68 ideas
| 17016 | Philosophy must abstract from the senses [Newton] |
| 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. |
| 18079 | Newton developed a kinematic approach to geometry [Newton, by Kitcher] |
| 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. |
| 9912 | There are no such things as numbers [Benacerraf] |
| Full Idea: There are no such things as numbers. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: Mill said precisely the same (Idea 9794). I think I agree. There has been a classic error of reification. An abstract pattern is not an object. If I coin a word for all the three-digit numbers in our system, I haven't created a new 'object'. |
| 9901 | Numbers can't be sets if there is no agreement on which sets they are [Benacerraf] |
| Full Idea: The fact that Zermelo and Von Neumann disagree on which particular sets the numbers are is fatal to the view that each number is some particular set. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: I agree. A brilliantly simple argument. There is the possibility that one of the two accounts is correct (I would vote for Zermelo), but it is not actually possible to prove it. |
| 9151 | Benacerraf says numbers are defined by their natural ordering [Benacerraf, by Fine,K] |
| Full Idea: Benacerraf thinks of numbers as being defined by their natural ordering. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Kit Fine - Cantorian Abstraction: Recon. and Defence §5 | |
| A reaction: My intuition is that cardinality is logically prior to ordinality, since that connects better with the experienced physical world of objects. Just as the fact that people have different heights must precede them being arranged in height order. |
| 13891 | To understand finite cardinals, it is necessary and sufficient to understand progressions [Benacerraf, by Wright,C] |
| Full Idea: Benacerraf claims that the concept of a progression is in some way the fundamental arithmetical notion, essential to understanding the idea of a finite cardinal, with a grasp of progressions sufficing for grasping finite cardinals. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xv | |
| A reaction: He cites Dedekind (and hence the Peano Axioms) as the source of this. The interest is that progression seems to be fundamental to ordianls, but this claims it is also fundamental to cardinals. Note that in the first instance they are finite. |
| 17904 | A set has k members if it one-one corresponds with the numbers less than or equal to k [Benacerraf] |
| Full Idea: Any set has k members if and only if it can be put into one-to-one correspondence with the set of numbers less than or equal to k. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: This is 'Ernie's' view of things in the paper. This defines the finite cardinal numbers in terms of the finite ordinal numbers. He has already said that the set of numbers is well-ordered. |
| 17906 | To explain numbers you must also explain cardinality, the counting of things [Benacerraf] |
| Full Idea: I would disagree with Quine. The explanation of cardinality - i.e. of the use of numbers for 'transitive counting', as I have called it - is part and parcel of the explication of number. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I n2) | |
| A reaction: Quine says numbers are just a progression, with transitive counting as a bonus. Interesting that Benacerraf identifies cardinality with transitive counting. I would have thought it was the possession of numerical quantity, not ascertaining it. |
| 9898 | We can count intransitively (reciting numbers) without understanding transitive counting of items [Benacerraf] |
| Full Idea: Learning number words in the right order is counting 'intransitively'; using them as measures of sets is counting 'transitively'. ..It seems possible for someone to learn the former without learning the latter. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: Scruton's nice question (Idea 3907) is whether you could be said to understand numbers if you could only count intransitively. I would have thought such a state contained no understanding at all of numbers. Benacerraf agrees. |
| 17903 | Someone can recite numbers but not know how to count things; but not vice versa [Benacerraf] |
| Full Idea: It seems that it is possible for someone to learn to count intransitively without learning to count transitively. But not vice versa. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: Benacerraf favours the priority of the ordinals. It is doubtful whether you have grasped cardinality properly if you don't know how to count things. Could I understand 'he has 27 sheep', without understanding the system of natural numbers? |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| Full Idea: The application of a system of numbers is counting and measurement. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], I) | |
| A reaction: A simple point, but it needs spelling out. Counting seems prior, in experience if not in logic. Measuring is a luxury you find you can indulge in (by imagining your quantity) split into parts, once you have mastered counting. |
| 18082 | Quantities and ratios which continually converge will eventually become equal [Newton] |
| 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'. |
| 9900 | For Zermelo 3 belongs to 17, but for Von Neumann it does not [Benacerraf] |
| Full Idea: Ernie's number progression is [φ],[φ,[φ]],[φ,[φ],[φ,[φ,[φ]]],..., whereas Johnny's is [φ],[[φ]],[[[φ]]],... For Ernie 3 belongs to 17, not for Johnny. For Ernie 17 has 17 members; for Johnny it has one. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: Benacerraf's point is that there is no proof-theoretic way to choose between them, though I am willing to offer my intuition that Ernie (Zermelo) gives the right account. Seventeen pebbles 'contains' three pebbles; you must pass 3 to count to 17. |
| 9899 | The successor of x is either x and all its members, or just the unit set of x [Benacerraf] |
| Full Idea: For Ernie, the successor of a number x was the set consisting of x and all the members of x, while for Johnny the successor of x was simply [x], the unit set of x - the set whose only member is x. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: See also Idea 9900. Benacerraf's famous point is that it doesn't seem to make any difference to arithmetic which version of set theory you choose as its basis. I take this to conclusively refute the idea that numbers ARE sets. |
| 8697 | Disputes about mathematical objects seem irrelevant, and mathematicians cannot resolve them [Benacerraf, by Friend] |
| Full Idea: If two children were brought up knowing two different set theories, they could entirely agree on how to do arithmetic, up to the point where they discuss ontology. There is no mathematical way to tell which is the true representation of numbers. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: Benacerraf ends by proposing a structuralist approach. If mathematics is consistent with conflicting set theories, then those theories are not shedding light on mathematics. |
| 8304 | No particular pair of sets can tell us what 'two' is, just by one-to-one correlation [Benacerraf, by Lowe] |
| Full Idea: Hume's Principle can't tell us what a cardinal number is (this is one lesson of Benacerraf's well-known problem). An infinity of pairs of sets could actually be the number two (not just the simplest sets). | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965]) by E.J. Lowe - The Possibility of Metaphysics 10.3 | |
| A reaction: The drift here is for numbers to end up as being basic, axiomatic, indefinable, universal entities. Since I favour patterns as the basis of numbers, I think the basis might be in a pre-verbal experience, which even a bird might have, viewing its eggs. |
| 9906 | If ordinal numbers are 'reducible to' some set-theory, then which is which? [Benacerraf] |
| Full Idea: If a particular set-theory is in a strong sense 'reducible to' the theory of ordinal numbers... then we can still ask, but which is really which? | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIB) | |
| A reaction: A nice question about all reductions. If we reduce mind to brain, does that mean that brain is really just mind. To have a direction (up/down?), reduction must lead to explanation in a single direction only. Do numbers explain sets? |
| 9907 | If any recursive sequence will explain ordinals, then it seems to be the structure which matters [Benacerraf] |
| Full Idea: If any recursive sequence whatever would do to explain ordinal numbers suggests that what is important is not the individuality of each element, but the structure which they jointly exhibit. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This sentence launched the whole modern theory of Structuralism in mathematics. It is hard to see what properties a number-as-object could have which would entail its place in an ordinal sequence. |
| 9908 | The job is done by the whole system of numbers, so numbers are not objects [Benacerraf] |
| Full Idea: 'Objects' do not do the job of numbers singly; the whole system performs the job or nothing does. I therefore argue that numbers could not be objects at all. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This thought is explored by structuralism - though it is a moot point where mere 'nodes' in a system (perhaps filled with old bits of furniture) will do the job either. No one ever explains the 'power' of numbers (felt when you do a sudoku). Causal? |
| 9909 | The number 3 defines the role of being third in a progression [Benacerraf] |
| Full Idea: Any object can play the role of 3; that is, any object can be the third element in some progression. What is peculiar to 3 is that it defines that role, not by being a paradigm, but by representing the relation of any third member of a progression. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: An interesting early attempt to spell out the structuralist idea. I'm thinking that the role is spelled out by the intersection of patterns which involve threes. |
| 9911 | Number words no more have referents than do the parts of a ruler [Benacerraf] |
| Full Idea: Questions of the identification of the referents of number words should be dismissed as misguided in just the way that a question about the referents of the parts of a ruler would be seen as misguided. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: What a very nice simple point. It would be very strange to insist that every single part of the continuum of a ruler should be regarded as an 'object'. |
| 8925 | Mathematical objects only have properties relating them to other 'elements' of the same structure [Benacerraf] |
| Full Idea: Mathematical objects have no properties other than those relating them to other 'elements' of the same structure. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], p.285), quoted by Fraser MacBride - Structuralism Reconsidered §3 n13 | |
| A reaction: Suppose we only had one number - 13 - and we all cried with joy when we recognised it in a group of objects. Would that be a number, or just a pattern, or something hovering between the two? |
| 9938 | How can numbers be objects if order is their only property? [Benacerraf, by Putnam] |
| Full Idea: Benacerraf raises the question how numbers can be 'objects' if they have no properties except order in a particular ω-sequence. | |
| From: report of Paul Benacerraf (What Numbers Could Not Be [1965], p.301) by Hilary Putnam - Mathematics without Foundations | |
| A reaction: Frege certainly didn't think that order was their only property (see his 'borehole' metaphor in Grundlagen). It might be better to say that they are objects which only have relational properties. |
| 9910 | Number-as-objects works wholesale, but fails utterly object by object [Benacerraf] |
| Full Idea: The identification of numbers with objects works wholesale but fails utterly object by object. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], IIIC) | |
| A reaction: This seems to be a glaring problem for platonists. You can stare at 1728 till you are blue in the face, but it only begins to have any properties at all once you examine its place in the system. This is unusual behaviour for an object. |
| 9903 | Number words are not predicates, as they function very differently from adjectives [Benacerraf] |
| Full Idea: The unpredicative nature of number words can be seen by noting how different they are from, say, ordinary adjectives, which do function as predicates. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: He points out that 'x is seventeen' is a rare construction in English, unlike 'x is happy/green/interesting', and that numbers outrank all other adjectives (having to appear first in any string of them). |
| 9904 | The set-theory paradoxes mean that 17 can't be the class of all classes with 17 members [Benacerraf] |
| Full Idea: In no consistent theory is there a class of all classes with seventeen members. The existence of the paradoxes is a good reason to deny to 'seventeen' this univocal role of designating the class of all classes with seventeen members. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], II) | |
| A reaction: This was Frege's disaster, and seems to block any attempt to achieve logicism by translating numbers into sets. It now seems unclear whether set theory is logic, or mathematics, or sui generis. |
| 17011 | I suspect that each particle of bodies has attractive or repelling forces [Newton] |
| 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'. |
| 8495 | The distinction between particulars and universals is a mistake made because of language [Ramsey] |
| Full Idea: The whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality what is merely a characteristic of language. | |
| From: Frank P. Ramsey (Universals [1925], p.13) | |
| A reaction: [Fraser MacBride has pursued this idea] It is rather difficult to deny the existence of particulars, in the sense of actual objects, so this appears to make Ramsey a straightforward nominalist, of some sort or other. |
| 8493 | We could make universals collections of particulars, or particulars collections of their qualities [Ramsey] |
| Full Idea: The two obvious methods of abolishing the distinction between particulars and universals are by holding either that universals are collections of particulars, or that particulars are collections of their qualities. | |
| From: Frank P. Ramsey (Universals [1925], p.8) | |
| A reaction: Ramsey proposes an error theory, arising out of language. Quine seems to offer another attempt, making objects and predication unanalysable and basic. Abstract reference seems to make the strongest claim to separate out the universals. |
| 8494 | Obviously 'Socrates is wise' and 'Socrates has wisdom' express the same fact [Ramsey] |
| Full Idea: It seems to me as clear as anything can be in philosophy that the two sentences 'Socrates is wise' and 'wisdom is a characteristic of Socrates' assert the same fact and express the same proposition. | |
| From: Frank P. Ramsey (Universals [1925], p.12) | |
| A reaction: Could be challenged. One says Socrates is just the way he is, the other says he is attached to an abstract entity greater than himself. The squabble over universals has become a squabble over logical form. Finding logical form needs metaphysics! |
| 17028 | Particles mutually attract, and cohere at short distances [Newton] |
| 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. |
| 17014 | The place of a thing is the sum of the places of its parts [Newton] |
| 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. |
| 9905 | Identity statements make sense only if there are possible individuating conditions [Benacerraf] |
| Full Idea: Identity statements make sense only in contexts where there exist possible individuating conditions. | |
| From: Paul Benacerraf (What Numbers Could Not Be [1965], III) | |
| A reaction: He is objecting to bizarre identifications involving numbers. An identity statement may be bizarre even if we can clearly individuate the two candidates. Winston Churchill is a Mars Bar. Identifying George Orwell with Eric Blair doesn't need a 'respect'. |
| 17546 | If you changed one of Newton's concepts you would destroy his whole system [Heisenberg on Newton] |
| 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. |
| 17027 | Science deduces propositions from phenomena, and generalises them by induction [Newton] |
| 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. |
| 17022 | We should admit only enough causes to explain a phenomenon, and no more [Newton] |
| 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'. |
| 17021 | Natural effects of the same kind should be assumed to have the same causes [Newton] |
| 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. |
| 17026 | From the phenomena, I can't deduce the reason for the properties of gravity [Newton] |
| 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). |
| 6421 | Newton's four fundamentals are: space, time, matter and force [Newton, by Russell] |
| 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. |
| 13470 | Mass is central to matter [Newton, by Hart,WD] |
| 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]. |
| 17020 | An attraction of a body is the sum of the forces of their particles [Newton] |
| 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. |
| 23012 | Newtonian causation is changes of motion resulting from collisions [Newton, by Baron/Miller] |
| 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. |
| 17008 | You have discovered that elliptical orbits result just from gravitation and planetary movement [Newton, by Leibniz] |
| 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. |
| 17010 | We have given up substantial forms, and now aim for mathematical laws [Newton] |
| 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. |
| 17023 | I am not saying gravity is essential to bodies [Newton] |
| 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). |
| 15866 | Newton reclassified vertical motion as violent, and unconstrained horizontal motion as natural [Newton, by Harré] |
| 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. |
| 15958 | Inertia rejects the Aristotelian idea of things having natural states, to which they return [Newton, by Alexander,P] |
| 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. |
| 17017 | 1: Bodies rest, or move in straight lines, unless acted on by forces [Newton] |
| 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. |
| 17018 | 2: Change of motion is proportional to the force [Newton] |
| 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. |
| 17019 | 3: All actions of bodies have an equal and opposite reaction [Newton] |
| 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'? |
| 20968 | Newton's Third Law implies the conservation of momentum [Newton, by Papineau] |
| 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). |
| 17547 | Newton's idea of force acting over a long distance was very strange [Heisenberg on Newton] |
| 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? |
| 20966 | Newton introduced forces other than by contact [Newton, by Papineau] |
| 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. |
| 20967 | Newton's laws cover the effects of forces, but not their causes [Newton, by Papineau] |
| 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. |
| 16708 | Newton's forces were accused of being the scholastics' real qualities [Pasnau on Newton] |
| 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. |
| 13153 | I am studying the quantities and mathematics of forces, not their species or qualities [Newton] |
| 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. |
| 12724 | The aim is to discover forces from motions, and use forces to demonstrate other phenomena [Newton] |
| 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. |
| 13593 | Newton showed that falling to earth and orbiting the sun are essentially the same [Newton, by Ellis] |
| 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. |
| 20969 | Early Newtonians could not formulate conservation of energy, having no concept of potential energy [Newton, by Papineau] |
| 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. |
| 17013 | Absolute space is independent, homogeneous and immovable [Newton] |
| 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. |
| 22915 | Newton needs intervals of time, to define velocity and acceleration [Newton, by Le Poidevin] |
| 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. |
| 22893 | Newton thought his laws of motion needed absolute time [Newton, by Bardon] |
| 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. |
| 17012 | Time exists independently, and flows uniformly [Newton] |
| 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'. |
| 14012 | Absolute time, from its own nature, flows equably, without relation to anything external [Newton] |
| 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. |
| 22954 | Newtonian mechanics does not distinguish negative from positive values of time [Newton, by Coveney/Highfield] |
| 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. |
| 17015 | If there is no uniform motion, we cannot exactly measure time [Newton] |
| 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) |
| 17025 | If a perfect being does not rule the cosmos, it is not God [Newton] |
| Full Idea: A being, however perfect, without dominion is not the Lord God. | |
| From: Isaac Newton (Principia Mathematica [1687], Bk 3 Gen Schol) |
| 17024 | The elegance of the solar system requires a powerful intellect as designer [Newton] |
| 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) |