William D. Whitney to Henry Whitney, 26 June 1889, Yale (Beineke).
40. Peirce did not mention Ann Arbor in this letter, but that was probably an oversight.
41. The National Archives “Register of Records” indicates that this report was received and stored as GO-401, 902 HG in Box 395. It is now missing.
42. Brent, p. 195.
43. Victor F. Lenzen, “An Unpublished Scientific Monograph by C. S. Peirce,” Transactions of the Charles S. Peirce Society 5 (1969): 5–24.
44. In his definition of “gravity” for the Century Dictionary, Peirce wrote: “The words gravity and gravitation have been more or less confounded; but the most careful writers use gravitation for the attracting force, and gravity for the terrestrial phenomenon of weight or downward acceleration which has for its two components the gravitation and the centrifugal force.”
45. Lenzen (1969), p. 13.
46. Victor F. Lenzen and Robert P. Multhauf, “Development of Gravity Pendulums in the 19th Century,” Contributions from the Museum of History and Technology (Smithsonian Institution, Bulletin 240,1966), pp. 301–47.
47. Report of the Superintendent of the U. S. Coast and Geodetic Survey for the Fiscal Year Ending June 30,1891, part II, Appendix no. 15, pp. 503–64.
48. See Lenzen (1969), pp. 6–7.
49. See Lenzen (1969), passim.
50. Peirce’s best value for gravity at the Smithsonian was 980.1037 cm/sec2, but that was not the value given in the 1889 report; it comes from a letter of 3 July 1890 from Peirce to Herbert Nichols, Professor of Physics at Cornell University. The value from the report is 99.095 cm (as the length of the mean equatorial seconds’ pendulum), which converts to an acceleration slightly less than Peirce’s “best value.” Lenzen points out, however, that the value given in the 1889 report had not been corrected for flexure, which may account for the difference (see Lenzen 1969:17–20).
51. Lenzen (1969), p. 20.
52. See Brent, pp. 14–15, especially in revised edition.
53. This opinion was expressed in a private communication.
54. See De Tienne’s “The Mystery of Arisbe,” Peirce Project Newsletter 3 (1999): 11–12.
55. The first two lines of this letter of 22 April 1890 have been heavily crossed out. This reading is based on Max H. Fisch’s study of the document.
56. See Brent, pp. 303–08.
57. See the textual editor’s headnote to selection 44 (pp. 658–663) for further discussion of Peirce’s relations with Metcalf and the import on Peirce’s composition.
58. Max H. Fisch, Peirce, Semeiotic and Pragmatism, eds. K. L. Ketner and C. J. W. Kloesel, (Indiana University Press, 1986) and Murray G. Murphey, The Development of Peirce’s Philosophy, (Harvard University Press, 1961; Indianapolis: Hackett Publishing Co., 1993).
59. See Murphey, pp. 301–03.
60. Murphey, p. 396.
61. Ibid.
62. Fisch, p. 190.
63. Don D. Roberts, “On Peirce’s Realism,” Transactions of the Charles S. Peirce Society 6 (1970): 67–83.
64. Fred Michael, “Two Forms of Scholastic Realism in Peirce’s Philosophy,” Transactions of the Charles S. Peirce Society 24 (1988): 317–48.
65. T. L. Short, “Review Essay,” Synthese 106 (1996): 409–30.
66. See Murphey, pp. 327–48.
67. Fisch, p. 229.
68. It is commonly believed that Peirce’s allusion to “the riddle” and his reference to the Sphinx were beholden to Emersons poem, “The Riddle of the Sphinx.” But the story is more complicated: see the introduction to W5, pp. xli–xlii and annotation 165.title in this volume on pp. 438–39.
Writings of Charles S. Peirce
Boolian Algebra—Elementary Explanations
| Fall 1886 | Houghton Library |
There is a very convenient system of signs by which very intricate problems of reasoning can be solved. I shall now introduce you to one part of this system only, and after you are well exercised in that, we will study some additional signs which give the method increased range and power. We use letters in this system to signify statements or facts, real or fictitious. We change their signification to suit the different problems. Two statements a and b are said to be equivalent when equal, provided that in every conceivable state of things in which either is true, the other is true, so that they are true and false together, and we then use a sign of equality between them, and write a = b. We use the words addition, sum, etc., and the symbol + in such a sense that, if a is one fact, say that the moon is made of green cheese, and b is another fact, say that some nursery tales are false, that is a + b, or a added to b, or the sum of a and b, signifies that one or the other (perhaps both) of the facts added are true, so that a + b is a statement; true if one or both of the statements a and b are true and false if both are false. Giving to a and b the above significations, it would mean that the moon is made of green cheese, or some nursery tales are false, or both. In translating it into ordinary language, you generally omit the words “or both” as unnecessary.
We use the words multiplication, product, factor, etc., and the signs of multiplication, or we write the two factors one after the other with no sign between them to mean that both of the two statements multiplied are true, so that ab is a statement which is true only if both the statements a and b are true, and false if either a or b is false. With the above significations it would mean that the moon is made of green cheese, and that some nursery tales are false. When we wish to signify the multiplication of a whole sum by any factor, we write that sum in parenthesis. Thus, (a + b)c would mean the product of a + b into c while a + bc would mean the sum of a and of the product of b and c; giving the above significations to a and b, and letting c mean some proverbs were false, (a + b)c, there we signify the combined statements of, some proverbs are false, and that either the moon is made of green cheese, or some nursery tales are false, while a + bc would mean that either the moon is made of green cheese, or else some proverbs and some nursery tales are false. There are certain rules which facilitate the application of these symbols to reasoning. Thus, a + a will mean neither more nor less than a written alone, so that we may write a + a = a, for a + a, according to what has been said, is that statement which is true if a is true, and is false only if a is false.
The statement aa is also the same as a standing alone, for it merely asserts the fact a twice over so that we may write aa = a. We also say that a + b is the same as b + a and that ab is the same as ba. This is usually expressed by saying that addition and multiplication are commutative operations. Also that (a + b) + c is the same as a + (b + c), and (ab)c is the same as a(bc). This is usually expressed by saying that addition and multiplication are associative operations. We also have (a + b)c = (ac + bc), for if we say that c is true and also that either a or b is true, we state neither more nor less than if we say that either both a and c are true, or both