by Scott Soames
11. See section 3.4 of chapter 8 of Soames (2018), and the references cited there.
12. Gödel (1932).
13. This theorem is discussed in section 4 of chapter 8 of Soames (2018).
14. Church (1936b).
15. Church (1936a).
16. See A fuller discussion is found in section 5.1 of chapter 8 of Soames (2018).
17. Turing (1936/37).
18. Church (1937).
19. A more extensive explanation is found in sections 5.2 and 5.3 of chapter 8 of Soames (2018).
CHAPTER 7
1. The Logical Structure of Linguistic Theory—Chomsky ([1955] 1975)—was written when Chomsky was at the Harvard Society of Fellows, but it wasn’t published until 1975. Syntactic Structures—Chomsky (1957)—is a much shortened summary of the main themes of that work. Aspects of a Theory of Syntax—Chomsky (1965)—revises his original conception of the organization of a grammar while articulating an explicitly mentalistic conception of the nature of linguistic theories, of which there had merely been some hints in Chomsky ([1955] 1975). Although his leading ideas about syntax, and its relation to semantics, have undergone many changes since then, this mentalistic philosophy of language has remained central to his thought. His entire professional life, after the Harvard Society, has been spent as a professor at MIT.
2. Pages 146–47 of Miller, Galanter, and Pribram (1960).
3. See Soames (1984) for an alternative to Chomsky’s heavily psychological conception of linguistics that nevertheless preserves the significance of linguistics for psychology, and conversely.
4. See Soames (2016a) and chapter 2 of Soames (2010b).
5. The placeholder view is examined and rejected in chapter 5 of Soames (2010b).
6. Russell’s conception of our passive awareness of propositions is stated on p. 60 of Russell (1904). Its significance is discussed on pp. 71–72 of Soames (2014c). See also Soames (2016a, chapter 2 of 2010b).
7. See sections 3, 4, and 5 of chapter 9 of Soames (2014b).
8. For discussion, see Soames (2016b), and chapter 2 of Soames (2018).
9. For discussion, see Soames (2008a).
10. Soames (1987, 2008b).
11. King (2007), Soames (2010a, 2013a, 2015b), Jesperson (2010, 2012), King, Soames, and Speaks (2014), Hanks (2015), and Moltmann (2017).
12. How a proposition represents things is read off the acts with which it is identified, from which we derive its truth conditions. A proposition p is true at world-state w if and only if, were the world actually in state w, things would be as p represents them—where what p represents is what any conceivable agent who entertains p would represent. No one has to entertain p for p to be true.
13. Nevertheless, one who says “it is a necessary truth that Hesperus is Phosphorus” does not assert that it is a necessary truth that the body in question is seen both in the morning and the evening. For explanation and discussion of the significance of this fact, see Soames (2015b), pp. 85–93.
14. See chapters 3–6 and chapter 9 of Soames (2015b).
15. Kaplan (1979, 1989).
16. Chapter 7 of Soames (2010a).
17. Soames (2008c).
18. Paul Grice, “Logic and Conversation,” given as The William James Lecture in 1967 at Harvard University, first published in Grice (1989).
CHAPTER 8
1. Tautologies—like Either I roll a 7 or ~ I roll a 7—are assigned probability 1. Their negations are assigned 0.
2. Kolmogorov ([1933] 1950).
3. A countable infinity is one the members of which can be uniquely and exhaustively paired with the natural numbers without remainder.
4. In such a case the agent believes each of the following: There are exactly n tickets; ticket 1 won’t win, ticket 2 won’t win … ticket n won’t win; one of the tickets will win.
5. Ramsey ([1926] 1990).
6. Ibid., p. 78.
7. Skyrms (1994).
8. Kemeny (1955).
9. P. 67 of Ramsey (1926 [1990]).
10. Ibid., p. 69.
11. Ibid., p. 70.
12. Ibid., p. 70.
13. Ibid., pp. 72–73.
14. Von Neumann and Morgenstern (1944), Savage (1954), Jeffrey (1965, 2004).
15. Becker ([1964] 1993, 1965, 1969, 1971,1973, 1974a, 1974b, [1981] 1991, 1985, 1992).
16. Becker (1992), p. 39.
17. The short but fascinating life of Ramsey is discussed at length in a book written by his sister (Paul 2012), which in turn is reviewed in Monk (2016).
18. Butler (2012), pp. 21–22.
19. Stigler and Friedland (1962) and Stigler (1971).
20. In contrast to his negative results concerning public choice, Arrow achieved an important positive result by showing that if a government (rightly or wrongly) wishes to redistribute wealth generated by a free, competitive economy, efficiency can be maximized by using taxes to accomplish redistribution, instead of controlling prices to redistribute income. Ever since, most economists have found this result compelling.
21. Buchanan (1986).
22. Ibid. Knute Wicksell, mentioned in the passage, was an important predecessor on whom Buchanan based much of his own approach.
CHAPTER 9
1. See chapter 7.
2. See Kripke (1980), chapters 14 and 17 of Soames (2003), and Soames (2007).
3. Soames (1989).
4. Place (1956), Smart (1963), Lewis (1966), and Armstrong (1968).
5. Kripke (1959).
6. Kripke (1971), pp. 152–53.
7. See Putnam (1967).
8. Kripke (1980), pp. 150–51.
9. Fodor (1981), p. 183.
10. As argued in Soames ([1990] 2009b), Fodor’s own discussion is ambiguous between a thesis with this force vs. other, stronger but more doubtful theses.
11. Fodor (1981), pp. 189–90.
12. Ibid., p. 183.
13. See Kripke (1980), Putnam (1975a), Kaplan (1989), and chapter 4 of Soames (2010a).
14. For further discussion, see Soames ([1990] 2009b).
CHAPTER 10
1. The passage quoted is from the sixth page of “Notes for an Autobiography,” published in The Saturday Review of Literature on November 26, 1949, which is a shortened version of the autobiographical statement in Einstein (1948).
2. Letter to Schlick in Einstein (1998), p. 220. For a brief discussion of Ernst Mach’s influence on the logical empiricist school of philosophy of which Schlick was a part, see Soames (2018), pp. 109–12; for Einstein’s influence on Schlick, see pp. 114–22.
3. See Norton (2010).
4. Here I follow the illuminating discussion of chapter 3 of Maudlin (2012), which the reader should consult for details.
5. Einstein ([1905] 1989).
6. The example is explained on p. 134 of Grünbaum (1967).
7. Ibid., pp. 134–35.
8. Ibid., p. 136.
9. Einstein ([1920] 2002).
10. See Norton (2010).
11. Chapter 4 of Maudlin (2012) discusses these points, including the fact that the law of inertia also covers bodies outside the light-cone plus the fact that in special relativity the paths of two physical entities not subject to external forces can’t intersect more than once.
12. Maudlin (2012), pp. 77–79.
13. Ibid., p. 78.
14. Ibid., p. 71. See pp. 72–74 for discussion of the physical interpretation of what these calculations are.
15. Ibid., p. 76. See also pp. 79–83 for widespread, and seemingly authoritative, but nevertheless misleading, confusions to be avoided.
16. See Maudlin (2012), pp. 89–94, for an explanation of how we could set up and calibrate accurate clocks and relate them to one another on parallel trajectories through space-time. Although one can calibrate some chosen pair of such co-mo
ving clocks and thereby assign simultaneity relations to arbitrarily distant space-time events, the assignment is conventional rather than objective, since selecting a pair of co-moving clocks on a different trajectory would result in a different simultaneity assignment. Simultaneity is not an objective physical notion in relativity theory. The point is extended to speed on pp. 95–96. How the twins A and B would look to each other during A’s journey is described on pp. 103–5.
17. For Einstein in 1905, speed was roughly speed as measured in a given “inertial reference frame”—a system of space-time points the coordinates of which, with respect to which bodies are not acted on by forces, move in a straight line at a constant rate. He imagined an observer in such a frame who sees a second observer moving past him at what the first observer measures to be a constant rate. Einstein’s principles—(i) that the speed of light in a reference frame doesn’t depend on the motion of the light source and (ii) that the same physical laws apply in all reference frames—led him to predict that a clock stationary in the second reference frame (moving relative to the first observer) will be measured by the clock in the first frame to be ticking slowly, and, similarly, that the first observer’s clock will be measured by the second observer’s clock to be running slowly. He also predicted that a rigid rod in the second reference frame will have shrunk when measured by rigid rods in the first reference frame, and similarly for rods in the first frame measured by rods in the second.
18. Maudlin (2012), chapter 5.
19. The nature of rigid rods and the contractions (and expansions) they undergo when subjected to trajectory changing forces in space-time are explained by the philosophically minded physicist John Bell, in “How to Teach Special Relativity,” which is chapter 9 of Bell (2008). See also pp. 116–20 of Maudlin (2012).
20. This is a version of the Michelson-Morley experiment in 1887, which Einstein was aware of, and accommodated in his theory of special relativity.
21. EarthSky (2011).
22. Feynman, Leighton, and Sands (1975), vol. 2.
23. Maudlin (2012), p. 138.
24. For discussion of a range of similar examples, see chapter 1 of Albert (1992).
25. Even this is a bit strange, at least terminologically, since normal functions are thought only to have mathematical, rather than physical, existence. Some contemporary physicists and philosophers of physics think of the wave function as a “nomological entity”—something like a law that “tells” the full-fledged physically existing things how to move through space-time. This too is, of course, hard to get one’s head around. (Thanks to Porter Williams for informing me of this.)
26. Thanks again to Porter Williams for helpful discussion.
27. For a fuller discussion, see chapter 11 of Carroll (2010).
28. Bohm (1951, 1952).
29. See, e.g., Everett (1973).
30. Deutsch (1997), Wallace (2012), and Carroll (2010).
CHAPTER 11
1. Hayek (1960), Rawls (1971), and Gauss (2016).
2. Hayek (1960), p. 42.
3. Ibid., p. 44.
4. Ibid., pp. 44–45.
5. Ibid., p. 93.
6. Ibid., p. 94.
7. Ibid., p. 97.
8. Ibid., p. 98.
9. Ibid., p. 96.
10. Ibid., p. 96.
11. Thanks to Jake Ross for bringing this to my attention.
12. See chapter 7 of Robert Nozick (1974).
13. Ibid., p. 157.
14. There is reason to think he would welcome this. On p. 87 of Hayek (1960) he says, “Our objection is against all attempts to impress upon society a deliberately chosen pattern of distribution.” What he may not have seen was that this prohibition applies to his own conclusion that in a free society distribution will roughly correspond to the value society perceives in a person’s actions.
15. Nozick (1974), p. 161.
16. The decades-long eclipse of normative inquiry is discussed in chapters 12 and 13 of Soames (2018).
17. On page 19 Rawls (1971) justifies the exclusion of agents’ “undeserved” personal characteristics from a fair decision procedure for choosing rules governing social cooperation on the grounds that such characteristics set people at odds and allow them “to be guided by their prejudices” (my emphasis). On page 74 he says that because natural assets are the outcome of a “natural lottery,” the possession of those assets is “arbitrary from a moral perspective.” He adds that “there is no more reason to permit the distribution of income and wealth by natural assets than by historical and social fortune.… Even the willingness to make an effort, to try, and so to be deserving in the ordinary sense is itself dependent upon happy family and social circumstances” (my emphasis).
18. Rawls (1971), p. 141 (my emphasis).
19. Ibid., pp. 136–37.
20. Ibid., pp. 143–44.
21. Ibid., 148 (my emphasis).
22. Ibid., p. 144.
23. Ibid., p. 145.
24. Ibid., p. 145.
25. Ibid., section 28.
26. Ibid., p. 169.
27. Ibid., p. 169.
28. See ibid., section 26.
29. Ibid., p. 176.
30. Again, thanks to Jake Ross for articulating this possibility.
31. See pages 74 and 101–2 of Rawls (1971).
32. Ibid., p. 100.
33. Ibid., 90–91.
34. If one asks what property of societies Gaus attempts to model—overall goodness or overall justice—one doesn’t get a clear answer. He tends to follow Rawls’s terminology, often speaking of overall justice. However, his conception seems not to be fundamentally focused on fairness, but rather on overall goodness, which includes justice or fairness along with other things.
35. See section 2.1 of chapter 2 of Gaus (2016).
36. Ibid., p. 68.
37. Ibid., p. 73.
38. Ibid., pp. 76–77.
39. Ibid., p. 81, my emphasis.
40. Ibid., p. 82.
41. Ibid., pp. 142–43.
42. Thanks to Jake Ross for bringing this to my attention.
43. Gaus (2016), chapter 4, sections 1.3–1.4.
44. Ibid., chapter 4, section 2.2.
45. Ibid., chapter 4, sections 3.1–3.3.
46. Ibid., all of chapter 4.
47. Ibid., pp. 215–220.
48. Ibid., pp. 217–18.
49. See section 3, “Marxism as a source of Leninism,” of chapter 16, book 1, volume 1 of Kołakowski ([1978] 2005).
50. Quoted in Kołakowski ([1978] 2005) at page 43.
51. Ibid., p. 223.
52. For useful discussion, see pp. 227–30 of Kołakowski ([1978] 2005).
53. Marx (1970), vol. 1, chapter 14, section 5.
54. Ibid., chapter 15, section 4.
55. Ibid., chapter 25, section 4.
56. Kołakowski ([1978] 2005), p. 252.
57. Ibid., pp. 255–56.
58. Ibid., p. 341.
59. Ibid., pp. 342–43.
60. Ibid., p. 343, my emphasis.
61. Ibid. pp. 343–44, my emphasis.
CHAPTER 12
1. Hart ([1961] 2012).
2. According to Hart, it is a necessary condition for a system of social rules to have this authority in order to count as a legal system. He does not, as far as I can see, assert that it is both necessary and sufficient.
3. It is enough to satisfy the Hartian necessary condition for being a legal system noted in the previous note.
4. Ibid., pp. 171–72.
5. Ibid., p. 210.
6. Ibid., p. 203.
7. 18 U.S. code section 924(c)(1) (2006).
8. Ibid., p. 242, my emphasis.
9. Ibid., p. 242, n. 1, my emphasis.
10. Ibid., p. 228.
11. See Soames (2013b).
12. Ibid.
