1669 | Universal Arithmetick |
p.407 | 17783 | A number is not a multitude, but a unified ratio between quantities | |
Full Idea: By a Number we understand not so much a Multitude of Unities, as the abstracted Ratio of any Quantity to another Quantity of the same Kind, which we take for unity. | |||
From: Isaac Newton (Universal Arithmetick [1669]), quoted by John Mayberry - What Required for Foundation for Maths? p.407-2 | |||
A reaction: This needs a metaphysics of 'kinds' (since lines can't have ratios with solids). Presumably Newton wants the real numbers to be more basic than the natural numbers. This is the transition from Greek to modern. |
1687 | Principia Mathematica |
p.8 | 22915 | Newton needs intervals of time, to define velocity and acceleration | |
Full Idea: Both Newton's First and Second Laws of motion make implicit reference to equal intervals of time. For a body is moving with constant velocity if it covers the same distance in a series of equal intervals (and similarly with acceleration). | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Robin Le Poidevin - Travels in Four Dimensions 01 'Time' | |||
A reaction: [Le Poidevin spells out the acceleration point] You can see why he needs time to be real, if measured chunks of it figure in his laws. |
p.12 | 6421 | Newton's four fundamentals are: space, time, matter and force | |
Full Idea: Newton works with four fundamental concepts: space, time, matter and force. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Bertrand Russell - My Philosophical Development Ch.2 | |||
A reaction: The ontological challenge is to reduce these in number, presumably. They are, notoriously, defined in terms of one another. |
p.26 | 15866 | Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural | |
Full Idea: Following Kepler, Newton assumed a law of universal gravitation, thus reclassifying free fall as a violent motion and, with his First Law, fixing horizontal motion in the absence of constraints as natural | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Rom Harré - Laws of Nature 1 | |||
A reaction: This is in opposition to the Aristotelian view, where the downward motion of physical objects is their natural motion. |
p.38 | 13470 | Mass is central to matter | |
Full Idea: For Newton, mass is central to matter. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by William D. Hart - The Evolution of Logic 2 | |||
A reaction: On reading this, I realise that this is the concept of matter I have grown up with, one which makes it very hard to grasp what the Greeks were thinking of when they referred to matter [hule]. |
p.53 | 22893 | Newton thought his laws of motion needed absolute time | |
Full Idea: Newton's reason for embracing absolute space, time and motion was that he thought that universal laws of motions were describable only in such terms. Because actual motions are irregular, the time of universal laws of motion cannot depend on them. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Adrian Bardon - Brief History of the Philosophy of Time 3 'Replacing' | |||
A reaction: I'm not sure of the Einsteinian account of the laws of motion. |
p.54 | 22954 | Newtonian mechanics does not distinguish negative from positive values of time | |
Full Idea: In Newton's laws of motion time is squared, so a negative value gives the same result as a positive value, which means Newtonian mechanics cannot distinguish between the two directions of time. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by P Coveney / R Highfield - The Arrow of Time 2 'anatomy' | |||
A reaction: Maybe Newton just forgot to mention that negative values were excluded. (Or was he unaware of the sequence of negative integers?). Too late now - he's done it. |
p.57 | 15958 | Inertia rejects the Aristotelian idea of things having natural states, to which they return | |
Full Idea: Newton's principle of inertia implies a rejection of the Aristotelian idea of natural states to which things naturally return. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Peter Alexander - Ideas, Qualities and Corpuscles 02.3 | |||
A reaction: I think we can safely say that Aristotle was wrong about this. Aristotle made too much (such as the gravity acting on a thing) intrinsic to the bodies, when the whole context must be seen. |
p.82 | 17546 | If you changed one of Newton's concepts you would destroy his whole system | |
Full Idea: The connection between the different concept in [Newton's] system is so close that one could generally not change any one of the concepts without destroying the whole system | |||
From: comment on Isaac Newton (Principia Mathematica [1687]) by Werner Heisenberg - Physics and Philosophy 06 | |||
A reaction: This holistic situation would seem to count against Newton's system, rather than for it. A good system should depend on nature, not on other parts of the system. Compare changing a rule of chess. |
p.83 | 17547 | Newton's idea of force acting over a long distance was very strange | |
Full Idea: Newton introduced a very new and strange hypothesis by assuming a force that acted over a long distance. | |||
From: comment on Isaac Newton (Principia Mathematica [1687]) by Werner Heisenberg - Physics and Philosophy 06 | |||
A reaction: Why would a force that acted over a short distance be any less mysterious? |
p.106 | 17008 | You have discovered that elliptical orbits result just from gravitation and planetary movement | |
Full Idea: You have made the astonishing discovery that Kepler's ellipses result simply from the conception of attraction or gravitation and passage in a planet. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Gottfried Leibniz - Letter to Newton 1693.03.07 | |||
A reaction: I quote this to show that Newton made 'an astonishing discovery' of a connection in nature, and did not merely produce an equation which described a pattern of behaviour. The simple equation is the proof of the connection. |
p.125 | 13593 | Newton showed that falling to earth and orbiting the sun are essentially the same | |
Full Idea: Newton showed that the apparently different kinds of processes of falling towards the earth and orbiting the sun are essentially the same. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Brian Ellis - Scientific Essentialism 3.08 | |||
A reaction: I quote this to illustrate Newton's permanent achievement in science, in the face of a tendency to say that he was 'outmoded' by the advent of General Relativity. Newton wasn't interestingly wrong. He was very very right. |
p.149 | 23012 | Newtonian causation is changes of motion resulting from collisions | |
Full Idea: In the Newtonian mechanistic theory of causation, ….something causes a result when it brings about a change of motion. …Causation is a matter of things bumping into one another. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Baron,S/Miller,K - Intro to the Philosophy of Time 6.2.1 | |||
A reaction: This seems to need impenetrability and elasticity as primitives (which is partly what Leibniz's monads are meant to explain). The authors observe that much causation is the result of existences and qualities, rather than motions. |
p.232 | 18079 | Newton developed a kinematic approach to geometry | |
Full Idea: The reduction of the problems of tangents, normals, curvature, maxima and minima were effected by Newton's kinematic approach to geometry. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.1 | |||
A reaction: This approach apparently contrasts with that of Leibniz. |
p.237 | 20966 | Newton introduced forces other than by contact | |
Full Idea: Newton allowed forces other than impact. All the earlier proponents of 'mechanical philosophy' took it as given that all physical action is by contact. ...He thought of 'impressed force' - disembodied entities acting from outside a body. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by David Papineau - Thinking about Consciousness App 3 | |||
A reaction: This is 'action at a distance', which was as bewildering then as quantum theory is now. Newton had a divinity to impose laws of nature from the outside. In some ways we have moved back to the old view, with the actions of bosons and fields. |
p.238 | 20967 | Newton's laws cover the effects of forces, but not their causes | |
Full Idea: Newton has a general law about the effects of his forces, ...but there is no corresponding general principle about the causes of such forces. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by David Papineau - Thinking about Consciousness App 3 | |||
A reaction: I'm not sure that Einstein gives a cause of gravity either. This seems to be part of the scientific 'instrumentalist' view of nature, which is incredibly useful but very superficial. |
p.239 | 20968 | Newton's Third Law implies the conservation of momentum | |
Full Idea: Newton's Third Law implies the conservation of momentum, because 'action and reaction' are always equal. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by David Papineau - Thinking about Consciousness App 3 | |||
A reaction: That is, the Third Law implies the First Law (which is the Law of Momentum). |
p.239 | 20969 | Early Newtonians could not formulate conservation of energy, having no concept of potential energy | |
Full Idea: A barrier to the formulation of an energy conservation principle by early Newtonians was their lack of a notion of potential energy. | |||
From: report of Isaac Newton (Principia Mathematica [1687]) by David Papineau - Thinking about Consciousness App 3 n5 | |||
A reaction: Interestingly, the notions of potentiality and actuality were central to Aristotle, but Newtonians had just rejected all of that. |
p.426 | 16708 | Newton's forces were accused of being the scholastics' real qualities | |
Full Idea: Newton's reliance on the notion of force was widely criticised as marking in effect a return to real qualities. | |||
From: comment on Isaac Newton (Principia Mathematica [1687]) by Robert Pasnau - Metaphysical Themes 1274-1671 19.7 | |||
A reaction: The objection is to forces that are separate from the bodies they act on. This is one of the reasons why modern metaphysics needs the concept of an intrinsic disposition or power, placing the forces in the stuff. |
Pref | p.41 | 17011 | I suspect that each particle of bodies has attractive or repelling forces |
Full Idea: Many things lead me to a suspicion that all phenomena may depend on certain forces by which the particles of bodies, by causes not yet known, either are impelled toward one another and cohere in regular figures,or are repelled from one another and recede. | |||
From: Isaac Newton (Principia Mathematica [1687], Pref) | |||
A reaction: For Newton, forces are not just abstractions that are convenient for mathematics, but realities which I would say are best described as 'powers'. |
Preface | p.41 | 17010 | We have given up substantial forms, and now aim for mathematical laws |
Full Idea: The moderns - rejecting substantial forms and occult qualities - have undertaken to reduce the phenomena of nature to mathematical laws. | |||
From: Isaac Newton (Principia Mathematica [1687], Preface) | |||
A reaction: This is the simplest statement of the apparent anti-Aristotelian revolution in the seventeenth century. |
1.1.11 Sch | p.86 | 13153 | I am studying the quantities and mathematics of forces, not their species or qualities |
Full Idea: I consider in this treatise not the species of forces and their physical qualities, but their quantities and mathematical proportions. | |||
From: Isaac Newton (Principia Mathematica [1687], 1.1.11 Sch) | |||
A reaction: Note that Newton is not denying that one might contemplate the species and qualities of forces, as I think Leibniz tried to do, thought he didn't cast any detailed light on them. It is the gap between science and metaphysics. |
1.II.Schol | p.86 | 17020 | An attraction of a body is the sum of the forces of their particles |
Full Idea: The attractions of the bodies must be reckoned by assigning proper forces to their individual particles and then taking the sums of those forces. | |||
From: Isaac Newton (Principia Mathematica [1687], 1.II.Schol) | |||
A reaction: This is using the parts of bodies to give fundamental explanations, rather than invoking substantial forms. The parts need not be atoms. |
Axioms | p.70 | 17017 | 1: Bodies rest, or move in straight lines, unless acted on by forces |
Full Idea: Law 1: Every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by forces impressed. | |||
From: Isaac Newton (Principia Mathematica [1687], Axioms) | |||
A reaction: This is the new concept of inertia, which revolutionises the picture. Motion itself, which was a profound puzzle for the Greeks, ceases to be a problem by being axiomatised. It is now acceleration which is the the problem. |
Axioms | p.71 | 17019 | 3: All actions of bodies have an equal and opposite reaction |
Full Idea: Law 3: To any action there is always an opposite and equal reaction; in other words, the action of two bodies upon each other are always equal and always opposite in direction. | |||
From: Isaac Newton (Principia Mathematica [1687], Axioms) | |||
A reaction: Is this still true if one body is dented by the impact and the other one isn't? What counts as a 'body'? |
Axioms | p.71 | 17018 | 2: Change of motion is proportional to the force |
Full Idea: Law 2: A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed. | |||
From: Isaac Newton (Principia Mathematica [1687], Axioms) | |||
A reaction: This gives the equation 'force = mass x acceleration', where the mass is the constant needed for the equation of proportion. Effectively mass is just the value of a proportion. |
Bk 3 Gen Schol | p.90 | 17025 | If a perfect being does not rule the cosmos, it is not God |
Full Idea: A being, however perfect, without dominion is not the Lord God. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) |
Bk 3 Gen Schol | p.90 | 17024 | The elegance of the solar system requires a powerful intellect as designer |
Full Idea: This most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) |
Bk 3 Gen Schol | p.92 | 17027 | Science deduces propositions from phenomena, and generalises them by induction |
Full Idea: In experimental philosophy, propositions are deduced from the phenomena and are made general by induction. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) | |||
A reaction: Sounds easy, but generalising by induction requires all sorts of assumptions about the stability of natural kinds. Since the kinds are only arrived at by induction, it is not easy to give a proper account here. |
Bk 3 Gen Schol | p.92 | 17026 | From the phenomena, I can't deduce the reason for the properties of gravity |
Full Idea: I have not as yet been able to deduce from the phenomena the reason for the properties of gravity. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) | |||
A reaction: I take it that giving the reasons for the properties of gravity would be an essentialist explanation. I am struck by the fact that the recent discovery of the Higgs Boson appears to give us a reason why things have mass (i.e. what causes mass). |
Bk 3 Gen Schol | p.93 | 17028 | Particles mutually attract, and cohere at short distances |
Full Idea: The particles of bodies attract one another at very small distances and cohere when they become contiguous. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) | |||
A reaction: This is the sort of account of unity which has to be given in the corpuscular view of things, once substantial forms are given up. What is missing here is the structure of the thing. A lump of dirt is as unified as a cat in this story. |
Bk 3 Rule 1 | p.87 | 17022 | We should admit only enough causes to explain a phenomenon, and no more |
Full Idea: No more causes of natural things should be admitted than are both true and sufficient to explain the phenomena. …For nature does nothing in vain, …and nature is simple and does not indulge in the luxury of superfluous causes. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Rule 1) | |||
A reaction: This emphasises that Ockham's Razor is a rule for physical explanation, and not just one for abstract theories. This is something like Van Fraassen's 'empirical adequacy'. |
Bk 3 Rule 2 | p.87 | 17021 | Natural effects of the same kind should be assumed to have the same causes |
Full Idea: The causes assigned to natural effects of the same kind must be, so far as possible, the same. For example, the cause of respiration in man and beast. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Rule 2) | |||
A reaction: It is impossible to rule out identical effects from differing causes, but explanation gets much more exciting (because wide-ranging) if Newton's rule is assumed. |
Bk 3 Rule 3 | p.88 | 17023 | I am not saying gravity is essential to bodies |
Full Idea: I am by no means asserting that gravity is essential to bodies. | |||
From: Isaac Newton (Principia Mathematica [1687], Bk 3 Rule 3) | |||
A reaction: Notice that in Idea 17009 he does not rule out gravity being essential to bodies. This is Newton's intellectual modesty (for which he is not famous). |
Def 8 Schol | p.64 | 17013 | Absolute space is independent, homogeneous and immovable |
Full Idea: Absolute space, of its own nature without reference to anything external, always remains homogeneous and immovable. | |||
From: Isaac Newton (Principia Mathematica [1687], Def 8 Schol) | |||
A reaction: This would have to be a stipulation, rather than an assertion of fact, since whether space is 'immovable' is either incoherent or unknowable. |
Def 8 Schol | p.64 | 17012 | Time exists independently, and flows uniformly |
Full Idea: Absolute, true, and mathematical time, in and of itself and of its own nature, without reference to anything external, flows uniformly and by another name is called duration. | |||
From: Isaac Newton (Principia Mathematica [1687], Def 8 Schol) | |||
A reaction: This invites the notorious question of, if time flows uniformly, how fast time flows. Maybe we should bite the bullet and say 'one second per second', or maybe we should say 'this fact is beyond our powers of comprehension'. |
Def 8 Schol | p.65 | 17014 | The place of a thing is the sum of the places of its parts |
Full Idea: The place of a whole is the same as the sum of the places of the parts, and is therefore internal and in the whole body. | |||
From: Isaac Newton (Principia Mathematica [1687], Def 8 Schol) | |||
A reaction: Note that Newton is talking of the sums of places, and deriving them from the parts. This is the mereology of space. |
Def 8 Schol | p.66 | 17015 | If there is no uniform motion, we cannot exactly measure time |
Full Idea: It is possible that there is no uniform motion by which time may have an exact measure. All motions can be accelerated and retarded, but the flow of absolute time cannot be changed. | |||
From: Isaac Newton (Principia Mathematica [1687], Def 8 Schol) |
Def 8 Schol | p.66 | 17016 | Philosophy must abstract from the senses |
Full Idea: In philosophy abstraction from the senses is required. | |||
From: Isaac Newton (Principia Mathematica [1687], Def 8 Schol) | |||
A reaction: He particularly means 'natural philosophy' (i.e. science), but there is no real distinction in Newton's time, and I would say this remark is true of modern philosophy. |
I:Schol after defs | p.145 | 14012 | Absolute time, from its own nature, flows equably, without relation to anything external |
Full Idea: Absolute, true, and mathematical time, of itself, and from its own nature, flows equably, without relation to anything external. | |||
From: Isaac Newton (Principia Mathematica [1687], I:Schol after defs), quoted by Craig Bourne - A Future for Presentism 5.1 | |||
A reaction: I agree totally with this, and I don't care what any modern relativity theorists say. It think Shoemaker's argument gives wonderful support to Newton. |
Lemma 1 | p.238 | 18082 | Quantities and ratios which continually converge will eventually become equal |
Full Idea: Quantities and the ratios of quantities, which in any finite time converge continually to equality, and, before the end of that time approach nearer to one another by any given difference become ultimately equal. | |||
From: Isaac Newton (Principia Mathematica [1687], Lemma 1), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.2 | |||
A reaction: Kitcher observes that, although Newton relies on infinitesimals, this quotation expresses something close to the later idea of a 'limit'. |
Pref 1st ed | p.173 | 12724 | The aim is to discover forces from motions, and use forces to demonstrate other phenomena |
Full Idea: The basic problem of philosophy seems to be to discover the forces of nature from the phenomena of motions and then to demonstrate the other phenomena from these forces. | |||
From: Isaac Newton (Principia Mathematica [1687], Pref 1st ed), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 4 | |||
A reaction: This fits in with the description-of-regularity approach to laws which Newton had acquired from Galileo, rather than the essentialist attitude to forces of Leibniz, though Newton has smatterings of essentialism. |
1692 | Letters to Bentley |
1692.12.10 | p.94 | 15863 | The principles of my treatise are designed to fit with a belief in God |
Full Idea: When I wrote my treatise about our system, I had an eye upon such principles as might work with considering men, for the belief of a deity. | |||
From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |||
A reaction: Harré quotes this, and it shows that the rather passive view of nature Newton developed was to be supplemented by the active power of God. Without God, we need a more active view of nature. |
1692.12.10 | p.95 | 13150 | The motions of the planets could only derive from an intelligent agent |
Full Idea: The motions which the planets now have could not spring from any natural cause alone, but were impressed by an intelligent agent. | |||
From: Isaac Newton (Letters to Bentley [1692], 1692.12.10) | |||
A reaction: He is writing to a cleric, but seems to be quite sincere about this. Elsewhere he just says he doesn't know what causes gravity. |
1693.01.17 | p.99 | 13151 | Not all infinites are equal |
Full Idea: It is an error that all infinites are equal. | |||
From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |||
A reaction: There follows a discussion of the mathematicians' view of infinity. Cantor was not the first to notice that there is more than one sort of of infinity. |
1693.01.17 | p.100 | 8340 | I do not pretend to know the cause of gravity |
Full Idea: You sometimes speak of gravity as essential and inherent in matter. Pray do no ascribe that notion to me; for the cause of gravity is what I do not pretend to know. | |||
From: Isaac Newton (Letters to Bentley [1692], 1693.01.17) | |||
A reaction: I take science to be a two-stage operation - first we discern the regularities, and then we explain them. Evolution was spotted, then explained by Darwin. Cancer from cigarettes was spotted, but hasn't been explained. Regularity is the beginning. |
1693.02.25 | p.102 | 12178 | That gravity should be innate and essential to matter is absurd |
Full Idea: That gravity should be innate, inherent and essential to matter ...is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it. | |||
From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |||
A reaction: He is replying to some sermons, and he pays vague lip service to a possible divine force. Nevertheless, this is thoroughgoing anti-essentialism, and he talks of external 'laws' in the next sentence. Newton still sought the cause of gravity. |
1693.02.25 | p.103 | 13152 | We can talk of 'innumerable number', about the infinite points on a line |
Full Idea: If any man shall take the words number and sum in a larger sense, to understand things which are numberless and sumless (such as the infinite points on a line), I could allow him the contradictious phrase 'innumerable number' without absurdity. | |||
From: Isaac Newton (Letters to Bentley [1692], 1693.02.25) | |||
A reaction: [compressed] I take the key point here to be the phrase of taking number 'in a larger sense'. Like the word 'atom' in physics, the word 'number' retains its traditional reference, but has considerably shifted its scope. Amateurs must live with this. |
1693 | Letters to Leibniz 1 |
1693.10.16 | p.109 | 17009 | I won't object if someone shows that gravity consistently arises from the action of matter |
Full Idea: If someone explains gravity along with all its laws by the action of some subtle matter, and shows that the motion of the planets and comets will not be disturbed by this matter, I shall be far from objecting. | |||
From: Isaac Newton (Letters to Leibniz 1 [1693], 1693.10.16) | |||
A reaction: Important if you think that Newton is the hero of the descriptive regularity theory of laws. Newton probably thought laws came from God, but he wouldn't object to Leibniz's view, that God planted the laws within the matter. |
1721 | Queries to the 'Opticks' |
q 31 | p.544 | 16746 | Principles of things are not hidden features of forms, but the laws by which they were formed |
Full Idea: The (active) principles I consider not as occult qualities, supposed to result from the specific forms of things, but as general laws of nature, by which the things themselves are formed. | |||
From: Isaac Newton (Queries to the 'Opticks' [1721], q 31), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 23.6 | |||
A reaction: This is the external, 'imposed' view of laws (with the matter passive) at its most persuasive. If laws arise out the stuff (as I prefer to think), what principles went into the formulation of the stuff? |