence for Plato's view of his own theory of Forms, i.e., as cosmological scientific theory that aims to compete with and replace other scientific cosmologies. His epistemological arguments for the existence of Forms in the Theaetitus, Meno and the Republic are consistent with this because they all presuppose a cosmological theory of knowledge, see Hintikka (1971). 5 Aristotle failed to see this and so reproduced the "Third Man" argument (Met. 1039a2, 990b17, 991a1), which Plato had dismissed long before (Parmenides 132A-B, D-133A, and also Republic 596A, 597C, Timaeus 31A). This was a constant blindness in Aristotle, as seen again in his critique of the Ideas, being non-spatial, as movers of spatial things and of Plato's geometrical atoms, being weightless and two-dimensional, the causes of heavy, three-dimensional bodies (De Gen. et Corr. 315b30, 316b5, 20, De Caelo 299a26). See Cherniss (1962):39-40, 293-300, 375, 316-18, 408, 453, 459, notes 378,379,406,409. 6 See note 3 above. 7 Aristotle is, nevertheless, the source of the tradition that views Socrates as an Aristotel­ian who "never treated universals or definitions as existing separately" (Met. 1078b30). 8 Aristotle views Plato's Ideas as examples of his own potentials (Met. 1071b14-20, 1075a32-6, b20-24) and so holds that they cannot be separate. 9 The soul is both 6fJ-ol.6Tt;pov and CTU"('YEVET€POV with Forms. See Hackforth (1955):85. 10 Plato holds that change is an essential feature of the visible world (Phaedo 78D-E, 79A9-1O; Symposium 207D-208B; Philebus 59A2-B3; Timaeus 27D-28A4, 49C7-E7, 52A4-7). Hence essential change is possible at all only if a changeless, eternally immu­table world of entities exists (Timaeus 49D9-E4, 51D5-7). Thus an absolute relativism is self destroying and therefore an inconsistent theory. Influenced by Plato's argument (in the Theaetitus 178C, 171AC, 158A-E) Aristotle attacks the relativists in the same manner (Met. 101OB12, 1012BI3-18, l009BI-11).

526 NOTES

11 See Vlastos (1965), Allen (1960). 12 Plato executes a kind of a transcendental argument which feeds on epistemological facts and concludes to the ontological features of Forms as changeless primary realities (See Phaedo 74C-75B, Timaeus 49D-E, 5IB4-6, and Cornford (1937):178-181, 188-191). 13 A direct consequence of this consideration is that the Form will never actualise in matter, i.e., that its material manifestations are necessarily imperfect. Also it seems to me that this entails that there could be Forms with no material manifestation at all, i.e., "empty Forms". The argument against this, proposed in M.D.Bohr (1981), is unconvinc­ing since it depends entirely on accidental elements in Plato's texts. The doctrine of the Timaeus about the work of the Forms as persuasion of necessity seems to me to lead to the same consequence. Hence the teleological interpretation of his cosmology in Morrow (1950) is unsatisfactory. Also Vlastos (1939) and (1964) seem to me a conclusive argument in favor of the interpretation that according to the Timaeus the material world was created, hence the Forms had existed unmanifested until then. 14 I take this mythical formulation to be a main achievement of Plato's informationist view of knowledge and predication. See Hicken (1957), Ackrill (1955), (1957), Mates (1979). 15 Mainly 251A-258B, see Cornford (1935):252-294. In 253C-D Dialectic is the science that discovers how the "Greatest Kinds" are "joined" and "separated" among them­selves. 16 So Ross (1971):34. 17 It is this argument from the actuality of the Forms and their relations, grounding the science of Dialectic, that is the strongest case against the thesis that Plato held a version of the plenitude principle, e.g., M.D.Bohr (1981). See note 13 above. That any Form can at all perfectly materialise must mean for it to be divisible and changeable, hence a contradiction in the midst of Plato's ontology. That Plato does not take potentiality of manifestation in action as identical with the real is seen in that this doctrine is suggested by the Stranger in the Sophist 248A-249D but only as an ad-hominem argument against the materialists, and see Cornford's view in his (1935):238-9. 18 See the exasperating exercise in the dialectic of the Form "One" in the second part of the Parmenides (137Cff.), e.g., the paradoxes ensuing from its relation to the Forms Motion, Rest, and Time. And see Gosling's commentary on the Philebus in his (1975):139-153. 19 See also the discourse within the world soul where the circle of the Different forms true belief about matter, 37B. See Cornford (1937):96-7, and Sophist 252E in Cornford's commentary (1935):260. 20 That is why the Demiurge molds "within the soul all that is bodily" and why the soul is made "everywhere inwoven from the center to the outermost heaven and enveloping the heaven all round on the outside" Timaeus 36D-E, and also 34B. The same goes for the human soul, whose divine part envelopes the head and controls the rest of the body as a "vehicle" (44E). See Cornford (1937):28lff. 21 See a detailed treatment in ch. 9.3, 7.14 and 7.6 below.

NOTES TO THE INTRODUCTION TO PART II

1 The case of Kepler has been thoroughly analysed through his dispute against the hypothetism of Ursus in Jardine (1984).

NOTES 527

2 See Cusanus (1979): II, ch. 3 and 5, III ch. 3 according to which human nature "contains in itself the intellectual and the sensible natures" and is therefore a "microcosm or a world in miniature" (p. 135). See also Cassirer (1964):ch. 1, 2.

NOTES TO CHAPTER FOUR

1 "To save the phenomena of the planets" by "admitting as hypotheses" only "circular, uniform and regular" motions, is a problem Plato "set the mathematicians", according to a tradition reported by Simplicius in his commentary on Aristotle's De Caelo, quoted in Duhem (1908):5. An examination of the prevalence of instrumentalism in ancient astronomy is offered in Lloyd (1978), exposing Duhem's distortions of the Platonism of Proclus, of the famous physics vs. mathematics commentary which Simplicius quotes from Geminus (Duhem ibid: 10), of Ptolemy and other Greek astronomers. Further cutting critique is in Jardine (1979). See my reading of the Platonic meaning of saving the phenomena, ch. 3.2.3. 2 I employ here Aaboe's qualitative account in his (1963). 3 See Dreyer (1906):156, Neugebauer (1962):198-204. The most detailed and friendly introduction to the technical astronomy of Ptolemy and Copernicus is, still, Small's (1804):2-90. 4 On the power of the epicyclic method in general, being in essence an application of Fourier analysis, see Hanson on Ptolemy and prediction in his (1973):101-115. In consequence of the "cellular" character of the Ptolemaic system, it turned out to be mathematically simpler than that of Copernicus, who employed the same analysis (ibid:233). So also Neugebauer (1962):204-5. Since questions of worth, elegance, simpli­city, originality, etc. seem to me at best mere emotive, pseudo-problems, I ignore them completely in the text. S Take, as just one example, Maimonides' evaluation in his Guide to the Perplexed part II ch. 24, where the contemporary anti-Ptolemaic critical tradition is reviewed. 6 "The equants violation of the principle of uniform motion was Copernicus' chief reason for breaking away from the Ptolemaic astronomy", Rosen (1984):67. The same point is made by Kuhn (1957):70, who adduces it as a confirmation of Copernicus' staunch Aristotelianism. See also Neugebauer's remark in Price (1959):217 n.6 and Grant (1962a) (1962b). In his (1984) Grant shows, however, that the Aristotelian reaction to Copernicus was not uniformly hostile, and that a conviction for the need of some compromises was also experienced. Some of the Aristotelians even tried to set the earth in motion (e.g., Cesalpino and Thomas White). Guerlac (1968) attacks the conception of Copernicus as an Aristotelian, mainly as presented in Holton (1973):71, who bases his view on a corrupt translation of De Revolutionibus:514. About 17th century extensions of Aristotelian cosmology see Grant (1985a). As regards the equant business, there is no doubt that it could be eliminated in favour of an excentric-epicycle combination within the Ptolemaic system, had anyone put his mind to it. Certainly Copernicus could do it. 7 Koyre, like Kuhn, was taken in by this red herring in his (1973) (which was published in 1961, some 4 years after Kuhn's work, which it never mentions) see ibid:40, 49, 59 which he himself shows to be irrelevant to heliocentrism, pp. 48-9, but fails to see his own interpretation-fallacy.

528 NOTES

8 Neugebauer's authoritative pronouncement on this issue in his (1968) should make it definite that (1) Copernicus' astronomy is literally the transformation of Ptolemy's struc­tures to a heliocentric reference system, and so (2) is not and cannot possibly be any bit more accurate in its predictions, (3) neither does it happen to be simpler (4) nor can it get rid of the equant. Copernicus' declared he got rid of the equant but he merely transferred it to an epicyclic construction of the planet, and so he was wrong in this declaration. However, I think that Neugebauer is wrong in saying that "Copernicus considered this," i.e., an equant-free model, as his "main achievement" (ibid:95). What was his main achievement I propose in the following, and there show that this was what he considered as such. 9 Though Kuhn views this harmony as the central issue of Copernicus, he manages to reduce it finally to merely an esthetic affair, "a matter of taste" in his (1957):172, 181. Similarly, Hanson's defence of Copernicus' "originality" in his (1964) (also in his 1973:200-235) as well as Price's attack in his (1959), bog down in a boring finesse about the jargon of equivalence. Thus Hanson's final discovery is that Copernicus' originality lay in the fact that he transferred the center of the geometry to the sun, and so his and Ptolemy's orbits are different. A rather meagre crop to gather from such sharp and cutting analyses. 10 Basically this means that the Copernican system constituted a change in the concept of causal linkage. That this is always involved in scientific revolutions was argued in Pitt and Tavel (1977) who, however, do not deal with Copernicus. Implied in this is the reversal of roles which Westman (1980) argues for, i.e., the priority of the formal aspect in dictating a cosmological conclusion. See also Jardine (1982): 184ff. 11 Hence it is incomprehensible to me that Hanson, who saw the "systematic" element in Copernicus as its main innovation and meant roughly what I call here informativity, could have regarded this as a mere "disturbance" as compared with Kepler's "revolution" in his (1961):176-7, and also that he failed to see this element as the real claim to originality in his dispute about Copernicus' "originality", see n.9 above. 12 But I do not think that these are good reasons for preferring the Copernican system, as is customarily accepted today. Questions of preference evaluation, be it as "rational" as may, are empty for "rationality" has never been and never will be elucidated prior to and independent of questions of preference. Hence, e.g., the whole Lakatosian school is an enormous development of non-informative sophisticated apology. See also Bechler (1980). A great example is described in Westman (1975): The Wittenberg circle around Melanchton preferred Copernicus but rejected the movement of the earth and ignored the whole novelty of discovering the linear relative (and even absolute) distances of the planets. And so did "every author of the generation which first received the work of Copernicus" (ibid:167). What convinced Galileo to become a Copernican were a set of interlinked errors, see Drake (1987). 13 It was this insight, I think, that was Kepler's main philosophical discovery in his defence of Copernicanism against the sceptic attack, see Jardine (1979):156ff. where Kepler argues that the truth of the conclusion does indeed entail the truth of the premises. This is the great revolution in logic which Copernicus' system announced, even though Kepler saw it in terms of causality, and rightly so, see Gingerich (1973):52o£f.

NOTES 529

NOTES TO CHAPTER FIVE

1 See also

I am attempting a far greater work: for it is not merely calculations or predictions that I aim at, but philosophy: such a philosophy I mean as may inform the human understanding not only of the motion of the heavenly bodies and the period of that motion, but likewise of their substance, various qualities, powers, and influences ... what is found in nature herself and is actually and really true. (Works, V:511 and also V:556)

See the link between this critique of astronomy and Bacon's Paracelsian cosmology in Rees (1975):91-8. For his renaissance links to neo-Platonic nature philosophy see Rossi (1968). Notice that Bacon rejects contemporary astronomy (including Copernicus') not as false, or useless, or even as not "guaranteed as true" (L.Jardine 1974:77) but strictly as "superficial", i.e., not-informative, irrespective of his belief that the notion of the earth's motion is false (Works, IV:349). 2 See Hesse (1964):146-9 for an analysis. It was Hesse's essay which first encouraged me in the interpretation of Bacon as a platonic, informationist philosopher of science, con­trary to a prevalent view which sees his induction as a method of generalisation. This distortion of Bacon may have been the motive behind the modern Popperian notion of "inductivism" . 3 For Bacon's constant admonition, insinuating his self-perception as a successor of and improver upon Plato, see Novum Organum II, §105. 4 Horton fastens on this passage and on the constant involvement of "law" in the various definitions of Form in order to identify them (see her 1973:243, "Forms are therefore no more nor less than the laws of nature"). But I have grave doubts (in spite of Novum Organum II, §2, §17, above), since law is not a physical entity but Form certainly is. That is why a given Form is indeed "what we would call a necessary and sufficient condition for the occurrence of any nature" (ibid:244) but law is not. Obviously the Form of heat, i.e., such and such motion, is not a law, for it is motion. But Horton's decision slowly corrupts her interpretation, pushing her to identify Form with a "statement" (ibid:245) which obviously cannot be a condition, necessary or sufficient. 5 Hence the importance of Bacon's inductivism as adopted by corpusculists and spirit­physicists such as Descartes and Hooke. See Hesse (1964) and (1965) and Lalande (1911) as well as Milhaud's (1921):ch. III and ch. X: 213-227. 6 The inductivist tradition in the 19th century, stemming indirectly from Bacon's Novum Organum, shared this double feature (until Mill revolted against it) but viewed induction as inherently an analysis rather than a generalisation. See Herschel's (1851):191, 202 on the aim of science as "analysis of phenomena and knowledge of hidden processes", and Duhem on Newton's induction (see ch. 14.1 and 14.3 below). 7 Ignoring this point led such a sharp mind as A.E. Taylor to a complete misunderstanding of both Bacon and Mill, see his (1926). 8 See also Novum Organum, II §106, where he explicitly conditions the validity of an abstracted Form upon its informativity, i.e., being "larger and wider" than "those particulars" from which it was inferred. Only then, i.e., when its "wideness" is "con­firmed" does it acquire a "collateral security" that it is a Form "solid and realised in

530 NOTES

matter" and not "shadows and abstract forms". About the incongruity of Bacon's various pronouncements on the "certainty" of his method, see Urbach's (1982) esp. pp. 128-130. 9 Hence the similarity he saw between his new induction and Plato's in that both "analyse nature by proper rejections and exclusions

and then, after a sufficient number of negatives, come to a conclusion on the affirmative instances; which has not yet been done or even attempted save only by Plato, who does indeed employ this form of induction to a certain extant for the purpose of discussing definitions and ideas. (Novum Organum I, §105)

In ch. 13 below I offer a suggestion as to how the rumour about the Baconian method arose according to which it depends on amassing repeated instances to prove some "generalisation." That the rumour is still going strong may be seen in Larsen (1962) who concludes that Bacon was a straight Aristotelian and that his Forms are nothing more than "descriptive generalisations" (ibid:443), as well as L. Jardine (1974):ch. 5, 6,7 (e.g., p. 1(0) who does not produce even one passage from Bacon in evidence, seems to confuse "universal laws" with "generalisations", and strangely ignores Bacon's outspoken and disdainful rejection of generalisations even though she quotes it (p. 86). 10 This led Ellis to argue that (1) the "doctrine of Forms is in reality an extraneous part of Bacon's philosophy" and (2) that as it stands his method is either useless or a simple petitio principi, blaming it on "the kind of realism that runs through Bacon's system" (1858):22-24. Ellis, the Cambridge Plumian professor of mathematics during the 1840's and Fellow of Trinity, was a staunch Whewellian, and Bacon's informationism was for him a simple blunder. But he was right on it, for since the "doctrine of Forms" is in fact the essence of Bacon's philosophy, his method is indeed both useless (for obtaining Whewellian certain knowledge) and petitio principi (as I shall show now). Ellis created a tradition of evaluating Bacon according to future science, as partly a precursor of modern science and partly an obsolete transition figure, e.g., Hattaway (1978) and Horton's reply (1982) in sequence of her "defence" in (1973). This whole perspective is, to me, of no interest. 11 Little wonder that Hooke, who regarded Bacon as the source of his own method of hypotheses(see his Micrographia:93) compares it to the circulation of the blood (ibid. preface) from hands and eyes, via memory and reason, back to hands and eyes. See Hesse (1965):267. The link with Bacon's animism is pointed out in Hattaway (1978):188-191.

NOTES TO CHAPTER SIX

1 In all that follows I shall systematically refrain from dealing with the rhetoric, propagan­distic, or indeed political side of Galileo's statements. There is no doubt that the political circumstances under which he wrote are irretrievably mixed with his philosophical views and that he wrote, as any of us always does, with eyes directed to thousand directions. There is no such thing as "Galileo's intention". I abstract from all these interferences, obstacles, etc., as the platonist must always do. 2 Galileo's custom tailored Aristotelian is more real than one might expect. Agostino Nifo writes in the course of an exposition of his view of the status of regressus, that

NOTES 531

Aristotle's syllogism "why", in which the middle term is the cause, is merely an ex conditione demonstration:

The second process, indeed, by which the reason for the effect is syllogised through the discovery of the cause, is demonstratio propter quid, not that which makes us know absolutely (simpliciter) but rather ex conditione, given that is the cause, or given that the propositions are true which represent it as the cause, and given that there can be no other cause (quoted in Jardine 1976:292).

Since the minor premise in the propter quid syllogism states a causal proposition, Nifo's view is that this makes the whole explanation non-demonstrative, or explanatory on the condition that the minor is known to be true or shown to be the only possible. This is also what Simplicio says of Galileo's explanation. 3 But see Drake (1970):ch. 7 (1978):498, defending Galileo's argument as "more cogent than generally acknowledged" on the basis of the "rule of parsimony". But this is exactly Simplicio's generous help which he offers according to Aristotle's rule, in fact, signifying the failure of Galileo's claim for the argument as demonstrative! 4 Wallace (who for some reason confusedly attributes Simplicio's words to Sagredo ) calls Salviati's full admission "coming to the rescue", and "rising in Galileo's defense" (Wal­lace 1974:91), with the confusion about Simplicio unamended in the collected papers version (1981):141. 5 Contrary to Wisan (1974):125 and see 6.4 below. 6 They are reported in vol. 72 folio 116v of the Galilean MS collection at the Biblioteca Nazionale di Firenze, and were published by Drake in his (1973a). Why Galileo never reported or mentioned them in any of his published work "will remain a mystery", says Naylor (1974):106. 7 This argument was previously noted by Wisan in her (1978):53, n.38, to whom (as well as to Machamer 1978 and McMullin 1978a) Wallace answers in the appendix he added to the later version of his (1974) in his (1981):150-156. His proposal in the appendix is based on the sex t2 relation and the findings in folio 116v that v2 ex h and for the case of hex s the needed relation v2 ex e or vex t is deducible. My point about the compatibility of both phenomenal relations with a micro quantal relation where v ex t fails still holds. I am not certain, however, that I really understand Wallace correctly, since for his defence of the regressus against charges of circularity he refers the reader to his (1972):118-149 where he had allegedly "already rejected" it (see his 1983:629 n.72), but there I found only Paul of Venice and Nifo's rejections, not Wallace's. Nifo, as is well known, defended the regressus as apodeictic non-circular but later on rejected this and viewed the regressus as a merely syllogismus conjecturalis, i.e., hypothetical, as Wallace reports (1972):141-143, and see n.2 above. 8 Wallace explained his reasons more amply in his (1981a). 9 See Wisan (1978):38, 45. 10 This was the common view of mixed sciences at Galileo's time. My view of the full implication of Aristotle's theory is different, see my (1989a):ch. 4. But see also Lennox (1986). 11 For this interpretation Wisan refers to Galileo's well known comparison of his theory with Archimedes' theorems concerning the spiral (in his Letter to Carcavi, p. 109 above),

532 NOTES

where he characterises it as ex-suppositione (Wisan 1984:233). Wisan then rejects the interpretations of Wallace and Mertz (1982). 12 Galileo uses to call this definition of natural accelerated motion the "essence". He uses both terms in this sense in Discorsi: 160 [197] see p. 109 above. 13 See the history of this affair in Drake's pre-I970 papers, mainly (1970):ch. 11, (1958), (1969a), (1970-1), and also in his (1978):84-104, 110-116. Compare with this Koyre's (1978):67-68,95-107. The switch to the v ex t definition occurred around 1610 consequent upon Galileo's discovery of the parabolic motion of projectiles, see Naylor (1976), (1977), and Wisan (1974):227-9. 14 E.g., Discorsi: 164-5 [201]. 15 Discorsi: 162 [199]: "starting from infinite slowness, i.e., from rest". 16 This feature was pointed out in detail by Drake in his (1974a). 17 Wisan is wrong on this point, see her (1978):54, n.38. 18 Related matters are discussed in Drake's (1973), (1974). 19 Moody's classical (1951) traces the medieval history of this difference function to Avempace, who was a Platonic commentator on Aristotle. The Platonic nature of the difference function goes back to Philoponus (see notes 21 and 43). A critique of Moody's interpretation of Aquinas was sketched out in Wallace (1981):341-8. 20 The full conceptual significance of the difference function did not sink even in Moody who, after discovering a major problem ("Why did this paradox not bother Galileo?" in his 1951:174) answers it as superficially as the traditional historiography is conditioned to do (ibid). The history of the problem is told in Grant (1981), but the erroneous notion that Aristotle rejected motion in the void because of its instantanity still persists. Moody compounds this error by holding that since Dl/0 = D2/0 all bodies in the void move equally fast! (ibid: 177). 21 Philoponus, who initiated the difference function in his critical commentary on Aristot­le's physics, along with his concept of impetus, introduced these concepts under the platonic philosophy of nature in which "nature" is a non-material universal force disper­sed in bodies and causing their natural motions as an efficient, separate but internal cause or force. See Sambursky (1962):74ff., 85-7 (but notice Sambursky's silence about the inconsistency of Philoponus' theory of weight-velocity proportionality). Philoponus' com­mentary was first translated into Latin only in 1539 and again in 1558. On the possible influence of this platonised Aristotle on Galileo, via Vitelleschi of the Collegio Romano, see Wallace (1981):ch. 7, 13, and Galileo's own notes in Galileo (1977). 22 On Aristotle's philosophy of mathematics and its ultimately formalistic sense of truth, see Bechler (1989a): ch. 5. 23 But see Koertge (1977) esp. p. 403 compared with p. 407. 24 Compare Galileo's remarks on the observational fit of theory (1960):37-8, 68, 107, with Descartes (ch. 7.14 below). Both refer to a fully existent realm of being, the realm of the physical yet mathematical, which is the realm of the actual potential. This is contrary to the accepted interpretation of the mathematical content of laws of nature in the scientific revolution as true by "idealisation", i.e., not in the concrete. See, e.g., Koyre (1978):28-38, 129-135, and recently Funkenstein (1975), (1981), (1986): 174-179, McMullin (1985), and see ch. 6.10 below. 25 My emphasis on the importance of infinitesimal atomisation of the continuum should be compared with the hesitant argument of Smith (1976) esp. pp. 587-8. 26 I cannot see any justification for Drake's remark that Galileo did not propose this equality as a conclusion to be accepted "but solely to stimulate careful thought", nor

NOTES 533

does Sagredo's reply bear out this interpretation, Discorsi D:37, n. See also Quan's analysis of the Galilean solution in his (1968). 27 See Settle (1961), (but compare Naylor 1974,1976,1977,1980, 1980a) and its influence in Wisan (1984). Also the important Drake (1974). Drake argued in his (1975) for the experimental origin of Galileo's soc e law. Drake's work was duplicated and contested in Naylor's works, especially (1980), see pp. 373-7. Naylor's view fits well my suggestion. 28 See, e.g., Funkenstein (see note 24 above). Since both Plato and Aristotle demand necessary truth as the basic principles of scientific knowledge, and since both accept that sense experience cannot provide a guarantee of such truth, the twin traditional categories of rationalism vs. empiricism are ill fitted to capture the distinction between platonists and aristotelians. This is the main reason I avoid any use of those beloved categories. 29 See ch. 10, and mainly lOA below. This aristotelian interpretation of Newton's physics began with Berkeley, and through d'Alembert via Mach reached modern historiography. 30 The only exception is Gassendi, who is crystal clear in his rejection of any impetus theory (Koyre 1978:250-1). This is a direct outcome of his rigid materialism, structurally identical to Ockham's nominalistic rejection of impetus (Shapiro 1957:ch. 2, 3, esp. pp. 36-41). The close conceptual affinity of materialists such as Hobbes and Gassendi, or aspectists such as Spinoza, with aristotelism is obvious and explains their being grouped together during the 17th and 18th centuries. It is in this context that Gassendi's acceptance of the void is problematic. All of Koyre's other examples, such as Bruno, Cavalieri, Torriceli, do not bear his claim (Koyre 1978:138, 237-250). Concerning Gassendi, see Descartes' disdainful attitude to him as a backward Aristotelian, 5'37 n.7 below. But though Koyre's evidence from Gassendi is clinching, Gassendi's extant texts are far from being as clear, see Pav (1966):30. Koyre himself adduced other, conflicting evidence in his 1957 paper on Gassendi, (1966a):284-296. All this has almost nothing to do with the fact that Gassendi was a discontent Aristotelian, as told in Brundell (1987). 31 On the survival of the Aristotelian "natural motions" and "elements" in Galileo see Brown (1976), who shows definitely that Galileo used these categories in his late proof from the tides and elsewhere. I have no satisfactory explanation for this. However, it must be noticed that since only "earth" has "natural" motion (i.e., circular), but neither "water" nor "air", Galileo would be in a tough spot were he confronted with the fact that "earth" and "water" fall exactly in the same way from high towers, as well as from masts of sailing ships. He would then come to see that the notion of natural motion of "earth" cannot be maintained, for the impetus of the tower would have to be added on to its natural motion and so its resultant motion could not be the same as that of "water" , contrary to fact. 32 This is contradicted by accepted historiography, according to which Galileo abandoned his early impetus theory which he inherited from 14th century scholastics, and only because of this came to create his novel inertial conception as presented in the 1638 Discorsi. See Koyre (1978):30-36; Hall (1962):ch. 1,3; Maier (1949):1ff., 132ff. See also notes 47 and 48 p. 536-7 below. 33 See Galileo (1960):66-7, also in his mature Dialogo:143-5, Discorsi:181 [215], 244 [268]. It was known before him, e.g., by Cardano and Benedetti, see Wisan (1974):159. 34 About circular inertia in Galileo see the arguments of Drake (1970):ch. 13, Coffa (1968). Drake's argument analyses Koyre's (1978) thesis of circular inertia in Galileo and refutes it. His arguments seem to me convincing, in particular the one that the planetary circular motion could not be held by Galileo who knew some astronomy, and that Galileo simply had no explanation for their motions. See Shapere's reply in his (1974):112-119.

534 NOTES

For the view that Galileo held a principle of circular inertia see Koyre (1978):154-8, using as evidence the well known opening discussion in Dialogo:19. Also Dijksterhuis (1961):349-50, Wisan (1974):263. Another view, which rejects circular inertia but also denies a principle of linear inertia in Galileo is in Chalmers and Nicholas (1983):334-6. 35 The case against Galileo's circular inertia is explored in Drake (1970):ch. 13, and is here adapted to the impetus theory. 36 On Galileo's impetus theory and its relations to Buridan's and Benedetti's see Drake (1975), (1976), and Franklin's critique in his (1977). Its link with his Copernicanism see Drake (1987), Chalmers and Nicholas (1983), and most importantly Wolff (1987). 37 "Duhem's thesis", expounded in his (1906), to the effect that Galileo's inertial concept was created in the 14th century by the Paris impetus theoreticians, was rejected by Maier (1949), (1951) on logical grounds of the incompatibility of inertial and impetus motion. Maier's thesis is premised on the accepted view of inertial motion as absolutely non enforced. This view she never supports. Since my thesis is that this is strictly an aristotelian interpretation of modern physics, and must be rejected on this account, her argument is really a petitio principi. Against her view see Moody (1966) :32 who says that he does not think that the alleged incompatibility between Buridan's impetus theory and inertia can be shown. However, Moody held that Galileo's early impetus theory was of the self­perishing kind, and that in his mature theory he abandoned it (ibid:31). This seems to me to be a double mistake, i.e., neither did Galileo hold a self-perish version of impetus in his early period, nor did he ever abandon the permanent version later on. Duhem's thesis has received a new push with the discovery of Galileo's close links with the Jesuits of the Collegio Romano, see Wallace (1981):111 and Crombie (1975), and also Unguru's (1982) and McMullin's critique (1983). Wallace replied in his (1984), as well as (1988). See the recent evaluation of both Duhem's claims and of the 1277 condemnations in Grant (1979), (1982) and (1985). Grant refutes the anti-Duhemian thesis in Koyre (1978) and reaffirms Duhem's thesis in the sense that it was "only after 1277, and because of the condemnation, that the principle of God's absolute power came to be used widely in the analysis and discussion of numerous physical problems" (1979):217. Funkenstein dismisses Grant's detailed evidence-packed (1982) paper with the remark that he "exag­gerates, perhaps, the impact of the condemnation" (1986):63 and ignores his important (1985) paper. 38 See Drake (1970):ch. 12, Maier (1951), Koyre (see note 32 above). The whole outlook of existing historiography is conditioned by its interpretation of Aristotle's theory of motion which is, uniformly, that one "cardinal tenet of [it] ... was that any moving body must have a mover other than itself" (Drake, ibid:242-3). Consequently impetus theory is interpreted as an Aristotelian offshoot (mainly by Maier) and so inertia in the new physics must be anti-impetus if it is anti-Aristotelian (Maier, ibid:304-6). Galileo's theory must be therefore of the self-expending impetus so as to accommodate a non­impetus uniform motion, i.e., inertial motion, if it is both anti-Aristotelian and anti­impetus. My argument is that Galileo's view is properly anti-Aristotelian and hence rejects the notion of natural, forceless motion, hence its impetus must be conserved. Drake also takes GaliJeo's impetus to be self perishing, e.g., (1976):328.

To characterise inertial motion as, among other characteristics, "uncaused (or 'natu­ral'), that is, it takes place without a pushing agency, external or internal" (Shapere 1974:122) is to prejudge the whole issue and beg the question about the principle of inertia in the scientific revolution. Most alarmingly, no such motion is physically possible even under most ideal conditions, since a body that is not initially pushed will not move,

NOTES 535

hence its motion must be caused. To qualify, in response to this challenge, the "uncaused (or 'natura!')" by "not continuously caused, that is," is either to beg the question about the nature of the force of inertia or to take the risk that the law of inertia was introduced into Newton's physics sometime in the 18th century. The issue becomes then verbal. 39 See Grant (1965), (1965a). 40 Maier's (1949), (1951) is a sustained argument that actual impetus theory was incompat­ible with inertial motion taken as infinite, non-externally enforced motion. Since Burid­an's theory flatly refutes this thesis, she was led to deny Buridan's own statement that in the absence of external obstructions, motion by impetus would be infinite (and so compat­ible with inertial motion). This she does by conjuring up an inclinatio ad quietem in matter which would lead to the perishing of the impetus even then. But there is no such concept of matter in Buridan, nor does Maier ever provide any hint of evidence that there is. See Moody (1966):32, who reports on this and points out that Buridan repeatedly asserted that "prime matter" has no resistance to motion. 41 See Fredette (1972). The argument links with that of Brown (1976) about natural motions. On pp. 338-9 Fredette proposes the thesis that "Galileo's theory of motion rests exclusively on his theory of weight", and the peripheral role of impetus in it. He ignores the fact that "weight" is itself now explicated in terms of impetus. 42 He could hold Buridan's suggestion, i.e., Clagett (1959):536. In fact he did not, and my guess is that this is because Galileo's impetus was linear while Buridan's was circular in the case of the planets. Galileo could at most explain the eternal circular motion of a heavy body along a rigid support concentric with the earth's center as caused by composi­tion of two linear forces, but he could not apply this where the combination heaviness­cum-support is absent, as in the case of the planets. Only Newton's gravitation supplied the second linear force, and even here the support is absent. Buridan's concept of impetus as "distinct from the local motion in which the projectile is moved" (Clagett, ibid:537) is of a force (motive force, virtus motiva ibid:534), and is clearly informative. Not that it was consistently so (e.g., the impetus is strictly proportional to the observed motion, it is corrupted by the presence not only of external impediments but also by the presence of internal conflicting tendency such as weight, and it does not compose with it), but the concept was there. 43 Hence John Philoponus, the initiator of the impetus concept in late antiquity, who was a Platonic commentator on Aristotle's corpus, insisted on interpreting weight as an efficient cause, see Cohen and Drabkin eds. (1948):217, and Clagett (1955):211-2. 44 Notice, by the way, how Galileo views the rule that everything in motion is moved by another, as anti Aristotelian, and uses his hydrostatic model to refute Aristotle's argument against the atomists in De Caelo 227bl-8. There Aristotle refutes the atomists theory that "an external agent is the cause of the elements moving up or down, or that they are moved by force (bia), the extrusion which some allege". Aristotle's refutation is by the proportionality of velocity to the quantity of matter moved in natural motion. 45 Notice that Galileo moves in his argumentation from the definition of natural motion by natural places to a novel definition by noninfiniteness, to still another definition by non externality of the moving force. It is this slow shift that permits his inference of a third category between natural and enforced, i.e., "neutral", in his (1960):66. This may also be the solution to Wolff's puzzle in his excellent (1987):247ff. Galileo infers this from a new definition of natural motion, i.e., as non-externally enforced cum finite motion. The novel motion which he discovered is non-externally enforced but infinite, and hence is not natural (and only internally enforced). Remember that his impetus

536 NOTES

interpretation showed natural motion such as free fall to be internally enforced. Hence he did not see any incompatibility between internal enforcement and naturality of motion. 46 This image of static streaming of force from support to the weight became ingrained in 17th century thought, e.g., Hooke's theory of weight in Gunther (1938) VIII:184, and see Hankins (1967) for the entailed view of force and the second law, also Dijksterhuis (1961):473. See ch. 11 below. 47 As noted above (note 32) this view of Galileo's dynamical philosophy of nature is rejected by all contemporary Galileo students. To take one curious example, Drake, who in his (1969) (read as early as 1966 as a lecture in the University of Toronto) agreed that impetus theory was "thoroughly un-Aristotelian", and that "the notion of inertia was sure to appear as soon as anyone conceived of impetus as a force that did not decay with time", so that "an anti-Aristotelian could take this step", started repenting by 1970. For now the essence of Galileo's inertia became the "body's indifference to motion or to rest" and this idea is "not derived from, or even compatible with, impetus theory, which assumed a natural tendency of every body to come to rest," (Drake 1970:251). This, however, is printed just five lines below a quotation from Galileo's 1613 treatise on sunspots which ends with this statement:

Thus a ship ... having once received some impetus through tranquil sea, would move continually around our globe without ever stopping. . . if. .. all extrinsic impediments could be removed. (ibid)

This is a flat refutation of the alleged incompatibility and of Drake's notion that impetus theory demanded a natural tendency of body to come to rest. By 1986 the conversion was complete, and Drake came to reject out of hand the view of Galileo's physics as "a kind of dynamics, either medieval with impetus as an impressed force, or Newtonian, with inertia as inhering force" (1986):167. At this stage the aristotelianism of Galileo reached its peak:

Galileo, as Aristotle, regarded force as contrary to nature by definition, depriving it of any proper place in physics as the science of nature. The "natural" motions to which Galileo's physics was restricted were those undertaken spontaneously by heavy bodies ... (ibid:167)

Galileo the aristotelian now differed from Aristotle only in the matter of light bodies and circular motions which now also belonged to terrestrial bodies. Drake now completed his view by arguing that Galileo identified impetus with velocity and not with force, referring to Dialogo pp. 25, 27 (of which p. 25 is irrelevant) and that Salviati "promptly removed" the idea (in ibid:149-51, 156) (Drake 1986:167-8). But on pp. 144-151, far from "promptly removing" it, Salviati in fact is the one who introduces the theory and it is Simplicio who rejects it! (see p. 157 below). And on p. 156 Salviati identifies the impetus with motion only because he is refuting Simplicio who previously declared this identity.

Drake's conflicting views of Galileo merely reflect the prevailing general confusion in regard to Aristotle and aristotelian philosophy of nature, as will become more clear in the case of Newtonian historiography. 48 The whole plea for Galileo's positivism breaks down in the face of the passages quoted above (with Sagredo and not Simplicio as the expounder!) as well as his argument for

NOTES 537

the perpendicularity of the freely falling stone, which explicitly uses impetus as a con­served force against the Aristotelians, see 6.15 below and previous note. Let it be noted, however, that Drake's positivising-drive stops at Newton who, Drake graciously admits, took inertia as "an inhering force", Galileo and "we", however, seeing the matter differently (Drake ibid:167 n.15, 168). 49 About the details and importance of this argument in Galileo's eyes, see Burstyn (1962), Shea (1970a), Brown (1976), Mertz (1982), Drake (1978):319 (1986):158-161 (1987). Galileo found his theory of tides as early as 1595 (Drake 1970:ch. 10, pp. 201-2) and it was this discovery that probably turned him into a Copernican. The whole Dialogo was conceived as a treatise on tides, and the comparison of the two systems of the world was a pretext for presenting the theory of tides, Drake (1978):309ff., and 495 n.25. 50 See Bechler (1989a):ch. 5 for my interpretation of Aristotle's "abstraction" in mathe­matics. 51 Hence the naivety of that brand of the historiography of the scientific revolution which sees Galileo's role as that of the discoverer of laws and the abolisher of the search for causes and essences, e.g., Cassirer (1946) mainly p. 295, and also Drake (1975a) who repeats Cassirer's thesis, e.g., p. 148,149,150,153. Drake further supported his view in his (1978a), even though its incompatibility with his own important discoveries in his (1974a), (1975), (1976) should have warned him against this. The view is also held by some Newtonian scholars about Newton, e.g., Westfall (1971):89.

NOTES TO CHAPTER SEVEN

1 Descartes saw danger in the syllogism's production of certainty exactly because of its automatism, see HR, 1:32. 2 See Passmore (1953). The circularity of the syllogism was a well known fact in the skeptic tradition stemming from Sextus Empiricus, see his Outline of Pyrrhonism II:ch. 14 (pp. 275-283 in the Loeb edition), and see Popkin (1964):34-38. Sextus was unknown in the middle ages, and was first translated into Latin in 1562, see ibid: 17. On the positivistic, pragmatistic, behavioristic, Humean aspects of Sextus see Chisholm (1941). 3 His 1628 Regulae is the only fairly detailed treatise on logic he managed to compose, and even this he left unfinished with two "parts" yet to go. The 1637 Discourse de la Method dedicates only two pages of the second chapter to method and logic. See Gibson (1898). 4 See Hintikka (1962), (1976). 5 From his answer to Mersenne, who was the first to formulate the charge of circularity in the Cogito, in the 2nd set of objections to the Meditations (HR, II:26). 6 But see more on the contingency of such a-priori truths in 7.6, 7.22 below. 7 See his letter to Clerselier, where Descartes says that Gassendi's

most important mistake here is that he supposes that the knowledge of particular propositions must always be deduced from universal ones, following the syllogistic order of Dialectic. This shows how little he knows the right way of seeking for truth; for in order to discover the truth one must assuredly begin with particular notions, and then go on to general ones afterwards. (Letter to Clerselier January 12 1646)

538 NOTES

8 Of recent analyses and solutions of the problem of Descartes' circularity, see Kenny (1968):172-199 (1970), and (1983) in which he defends his earlier thesis against Gewirth (1970) and others, Gewirth (1941), Hintikka (1962), Williams (1967), (1978):ch. 2, Tlu­mak (1978), Dreisbach (1978), Imlay (1977), Attig (1977), Odegard (1984). 9 Burman relates that Descartes told him that "attention" is all that is needed as a guarantor of the truth (Burman:6). 10 But this point, so essential to Descartes, is still ignored today, see Funkenstein (1975a):185 where God's goodness is stated to be the basis of the clarity and distinctness criterion of truth. 11 See Kenny (1968): 125ff. for an analysis which sees distinctness as a truth criterion. But Kenny fails to connect this with certainty and to deal with the ensuing puzzle that Descartes sees certainty as a criterion of truth, see n.16 below. 12 Frankfurt (1970):162-3 has argued against such an interpretation, i.e., the implication of truth by certainty. But the texts he uses (HR, 1:184, 158-9) fail to confirm his claim that Descartes uses certainty as a criterion of truth only after God's existence is proved: God is not mentioned in the first text, and in the second Descartes says that when he attends to a clearly and distinctly perceived proposition he is certain that no God could possibly deceive him in that. 13 It has been argued (by Dreisbach 1978:64), that Descartes never based his argument, up to the end of Meditations III, on the clarity and distinctness criterion of truth, or (by Markie 1979:101 in reference to a clarity and distinctness criterion of metaphysical certainty) that he never used it. But our passage (HR, 1:158) says that certainty about truth is the consequence of clarity and distinctness, and that it is a justified consequence. Indeed, it is the best justified consequence that ever could be, as also its sequence (which Kenny quotes, 1968:182-3) confirms, and hence that kind of certainty is indeed metaphysical. Hence this passage refutes both claims. Markie never even refers to it. 14 See Gewirth (1943) for a detailed analysis of the ensuing problems, and some qualifi­cation of my conclusions. 15 Check this against Principles I, §64, where the very same idea, hence the same perception, is distinct or confused according as it is "viewed as" mode or substance. "Viewing as" is obviously different from "perceiving", and is actually "interpreted as" or "understood as". 16 This epistemic circularity was pointed out by Kenny (1968):197-9, but he failed to see its link with the distinctness criterion of truth. 17 So Gewirth (1943):255, and his conclusion p. 258. 18 He may sound hedging on the existence of substance, saying that "we name the thing in which (attributes) exist a substance" (HR, 11:98), implying maybe that it is merely our human reaction but not a true inference. My point is that he actually does assume the existence of such a substratum, of which "we do not have immediate awareness" (ibid.) just as Locke would do. See ch. 12.1 below. 19 Hume in fact used in sequence Descartes' distinctness criterion of truth and then separability salva veritate, arguing in result that

As all distinct ideas are separable from each other, and as the ideas of cause and effect are evidently distinct, ... consequently the actual separation of these objects

NOTES 539

is so far possible, that it implies no contradiction or absurdity. (Hume Treatise, I, Pt. III, Sec. III p. 79)

20 See Kenny (1967) on innateness in Descartes as mere capacity. 21 See Bn!hier (1937) on the relations of Descartes' semi-tacit doctrine of created eternal truths and the Platonic and Neo-Platonic theories of Ideas. 22 The complicated issue of the concept of "idea" in the 17th century as an act, an object, a representation, and more, is sketched out in McRae (1965), and the important studies of Yolton (1975) and (1983). 23 See a strictly physicalist interpretation of Descartes' ideas in Reed (1981). 24 See Funkenstein (1975a) (reprinted in his 1986: 179-192) for an attempted nominalist­conceptualist interpretation of Descartes' eternal truths. Its failure, implied in Descartes' rejection of the natural causal link between the material object and its idea as an explanation of our having the idea, and confirmed by his affirmation of the necessity of some intuited essences even if the substance is non existent (ibid:184-5) should have made it clear that some kind of platonic realist ontology of ideas is inevitable for Descartes. Another attempt at a "conceptualist" interpretation of Descartes which may be used as its own refutation is Miller (1950) who based his case, partly, on Descartes' alleged "refusal to admit any kind of reality besides thinking and extended substances" (ibid:240), conveniently forgetting God as neither. 25 See his October 16 1639, letter to Mersenne, where he remarks that the word "truth" "denotes the conformity of thought with its object" (Letters:65-6). 26 Notice how Descartes' mind wanders and, undoubtedly thinking about Aristotle's potentials, he adds the confused remark that the real triangle exists in the drawn triangle "just as Mercury is contained in a rough block of wood" (HR, 11:228) thus, in effect, confusing the whole issue. Aristotle, in fact, denied this, e.g., Met. 1002a21-3, quoted in n.5 ch. 9 below. 27 See Cook (1975) for an opposed interpretation. 28 See Leclerc's inquiry into the Neo-Platonic affiliations of Descartes' ontology in his (1980). The standard interpretation is of Descartes as a sophisticated late Scholastic­Aristotelian, not only as in Gilson's classic work but also in Kenny (1967) and both his critics Halbfass (1969) and Lennon (1974). Koyre in his (1966) never mentions the problematics of the ontology of ideas, essences and eternal truths. 29 About the complete failure to see him as a conceptualist, see Miller's attempt in his (1950). 30 One version of this query was raised by G.Brown in his important (1980):36--7. My answer is more extreme than his, and is opposed to Kenny's answer in his (1970):692. Both, as well as Gewirth (1970):677-8 opt for the three level ontology without, however, sensing this. 31 An argument for the very close link between Malebranche's and Descartes' philosophies is given in Gueroult's (1954). 32 See on this the dispute between Lovejoy and Laird. Lovejoy (1923) argued that far from being a direct-realist, Arnauld was a standard idea-representationalist, contrary to his canonisation by the new-realism of the time. Laird, one of the canonisers, answered (1924) but failed to see the systematic centrality of Arnauld's ideas as necessary -according to Cartesian ontology - mediators of our knowledge. Both, however, and even

540 NOTES

Lovejoy's rejoinder (1924), fail to appreciate the fact that "representation" is used throughout as a technical, newly defined term, which voids the dispute of any logical content. (See also Watson 1966:85-88). 33 Cook (1974) sharply criticises previous analyses of the dispute for having failed to perceive the true nature of Arnauld's alleged representationist epistemology. Cook con­cludes that Arnauld did not hold an "object theory of ideas" but that his "ideas" are "acts by which one sees physical objects" (ibid:56). My analysis argues that this is a mere side issue in Arnauld's interpretation of Descartes. 34 Extending Descartes' declaration that the geometric triangle, even though non-physical, "is something and not nothing", Malebranche applied it to "false ideas". The chimera argument is repeated in regard to such chimeras as "a fiat sun", "a cubical earth" and the scandalous "mountain of gold" (Receuil de to utes les responses in his D.C. vol. VIII:910, letter III, March 19 1699). He is thus the link between the half hearted platonism of Descartes and the full blooded one of Meinong. 35 Introduced as a systematic principle in his reconstruction of the history of the principle of inertia, Koyre referred to the "equal ontological rank" of the two "states" of motion and rest (1968):4 (1978):114, 254. The notion was adopted by recent scholars and entitled "ontological identity", see Westfall (1971):58. See also note 11 ch. 11 below. 36 See Herivel's discussion of Descartes' conatus in his (1965):42-54, Sabra (1967):81-85, Schuster (1981):283-299, Gabbey's (1980) on Descartes' "determination". 37 The argument for the centrality of force in Descartes' ontology which is launched here and winds up in the actual potentiality of God's action (ch. 7.17 below) should be supplemented by the arguments of Gabbey (1980), Pendergast (1975), Clarke (1977a) and Hatfield (1979). 38 Relativism might be imputed to Descartes not merely in consequence of his own declarations in Principles, e.g., II:§62, III:§19, 26-29, but also, and more importantly, in consequence of the ontological equivalence of rest and motion. The conclusions here are in agreement with those of Mouy (1934):19-22, and Koyre (1978):263-6. 39 The scholastic origin of this complex category see in Wolfson (1929):99-113 and (1934):59-69. 40 Mode as limitation is used by Descartes in his letter to Mesland May 2 1644, where surface, line and point are modes of the substance body (Letters:151), also described as "manner of being which cannot be changed without a change in" the subject (ibid:155). 41 See also his letters to Arnauld (Letters:235), to Mesland (ibid:148), to Regius (ibid:129). 42 Respectively treated in Principles, I, §60, 61, 62. 43 Hence his pointed disregard of Kepler's and Galileo's laws in so far as they are observational. His own work on planetary motion was, he said, only general and qualita­tive (AT, V:259), and he "never examined questions which depend on measurement of velocity in detail" (Letter to De Beaune, April 30 1639, AT, II:542). He declared his seven laws of collision to be non-observable, since they describe potential situations which cannot possibly be realised, such as empty space (which is a contradictory concept), see Principles, II, §53. 44 This problematic role of experience in Descartes is a well known issue, see Liard (1882):ch. IV, Milhaud (1921):ch. 9, Gewirth (1941a), Shea (1984), Larmor (1980). 45 Principles, I, §57. For the following argument see Wahl (1920). 46 Informativity is rooted in God's omnipotence and in the identity of his knowledge and

NOTES 541

will, which entails that even the laws of logic are contingent, e.g., the law of contradiction (see his letter to Mesland, May 21644 Letters:151). The platonist's contingency of eternal trnths must, however, be carefully distinguished from the aristotelian's. With the latter it is, as in Kant, simply the outcome of the radical reduction of all laws (of logic, mathematics and of physics) to the contingent nature of human thought, but with the platonist it is the outcome of the contingent nature of the world created by the Judeo­Christian God. 47 See Suppes (1954):148-150. 48 See his 'Principles, IV, §205 for the cipher metaphor: Even if the text becomes intelligible, this does not entail the cipher's truth, and the only certainty such success allows is "moral", which counts as nothing where the infinity of God's power is concerned. 49 The whole history of the philosophy of science is a constant effort and failure to see and accept this implication of informativity. See Cotes' metaphor of the clock (ch. 13.4 below) as a sneering critique of Newton's failure, or Mill's puzzled disdain of Whewell's "consilience" as an employment of Descartes' metaphor (A System of Logic, III, xiv, §6) and compare it with the typical aristotelian attitude to it as in Leibniz's reference in his New Essays, IV, xii, 13. The unhappy end is the contemporary trivialisation of "realism" into "sophisticated realism" or "internal realism" which is a collapse into "idealism" as in Putnam's Meaning and the Moral Sciences (1978) Lecture IV.

NOTES TO CHAPTER EIGHT

1 See, however, Kitcher (1973), and note 5. 2 "In demonstrating propositions I always write down the letter 0 and proceed by the geometry of Euclides and Appolonius without any approximation. In resolving questions or investigating truths I use all sorts of approximations which I think will create no error in the conclusion and neglect to write down the letter 0, and this I do for making dispatch." (Corr. VI:136-7) 3 See Heath's commentary in Euclid (1956) III: 374-377. 4 Thus, Euclid XII:2, the theorem I used as an example, uses this assumption to derive the statements that the polygon inscribed in M is smaller than M and that the polygon inscribed in m is smaller than m. The theorem becomes a petitio principii if these are extended to equality. 5 This refutes Kitcher's assertions that in the Principia and the Quadrature Newton "founded the calculus on a firm geometrical basis" (Kitcher 1973:46), or that the method of infinitesimals was only a "temporary backing for algebraic" rigorous formulation (ibid), or that Lemma II of the Principia is a "generalisation of the exhaustion method" (ibid:47 n.55), or that Lemma I has a "proof which accords with traditional standards" (ibid:47). Kitcher thus misses the essence of Newton's conceptual innovation and the enormity of his revolt as expressed in Lemma I. 6 See, e.g., Aristotle's Phys. 231b15-20, De Gen. et Corr. 316a23-30 and my analysis in my (1989a):ch. 2.10. See also Feyerabend's treatment in his (1983a). The aristotelian argument delineated here by Newton will actually be picked up by Berkeley, see ch. 16.1-5 below. Newton, on the contrary, says that "if light were moving instantaneously

542 NOTES

then it would need infinite force" (Opticks, Query 28) but uses it as implying that infinite force is logically possible and that motion in an instant is not a logical absurd. See also Principia:372 on infinite pressure. 7 Archimedes, who formulated this axiom, attributed it to Eudoxus, see Heath's notes in Euclid (1956) III: 15-16 and in Archimedes (1912):xlviii, 4, 234, as well as Heath (1921) II:5. 8 Make no mistake: Indeed I take to heart Whiteside's ominous warning that any attempt to "argue that the Newtonian infinitesimal is non-Archimedean quantity" "should be­ware" of this declaration (Whiteside 1970, MWN 6:195, n.9). 9 Thus the Quadrature so called kinematic presentation is inevitably landed into circularity in its definition of the derivative, defining it by the concept of "fluxion", i.e., instan­taneous velocity, which in its turn cannot be defined independently of the concept of the derivative.

NOTES TO CHAPTER NINE

1 See the texts analysed in the following pages, which actually reverse the dependence relation and declare that God could not possibly have created space. 2 This is Plato's transcendental proof of the existence of the Ideas in his Phaedo:74-75. 3 The best and most important analysis to date of Newton's conception of space is McGuire's (1978), (1978a) and (1983), which contain, apart from their acute logical analysis, the full contemporary background. 4 Compare with Galileo's argument ch. 6.7 above. Descartes' principle that the distinction by the intuition entails separability, reflecting the priority of the potential, is also the principle which informs the Bohr-Einstein controversy over the nature of quantum mech­anical reality. The Einstein-Podolsky-Rosen argument presupposes this and Bohr's rebut­tals presuppose its contrary. See my analysis of Bohr's philosophy in my (1989): ch. 4 and of Einstein's platonism in my (1989b). 5 Contrast this with Aristotle's words:

no sort of shape is present in the solid more than any other, so that if the Hermes is not in the stone, neither is the half cube in the cube as something determinate, and therefore the surface is not in it either. (Met. l002a 21-3).

NOTES TO CHAPTER TEN

1 My hunch is that Mach's critique of Newton's physics, through its brilliant articulation in Reichenbach's writings, became the main influence on modern Newtonian historiogra­phy. I have analysed Mach's and Reichenbach's aristotelian ontology in my (1989):ch. 4.1 and 4.2 as a preliminary to the analysis of Einstein's theories of relativity. 2 See the extended analysis of Newton's bucket-type arguments in ch. 11 below, where the logical link with the informationist concept of inertia is the main theme. 3 Cf. Duhem (1906):32 where he says that in "the progress of experimental physics", "the purely representative part enters nearly whole in the new theory, bringing to it the inheritance of all the valuable possessions of the old theory" while the "explanatory

NOTES 543

part" is discarded. Contrary to the "explanations", which Duhem views as mere "intellec­tual symbolic abstractions", and which are discarded during a revolutionary change, the scientific tradition guards its real continuity by keeping this "purely representative part" intact across the change (ibid:33). 4 E.g., Principia: 10. See the argument p. 292-7 above. 5 The tight link between strict formalism in the philosophy of mathematics (even up to Hilbert's sense) and Aristotle's ontology is analysed in my (1989a):ch. 5. 6 Cohen has assembled a good sample of these declarations, see his (1982):51-53 and (1980):68-83.

NOTES TO CHAPTER ELEVEN

1 See ch. 15.1 below. The symmetry issue became crucial in Berkeley's theory, see 16.9 below. 2 Not that this was always clearly put by Clarke, who condensed the bucket argument by writing to Leibniz that it showed "from real effects, that there may be real motion where there is none relative, and relative motion, where there is none real" (Alexander 1956:48). Though the first clause is true as it stands (referring only to existence, and not to observability), the second is false. 3 On the bucket argument see Lacey (1970), Hooker (1971), Suchting (1967). 4 See the analysis of Mach's ontology of actuality as the basis of his critique in my (1989) :ch. 4.1.4. 5 "For to this end it was that I composed it" (Principia:12 and see full quotation p. 294 above). 6 See Leibniz' critique of Descartes' declared relativism, ch. 15.1 below. Leibniz de­veloped a version of spatial relativism and compensated for this by his dynamic absolut­ism. The same goes for Berkeley (see 16.9 below). Consequently they had to reject either the priority of the actual, or the reality of forces. Both choices were equally fatal to their ontologies. 7 See Koyre (1965):115-138 and Reichenbach (1924). 8 See Newton's Opticks:400. 9 See Herivel (1965):28ff. 10 This should supplement the argument against identifying measure with the measured pp. 282 above. 11 The notion of dynamic equivalence seems to be derived from Reichenbach's term "dynamic relativity" (e.g., his 1978 II:62) which Koyre adopted for his aristotelian interpretation of Galileo and Descartes (e.g., his conclusion that inertial motion must be a "relational state" in his 1978:130), from whom it passed on to us, as in Westfall "dynamic identity" e.g., (1971):347. See also note 35 ch. 7 above. 12 See document II in Herivel (1965):141-150, and in particular 146-7. 13 See the story of this important exchange in Koyre (1965):ch. V, and Corr. II, letters 236 to 239. 14 See Herivel ibid:311 ("Definition 13"). 15 See Cohen (1970), Westfall (1971):476-81 for a discussion of the problematics of Newton's proof of Principia I Prop. I and Prop II. Compare the solutions in Whiteside's commentary in MWN 6:31-37.

544 NOTES

16 See Westfall (1971):355-368; Ellis (1962), (1965); Hankins (1967) and (1970):ch. 8; Cohen (1970) and Whiteside's solution in Whiteside (1966a). 17 See the letters in Cohen ed:(1958):279-312. These words occur on p. 298 and 302, and see the accepted interpretation put on them, Koyre (1965):149-169. 18 On the voluntaristic theology of the Boyle Lectures and the link between Newtonianism and English protestantism, see the works of J. Jacob (1972), (1977) and M. Jacob (1969), (1971), (1976). 19 Compare McMullin's analysis in his (1978):59ff. Newton never suggested that action at a distance is "unacceptable" to him, but only objected to the notion that dead matter could act thus. My argument shows that dead matter could not act in any way, i.e., not even by contact, which implies that matter is not dead. Nowhere does Newton say or imply that matter as it now exists, is dead. 20 The most important work to date on Newton's conception of essentiality and matter is McGuire's (1967), (1968), (1968a). My view was heavily influenced and determined by McGuire's work. 21 Confusion of universality and essentiality is common among writers, e.g., McMullin says that "gravity does not satisfy Rule IlIon the ground of its being mutable", and that Newton "leaves the reader wondering how to reconcile conflicting claims as to whether gravity is a universal quality" McMullin (1978) :68. 22 See Tamny (1979). 23 It is quite a problem to try and formulate the exact point where an active principle can initiate new motion. If it is at any point in the present career of the universe then it would probably destroy the conservation of momentum and with it the laws of mechanics since conservation of momentum is a consequence of the three laws of motion. Inciden­tally, since momentum is actually not conserved in Newton's universe, according to his argument in Opticks:397-8, which serves as a main reason for introducing the notion of active principles, the validity of the laws of motion becomes thereby actually doubtful. Newton saw, nevertheless, the validity of Law I at least as a necessary condition for the stability of the frame of nature, see his letters to Cotes p. 359 above.

NOTES TO CHAPTER TWELVE

1 See Locke's Essay II, xxxi, 6; III, xi, 23; IV, iii, 25; IV, vi, 11; That Locke's "secondary qualities" are distinct from our sensations and "ideas" and are actually "powers" and capacities in the same body in which the "primary qualities" inhere was first conclusively argued in Jackson's classic (1929) and (1930). See also Yolton (1970):5ff. 2 On Locke's corpuscularism see Anderson (1925), Mandelbaum (1964):160. Mandel­baum's argument is that the atomic theory of nature was essential to Locke's epistemology and ontology. Laudan supported this in his (1967). See Yolton's dispute with both in his (1970):44-75. 3 In Essay II, xxxi, 6, Locke explains that our "ideas" "cannot be supposed to be any representation of" the real essence "at all". However, the ideas, nevertheless "must ... refer" "to such real essences, as to their archetypes". This is entailed by the consideration that were the idea a representation of the real essence itself, all the properties of the

NOTES 545

body would be "deducible from it, and their necessary connexion with it be known", which is not the case. 4 For Locke's theory of reference, see Kretzmann (1968). 5 This agrees with Lovejoy (1936):228, Wiggins (1974):336, Copi (1954):183-185. 6 This may serve as an answer to Uzgalis (1988) who argues against any such distinction within Locke's ontology, and bases his argument on the Essay III, vi, 39, and ibid:5. In these passages Locke argues for the ambiguity of any classification of the real essences themselves into species without any reference to invisibility. This however does not touch my thesis about his platonism, for it is an inner-platonic difficulty, formulable as, say, the problem of classifying Platonic Ideas: Why do the Ideas of Wolf, Fox, and Lion "fall under" the idea of Dog, or in what exactly do the Ideas of Dog and Wolf differ? 7 The crucial influence of the Principia was in Locke's correction of the mechanistic notion in the first edition of the Essay, see his story of this in his "second reply" to Stillingfleet (Locke's Works, IV:467f.), and 12.4 below. 8 Locke usually refers only to the visibility barrier, as in II, xxxi, 6; IV, iii, 25 and 26; IV, vi, 11. 9 In addition to the strong passage I cited from III, xi, 23, see also III, vi, 3, and IV, xvi, 14, where in addition to angels he suggests that the "spirits of just men made perfect" may equally reach "in a future state" such necessary knowledge. 10 Opticks:400. That Locke actually hints here at an idea suggested to him by Newton about the creation of matter and motion becomes plausible on the evidence of his French translator, Pierre Coste in his footnote to Essay, IV, x, 18, see Coste (1700):523 which I quoted above ch. 9.3 p. 262-3. 11 Compare ch. 1.11 above. The importance of the issue of supperaddition and its implications for Locke's whole philosophy was realised only in the last decade, and so Wilson could discover as late as 1979 that Locke's "reservations about the explanatory capacities of Boylean principles are not restricted to the mind-body problem but extend to phenomena that unequivocally fall within the range of physics" (Wilson 1979:148). Since I do not deal with Locke's "reservations" but rather with his philosophy's impli­cations, my conclusions are much more extreme. Shifting the center of importance from the epistemology of empiricism to the ontology of informationism exhibits the great conceptual similarity of Locke and Descartes even though the one is slow and hesitant in accepting the consequences while the other is quick but secretive about them. Ayers' (1981) dispute against Wilson's (1979) is an attempt to return to the old style of Yolton's (1970) view-point. Yolton mentions the Stillingfleet affair about superaddition and gravi­tation in a footnote (p. 24) but fails to make anything of it throughout his work. Woolhouse (1971) never mentions it at all. But Yolton made ample amends in his recent magnificent compilation work (1983) and (1983a). The notion that there ever was or could be an "intelligible universe of pure mechanism" possessing "intrinsic perspicuity" (Ayers 1981:211-2) in the intellectual context of the Judeo-Christian tradition should have died quickly after McGuire's trail blazing series (1966), (1967), (1968), (1968a) (1978) and (1978a). Little remains to be done after these epoch making papers but reorganize our view of the 17th century around a wholly new, ontologically oriented gestalt. Ayers and Wilson, however, as well as the majority of 17th century philosophical scholars, are quite oblivious to McGuire's work, with dire consequences.

546 NOTES

12 Such superaddition does not change the real essence, as Locke argued against Stilling­fleet (Locke's Works, IV:460-1). 13 See Axtell's (1965) and (1965a) for details. 14 It is a mark of the backward state of contemporary historiography of science that the enquiry about the interrelations of Locke's and Newton's theories has not yet surmounted its primitive state. Axtell's discovery in his (1965) remains to this day the only original attack on the problem. Such papers as Rogers (1982), (1978), (1979), take no notice of the Stillingfleet dispute, of the Cudworth connection (Locke's patron, Lady Masham, was his daughter), or of McGuire's discoveries. Thus, e.g., Rogers is unaware of the influence which Newton's refutation of the Cartesian gravitation mechanism in Book II of the Principia had on Locke as a confirmation of his conception of superaddition. 15 The issue of the innateness of some ideas is, therefore, not very important for Locke's empiricism: Had the case been decided by some controlled laboratory experiments that we are born with some such ideas, Locke could have simply extended the doctrine of God's superaddition to these inborn ideas, without any essential changes in the rest of his empiricism. 16 See also Essay II, xi, 13 as well as the draft notes on madness and its relations to memory, imagination, and error in King (1884):333-336. The earlier note dates from 1678, the time he was already at work on the program of Book IV, see Aaron (1955):53, Aaron and Gibb (1936):xxv. See also Locke's Journal note dating November 111677 in ibid:98. The interest in madness and the link he makes between it and prejudice and conditioning may be an outcome of Locke's theological dissidence, a feature he shared with Newton, and see Locke's notes on anti-trinitarism and "defence of non-conformity" in King ibid:342-358. 17 Aaron says that since the association chapter "only appeared in the 4th edition, this in itself suggests that it is not central to Locke's thinking" (Aaron 1955: 141), and that contrary to Hume where association is central, Locke "only uses it to account for aberrations from the normal" (ibid). I agree that the role of association is not manifest in the Essay, and this is because Locke seems to have discovered it only around 1700, after he finally succeeded to resign from his grinding administrative job, on account of his chronic illness (King 1884:246-251). This was late in the day for him, and so instead of re-writing the whole Essay, he simply added the relevant sections (4-18) and let it stay. It was a late discovery, as the April 26 1695 letter to Molyneoux shows (Works, III:554 cited in Nidditch's edition p. xxviii). That it explains much more than rare aberrations is also clear. Firstly, Locke says that (1) these aberrations happen to almost "anyone" (§1) and that even "men of fair minds ... are frequently guilty of it .. .in many cases" (§2), and "there is scarce a man so free from it" who is not at times "fitter for Bedlam than for civil conversation" (§4), and that it may be "a taint which so universally infects mankind" (§4). Secondly, Locke ends by attributing this taint to all intellectual controversies (§18), and some widespread philosophical doctrines as, e.g., materialism (§17) which identifies being with matter in consequence of such an association. 18 See Letter to Molyneux, April 26 1695, Works, III:554, see note 17. 19 See Bechler (1989a):ch. 5. 20 This, however, was how T.H. Green interpreted the issue in his (1874):97. My indebted­ness to Green's penetrating analysis of Locke should, nevertheless, be evident. 21 This interpretation may take care of Woolhouse's suggestion to view Locke as a "rationalist" in accordance with a modified definition of "rationalism" (1971:25). See also Rogers (1979a):23-25.

NOTES 547

22 Such analysis is imputed to Locke by O'Connor (1952):169. 23 See title of II, xiii, 28, where "equally intelligible" was changed in Coste's 1700 French translation into "equally unintelligible", Nidditch:311.

NOTES TO CHAPTER THIRTEEN

1 The puzzle about the tardiness in the rise of the problem of induction is never raised in the literature. The connection of Hume to Newton's science is discussed in Smith (1941):53-79; Stroud (1977):ch. 1; Noxon (1973):ch. 2, 3. 2 On the reasons for Barrow's resignation see Whiteside ed.(1970) MWN III:xiv n.14. Though Barrow's intention was only to epitomize existing knowledge, his presentation was unusual in that he applied the hypothetico-deductive method to optics in the form of deriving it axiomatically from six "primary and fundamental optical hypotheses [or] laws ... confirmed by experiment" (Barrow's Lectiones Opticae 1669:7-19). See, how­ever, Kargon (1965). 3 See Whiteside ed:(1970) MWN III:xix and Brewster (1855) II:92. 4 See Shapiro ed.(1984) 1:50-63. 5 See Shapiro's masterly work on the development of Newton's optical thought in Shapiro (1974), (1975), (1980). The story I tell here has been told in my (1974), and compare also Westfall (1962), (1962a), (1963), (1966). See also Kuhn (1958). 6 Concerning the reviews, see Cohen (1971):145-157 (1980):96-99. Of the four reviews published in 1687-8, only the one in the Journal des Sr;avans, vol. 16 (1688: 237-8) was critical. The others, by Halley, Locke and Mencke (see Cohen 1971:155, n.lO) were either laudatory, or, at most, neutral. 7 On Newton and hypotheses see Cohen (1966), Koyre (1965):ch. II. 8 See Bechler (1974) for this point. The most thorough treatment is Sabra's (1967):ch. X, XI, XII. 9 On Cotes see Gowing (1983). Gowing's view of Cotes is incompatible with mine, ibid:13, 17, 140. 10 But at that age he became also the Bursar of Trinity for the next three years. 11 About the editorship of Cotes see Cohen (1971):216-256, Hall (1974). 12 Corr. V:167, text to note 5, p. 179; text to note 3, p. 183, and finally p. 215. Hall's and Tilling's remarks on this dispute are confused and perplexing: Admitting that "Cotes' objection is not trivial" (ibid:I71) they refer to it later as "irrelevant" (p. 185), blame him as ambiguous when he merely uses Newton's terms ("uniform") (p. 185), call his proposal "invalid" (p. 185) without explaining why, and finally, when it becomes clear that Cotes was right all the time, merely note this "with some surprise" (p. 216). On Newton's rude disregard of Cotes see Cotes' letter to Jones ibid:195 and the answer p. 215. Newton woke up from his lofty "other Business" (after having halted the printing for half a year), as a consequence, I think, of the rise of a new wave of Continental criticism against his theory of gravitation and the start of the calculus dispute with Leibniz: Just two days before he wrote his reply letter to Cotes, Leibniz' letter to Sloane, the secretary of the Royal Society, was read to the Society and was "Delivered to the President to consider of the contents thereof" (ibid:208). 13 Cotes argued that the proportionality of inertia and matter must be added as a separate axiom for it cannot be proved a-posteriori (Corr. V:242) or a-priori (since it is not "impossible that God should give different vires inertiae to" equal volumes filled plen-

548 NOTES

ically with matter, and so "I think it cannot be said that they must necessarily have the same or an equal Vis inertiae" (Corr. V:228). Newton's suggested corrections were twice rejected by Cotes, and only Newton's third rewriting of the argument one month later was finally acceptable to Cotes. 14 On the calculus dispute see Hall (1980). The same background is also covered in Shapin (1981). 15 See Koyre (1965):ch. VII. 16 See Mouy (1934):256 who suggests it was Pierre Sylvain Regis. The review was published in the August 1688 issue of the Journal des S<;avans, 16:237-8. It is reviewed in Cohen (1971):156-7. 17 Cohen interprets the reviewer's accusation of "arbitrary hypotheses" as referring to the "Hypotheses" which open Book III in the first edition, but this is not plausible since these could not possibly be regarded as arbitrary (see Cohen 1980:97-9). 18 Thus were created two traditions of deriving the universality of gravitation. See Whewell's Treatise on Dynamics in which ch. VI (newly added in the 3rd edition, 1836) neglects all mention of Law III in its derivation, even in the case of touch action. In fact Whewell argued that gravitation was action at a distance, ibid:21O. 19 The invalidity of Cor. 3 is generally overlooked, e.g., Cohen states that from the proof that a force acts in each of the planetary subsystems "it would logically follow that the planets must also attract one another" and "That is, there is a logical step from an interactive two-body system to an interactive many-body system" (1982:43, 44) and he repeats Newton's mistake on other occasions (ibid:89 n.11, 1980:89, and 270 where he writes: "it follows at once that if planets are centers of attraction, as well as subjects of attraction, they should attract one another"). 20 See Laudan (1966). 21 There exists a draft variant of the preface which seems to have been written much earlier than March 1713, which has this as its last sentence:

In publishing all this the very learned Mr. Roger Cotes, Professor of Astronomy at Cambridge, has been my collaborator: he corrected the errors in the former edition and advised me to reconsider many points. Whence it has come about that this edition is more correct that the former one. (Corr. V:114)

This was written probably around the same time as the Commercium Epistolicum committee review was drafted, hence around the time the protest letter to the Memoirs editor was written. The identical date of Newton's published preface and his second answer letter to Cotes has escaped the notice of the Correspondence editors (see pp. xxxvi-xxxvii) . 22 Care should be exercised in reading the set of Corollaries III to VI appended to the "Laws of Motion". These argue in sum that mass clusters behave as one single mass which obeys Law I. Thus, if all forces are internal, the cluster will move inertially as if all its mass is concentrated at its center of mass. These Corollaries are proved, however, only in regard to collision interactions, making the legitimate use of Law III. In this case the cluster obeys Law I since all involved motions are inertial and the inertial motion of the cluster's center of mass is a straightforward formal result of this fact and of the fact that ~miAvi = 0 on collisions. The extension of Law I from mass singletons to clusters, however, cannot be further extended along this route to clusters under non-collision interactions.

NOTES 549

Thus, these corollaries become circular demonstrations if they are to be applied to attracting bodies, since they are based on applying Law III to the cluster's components in the first step of the proof ("For action and its opposite reaction are equal, by Law III, and therefore by Law II they produce in the motions equal changes towards opposite sides", p. 17), thus presupposing Law I to be true of the cluster as a whole. If Newton used these corollaries also in his Book III propositions, then you have another circle on your hand. 23 The last sentence of the proof of Law III was added in the Cotes edition, promising a separate proof for the case of attracting bodies in the Scholium, which appears in Principia:25, with the example of the earth (p. 26) also added in the Cotes edition. For a recent presentation of the role of Law III in Newton's structure see Cohen (1987). 24 That the application of Law III depends on the nature of the entities on which the forces involved act is exemplified by Lorentz's 1895 theory of electrons, in which the ponderomotive force of the ether acts on "electrons" but they do not act on the ether in return. Lorenz remarked on Law III: "As far as I see, nothing compels us to elevate that proposition to a fundamental law of unlimited validity" (Quoted in Silberstein 1914:45 and see summary ibid:50). Poincare tried in 1900 to attack Lorenz for this reason but gave up soon afterwards. See his comments in Poincare (1905):175-7 (1908):222-5. See also Agassi (1971):48-50 on the same question in field theories. 25 Newton's diffidence in introducing Law III extends up to the time of his composition of the various tracts De Motu, one of which (probably the first, composed in 1684) does not even list it among its premises (Herivel:257-8). Law III was known and used by Newton for more than ten years prior to 1684, but only for contact action. 26 The last known return to vortical mechanism in astronomical theory occurs in Newton as late as 1682, see Whiteside (1970):14. 27 Compare Cohen's dating of Newton's discovery of the universality of gravitation by his admission of the mere approximate truth of Kepler's laws, Cohen (1980):269-270; (1982):42-5. 28 The attitude of modern historians towards the relevant conceptual problematics, as distinct from socio-psychological ones, is best exemplified in Westfall's magnificent biogra­phy of Newton. Westfall ignores the whole Cotes affair even though he reports on Cotes' editorship in great detail (1980):698-712, 729-751. 29 But the tradition of deriding Cotes for his cheek in daring criticise Newton goes back to Edleston, see his note on the occasional feeble mindedness of great minds (1850):152n. 30 Two examples will suffice. Cotes' mathematical ability is graded by the editors as "brilliant" when explaining his being the editor chosen by such dignitaries as Bentley and Newton, but he becomes "no more than a superb second class mathematician" when Newton's degrading conduct is defended by them (Corr. V:xxxvii). A similar treatment is meted out to him in the affair of the half year delay, where the editors decide Cotes was in error (though they admit they don't understand him!) and as a result blame him for the delay. See note 12 above. 31 On the dispute see Priestley (1970), and a brilliant analysis of Newton's role in it in Koyre and Cohen (1962). Social circumstances are the focus of litis (1973), Hall (1980) and Shapin (1981). 32 Leibniz' letter was published in Memoirs of Literature 1712, II no.18 (May 5 1712) pp. 137-43. It was written around 10 February 1711 and published first in Memoires pour I'Histoire des Sciences et des Beaux Arts, March 1712 (also known as Memoires de Trevoux ) and later reprinted in the Journal des Sfavans December, 1712. The Leibniz-

550 NOTES

Hartsoeker correspondence is included in the Gerhardt edition of Leibniz' Philosophische Schriften vol. III. Newton drafted a response but never sent it (Corr. V:298-300) to the Journal. 33 Concerning these rules see McGuire (1970), Koyre (1965):ch. VI, Butts (1970) and Mandelbaum (1964):ch. 2. 34 See Mandelbaum (1964):ch. 2, who introduced the term "transdiction" ibid:61 (bor­rowing it from D. Williams) as "vertical" inference. 35 See Newton's explicit assertions about the contingency of the physical world p. 362 aboye, or in Opticks:404. The impact of this view on Newton's concept of essentiality (p. 369 above) should be contrasted with Leibniz' concept.

NOTES TO CHAPTER FOURTEEN

1 See Duhem (1906):ch. 6.4, pp. 190-195. 2 See his critique of Bacon's induction (1906):188-190 where he outlines his refutation of crucial experiments. 3 On the method of analysis and synthesis in classical physics see Hintikka and Remes (1974) (especially ch. 9:105-117) (1976), Lakatos (1978a). 4 Newton, approving Cotes' suggestion, regarded the structure as follows: By Prop. 2 and 3, centripetal force is derived, and by Prop. 4, Cor. 6 or by Prop. 45 Cor. 1, the inverse square function is derived. Cotes suggests, and Newton approves these two alternatives (see Edleston 1850:152, Corr. V:398) for the first depends on KIll, whereas the second depends on the stationary apse-line. For some reason the editors of Corr. v, A.R. Hall and L. Tilling, replaced in Cotes' letter Prop. 45 Cor. 1 by Prop. 4 Cor. 1. I have not checked the original draft, but this seems an error both from Newton's approval (ibid.) and from the fact that Cotes regarded these as alternatives (see his following sentence: "But tis agreed on by Astronomers, that etc., or etc. Therefore [ ... j" ibid). Prop. 4 Cor. 1 is no alternative to Prop. 4. Cor. 6. The editors do not comment on this difference between their version and Edleston's and Newton's. 5 "Apply" in this sense is used by Newton in his description of this structure, see his paraphrase of Cotes' summary in his draft letter (Corr. V:398). 6 Strictly formally, Stage (3) is free of any assumed Kepler's laws. It assumes only what Stage (2) supplies to it, i.e., the plurality of planetary restricted gravitation laws. 7 Strictly formally, again, there is no contradiction between the law of universal gravitation and the set of laws of restricted gravitation, as the fact that the former entails the latter proves. If Duhem meant that they contradict because they entail respectively two mutually contradicting consequences (i.e., N.St.K and St.K. motions), then he was wrong again since restricted gravitation entails N.St.K. motions as well. 8 This is proved already in Newton's elementary perturbation theory in Principia I Prop. 57-68. 9 This point will be developed fully in 14.1.3 below. 10 Popper's revival of Duhem's argument, as reproduced in his (1972):358 and 201-2, and in his (1962):62, was taken up by Agassi (1963):113, Lakatos (1968):320, Feyerabend (1965):168. Feyerabend is the only one who seems to me to be in doubt about this, since he never mentions the issue in either of his (1963), (1970), (1970a) which are the main loci of his attack on classical empiricism.

NOTES 551

11 Popper's argument is that whereas KIll says that a3/T2 = constant for planetary motion, from the restricted gravitation law it follows that a3/T2 = K(M + m) (where M and m are the sun's and the planets' masses respectively) which contradicts KIll. The factor M + m expresses the fact that both sun and planet are in fact accelerated in consequence of LIII. Hence it follows that taking M as the origin of reference will eliminate m from the equation, as KIll demands. Such a reference may be justified by assuming M to be in absolute rest. This at once refutes Popper's formal argument, for we see that the assumed and derived Kepler laws (i.e., before universal gravitation is induced, as Popper's argument demands) are not necessarily inconsistent. They may (and most probably actually are) inconsistent since the sun may and most probably does accelerate absolutely, but this is beside the point. Thus, for example, Newton posited as Hypothesis 1 in Book III the absolute rest of the sun, and kept coming back to it in Prop. 11, and Prop. 12, for there is no a-priori reason against this. Popper's is a formal argument, and strictly formally, therefore, it is both unsound and invalid (compare, however, Cohen 1980:223-4). A more exact proof may now be added, for it is quite elementary:

Limiting the argument to one dimension, take the x axis of an absolute reference system to pass through the two masses ml and m2, and let their coordinates be Xl and X2, respectively.

Case 1: Assuming both ml and m2 to be accelerated in relation to the absolute reference­frame X, their equations of motions, in accordance with Newton's law of gravitation, will be:

(1) mld2x/dt2 = Kmlm2(xl-x2)/r.3

(2) m2d2x/dt2 = Kmlm2(x2-xl)/r.3

These express the absolute forces and accelerations of ml and m2, and both are different from zero. The relative acceleration of m2 with respect to ml is obtained by substracting (1) from (2):

(3) d2(xz-xl)/de = K(ml + m2)(xZ-xl)/r.3

or, transforming to the origin of ml so that Xl = 0 and X2 = x we get

which describes the acceleration of m2 relatively to ml, the latter taken as the origin, and on the assumption that this origin is in absolute acceleration. On this assumption, d2x/dt2 is merely the relative acceleration of m2, relative to ml as though it were fixed but taking into account that actually it is not fixed. What will (4) look like when ml is assumed truly fixed in absolute space? Case 2: Assuming ml to be absolutely fixed, the equations of motion now will be :

(1') mld2xl/dt2 = o.

(2') m2d2x2/dt2 = Kmlm2(x2-xl)/r.3

The relative motion of m2 in relation to mb obtained by substraction, is now:

552 NOTES

and transforming the origin to ml as before

which shows that the relative acceleration d2x/dt2 of m2 with respect to ml is equal to its absolute acceleration on the assumption that ml is absolutely at rest.

This simple demonstration shows that in Newton's conceptual framework, observations from the earth, which is assumed to be absolutely accelerated, should show that the accelerations of bodies moving under the earth's force of gravitation, are not constant but depend on the masses of those bodies. On the other hand, planetary motions related to the sun, on the assumption that the sun is fixed in absolute space, will be independent of the masses of these planets. Obviously, KIll as derived under the assumptions of case 1, will depend of the planet's mass as well as the sun's mass, while if derived under the assumptions of case 2 will depend on the sun's mass only. 12 On Duhem's general philosophy and full bibliography see Jaki (1984) ch. 9:319-375. Typically the Duhem-Popper argument is mentioned only in n.199 on p. 369. 13 Duhem's instrumentalism legitimises self contradiction since it rejects the status of proposition to the sentences of a theory, denying them any truth value:

[W]e can see the same physical law simultaneously adopted and rejected by the same physicist in the course of the same work. If a law of physics could be said to be true or false, that would be a strange paradox; the same proposition would be affirmed and denied at the same time, and this would constitute a formal contradiction. (Duhem 1906:173)

See also Duhem's view of science as "symbolic", ibid: 168, which grounds his denial of any truth value to theories. 14 Hence, Cohen's concept of the "Newtonian Style" could serve as a basis for a very different solution. 15 On Hooke's influence on Newton, which I take to be crucial and incontestable, see Patterson (1949), Westfall (1967), Whiteside (1964a) and (1970):vol. 6:9-16, Cohen (1980):241-258, Koyre (1965):ch. V, Herivel (1965):ch. 3, Lohne (1960). 16 Principia I, Prop. 73. 17 See 14.1.2 above, and Principia I, Prop. 74-78. 18 Concerning the status of Kepler's laws in Newton's time see Whiteside (1964a), Russell (1964), Wilson (1968), (1970), Brackenbridge (1982). 19 This may be taken as the best refutation of Cartwright's aristotelian thesis against the reality of components (see her 1983:ch. 3). For in Newton's physics there is no doubt that there fully exist the micro-gravitational forces between each pair of atomic particles, and also it is an easily proven theorem that no resultant gravitation force acting on any such particle is ever conformable to the law of gravitation. See also Hooker (1974) and (1974a). 20 Compare, however, Wilson (1970):235 on the power of Prop. 1.2. Wilson's unawareness is endemic. 21 See Lohne (1968), (1961), Shapiro (1975), Westfall (1962a), Sabra (1967):231-250. 22 On the close link between the theory of forces assumed in the Opticks proof and Newton's dynamics in the Principia, see Bechler (1973).

NOTES 553

23 Compare this structure with Mertz's (1982) proposal (discussed above ch. 6.16) which attempts to recover linearity in Galileo.

NOTES TO CHAPTER FIFTEEN

1 On Leibniz' Aristotelian genealogy, see his own early account in Loemker:94-103. He never changed his warm allegiance to Aristotle, as his lifelong defence of his entelechy and substantial form testify, e.g., the 1695 Specimen Dynamicum, Loemker:436-7. 2 Leibniz read Newton's Principia during his stay in Italy (starting in 1690) and before his 1692 letters to Huygens (Loemker:413ff.). His earlier critique of Descartes' laws of motion was published in 1686 in the "Brief Demonstration" paper (Loemker:296). He summarised it in the Discourse on Metaphysics:§17. 3 For general analysis of Leibniz' principle of the identity of indiscernibles see Russell (1900):ch. V, Rescher (1967):ch. II, Broad (1975):39-42. 4 See also Leibniz' simplicity criterion of truth in the same letter to Huygens, p. 471 above. 5 Leibniz used to distinguish between two sorts of forces - the primitive and the derived, and he needed this in order to distinguish between the inner force which is unobservable but constant and the observable manifestation (or "limitation") of it. The second he identified with the vis viva which is not constant for one subject but only for the whole universe. (G.M. VI:236). 6 See the influence of Hobbes on Leibniz through his view of force and conatus in Bernstein (1980). The link with aristotelian ontology is clear also via the tight relation the concept of conatus has with the nature of infinity (ibid:26-7, and see reference to Westfall's interpretation p. 31). On Leibniz' alleged relation to Plato's ontology see Bregman (1984) and Castaneda (1982). 7 On the connection, or rather lack of it, between Leibniz' philosophy of nature and his physics, see L.J.Russell (1976). 8 On the reality of Leibniz' derivative and primitive forces see Gueroult (1967):ch. VII. 9 See the text quoted on p. 453 above. 10 See, however, Russell's argument to the effect that Leibniz laboured under an unsoluble confusion stemming from his adherence to absolute motion but denial of absolute space (Russell 1900:84-9). Russell's argument labours under his assumption that Leibniz' force is a separate entity. See also Broad (1975):54-66,102-107, Rescher (1967):88-104. 11 See Bechler (1989a):ch. 1.10. 12 Hence, every kind of motion must be a real change in the substance's predicates since all space and time predicates are relational and so their changes are real changes in the predicate sequence P. 13 See a good detailed interpretation of Leibniz' theory of relations as monadic attributes and its consequences for his theory of definition and essence in Cox (1975) which ben­efitted me a lot. 14 See the analysis of the relations between Aristotle's logic and his ontology in my (1989a):ch. 4. 15 Other important aspects of this conceptual holism in Leibniz play essential roles in his theory of apology, see ch. 15.7 below and in particular the passage quoted on p. 458.

554 NOTES

16 Compare, however, Arnauld's dispute with Malebranche over the separate existence of concepts, ch. 7.8 above. 17 This interpretation is in conflict with the standard reading of Leibniz. See, for example, Leyden who holds that the subject-predicate doctrine is equivalent to holding that the subject is separate from its predicates (Leyden 1986: 177) and builds upon it the thesis that Leibniz' principle of identity is simply empirical. 18 Notice the parallel difficulty which hit Descartes in the course of his defence of the difference between distinctness and clarity or completeness and adequacy, ch. 7.4 above. 19 Hintikka (1981) has argued consistently enough for applying the plenitude consequence which he had argued for Aristotle, also for Leibniz. This is now obviously true, but only because of Leibniz' aristotelian ontology, which Hintikka ignores. 20 Hence Russell's major thesis, i.e., that the whole basis of Leibniz' system is the doctrine of the subject-predicate structure of all non-existential propositions, is too limited and, in a sense, false: If it implies the separate existence of the subject, then it is false, and if it does not imply it, then the basic doctrine is a different one, i.e., the ontological identity of the subject and its predicates. It is false on the first option because on such ontology the doctrine cannot entail pre-established harmony and non-dynamic necessity. 21 This at once prohibits the existence of non-inertial motions in Leibniz' ontology, a consequence which is equally applicable to all truly relativistic ontologies. The notion was realised in physical theory only by Einstein's general theory of relativity. See an expanded argument in ch. 15.9 below. 22 Compare the opposite interpretation which takes Leibniz as a platonic philosopher, such as Gabbey (1980):233, Gale (1974):32-3, who also argues that derivative forces must be "reduced" to primitive forces as their efficient causes. Gale can do this only by "distinguishing properly between Leibniz' physics and his metaphysics" (1970):123-4, which is to me meaningless. Similarly, see attempts to ground Leibniz' attack against Descartes' laws of motion on his view of force as "an absolute" in Gale (1973) and also Spector (1975). Nowhere is there an explanation why mv as a vector quantity is inferior to mv2 , or how can it be that v2 is absolute if v is not, but see Gueroult (1967):ch. V. 23 Here might be one important systematic reason for Leibniz' critique of Descartes' theory of extension as the essence of matter, i.e., Leibniz' nominalism dictating that there is no essence at all. See, however, Nason (1946). 24 There is no doubt that Leibniz held all true non-existential propositions to be analyti­cally true, see Russell (1900):ch. II. I find it unconvincing to argue, as Hacking (1974) argues, that such propositions are taken to be analytic only in the infinite limit. See also an attack on the Couturat-Russell interpretation in Ishiguru (1972):ch. 7. I failed to see its merit and suspect it to be based on a confusion between "analytic" and "necessary", e.g., ibid:120 bottom lines. 25 Hence the strictly metaphorical sense of Leibniz' description of possible worlds, striving to be selected by God for actualisation, see Blumenfeld (1973). 26 The detailed argument is in Bechler (1989):ch. 1.2.7 (1989a):ch. 2.12. 27 The soul acts as a motiveless entity, for "properly speaking, motives do not act upon the mind as weights do upon a balance" (5th letter to Clarke, in Alexander:59). 28 See however, a widely accepted counterargument by Ishiguru who admits that "strictly speaking, it is not the case that "Caesar did not cross the Rubicon" could be true" (Ishiguru 1972: 123), and that the counterpart possible world "does not contain Julius Caesar himself" (ibid:124). But if this is true "strictly speaking" then this is true period, and counteractual Caesar is, in Leibniz' ontology, a contradictory entity.

NOTES 555

29 Nor was Leibniz loath to acknowledge and fully adopt these conventionalistic conse­quences of his aristotelian principle of the primacy of the actual, see ch. 15.11 below. 30 L.J.Russell pointed out the closeness of Leibniz' view of causality with Hume's and suggested an instrumentalist way out for Leibniz as a solution of the contradiction between his physics and his ontology, see Russell (1977). 31 Proper names are, therefore, truly rigid designators in Leibniz' ontology even though they are definitely non-Kripkean. For since substance has no essence separate from its potential predicate-sequence in Leibniz but not in Kripke, it is meaningless for Leibniz to insist that the substance would remain essentially identical even if some of its predicates change. The confusion in Locke's theory of nominal essence gets a reaction in Leibniz' commentary, but the confusion sticks to him. See Jolley (1982) where the Kripke connec­tion is made, also Wren (1972). 32 This option was pointed out by Mach and then executed by Einstein for the case of gravitational forces in his general theory of relativity. I do not know what Leibniz' own choice was, or whether he was at all aware of the dilemma. See my analysis of Mach's and Einstein's theories as modem aristotelian conceptions in Bechler (1989):ch. 4.1, 4.2. 33 Thus, Leibniz' identity of indiscernibles is closely related to his concept of God and to his denial of the possibility of an absolutely willful divine action, i.e., an action which is not priorily justified by some sufficient reasor. The platonist God of Newton is above such limitations. See a good analysis in Wilson (1973). 34 The whole of Leibniz' critique of Newton's physics is contained in this well-known argument, detailed in Leibniz' 5th letter to Clarke (Alexander: 90-95). The rest of the correspondence is a mere introductory skirmish and illustrative commentary on this all­inclusive argument. I am not aware that the dispute was ever analysed satisfactorily, as a serious intellectual issue springing o.ut of two contradicting ontologies of the entity called law of nature. 35 Russell argued that there was no logical ground for this attack on the force of gravitation, and that it was nothing more than a "vulgar prejudice" (Russell 1900:93) concerning the necessity of action-by-contact. 36 Failure to perceive Leibniz' aristotelianism results in obvious distortions mainly about the concept of force. Thus, Gale is misled by this failure to accept Boscovich's misconcep­tion of the illusory affinity between Newton's gravitation theory and Leibniz' harmony. Classifying Boscovich as a Leibnizian who accepted action at a distance (Gale 1974:46) implies that Boscovich was a self contradictory thinker. Compare note 35. 37 See Alexander:92-3. 38 On Leibniz' concept of infinity see the brilliant paper of Bernstein (1977). 39 Leibniz published this half-page Memoir in the Journal de Trevoux of 1701 in response to a previously published paper in the Journal, which argued that the method of the infinitesimal calculus was "too far from the method of the Ancients", using as it does "infinity and infinity of infinity". Leibniz answered that, as I'Hospital already made clear, "one need not take the infinite here rigorously, but only as one says in optics that the rays from the sun come from a point infinitely far, and so are estimated parallel". One needs only compare this to Newton's piece on parallels which actually cut at infinity to see the huge difference. 40 See Bos (1974) for a somewhat different view. 41 See the three senses of identity and the two kinds of infinitesimals which Earman suggests for interpreting Leibniz in Earman (1975). This leads to consequences at variance with mine.

556 NOTES

42 See Bregman (1984). 43 See McGuire's brilliant (1976). 44 Russell, who argued that Leibniz rejected the actual infinity, ignores this enormous difficulty about Leibniz' concept of matter (1900):ch. 7. See also Gueroult (1946). 45 The exact potentiality status of the complete concept is tightly connected with the ontology of time and "the puzzle of the present" which Leibniz left dangling. See Rescher (1968). My guess would be that the whole predicate-sequence is simultaneously actual since time is merely phenomenal, and there is no real ontic difference between past, present and future that could be well grounded on the reality of monads. That is why Leibniz can say that not only matter and extension but also motion is "mere phenomenon like the rainbow and parhelia", See Bernstein (1977):175. The predicate-sequence exists as one whole and is the "potential as such". 46 See Blumenfeld (1982) for the notion of Leibniz' superessentialism.

NOTES TO CHAPTER SIXTEEN

1 See Brook (1973):174. But Brook has trouble with really perceiving the nature of Newton's contradiction, see ibid:185. See my analysis of Newton's infinitesimals ch. 8.3 above. 2 A public, if only implicit, validation of Berkeley's analysis of the logical situation, came only in 1784 when Lagrange initiated the prize subject of the Berlin Academy as the problem of the foundations of the calculus. However, Berkeley's critique became the manifest moving force behind the aristotelian program in the foundations of analysis which started with Robins' retort in 1736 (Cajori, 1919:100, 114) went through the attempts of Maclaurin, Lagrange and L. Carnot, and fruited in Bolzano's and Cauchy's sophisticated formulation (Grabiner, 1981:ch. 2). The main aim of the program was the finitisation of the derivative concept, either by developing Berkeley's thesis of compensat­ing errors (Lagrange and Carnot) or by redefining or creating a new limit concept that is independent of the actual infinite division of the continuum (Robins, Mclaurin), which eventually won the day in Cauchy's aristotelian theory. The only attempt to boldly reinstate Newton's platonic ontology of the infinitesimal was Jurin's 1735 retort to Berke­ley (Cajori, 1919:101-106). 3 Hence a need for an external explanation of Berkeley's critique, see Cantor (1984). 4 See, for example, Brook's assertion that "from the modern point of view, there is no necessary relation between an actually infinite number of divisions of a finite segment and the existence of infinitesimals" (1973):172, and his ensuing confusion about the logical status of the modern (Cauchy's) concept of the "sum" of an infinite series. The fact that the essence of Cauchy's solution is the definition and thereby the introduction of a new concept of "sum" and "limit" which is only homonymously similar to the old, platonic concepts, is not appreciated by most commentators on Berkeley, e.g., Wisdom (1941):81, which he will contradict in his (1942):41. 5 An analysis of Berkeley's critique from a so called methodological angle is given by Baum (1972) and Sherry (1987). 6 See the critical account of Gratan-Guiness (1970) as well as Wisdom's (1941). 7 But see also Wisdom's (1941) where the proof is developed explicitly. 8 The exact structure of Berkeley's thesis of compensation, i.e., where and how exactly

NOTES 557

does compensation occur, is a moot point in modem commentaries on Berkeley, including the otherwise masterly Wisdom (1941), (1942), (1953). Brook (1973):180 raises this question. 9 On this issue see Wisdom's (1953) which I follow here. I add to his interpretation merely this conclusion, i.e., that the calculus expressions for the time derivatives of a variable give only the mean and not the instantaneous value. 10 He was right, of course, and hence an answer to Hutchison's (1982). 11 See Agassi's review of Brook in Agassi (1975). 12 To judge by Leibniz' dynamic jargon, Berkeley was right in his diagnosis. Leibniz' jargon still misleads commentators on the vis viva controversy, e.g., Papineau (1977):150-1, Gueroult (1967):ch. II. 13 See ch. 2.8, 2.10 above and Bechler (1989a):ch. 1.10. 14 Berkeley, appropriately enough, rejected also the concept of component force, as one of the "strange paradoxes" associated with "force":

for instance, that contrary forces may at once subsist in the same quiescent body. (Alciphron in his Works VII:6).

15 See Aristotle's Phys. 215a20. This is to become the germ of d'Aiembert's proof of Law I (see Hankins 1970:ch. 8) which in 1743 signalled the beginning of the aristotelian reinterpretation of Newton's physics through the denial of all forces. 16 Much more lenient interpretations may be found in Brook (1973):125-145, Mirarchi (1977), Winkler (1986), Sklar (1974):193, Suchting (1967). 17 See, as a most typical representative, Popper's (1953). Others are Whitrow (1953) and (1953a). Suchting's (1967) was the first to challenge the validity of Berkeley's critique (p. 191) as well as the alleged relation to Mach (p. 193ff.). 18 See, for a nice try, Mirarchi (1977):711. 19 Berkeley refers to "true rest" in De Motu §64, but the context is not clear. 20 This agrees with Silver's (1973). I do not find Mirarchi's (1977) at all convincing. 21 Winkler suggested, following Mirarchi (1977), to understand the applied force as a momentary impressed force, the observable involved as collision, and the "denomination" of motion as conditioned by the history of the bodies P and Q (Winkler 1986). The main trouble with this suggestion is that it will tum all bodies into truly moving, for even if a given body has never collided with any other body, it must have been given some push by God Himself at the moment of creation, even if this caused it to "stay at rest". 22 That he actually ended up in such a contradiction was argued by Silver (1973). If my interpretation of Newton's inertial force (ch. 11 above) is true, then Silver'S argument may be avoided. Berkeley himself seems, however, to hold Silver's view of inertia. See also Silver's defence against Mirarchi (1977) in Silver (1977). Mirarchi's defence of Berkeley against Silver depends on fine distinctions of Berkeley's innocent texts. 23 See Berkeley's references to Leibniz in De Motu §11 and Winkler's references in his (1986):27-30. Berkeley declared that this was indeed his aim, Principles §114, where he says that all the "properties, causes and effects" of absolute motion (obviously referring to Newton's words in the Scholium on absolute motion) belong also to the newly defined "relative motion". 24 Suppose a two-masses universe with ml "" m2 and two applied forces FI and F2. Then

558 NOTES

if r"" const. for the relative distance is at all a necessary condition for true relative motion, then Newton's Law II would be violated if

1. neither mass is in true motion even though forces are applied to both, e.g., starting with r = const, apply forces FI '=(m1/m2)F2. -

2. the true relative motion diminishes though the force increases (e.g., FI = const, F2 increases, r diminishes such that d2r/dt2 diminishes) until the relative motion vanishes (at FI = F2max, r becoming constant if ml = m2 or in general if FI = [ml/m2J F2).

Many more variations can be devised, of course. 25 On Berkeley's semantics of "conceive" see Suchting (1967):198 and Brook (1973):133-5. Even if "conceive" is not in general the same as "imagine" in Berkeley, both agree that it is so here. 26 Winkler lists three possible strategies by which Berkeley could evade my interpretation: (1) deny that shape deformation means force; (2) deny that force means motion; (3) deny that the water is deformed when no rcrference body exists (Winkler 1986:38). His final view is that Berkeley could not take any of these without detriment to the factual content of Newton's physics (ibid:39-41). The fact that Berkeley does not in fact deal with any of these strategies indicates, I think, that the need for them did not even arise. Brook lists three similar strategies open for Berkeley in his troubled De Motu §60 (Brook 1973:140). 27 See attempts to explain it in Suchting (1967):194-5 and Brook (1973):137.

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physics, Isis 56. Wells, N.J. (1982) Descartes' uncreated eternal truths, New Scholas. 56. Westfall, R.S. (1962) Newton and his critics on the nature of color, Arch. Int. Hist. Sci.

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dence, Isis 57. Westfall, R.S. (1966a) The problem of force in Galileo's physics (in Golino, ed:1966). Westfall. R.S. (1967) Hooke and the law of universal gravitation, BfHS 3. Westfall, R.S. (1971) Force in Newton's Physics (London).

BIBLIOGRAPHY

Westfall, R.S. (1973) Newton and the fudge factor, Science 159. Westfall, R.S. (1979) Newtonus Absolutus, BJPS 30. Westfall, R.S. (1980) Never at Rest: A Biography of Isaac Newton (Cambridge). Westfall, R.S. (1987) Newton's scientific personality, JH148.

579

Westman, R.S. (1975) The Melanchton circle, Rheticus, and the Wittenberg interpreta­tion of the Copernican theory, Isis 66.

Westman, R.S. (1980) The astronomer's role in the 16th century: a preliminary study, Hist. Sci. 18.

Whiteside, D.T. (1962) The expanding world of Newtonian research, Hisl. Sci. 1. Whiteside, D.T. (1964) I.Newton: The birth of a mathematician N.R.R.S.L 19. Whiteside, D.T. (1964a) Newton's early thoughts on planetary motion - a fresh look,

BJHS 2. Whiteside, D.T. (1966) Newton's marvellous year: 1666 and all that, N.R.R.S.L. 21. Whiteside, D.T. (1966a) Newtonian dynamics, Hist. Sci. 5. Whiteside, D.T. (1967) Sources and strength of Newton's early mathematical thought,

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INDEX

Actuality priority of, in Aristotle 24-

Analysis and synthesis of the continuum, in Galileo 135 Cotes on 348 method of in Newton 345ff. in Newton's gravitation theory 347 in Newton's optics 345-6

Aristotle all necessary conditions included in

genuine potentiality 18 aristotelian vs. platonic explanation

ch.l aristotelian vs. platonic historiography

xv, 520n.4 attack on Plato 52 can everything in motion be moved

by another? 29-31 circularity, convertibility xvi, 42, 106 consistency potentiality 17, 18 and exhaustive method 240 explaining natural motion 32-6 the first mover theory 37ff. and Galileo's infinity 136, 138ff. and Galileo's informationism 157ff. and Galileo on motion in the void

126ff. and Galileo's natural motion 151 and Galileo's view of mathematics

128 genuine potentiality 18-23, 26-7 and infinity 44 instant actualisation of genuine

potentiality 19-20, 26 and Koyre 143ff. his law of free fall xiv, 1-3 logical determinism 26-7 his logical theory 39ff. and the Megarians 16-7, 22 and mixed deduction 43, 106 and Newton on space 266-7

his philosophy of nature ch.2 and plenitude 20, 25, 27 on potentiality 15-8, 542n.5 potentiality is a non-entity 23-4 priority of actuality 24 and quantum-jumps universe 27, 121-

2 the relation of his philosophy of

nature and his logic 39ff. the sea battle argument 27 the semen argument 21-2 his teleology 22, 31, 524n.5 his theory of motion 28-34 tradition's distortion of his physics 2-

3 what is the cause of natural motion

28, 34, 36, 37 Arnauld, A.

on adequacy 183 dispute with Leibniz 444--9 dispute with Malebtanche 205-8 Lovejoy and Laird on 539n.32

Bacon, F. as an Aristotelian 530n.9, 10 attack on non-informativity 93---6 his concept of law 97, 529n.4 his critique of astronomy 529n.1 and the inductivist tradition 529n.6 his informative program and

induction 98-9 platonic circularity 102-4, 529n.2,

530n.11 his platonic philosophy of Forms 96,

102 prediction as informativity 100--1

Barrow, I. 345, 546n.2 Bayle, P.

581

continuous creation entails identity of essence and existence 455

on God's goodness 456-7

582 INDEX

and priority of the potential 458 on soul and body 459

Bentley, R. and correspondence with Newton

about essentiality of gravitation 311-4

and Cotes 352 Berkeley, G.

and Aristotle 489, 491, 493, 494, 496, 502,557n.15

based on his aristotelism, his critique of Newton's calculus 485-9

contradicts Mach 503, 557n.17 his critique of Newton's Bucket 504-5 his critique of Newton's calculus,

476-85 his critique of Newton's dynamics 489 on explanation 495-6 his fictionalism 494 and force as occult quality 490 force is either motion or nothing 491-

2 on Galilean platonism 491 ineffective, his critique on Newton's

calculus 487 his instrumentalism and

phenomenalism 490, 494-6 and Leibniz 491, 492, 500, 502,

557n.23 neglects Newton's ontology, his

critique of Newton's calculus 478-9, 487

no force in rest or inertial motion 493 as the pioneer of modern renovation

of the calculus 556n.2 his priority of actuality 489 rejected components 557n.14 his "relative motion" 497ff.

Boscovitch, R. and Leibniz 555n.36

Bucket argument 287-95 and circular argumentation 426 either circular or not intended to

prove existence of absolute space 289, 292

and the General Scholium 351 Leibniz and Clarke on 291

Mach's failure in his critique of 289-90

its purpose 290-1 works by relative motions 294

Cartwright, N. 552n.19 Cassirer, E. 537n.51 Circularity

in both aristotelian and platonic science xvi

of the Bucket argument, see Bucket in Descartes 232-7 and deviant logic 434-6 Feyerabend xvi, 520n.3 in Galileo 156-70, 167-71 in Newton 420-36

Clarke, S. and Cotes on essentiality of

gravitation 314, 370 Cohen, LB.

on Cotes 380 on the derivation of universal

gravitation 381, 548n.19 on Newtonian Style 283-6 on Newton's inertia 277-83

Component as actual potentiality 413 and approximation 415, 422-3, 487 and approximation, in Newton 418 and "ideal" 258, 419 and limit 246-8.418-9 and logical circularity 171, 232

420ff. and refutation of Cartwright 552n.19

Componential reality in Descartes 223 of forces 300-1 in Galileo 126-8, 156 in Newton 245. 409ff. in the scientific revolution 413-6

Contingent necessity 6-7 in Descartes 229-30 in Locke 326-8 in Newton 308, 328, 396, 549n.35 and non-Euclidean geometry 183,

200-1 and platonist ontology 397

Copernicus, N. ch.4 claim of certainty 86 his concept of harmony 75, 87-101 and equants 527n.6 informativity and Ptolemy 92 his solution of the equivalence

problem 78 Cotes

analysis of his Preface 366ff. and Clarke on essentiality of

gravitation 314, 370 Cohen on 380 and dispute with Newton 353ff. Edleston on 549n.29 and the essentiality of extentsion 314 and the essentiality of gravitation 314 Hall and Tilling on 381-2, 547n.12,

549n.30 Koyre on 379 his mention in Newton's preface

cancelled 372, 548n.21 metaphor of the clock and Descartes

372, 541n.49 on Newton's method of analysis and

synthesis 348 his version of derivation of

universality of gravitation 367-9 Cusanus 73

Descartes, R. and abstraction 186 against the deductive syllogism 172-6 analysis and paradox 226-9 answer to Gassendi 185, 187, 194-5,

197, 537n.7 Arnauld's non-platonic interpretation

of 205-8 circularity in the Cogito 176ff. circularity and informativity 232-7 conatus and absoluteness of motion

208-10 his concept of conatus as actual

potentiality 208-12 and Copernicus' harmony 230 and essence of the wax 189 and Fermat 235 and identity of the wax 188

INDEX

inertia proved by nature of time 224-6

inertial motion 220ff. on infinity 226-7 informativity 228-37 informativity and causality 229-32 informativity and circularity 232-7 informativity and laws of logic

540n.46 on intuition as the basis of inference

174-6 invisibility and componential reality

220, 222, 223 Malebranche's platonic interpretation

of 200-5 mode as absolute 212-5 and Morrin 232ff. motion as mode 215-6, 540n.38 and nominalism 185-90 paradox, motion as 217,226-7 and Plato's Meno 196 and separate essences 190ff. state, motion is not a 218-9 time and law of inertia 224-6 on vision of ideas 177-80

Drake, S. 161-4, 531n.3, 532n.13, 16, 536n.47, 536n.48, 537n.51

Duhem, P. attack on Newton's induction 398-

405, 542n.3, 550n.l, 2, 7, 552n.12, 13

"Duhem's Thesis" 420, 534n.37 and induction 344, 368-70 and self-contradiction 552n.13

Einstein-Podolsky-Rosen argument 542n.4

Feyerabend, P. xvi, 520n.3, 525n.18, 550n.l0

and circularity in realism 520n.3 his early realism 521n.9 on Mach 521n.8

Forces as causes of absolute motion 305-6 as the causes of all motion in the

scientific revolution 151-2

583

584 INDEX

causing free fall in Galileo 126-7 components and resultants 298ff. composition of 298-300, 306 as the essence of the scientific

revolution 511 Galileo's "what moves moves by

force" 152, 535n.44 "grasping" 357,394 of inactivity and rest 147-9, 276 in informationism 9, 11, 144-7, 151-5 laws of, essential and universal in

Newton 304-5, 314-7 laws of, and contingent necessity 388-

9,396 maintainig, not only initiating, motion

144-7 in matter 313-{j, 543n.19, as separate entities in Newton 425 their separateness entails absolute

space and time 425

Galileo, G. and actual infinity 137 all motion is a process, not a state

153-{j on Aristotle's potentiality 137 and atomism 133 his circular arguments entailed by his

informationism 157-{j1 and circular inertia 145-6 and circular logic 156ff., 167-71 his concept of inertial motion 144-7 on Copernicus 118 and deviant logic (explaining wonder

by miracle) 134-5, 167-71 and difference function 124-6, 127 the difference function and the reality

of components 126 Drake on Galileo as hypothetical

positivist 161-4 essence of free fall 109, 119, 120,

532n.12 and experiment 114-4 and the fallacy of the consequence

105-7 heterogeneity of premises 106

and hypothetical demonstration 107-10

and impetus as permanent 148-51 on infinity 122-{j, 130 and Koyn!'s misconceptions of his

platonism and inertia 141-4 letter to Baliani 110, 119, 121 and mathematical exactness of physics

128-30 Mertz on Galileo and analogy 164-7 and mixed science 115, 167-71 on motion in the void 126-8 and natural motion 151-3 and paradoxes of infinity 130-9 as platonist 127-30 revolt against Aristotle 122, 124, 129 and step function 120 Wallace on his hypothetical

demonstration 110-4 Wisan on the fallacy of the

consequence 114-9 and Zeno's paradoxes 139-41 on zero 122-{j

Gassendi, P. 533n.30, 537n.7 against Descartes 185, 187, 194-5 Descartes on 537n.7 on essences 197-8

Gordon, G. and first critic of circularity in

Newton 431-4 Gravitation

as action at a distance 302

Hall, R.A. on Cotes 549n.30 on Law III 381-4

Hartley, D. 523n21 Herschel, J. 529n.6 Hintikka, J. 523n.2, 524n.4, 10, 17,

537n.4, and informativity 521n.11 and plenitude in Aristotle 523n.2

Historiography Newtonian as aristotelian 269-86 platonic and aristotelian xiii-xv,

520n.4

INDEX 585

Hooke on another kind of knowledge 327 on Bacon's circularism 530n.11 his influence on Newton 552n.15 and Newton's optics 346, 349 Newton's priority claim against

Hooke 405ff. his subtle spirits 536n.46 his theory of curved motion 302

Hume, D. 42, 188, 342, 397, 436

Induction is no difficulty for the platonist 342-5 platonic vs. aristotelian problems of

395-7 principle of induction and the Rules

of Philosophizing 393 problem of, introduced by Newton

355,385,390 Inertial force

cause of deformation 306-7 cause of motion 306-7 as centrifugal force 299, 301-3 distinct from mass 296, 298 distinct from motion 296, 298 as effects of absolute motion 295 and the essence of matter 309-11 as "force of motion" 296 and impetus 295 as inherent in matter 315 and Law III 376 in Law I and Law III 303, 304-5 and modern historiography 269-83 separate, superadded 308 splits on collision, exerted 295 as superadded to matter 317-8 transformed into impressed force 304

Inertial motion as actual potential 414 Informational philosophy

and absolute space and time 13-4 and God 10-1 and the irrationality of explanation 6-

8 the law of inertia in 10 and paradoxical entities 8-10

and the scientific revolution 5-14 and spirits 11-2

Informationist view entails occult causality 9 of explanation as heterogeneous 8-14 as irrational 5-7 place of God in 10-1 place of spirit in 11-2 platonist 8 qualitative definition of 5-6 role of absolute space and time in 13-

4

Kepler, J. on Copernican harmony 528n.13 laws 398ft. his laws relative to geocentric system

427-8 Newton's claim about Kepler's laws

405-6 KoynS, A.

on Copernican equants 527n.7 on the Cotes affair 379 on Galileo's circular inertia 533n.34 on Galileo's impetus theory 533n.32 on Galileo's platonism and inertia

141-4 on Gassendi 533n.30

Kuhn; T. and Copernicus 528n.9

Law III and action at a distance 378 Agassi on 548n.24 a branch of Law I 357, 375 entails mutuality of gravitation 359-60 and inertial forces 377 its logic of application 373-8 Lorentz and Poincare on 548n.24 misconceptions of Hall and Tilling

381-2 in Newton's proof of gravitation 355-

8,378 Laws of motion

and kinds of forces 304-5 Newton's - as informational 425

586 INDEX

Leibniz his absolute motion different from

Newton's 441 accepts absolute motion 438-9 accepts actual infinity 471 against Bayle 456-7 all motion is natural and inertial 452-

4, 456, 459-62, 464 his apologetic and Aristotle's sea

battle 449-50 as an aristotelian 437-75 and Aristotle's soul 451 conventionalism entailed by

equivalence 472-3, 475 counterfactuals are self-contradictory

463 his critique of Newton's gravitation

464-5 his critique of Principia 355, 371 dispute with Arnauld 444-9 dispute with Clarke 384-90 his dispute with Newton entailed by

his non-informationist ontology 465 his divine nominalism 444ff. on equivalent theories 439, 472 essence is predicate sequence 446 hypothetical necessity 450 his identity criterion non-practical

438ff. his infinitesimal calculus mere

instrument 467-9 letter to Hartsoeker 361-2, 549n.32 and modality, priority of actuality

457-9 on necessity in Hobbes and Spinoza

450 necessity vs. certainty 447-9 ontological conventionalist 471ff. and plenitude 451 no prediction by law and initial

conditions 463 primitive force as form 440 rejection of analysis 458 rejects actual infinity 466 rejects the Bucket argument, see

Bucket on space and time 441ff., 468, 470-1

Locke accepts necessity in re 325 apparent nominalist 322 and association of ideas 333, 546n.17 his contingently necessary truths 326-

8 Coste's story 262-3 dispute with Stillingfleet 322ff. and empiricism 319-41, 332 as essentialist 319-23 formulates Hume's problem 324 influence of Newton 262-3, 329 and informativity 331, 332, 339 and innateness 545n.15, 339-40 and madness 332, 546n.16 and mathematical truth 334-8 Ryle on 325 secondary qualities as powers 330-1,

544n.l and superaddition 328, 545n.ll and thinking matter 523n.19

Mach, E. and the Bucket argument 289-90 contradicted by Berkeley 503, 542n.l,

543n.4, 557n.17 and Newtonian historiography 272

Maier, A. 533n.32, 534n.37, 38, 535n.40 Malebranche, N.

his dispute with Arnauld 205-8 on false ideas 540n.34 as a platonist Cartesian 200-5

McGuire, E. 523n.20, 542n.3, 544n.20, 545n.ll

McMullin, E. 544n21, 543n.19 Mill, I.S. 541n.49 Moody, E.A. xiii, 532n.19, 20, 534n.37,

535n.40

Neugebauer, o. on the relative merits of Ptolemaic

and Copernican systems 528n.8 Newton, I.

and absolute space and time 13, 253 and actual infinity 238-9, 251 and Aristotle on space 266-7 and Bentley 311-4

and the Bucket argument 287-94 and the calculus 238-52 and centrifugal forces 298, 300-3 circularity in his physics 420-36 Cohen on "Newtonian Style" 283-{5 Cohen on Newton's inertia 277-83 and Cotes 351-73, 547n.2 distinctness of indiscernibles 253-8,

266 and essentiality 311-4 and exhaustion method 238, 240-2,

250,251 force as essential and universal 314-7 God 11, 265, 371, 395-6 Hall on Law III 381-4 Herivel on Newton's inertia 274-7 on Hooke 406ff. and hypothetical method 284-6 and induction ch.13 inertia 10, 265-8, 269-83, 287-318 the infinitesimal as medial entity 242-

7 influence on Locke 262-3 on Kepler 405ff. his Law III 357,373-8, 548n.22 his laws of motion as laws of forces

304-5 and Leibniz on gravitation 355, 361-2 letter to Haney 405-7 medials as actual potentials 253-6,

258-61, 264 and modern historiography 269-86 non-mechanistic explanations of force

315-7 his optics 346, 430-1 and the Popper-Duhem argument

398-400, 402-5 and proof of universal gravitation

400-2 Rules of Philosophizing 392-5 space and geometrical forms 261-5 his space and Plato's 310 Westfall on Newton's inertia 269-74

Nifo, A. on the regressus 530n2

Philoponus, 1. 532n.19, 21, 535n.43 Plato 45-71

INDEX

inevitability of circularity 70-1 as informationist 56-60 the informativity of Ideas 50-2 the notion of medial entities 65ff. paradox as inherent in science 67-70 his rejection of tautologous

explanation 62, 65 saving the phenomena 68, 77, 527n.l his story of Socrates 45-9 and the syllogism 63 teleology and the Ideas 53-6 the theory of Ideas and the reality of

components 60-5 Popper, K.

attack on Newton's induction 398-400,403-5,420, 550n.1O

on Berkeley 557n.17 Ptolemaic astronomy 77-83

possible refutation of 79, 81, 83 its relative low informativity 82-3

Quine, N.W. 344, 397

Reichenbach, H. 542n.l Ross, D.

on Aristotle's teleology 524n13 Ryle, G. on Locke 325

Sambursky, S. xviii, 520n.2, 532n.2l on Aristotle's law of free fall xiii,

520n.5 Scientific revolution

its essence and the notion of force 5 and informativity 5-7, 9-10, 59-{52,

92-3 wrong traditional view of 3-4

Sextus Empiricus, on the syllogism 537n.2

Socrates 45-9 and informativity 49 Plato's interpretation of 51-6 and teleological explanation 48

Stillingfleet 322, 323

587

588

Wallace, W. 531nA, 7, 8, 11 on Galileo's ex-suppositione 110-4

Westfall, R. on the Cotes affair 549n.28 on Mach 272 on Newton's inertia 269-74, 306

INDEX

Whewell, W. 548n.18 Whiteside, D.T. 541n.8 Wisan, W. 531n.5, 7, 9, 11

on Galileo's fallacia consequentis 114-9