See A. J. Ayer, “Editor’s Introduction,” in A. J. Ayer, ed., Logical Positivism, pp. 3-28; Rudolf Carnap, “The Elimination of Metaphysics <javascript:loadBrain(‘Metaphysics’)> through Logical Analysis of Language <javascript:loadBrain(‘Language’)>,” in Ayer’s Logical Positivism, pp. 3-81; Noam Chomsky <javascript:loadBrain(‘Chomsky,%20Noam’)>, Syntactic Structures (1957). For a review of Chomsky’s achievement and influence, see Frederick J. Newmeyer’s Linguistic Theory in America, 2nd ed., chapter 2, “The Chomskyan Revolution.”
9. This debate, in its technical and personal dimensions, is described in some detail in McCorduck’s Machines Who Think.
10. Plato <javascript:loadBrain(‘Plato’)>’s works are readily available in Greek and English in the Loeb Classical Library editions; some other English translations of individual <javascript:loadBrain(‘Individual’)> works are mentioned below. An excellent place to begin is any of several reference works: Gilbert Ryle, “Plato <javascript:loadBrain(‘Plato’)>,” in The Encyclopedia of Philosophy, vol. 6, pp. 324-333; D. J. Allan, “Plato <javascript:loadBrain(‘Plato’)>,” in The Dictionary of Scientific Biography, vol. 11, pp. 22-31 (New York: Charles Scribner’s Sons, 1975). A more detailed account can be found in J. N. Findlay, Plato and Platonism: An Introduction.
11. In Aristotle <javascript:loadBrain(‘Aristotle’)>: The Growth and Structure of His Thought, chapters 2 and 3, G. E. R. Lloyd describes Aristotle <javascript:loadBrain(‘Aristotle’)> as both a pupil and a critic of Plato <javascript:loadBrain(‘Plato’)>.
12. See “The Greek Academy,” in The Encyclopedia of Philosophy, vol. 3, pp. 382-385. The Academy is also treated in Ryle’s “Plato <javascript:loadBrain(‘Plato’)>,” pp. 317-319. In his excellent survey, A History of Greek Philosophy, vol. 4, p. 19, W. K. <javascript:loadBrain(‘C’)>. Guthrie explains that the Academy was by no means like our modern university: it had religious elements we might more readily associate with a medieval college. Volume 4 of this survey is devoted to Plato <javascript:loadBrain(‘Plato’)>; the Academy is discussed on pp. 8-38. The early years of Plato <javascript:loadBrain(‘Plato’)>’s Academy are described in the reprint edition of Eduard Zeller’s 1888 classic, Plato and the Older Academy. See note 17 below.
13. Guthrie (vol. 4, pp. 338-340) points out that Plato <javascript:loadBrain(‘Plato’)> was influenced by the mystery religions of his day, especially in the Phaedo.
14. Plato <javascript:loadBrain(‘Plato’)> describes the movements of the planets in important passages in the Republic and the Timaeus; In Plato’s Timaeus, pp. 33-35, Francis Cornford provides a useful summary of the kinds of motion <javascript:loadBrain(‘Motion’)> Plato <javascript:loadBrain(‘Plato’)> describes in the Timaeus. G. E. R. Lloyd has a lucid and concise discussion of Plato <javascript:loadBrain(‘Plato’)>’s astronomy <javascript:loadBrain(‘Astronomy’)> in chapter 7 of Early Greek Science: Thales to Aristotle, pp. 80-98. The nature <javascript:loadBrain(‘Nature’)> of Plato <javascript:loadBrain(‘Plato’)>’s astronomy <javascript:loadBrain(‘Astronomy’)>, long a controversial subject for the history <javascript:loadBrain(‘History’)> of science <javascript:loadBrain(‘Science’)>, is analyzed in John D. Anton’s Science and the Sciences in Plato.
15. The myth of Er in the Republic (617-618) was Plato <javascript:loadBrain(‘Plato’)>’s version of a scheme originally developed by the Pythagorean philosopher Philolaus, who put fire at the extremity and at the center of the universe <javascript:loadBrain(‘Universe’)>, thus displacing the earth from its central position (G. S. Kirk, J. E. Raven, and M. Schofield, The Presocratic Philosophers, p. 259). The Pythagorean concept <javascript:loadBrain(‘Concept’)> of a central fire is described by S. Sambursky in The Physical World of the Greeks, pp. 64-66.
16. The discovery of irrational numbers eventually resulted in the rejection of a Pythagorean “geometric atomism” and led to the concept <javascript:loadBrain(‘Concept’)> of the continuum (S. Sambursky, The Physical World of the Greeks, pp. 33-35). In Plato <javascript:loadBrain(‘Plato’)>’s Theaetetus, the mathematician Theodorus demonstrates the irrationality of nonsquare numbers up to the root of 17. Plato <javascript:loadBrain(‘Plato’)> then claims that the roots of all numbers that are not squares are irrational. According to G. E. R. Lloyd (Early Greek Science: Thales to Aristotle, pp. 32-34), the irrationality of the square root of 2 was known even before the time of Plato <javascript:loadBrain(‘Plato’)>. The Greeks commonly expressed the proof in geometrical terms, by showing that the diagonal of a square is not commensurable with its side. (The proof assumes this commensurability, then shows that it leads to an impossibility because the resulting number <javascript:loadBrain(‘Number’)> is both odd and even.) The discovery that some magnitudes are incommensurable (c. 450-441 B.<javascript:loadBrain(‘C’)>.) is attributed to Hippacos of Mepontum, a member of the Pythagorean Brotherhood, in Alexander Helleman and Bryan Bunch, The Timetables of Science, p. 31.
17. E. R. Dodds, The Greeks and the Irrational is a classic treatment of this subject. Ananke is described in detail in F. M. Cornford, Plato’s Cosmology, pp. 159-177. A more recent work is Richard R Mohr’s Platonic Cosmology.
18. In the Phaedo and The Republic, Plato <javascript:loadBrain(‘Plato’)> opposes the activity of intellect to the “brutish” passivity of desire (Martha Nussbaum, “Rational Animals and the Explanation of Action <javascript:loadBrain(‘Action’)>,” in The Fragility of Goodness: Luck and Ethics in Greek Tragedy and Philosophy, p. 273). In this book Nussbaum explores the antithesis in Greek philosophy <javascript:loadBrain(‘Philosophy’)> between the controlling power of reason <javascript:loadBrain(‘Reason’)> and events beyond one’s control, an antithesis central to Plato <javascript:loadBrain(‘Plato’)>’s dialogues.
19. The first mention of the Forms is in the Phaedo; an excellent discussion can be found in Gilbert Ryle’s article (pp. 320-324) in The Encyclopedia of Philosophy.
20. Plato <javascript:loadBrain(‘Plato’)>’s theory of matter <javascript:loadBrain(‘Matter’)> in the Timaeus, where the smallest particles are triangles, is a blend of Pythagorean ideas and Democritan atomism (see S. Sambursky, The Physical World of the Greeks, p. 31).
21. Cornford, in Plato’s Cosmology, pp. 159-177, provides a lucid discussion of this tension between necessity and reason <javascript:loadBrain(‘Reason’)>.
22. On the dialog as Plato <javascript:loadBrain(‘Plato’)>’s chosen form, see D. Hyland’s “Why Plato <javascript:loadBrain(‘Plato’)> Wrote Dialogues,” Philosophy and Rhetoric 1 (1968): 38-50.
23. Physicist Werner Heisenberg <javascript:loadBrain(‘Heisenberg,%20Werner’)> describes how he arrived at his uncertainty principle <javascript:loadBrain(‘Uncertainty%20Principle’)>, which he formulated in 1927 in chapter 6 of his gracefully written and entertaining volume Physics and Beyond: Encounters and Conversations. Heisenberg was influenced by Plato <javascript:loadBrain(‘Plato’)>’s corpuscular physics <javascript:loadBrain(‘Physics’)>, and he explores the relation between Plato <javascript:loadBrain(‘Plato’)>’s ideas and quantum theory in chapter 20, “Elementary Particles and Platonic Philosophy <javascript:loadBrain(‘Philosophy’)> (1961-1965).”
24. A refreshing new interpretation of the Phaedrus emphasizing the role of paradox <javascript:loadBrain(‘Paradox’)> is Martha Nussbaum’s “‘This Story Isn’t True’: Madness, Reason <javascript:loadBrain(‘Reason’)>, and Recantation in the Phaedrus,” chapter 7 in The Fragility of Goodness, pp. 200-228.
25. D. A. Rees, “Platonism and the Platonic Tradition,” p. 336. It was Xenocrates, who headed the Academy after the death of Speusippus, Plato <javascript:loadBrain(‘Plato’)>’s immediate successor, who identified the Platonic Ideas with mathematical numbers, not the “ideal” numbers postulated in the Academy under Plato <javascript:loadBrain(‘Plato’)> and discussed in the Phaedo. The fates of the various forms of Platonism are reviewed in several brief articles in the Dictionary of the History of Ideas (New York: Charles Scribner’s Sons, 1973), vol. 3: John Fisher’s “Platonism in Philosophy <javascript:loadBrain(‘Philosophy’)> and Poetry <javascript:loadBrain(‘Poetry’)>,” pp. 502-508; John Charles Nelson’s “Platonism in the Renaissance <javascript:loadBrain(‘Renaissance’)>,” pp. 508-515; and Ernst Moritz Manasse’s “Platonism since the Enlightenment <javascript:loadBrain(‘The%20Enlightenment’)>,” pp. 515-525.
26. D. H. Fowler, in The Mathematics of Plato’s Academy, reconstructs in detail the curriculum of the Academy. A particularly readable account of the work of the geometers can be found in chapter 3 of Francois Lasserre, The Birth of Mathematics in the Age of Plato. A more technical treatment can be found in chapter 3 of Wilbur Richard Knorr, The Ancient Tradition of Geometric Problems.
27. For a general overview of Plato <javascript:loadBrain(‘Plato’)>’s philosophy <javascript:loadBrain(‘Philosophy’)> of numbers, see “Plato <javascript:loadBrain(‘Plato’)>,” The New Encyclopedia Britannica, vol. 14, p. 538. For the text of the Epinomis in Greek and English, see W. R. M. Lamb, ed., Plato, Loeb Classical Library, vol. 8. In the Epinomis, 976 D-E, the speaker asks what science <javascript:loadBrain(‘Science’)> is indispensable to wisdom <javascript:loadBrain(‘Wisdom’)>: “it is the science <javascript:loadBrain(‘Science’)> which gave number <javascript:loadBrain(‘Number’)> to the whole race of mortals.” See also R. S. Brumbaugh, Plato’s Mathematical Imagination.
28. A superb introduction to Enlightenment thought <javascript:loadBrain(‘Thought’)> is Peter Gay’s two volumes, The Enlightenment: An Interpretation, vol. 1, The Rise of Modern Paganism and vol. 2, The Science of Freedom.
29. The definitive biography is Richard Westfall’s Never at Rest: A Biography of Isaac Newton. No one interested in Isaac Newton <javascript:loadBrain(‘Newton,%20Isaac’)>’s scientific achievement should fail to see I. Bernard Cohen’s Newtonian Revolution. Those who wish to tackle Newton in the original should see Isaac Newton <javascript:loadBrain(‘Newton,%20Isaac’)>’s Philosophiae Naturalis Principia Mathematica, 3rd edition (1726), assembled by Alexander Koyré, I. Bernard Cohen, and Anne Whitman.
30. Otto Mayr, Authority, Liberty, and Automatic Machinery in Early Modern Europe.
31. A useful overview of Descartes’s life and work can be found in The Dictionary of Scientific Biography, vol. 4, pp. 55-65. Descartes, by Jonathan Rée, is unsurpassed in giving a unified view of Descartes’s philosophy <javascript:loadBrain(‘Philosophy’)> and its relation to other systems of thought <javascript:loadBrain(‘Thought’)>.
32. The brief Discours de la Méthode appeared in 1637 and is written in a lively autobiographical manner. It is readily available in the Library of the Liberal Arts edition, which includes the appendixes in which Descartes introduced analytic geometry <javascript:loadBrain(‘Geometry’)> and his theory of refraction: Discourse on Method, Optics, Geometry, and Meteorology, trans. by Paul J. Olscamp.
33. Derek J. de Solla Price, “Automata and the Origins of Mechanism and Mechanistic Philosophy <javascript:loadBrain(‘Philosophy’)>,” Technology and Culture 5 (1964): 23.
34. See I. Bernard Cohen on Newton in the Dictionary of Scientific Biography, vol. 10, pp. 42-103, and Cohen’s Newtonian Revolution, mentioned above.
35. Charles Gillispie, The Edge of Objectivity, p. 140. The resulting prestige of science <javascript:loadBrain(‘Science’)> during the Enlightenment <javascript:loadBrain(‘The%20Enlightenment’)> is treated in chapter 5.
36. For a readable and lucid introduction to relativity <javascript:loadBrain(‘Relativity’)>, see the 1925 classic by Bertrand Russell, The ABC of Relativity, 4th rev. ed. A more detailed treatment may be found in Albert Einstein <javascript:loadBrain(‘Einstein,%20Albert’)>, Relativity: The Special and General Theory, a Popular Exposition, trans. Robert Lawson.
37. Gillispie, The Edge of Objectivity, pp. 145-150.
38. Leibniz’s criticism of the watchmaker God <javascript:loadBrain(‘God’)> can be found in a letter written in November 1715 to Samuel Clarke (1675-1729), a renowned disciple of Newton (see pp. 205-206 of Leibniz’s Philosophical Writings, G. H. R. Parkinson, ed.). For the famous debate this letter initiated, see The Leibniz-Clarke Correspondence, H. G. Alexander, ed.
39. W. T. Jones, Kant and the Nineteenth Century, p. 14. The legacy of Descartes is expressed in Kant’s own definition of the Enlightenment <javascript:loadBrain(‘The%20Enlightenment’)>, which is quoted by Ernst Cassirer in The Philosophy of the Enlightenment, p. 163: “Enlightenment is man’s exodus from his self-incurred tutelage. Tutelage is the inability to use one’s understanding without the guidance of another person. This tutelage is self-incurred if its cause lies not in any weakness of the understanding, but in indecision and lack of courage to use the mind without the guidance of another. ‘Dare to know’ (sapere aude)! Have the courage to use your own understanding; this is the motto of the Enlightenment <javascript:loadBrain(‘The%20Enlightenment’)>.”
40. Immanuel Kant <javascript:loadBrain(‘Kant,%20Immanuel’)>, Critique of Pure Reason, 1st ed. 1781; Prolegomena to Any Future Metaphysics, 1st ed. 1783. The relations between Kantian philosophy <javascript:loadBrain(‘Philosophy’)> and science <javascript:loadBrain(‘Science’)> are explored in Gordon G. Brittan, Jr., Kant’s Theory of Science.
41. A brief history <javascript:loadBrain(‘History’)> of logical positivism <javascript:loadBrain(‘Logical%20Positivism’)> can be found in A. J. Ayer, Logical Positivism, pp. 3-28. Moritz Schlick, center of the Vienna Circle in the 1920s, compares the Kantian and positivist treatments of reality <javascript:loadBrain(‘Reality’)> in “Positivism and Realism,” an essay published in 1932 or 1933 and reprinted in Ayer’s Logical Positivism (see p. 97).
42. Ayer, in Logical Positivism, p. 11, points out the positivist nature <javascript:loadBrain(‘Nature’)> of Hume’s attack on metaphysics <javascript:loadBrain(‘Metaphysics’)> and then claims that he could well have cited Kant instead, “who maintained that human understanding lost itself in contradictions when it ventured beyond the bounds of possible experience <javascript:loadBrain(‘Experience’)>.” Ayer claims that “the originality of the logical positivists lay in their making the impossibility of metaphysics <javascript:loadBrain(‘Metaphysics’)> depend not upon the nature <javascript:loadBrain(‘Nature’)> of what could be known but upon the nature <javascript:loadBrain(‘Nature’)> of what could be said” (Logical Positivism, p. 11).
27/08/2021 09:25:49 -0500