Rules_of_Reasoning_in_Philosophy

The article below is from http://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica Rules of Reasoning in Philosophy Perhaps to reduce the risk of public misunderstanding, Newton included at the beginning of Book 3 (in the second (1713) and third (1726) editions) a section entitled "Rules of Reasoning in Philosophy." In the four rules, as they came finally to stand in the 1726 edition, Newton effectively offers a methodology for handling unknown phenomena in nature and reaching towards explanations for them. The four Rules of the 1726 edition run as follows (omitting some explanatory comments that follow each): Rule 1: We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances. Rule 2: Therefore to the same natural effects we must, as far as possible, assign the same causes. Rule 3: The qualities of bodies, which admit neither intensification nor remission of degrees, and which are found to belong to all bodies within the reach of our experiments, are to be esteemed the universal qualities of all bodies whatsoever. Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, not withstanding any contrary hypothesis that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions. This section of Rules for philosophy is followed by a listing of 'Phenomena', in which are listed a number of mainly astronomical observations, that Newton used as the basis for inferences later on, as if adopting a consensus set of facts from the astronomers of his time. Both the 'Rules' and the 'Phenomena' evolved from one edition of the Principia to the next. Rule 4 made its appearance in the third (1726) edition; Rules 1–3 were present as 'Rules' in the second (1713) edition, and predecessors of them were also present in the first edition of 1687, but there they had a different heading: they were not given as 'Rules', but rather in the first (1687) edition the predecessors of the three later 'Rules', and of most of the later 'Phenomena', were all lumped together under a single heading 'Hypotheses' (in which the third item was the predecessor of a heavy revision that gave the later Rule 3). From this textual evolution, it appears that Newton wanted by the later headings 'Rules' and 'Phenomena' to clarify for his readers his view of the roles to be played by these various statements. In the third (1726) edition of the Principia, Newton explains each rule in an alternative way and/or gives an example to back up what the rule is claiming. The first rule is explained as a philosophers' principle of economy. The second rule states that if one cause is assigned to a natural effect, then the same cause so far as possible must be assigned to natural effects of the same kind: for example respiration in humans and in animals, fires in the home and in the Sun, or the reflection of light whether it occurs terrestrially or from the planets. An extensive explanation is given of the third rule, concerning the qualities of bodies, and Newton discusses here the generalization of observational results, with a caution against making up fancies contrary to experiments, and use of the rules to illustrate the observation of gravity and space. Isaac Newton’s statement of the four rules revolutionized the investigation of phenomena. With these rules, Newton could in principle begin to address all of the world’s present unsolved mysteries. He was able to use his new analytical method to replace that of Aristotle, and he was able to use his method to tweak and update Galileo’s experimental method. The re-creation of Galileo’s method has never been significantly changed and in its substance, scientists use it today. Reference: 1. ^ Among versions of the Principia online: [1]. 2. ^ a b Volume 1 of the 1729 English translation is available as an online scan; limited parts of the 1729 translation (misidentified as based on the 1687 edition) have also been transcribed online. 3. ^ Newton, Isaac. "Philosophiæ Naturalis Principia Mathematica (Newton's personally annotated 1st edition)". 4. ^ a b [In Latin] Isaac Newton's Philosophiae Naturalis Principia Mathematica: the Third edition (1726) with variant readings, assembled and ed. by Alexandre Koyré and I Bernard Cohen with the assistance of Anne Whitman (Cambridge, MA, 1972, Harvard UP) 5. ^ J M Steele, University of Toronto, (review online from Canadian Association of Physicists) of N Guicciardini's "Reading the Principia: The Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736" (Cambridge UP, 1999), a book which also states (summary before title page) that the "Principia" "is considered one of the masterpieces in the history of science". 6. ^ (in French) Alexis Clairaut, "Du systeme du monde, dans les principes de la gravitation universelle", in "Histoires (& Memoires) de l'Academie Royale des Sciences" for 1745 (published 1749), at p.329 (according to a note on p.329, Clairaut's paper was read at a session of November 1747). 7. ^ G E Smith, "Newton's Philosophiae Naturalis Principia Mathematica", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), E N Zalta (ed.). 8. ^ a b The content of infinitesimal calculus in the 'Principia' was recognized both in Newton's lifetime and later, among others by the Marquis de l'Hospital, whose 1696 book "Analyse des infiniment petits" (Infinitesimal analysis) stated in its preface, about the 'Principia', that 'nearly all of it is of this calculus' ('lequel est presque tout de ce calcul'). See also D T Whiteside (1970), "The mathematical principles underlying Newton's Principia Mathematica", Journal for the History of Astronomy, vol.1 (1970), 116–138, especially at p.120. 9. ^ a b Or "frame" no hypotheses (as traditionally translated at vol.2, p.392, in the 1729 English version). 10. ^ From Motte's translation of 1729 (at 3rd page of Author's Preface); and see also J. W. Herivel, The background to Newton's "Principia," Oxford University Press, 1965. 11. ^ The De motu corporum in gyrum article indicates the topics that reappear in the Principia. 12. ^ Newton, Sir Isaac (1729). "Definitions". The Mathematical Principles of Natural Philosophy, Volume I. p. 1. 13. ^ Newton, Sir Isaac (1729). "Axioms or Laws of Motion". The Mathematical Principles of Natural Philosophy, Volume I. p. 19. 14. ^ Newton, Sir Isaac (1729). "Section I". The Mathematical Principles of Natural Philosophy, Volume I. p. 41. 15. ^ Newton, Sir Isaac (1729). "Section II". The Mathematical Principles of Natural Philosophy, Volume I. p. 57. 16. ^ This relationship between circular curvature, speed and radial force, now often known as Huygens' formula, was independently found by Newton (in the 1660s) and by Huygens in the 1650s: the conclusion was published (without proof) by Huygens in 1673.This was given by Isaac Newton through his Inverse Square Law. 17. ^ Newton, Sir Isaac; Machin, John (1729). The Mathematical Principles of Natural Philosophy, Volume I. pp. 79–153. 18. ^ Newton, Sir Isaac (1729). "Section IX". The Mathematical Principles of Natural Philosophy, Volume I. p. 177. 19. ^ Newton, Sir Isaac (1729). "Section XI". The Mathematical Principles of Natural Philosophy, Volume I. p. 218. 20. ^ Newton, Sir Isaac (1729). "Section XI, Proposition LXVI". The Mathematical Principles of Natural Philosophy, Volume I. p. 234. 21. ^ Newton, Sir Isaac; Machin, John (1729). The Mathematical Principles of Natural Philosophy, Volume I. pp. 239–256. 22. ^ Newton, Sir Isaac (1729). "Section XII". The Mathematical Principles of Natural Philosophy, Volume I. p. 263. 23. ^ Eric J Aiton, The Cartesian vortex theory, chapter 11 in Planetary astronomy from the Renaissance to the rise of astrophysics, Part A: Tycho Brahe to Newton, eds. R Taton & C Wilson, Cambridge (Cambridge University press) 1989; at pp. 207–221. 24. ^ Newton, Sir Isaac (1729). "Scholium to proposition 53". The Mathematical Principles of Natural Philosophy, Volume II. p. 197. 25. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 252. 26. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 262. 27. ^ Newton, Sir Isaac (1729). "The Phaenomena". The Mathematical Principles of Natural Philosophy, Volume II. p. 206. 28. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 213. 29. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 220. 30. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 323. 31. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 332. 32. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 255. 33. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 305. 34. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 306. 35. ^ Newton, Sir Isaac (1729). The Mathematical Principles of Natural Philosophy, Volume II. p. 320. 36. ^ See Curtis Wilson, "The Newtonian achievement in astronomy", pages 233–274 in R Taton & C Wilson (eds) (1989) The General History of Astronomy, Volume, 2A', at page 233). 37. ^ Newton, Sir Isaac (1729). "Proposition 12, Corollary". The Mathematical Principles of Natural Philosophy, Volume II. p. 233. 38. ^ a b Newton, Sir Isaac (1729). "Proposition 11 & preceding Hypothesis". The Mathematical Principles of Natural Philosophy, Volume II. p. 232. 39. ^ Newton, Sir Isaac (1729). "Proposition 8, Corollary 2". The Mathematical Principles of Natural Philosophy, Volume II. p. 228. 40. ^ Newton, Sir Isaac (1729). "Proposition 22". The Mathematical Principles of Natural Philosophy, Volume II. p. 232. Newton's position is seen to go beyond literal Copernican heliocentrism practically to the modern position in regard to the solar system barycenter. 41. ^ See online Principia (1729 translation) vol.2, Books 2 & 3, starting at page 387 of volume 2 (1729). 42. ^ Edelglass et al., Matter and Mind, ISBN 0-940262-45-2, p. 54. 43. ^ See online Principia (1729 translation) vol.2, Books 2 & 3, at page 392 of volume 2 (1729). 44. ^ Snobelen, Stephen. "The General Scholium to Isaac Newton's Principia mathematica". Retrieved 2008-05-31. 45. ^ Ducheyne, Steffen. "The General Scholium: Some notes on Newton’s published and unpublished endeavours, Lias: Sources and Documents Relating to the Early Modern History of Ideas, vol. 33, n° 2, pp. 223–274.". Retrieved 2008-11-19. 46. ^ Paraphrase of 1686 report by Halley, in H. W. Turnbull (ed.), 'Correspondence of Isaac Newton', Vol.2, cited above, pp. 431–448. 47. ^ 'Cook, 1998': A. Cook, Edmond Halley, Charting the Heavens and the Seas, Oxford University Press 1998, at pp.147 and 152. 48. ^ As dated e.g. by D. T. Whiteside, in The Prehistory of the Principia from 1664 to 1686, Notes and Records of the Royal Society of London, 45 (1991) 11–61. 49. ^ Cook, 1998; at p. 147. 50. ^ 'Westfall, 1980': R S Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge University Press 1980, at p.404. 51. ^ Cook, 1998; at p. 151. 52. ^ Westfall, 1980; at p. 406, also pp. 191–2. 53. ^ Westfall, 1980; at p.406, n.15. 54. ^ Westfall, 1980; at pp. 153–156. 55. ^ The fundamental study of Newton's progress in writing the Principia is in I. Bernard Cohen's Introduction to Newton's 'Principia' , (Cambridge, Cambridge University Press, 1971), at part 2: "The writing and first publication of the 'Principia' ", pp.47–142. 56. ^ Newton, Sir Isaac (1729). "Introduction to Book 3". The Mathematical Principles of Natural Philosophy, Volume II. p. 200. 57. ^ Newton, Isaac (1728). A Treatise of the System of the World. 58. ^ I. Bernard Cohen, Introduction to Newton's A Treatise of the System of the World (facsimile of second English edition of 1731), London (Dawsons of Pall Mall) 1969. 59. ^ Newton, Sir Isaac (1740). The System of the World: Demonstrated in an Easy and Popular Manner. Being a Proper Introduction to the Most Sublime Philosophy. By the Illustrious Sir Isaac Newton. Translated into English. A 'corrected' reprint of the second edition. 60. ^ Richard Westfall (1980), Never at Rest, p. 453, ISBN 0-521-27435-4 61. ^ "Museum of London exhibit including facsimile of title page from John Flamsteed's copy of 1687 edition of Newton's ''Principia''". Museumoflondon.org.uk. Retrieved 2012-03-16. 62. ^ a b D T Whiteside, "The pre-history of the 'Principia' from 1664 to 1686", Notes and Records of the Royal Society of London, 45 (1991), pages 11–61; especially at 13–20. [2] 63. ^ See J. Bruce Brackenridge, "The key to Newton's dynamics: the Kepler problem and the Principia", (University of California Press, 1995), especially at pages 20–21. 64. ^ See page 10 in D T Whiteside, "Before the Principia: the maturing of Newton's thoughts on dynamical astronomy, 1664–1684", Journal for the History of Astronomy, i (1970), pages 5–19. 65. ^ a b Hooke's 1674 statement in "An Attempt to Prove the Motion of the Earth from Observations", is available in online facsimile here. 66. ^ See page 239 in Curtis Wilson (1989), "The Newtonian achievement in astronomy", ch.13 (pages 233–274) in "Planetary astronomy from the Renaissance to the rise of astrophysics: 2A: Tycho Brahe to Newton", CUP 1989. 67. ^ a b c d e H W Turnbull (ed.), Correspondence of Isaac Newton, Vol 2 (1676–1687), (Cambridge University Press, 1960), giving the Hooke-Newton correspondence (of November 1679 to January 1679/80) at pp.297–314, and the 1686 correspondence over Hooke's priority claim at pp.431–448. 68. ^ 'Correspondence' vol.2 already cited, at p.297. 69. ^ Several commentators have followed Hooke in calling Newton's spiral path mistaken, or even a 'blunder', but there are also the following facts: (a) that Hooke left out of account Newton's specific statement that the motion resulted from dropping "a heavy body suspended in the Air" (i.e. a resisting medium), see Newton to Hooke, 28 November 1679, document #236 at page 301, 'Correspondence' vol.2 cited above, and compare Hooke's report to the Royal Society on 11 December 1679 where Hooke reported the matter "supposing no resistance", see D Gjertsen, 'Newton Handbook' (1986), at page 259); and (b) that Hooke's reply of 9 December 1679 to Newton considered the cases of motion both with and without air resistance: The resistance-free path was what Hooke called an 'elliptueid'; but a line in Hooke's diagram showing the path for his case of air resistance was, though elongated, also another inward-spiralling path ending at the Earth's centre: Hooke wrote "where the Medium ... has a power of impeding and destroying its motion the curve in wch it would move would be some what like the Line AIKLMNOP &c and ... would terminate in the center C". Hooke's path including air resistance was therefore to this extent like Newton's (see 'Correspondence' vol.2, cited above, at pages 304–306, document #237, with accompanying figure). The diagrams are also available online: see Curtis Wilson, chapter 13 in "Planetary Astronomy from the Renaissance to the Rise of Astrophysics, Part A, Tycho Brahe to Newton", (Cambridge UP 1989), at page 241 showing Newton's 1679 diagram with spiral, and extract of his letter; also at page 242 showing Hooke's 1679 diagram including two paths, closed curve and spiral. Newton pointed out in his later correspondence over the priority claim that the descent in a spiral "is true in a resisting medium such as our air is", see 'Correspondence', vol.2 cited above, at page 433, document #286. 70. ^ See page 309 in 'Correspondence of Isaac Newton', Vol 2 cited above, at document #239. 71. ^ See Curtis Wilson (1989) at page 244. 72. ^ See "Meanest foundations and nobler superstructures: Hooke, Newton and the 'Compounding of the Celestiall Motions of the Planetts'", Ofer Gal, 2003 at page 9. 73. ^ See for example the 1729 English translation of the 'Principia', at page 66. 74. ^ R S Westfall, 'Never at Rest', 1980, at pages 391–2. 75. ^ The second extract is quoted and translated in W.W. Rouse Ball, "An Essay on Newton's 'Principia'" (London and New York: Macmillan, 1893), at page 69. 76. ^ The original statements by Clairaut (in French) are found (with orthography here as in the original) in "Explication abregée du systême du monde, et explication des principaux phénomenes astronomiques tirée des Principes de M. Newton" (1759), at Introduction (section IX), page 6: "Il ne faut pas croire que cette idée ... de Hook diminue la gloire de M. Newton", [and] "L'exemple de Hook" [serves] "à faire voir quelle distance il y a entre une vérité entrevue & une vérité démontrée". 77. ^ Newton, Isaac. "Philosophiæ naturalis principia mathematica". Cambridge Digital Library. Retrieved 3 July 2013. 78. ^ Newton, Isaac (1687). "Philosophiae naturalis principia mathematica" (in Latin). Swem Library: Jussu Societatis Regiae ac Typis Josephi Streater. 79. ^ "The Crawford collection at the Royal Observatory Edinburgh". The Royal Observatory, Edinburgh. Retrieved 3 July 2013. 80. ^ http://www.uu.se/press/pm.php'typ=pm&id=470[dead link] 81. ^ The Correspondence of Isaac Newton, vol.4, Cambridge University Press 1967, at pp.519, n.2. 82. ^ The Correspondence of Isaac Newton, vol.4, Cambridge University press 1967, at p.42. 83. ^ I Bernard Cohen, Introduction to the Principia, Cambridge 1971. 84. ^ Richard S. Westfall. Never at Rest: A Biography of Isaac Newton. Cambridge U. Press. 1980 ISBN 0-521-23143-4, at p.699. 85. ^ The Correspondence of Isaac Newton, vol.4, Cambridge University press 1967, at pp.518–20. 86. ^ The Correspondence of Isaac Newton, vol.5, Cambridge University press 1975. Bentley's letter to Newton of October 1709 (at p.7-8) describes Cotes' perhaps unenviable position in relation to his master Bentley: "You need not be so shy of giving Mr. Cotes too much trouble: he has more esteem for you, and obligations to you, than to think that trouble too grievous: but however he does it at my Orders, to whom he owes more than that." 87. ^ Westfall, pp.712–716. 88. ^ Westfall, pp.751–760. 89. ^ Westfall, p.750. 90. ^ Westfall, p.802 91. ^ [In Latin] Isaac Newton, Philosophiae naturalis principia mathematica volume 1 of a facsimile of a reprint (1833) of the 3rd (1726) edition, as annotated in 1740–42 by Thomas LeSeur & François Jacquier, with the assistance of J-L Calandrini 92. ^ I Bernard Cohen (1968), "Introduction" (at page i) to (facsimile) reprint of 1729 English translation of Newton's "Principia" (London (1968), Dawsons of Pall Mall). 93. ^ See pages 29–37 in I. Bernard Cohen (1999), "A Guide to Newton's Principia", published as an introduction to "Isaac Newton: The Principia, Mathematical principles of natural philosophy, a new translation" by I Bernard Cohen and Anne Whitman, University of California Press, 1999.