Writings of Charles S. Peirce: A Chronological Edition, Volume 2. Charles S. Peirce

Peirce is dealing with relations or with relatives—that is, with the relation of being a servant, or with such classes as the class of servants or the class of servants of women. His choice of the term “relative” suggests a desire to distinguish his project from De Morgan’s, but in some cases his terms clearly stand for relations. The situation is complicated by the fact that many terms, such as “servant,” can stand for either a relation or a relative, depending upon the context. Perhaps it is safest to say that he deals with both relational and relative terms, but that he usually treats relational terms within the context of relative terms. While this seems true in general, the interpretation of particular formulas still remains puzzling.

      Other serious issues concern his treatment of conjugative terms and his elaborate and obscure mathematical analogies. More generally, one may ask whether DNLR is best studied by translating it into standard symbolic logic or by considering it in its own right. With the benefit of hindsight, DNLR cries out for the modern theory of quantifiers, to which Peirce was to make important contributions. Nevertheless, the core of its notation is of considerable power and can be studied separately. It remains of interest to those modern logicians and mathematicians who have taken an algebraic approach to the study of logic.²⁶

      ¹Ben began a promising career as a mining engineer at Marquette, Michigan, but died near there at the early age of twenty-six, on 22 April 1870.

      ²P. 288 below.

      ³Nevertheless, she married Edward H. Green later in 1867 and, as Hetty Green, was on her way to becoming “the witch of Wall Street.”

      ⁴In the interim, from 1872 to 1890, there had been a small “Graduate Department” and Jem, as secretary of the Academic Council, had been its administrator.

      ⁵He later obtained and distributed collective offprints of the fourth and fifth papers.

      ⁶This is a good point at which to remind our readers that even a twenty-volume edition of Peirce’s writings is only an anthology, and that statements about his views based on the anthology may be falsified (or at least may seem to be falsified) by writings it omits. Our first volume, for very good reasons, omits MS 52 (921). If it had been included, it would have come between pages 33 and 37. Past the middle of it there is a leaf whose recto was headed at first “Of Realism & Nominalism. 1859 July 25.” The “& Nominalism” was later deleted. The recto continues:

      It is not that Realism is false; but only that the Realists did not advance in the spirit of the scientific age. Certainly our ideas are as real as our sensations. We talk of an unrealized idea. That idea has an existence as neumenon in our minds as certainly as its realization has such an existence out of our minds. They are in the same case. An idea I define to be the neumenon of a conception.

      That is all. But on the verso there is a “List of Horrid Things I am.” They are: Realist, Materialist, Transcendentalist, Idealist. Why did Peirce delete “& Nominalism”? We can only guess. He was not yet twenty. Perhaps he had confused the sense of realism in which it is opposed to idealism with that in which it is opposed to nominalism, but settled on the former.

      ⁷For details see Max H. Fisch, “Peirce’s Progress from Nominalism toward Realism,” Monist 51(1967):159–78, at 160–65.

      ⁸For details see Max H. Fisch, “Peirce’s General Theory of Signs,” in Sight, Sound, and Sense, edited by Thomas A. Sebeok (Bloomington: Indiana University Press, 1978), pp. 31–70 at 33–38 and, for Berkeley, pp. 57, 63, 65. For Peirce’s early nominalism and its probable derivation from Whately, see also pp. 60–63. (It is worth adding here that Boole in An Investigation of the Laws of Thought after an introductory first chapter begins the investigation with Chapter II “Of Signs in General, and of the Signs appropriate to the science of Logic in particular; also of the Laws to which that class of signs are Subject”; and that Chapter III is headed “Derivation of the Laws of the Symbols of Logic from the Laws of the Operations of the Human Mind.”)

      ⁹Karl-Otto Apel, Charles S. Peirce: From Pragmatism to Pragmaticism, translated by John Michael Krois (Amherst: University of Massachusetts Press, 1981), pp. 53, 90, 153,196, 213nl07. Gerd Wartenberg, Logischer Sozialismus: Die Transformation der Kantschen Transzendentalphilosophie durch Charles S. Peirce (Frankfurt: Suhrkamp, 1971).

      ¹⁰John Fiske, Edward Livingston Youmans (New York: D. Appleton and Co., 1894), p. 340. (From a letter of Youmans reporting a visit with Clifford.)

      ¹¹See part three of the present introduction, by Daniel D. Merrill, and the literature there referred to.

      ¹²At a meeting of the much older American Academy of Arts and Sciences on 12 October 1869, “Professor Peirce made a communication on his investigations in Linear Algebra.”

      ¹³Cf. Carolyn Eisele, Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce (The Hague: Mouton, 1979), pp. 58 f., 251 f., and The New Elements of Mathematics by Charles S. Peirce, edited by Carolyn Eisele (The Hague: Mouton, 1976), 3:xxiii-xxvii.

      ¹⁴It was probably Peirce’s intention to use the title “Questions concerning Reality” for his first published article, but Harris advised against this in a letter of about 15 April 1868, and Peirce replied on 20 April: “Your remark upon my title is very just. I will make it ‘Questions concerning certain Faculties claimed for man’.”

      ¹⁵See Emily Michael, “An Examination of the Influence of Boole’s Algebra on Peirce’s Development in Logic,” Notre Dame Journal of Formal Logic 20(1979): 801–6.

      ¹⁶See “On an Improvement in Boole’s Calculus of Logic,” item 2 below, pp. 12–23.

      ¹⁷See Emily Michael, “Peirce’s Early Study of the Logic of Relations, 1865–1867,” Transactions of the Charles S. Peirce Society 10(1974):63–75.

      ¹⁸This interest culminates in “On a New List of Categories,” item 4 below, pp. 49–59.

      ¹⁹See Daniel D. Merrill, “De Morgan, Peirce and the Logic of Relations” Transactions of the Charles S Peirce Society 14(1978):247–84.

      ²⁰Ibid. See also R. M. Martin, “Some Comments on De Morgan, Peirce, and the Logic of Relations,” Transactions of the Charles S. Peirce Society 12(1976):223–30.

      ²¹Augustus De Morgan, “On the Syllogism, No. IV, and on the Logic of Relations,” Transactions of the Cambridge Philosophical Society 10(1864):331–58.

      ²²”Grounds of Validity of the Laws of Logic: Further Consequences of Four Incapacities,” item 23 below, pp. 242–72.

      ²³American Journal of Mathematics 4(1881):97–229, and as a separate volume paged 1–133 (New York: D. Van Nostrand, 1882).

      ²⁴“On the Application of Logical Analysis to Multiple Algebra,” Proceedings of the American Academy of Arts and Sciences n.s. 2(1874–75):392–94, which will be published in volume 3 of the present edition.

      ²⁵For analyses and interpretations of DNLR, see Chris Brink, “On Peirce’s Notation for the Logic of Relatives,” Transactions of the Charles S. Peirce Society 14(1978): 285–304; R. M. Martin, “Of Servants, Lovers and Benefactors: Peirce’s Algebra of Relatives of 1870,” Journal of Philosophical Logic 7(1978):27–48; Jacqueline Brunning, “Peirce’s Development of the Algebra of Relations,” diss. Toronto 1981; and Hans G. Herzberger, “Peirce’s Remarkable Theorem,” in Pragmatism and Purpose: Essays Presented to Thomas A. Goudge (Toronto: University of Toronto Press, 1981), pp. 41–58.

      ²⁶Alfred Tarski, “On the Calculus of Relations,” Journal of Symbolic Logic 6(1941):73–89.

      Writings of Charles S. Peirce

      Volume 2

      [The Logic Notebook]