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Introduction

I

The Decisive Year and Its Early Consequences

MAX H. FISCH

The most decisive year of Peirce’s professional life, and one of the most eventful, was 1867.

Superintendent Bache of the Coast Survey had been incapacitated by a stroke in the summer of 1864. He died on 17 February 1867. Benjamin Peirce became the third Superintendent on 26 February and continued in that position into 1874. He retained his professorship at Harvard and, except for short stays in Washington, he conducted the business of Superintendent from Cambridge. Julius E. Hilgard served as Assistant in Charge of the Survey’s Washington office. On 1 July 1867 Charles was promoted from Aide to Assistant, the rank next under that of Superintendent. He continued in that rank for twenty-four and a half years, through 31 December 1891.

National and international awareness of the Survey was extended by two related episodes beginning in 1867. A treaty with Russia for the purchase of Alaska, negotiated by Secretary of State William Henry Seward, was approved by the Senate on 9 April, but the House delayed action on the appropriation necessary to complete the transaction. Superintendent Peirce was asked to have a reconnaissance made of the coast of Alaska, and a compilation of the most reliable information obtainable concerning its natural resources. A party led by Assistant George Davidson sailed from San Francisco on 21 July 1867 and returned 18 November 1867. Davidson’s report of 30 November was received by Superintendent Peirce in January, reached President Johnson early in February, and was a principal document in his message of 17 February to the House of Representatives, recommending the appropriation. The bill was finally enacted and signed by the President in July.

Charles’s younger brother, Benjamin Mills Peirce, returned in the summer of 1867 from two years at the School of Mines in Paris. Seward wished to explore the possibility of purchasing Iceland and Greenland from Denmark. His expansionist supporter Robert J. Walker consulted Superintendent Peirce, who had his son Ben compile A Report on the Resources of Iceland and Greenland which he submitted on 14 December 1867, and which his father submitted to Seward on the 16th. With a foreword by Walker, it was published in book form next year by the Department of State. But congressional interest in acquiring the islands was insufficient and no action was taken.¹

Joseph Winlock had become the third Director of the Harvard College Observatory in 1866, and working relations between the Survey and the Observatory became closer than they had previously been. (Winlock had been associated with the American Ephemeris and Nautical Almanac from its beginning in 1852, and for the last several years had been its Superintendent, residing in Cambridge. Benjamin Peirce had been its Consulting Astronomer from the beginning. Charles had done some work for it in recent years. Assistant William Ferrel and he had observed the annular eclipse of the sun at St. Joseph, Missouri, 19 October 1865, and both had submitted written reports to Winlock which are still preserved.) By arrangement with Winlock, Charles began in 1867 to make observations at the Observatory that were reported in subsequent volumes of its Annals. In 1869 he was appointed an Assistant in the Observatory, where, as in the Survey, the rank of Assistant was next to that of Director.

In 1867 the Observatory received its first spectroscope. Among the most immediately interesting of the observations it made possible were those of the auroral light. In volume 8 of the Annals it was reported that “On April 15, 1869, the positions of seven bright lines were measured in the spectrum of the remarkable aurora seen that evening; the observer being Mr. C. S. Peirce.”

By that time, Peirce had begun reviewing scientific, mathematical and philosophical books for the Nation. His second review was of Roscoe’s Spectrum Analysis, on 22 July 1869, and it was both as chemist and as astronomer that he reviewed it. With Winlock’s permission, he reported that

In addition to the green line usually seen in the aurora, six others were discovered and measured at the Harvard College Observatory during the brilliant display of last spring, and four of these lines were seen again on another occasion. On the 29th of June last, a single narrow band of auroral light extended from east to west, clear over the heavens, at Cambridge, moving from north to south. This was found to have a continuous spectrum; while the fainter auroral light in the north showed the usual green line.²

Peirce was a contributor to the Atlantic Almanac for several years, beginning with the volume for 1868. In that for 1870 he had, among other things, an article on “The Spectroscope,” the last paragraph of which was devoted to the spectrum of the aurora borealis and the newly discovered lines.

As an Assistant both in the Survey and in the Observatory, Peirce was an observer of two total eclipses of the sun, at Bardstown, Kentucky, 7 August 1869, and near Catania, Sicily, 22 December 1870. And as late as 1894 he would write: “Of all the phenomena of nature, a total solar eclipse is incomparably the most sublime. The greatest ocean storm is as nothing to it; and as for an annular eclipse, however close it may come to totality, it approaches a complete eclipse not half so near as a hurdy-gurdy a cathedral organ.”

In 1871 the Observatory acquired a Zöllner astrophotometer and Winlock made Peirce responsible for planning its use. More of that in our next volume. And in 1871 Peirce’s father obtained authorization from Congress for a transcontinental geodetic survey along the 39th parallel, to connect the Atlantic and Pacific coastal surveys. This led to Charles’s becoming a professional geodesist and metrologist; but that too is matter for the third and later volumes. Back now to 1867.

One of the most famous cases that ever came to trial was the Sylvia Ann Howland will case, and the most famous of the many famous things about it was the testimony of the Peirces, 5 and 6 June 1867. The questions at issue were (1) whether Miss Howland’s signatures to the two copies of the “second page” codicil of an earlier will were genuine, or were forged by tracing her signature to the will itself, and (2) whether, supposing them genuine, the codicil invalidated a later will much less favorable to her niece, Hetty H. Robinson. The Peirces addressed themselves to the first of these questions. Under his father’s direction, Charles examined photographic enlargements of forty-two genuine signatures for coincidences of position in their thirty downstrokes. In 25,830 different comparisons of downstrokes, he found 5,325 coincidences, so that the relative frequency of coincidence was about a fifth. Applying the theory of probabilities, his father calculated that a coincidence of genuine signatures as complete as that between the signatures to the codicil, or between either of them and that to the will in question, would occur only once in five-to-the-thirtieth-power times. The judge was not prepared to base his decision on the theory of probabilities, but he decided against Miss Robinson on the second issue.³ In the Nation for 19 September 1867, under the title “Mathematics in Court,” there appeared a letter to the editor criticizing Benjamin Peirce’s testimony, and a long reply signed “Ed. Nation” but written by Chauncey Wright, concluding that “The value of the present testimony depends wholly on the judgment of his son in estimating coincidences, and does not depend on the judgment of either father or son as mathematical experts.” In a long article on “The Howland Will Case” in the American Law Review for July 1870 it was said that: “Hereafter, the curious stories of Poe will be thought the paltriest imitations.”

Through 1867 (and on beyond) Peirce made frequent additions to his library in the history of logic. In March and April he acquired early editions of Duns Scotus. On 1 January 1868 he compiled a “Catalogue of Books on Mediaeval Logic which are available in Cambridge”—more of them in his own library than at Harvard’s or anywhere else.

Charles W. Eliot became President of the University on 19 May 1869. Two days later he wrote to George Brush of Yale: “what to build on top of the American college.… This is what we have all got to think about.” His first thought was to try turning the University Lectures into sequences running through the academic year, with optional comprehensive examinations on each sequence at the end of the year. He arranged two such sequences for 1869–70; one in philosophy, the other in modern literature. For philosophy he enlisted Francis Bowen, John Fiske, Peirce, F. H. Hedge, J. Elliott Cabot, Emerson, and G. P. Fisher, in that order. Peirce’s fifteen lectures, from 14 December to 15 January, were on the history of logic in Great Britain from Duns Scotus to Mill. William James attended at least his seventh, on nominalism from Ockham to Mill, and wrote next day to his friend Henry P. Bowditch that “It was delivered without notes, and was admirable in matter, manner and clearness of statement. … I never saw a man go into things so intensely and thoroughly.” The Graduate School was not established until 1890, with James Mills (“Jem”) Peirce, Charles’s older brother, as Dean; but the experiment of 1869–70 was later called “The Germ of the Graduate School.”⁴

Back again to 1867. On 30 January Peirce was elected a Resident Fellow of the American Academy of Arts and Sciences. He presented three papers to the Academy at its meetings of 12 March, 9 April, and 14 May, and two further papers at those of 10 September (read by title only) and 13 November. The volume of the Academy’s Proceedings which included all five of these papers did not appear until the following year, but by November 1867 Peirce had obtained collective offprints of the first three under the title “Three Papers on Logic” and had begun distributing them. He began receiving responses early in December.⁵

The first philosophical journal in the United States—indeed the first in English anywhere—was the quarterly Journal of Speculative Philosophy, published in St. Louis and edited by William Torrey Harris. It began with the issue for January 1867. Peirce subscribed at first anonymously through a bookseller. But as soon as the collective offprints of “Three Papers on Logic” were ready, he sent Harris a copy. Harris responded with a letter dated 10 December 1867. He was especially interested in Peirce’s third paper, “On a New List of Categories.” (Peirce himself as late as 1905 called it “my one contribution to philosophy.”) In response to Harris, Peirce wrote a long letter on Hegel which he did not mail and a short letter dated 1 January 1868 which he did mail. Thus began the correspondence that led to five contributions by Peirce to the second volume of the Journal: two anonymous exchanges with the editor, and three articles under his own name in response to the editor’s challenge to show how on his nominalistic principles “the validity of the laws of logic can be other than inexplicable.” (These five contributions are examined in detail by C. F. Delaney in part II of the present introduction.)

In giving the title “Nominalism versus Realism” to the first exchange, Harris obviously meant to call Peirce a nominalist and Hegel and himself (and other followers of Hegel) realists. Peirce did not disclaim the nominalism. But was he a professing nominalist, and did Harris know that he was? And, if so, how did he know it?

That question takes us back again to 1867. At the end of the first of his “Three Papers on Logic” Peirce advocated a theory of probability for a fuller account of which he referred to his review of Venn’s Logic of Chance. In that review he called it the nominalistic theory, as opposed to the realistic and conceptualistic theories. But Venn, though he used the latter two terms, nowhere used the terms nominalism, nominalistic, or nominalist. (The terms he did use are “material” and “phenomenalist.”) Evidently, therefore, Peirce wished to make his own commitment to nominalism unmistakable.

When did Peirce become a professing nominalist? Probably in 1851, about the time of his twelfth birthday, when he read Whately’s Elements of Logic.

Where is the evidence in volume 1 of the present edition that he was a professing nominalist during the period of that volume? In what he says about the falsity of scholastic realism on pages 307 and 312 and in other relevant passages on pages 287, 306, and 360.⁶ And that he was still a professing nominalist when he began drafting his Journal of Speculative Philosophy articles, commonly called his “cognition series,” appears from what he says on pages 175, 180 and 181 of the present volume: “Thus, we obtain a theory of reality which, while it is nominalistic, in as much as it bases universals upon signs, is yet quite opposed to that individualism which is often supposed to be coextensive with nominalism.” “Now the nominalistic element of my theory is certainly an admission that nothing out of cognition and signification generally, has any generality. …” “If this seems a monstrous doctrine, remember that my nominalism saves me from all absurdity.”

But in the published form of the second article, in the paragraph on page 239 of the present volume, Peirce unobtrusively takes his first step from nominalism toward realism.⁷ “But it follows that since no cognition of ours is absolutely determinate, generals must have a real existence. Now this scholastic realism is usually set down as a belief in metaphysical fictions”—as Peirce himself had set it down on pages 287, 307, 311 and 312 of our first volume. It is the realism of Scotus to which he now commits himself. He takes a second and much more emphatic step in his Berkeley review three years later. He says there (on page 467 below) that Scotus “was separated from nominalism only by the division of a hair.” What was the hair that Scotus split, we might ask, and how did he split it? Instead, going back once more to 1867 and taking the “New List of Categories” together with the three articles of the cognition series (1868–1869) and the Berkeley review (1871), let us ask what hairs Peirce split and how he split them.

As we remarked on page xxvi of the introduction to volume 1, Peirce’s “is the first list of categories that opens the way to making the general theory of signs fundamental in logic, epistemology, and metaphysics.” We may add here that the “New List” together with the cognition series and the Berkeley review—five papers in all, and all five contained in the present volume—are now recognized as constituting the modern founding of semeiotic, the general theory of signs, for all the purposes of such a theory.⁸

Now for the hairsplitting. The Berkeley review is much more emphatic than the cognition series on the distinction between the forward and the backward reference of the term “reality” and the identification of nominalism with the backward and of realism with the forward reference. Which amounts to a semeiotic resolution of the controversy. Of the three central categories, quality is monadic, relation dyadic, and representation irreducibly triadic. The sign represents an object to or for an interpretant. But we may focus on the sign-object or on the sign-interpretant. If the question is whether there are real universals, the nominalists turn backward to the sign-object and do not find them; the realists turn forward to the sign-interpretant and find them (pp. 467 ff. below). That is primarily because the backward reference to the object is more individualistic, and the forward reference to the interpretant is more social. So realism goes with what has been called the social theory of logic, or “logical socialism.”⁹ If we were selecting key sentences from the Peirce texts in the present volume, they might well include these two: (1) “Thus, the very origin of the conception of reality shows that this conception essentially involves the notion of a COMMUNITY, without definite limits, and capable of an indefinite increase of knowledge” (p. 239). (2) “Whether men really have anything in common, so that the community is to be considered as an end in itself, and if so, what the relative value of the two factors is, is the most fundamental practical question in regard to every public institution the constitution of which we have it in our power to influence” (p. 487).

The forward reference and the community emphasis owed something to Charles’s wife Zina. By 1865 they were settled in a home of their own at 2 Arrow Street in Cambridge, and it remained their home throughout the period of the present volume. Arrow Street shot eastward from Bow Street into what was then Main Street but is now Massachusetts Avenue. The Arrow Street years were a period of experimentation and productivity for Zina as well as for Charles. Her major concerns were three: (1) reducing the burden of housekeeping drudgery for married women, (2) creating institutions to give women a voice in public affairs without their having to compete with men, and (3) higher education for women. For the first she advocated “Co-operative Housekeeping” in a series of five articles in the Atlantic Monthly from November 1868 through March 1869, when Charles’s Journal of Speculative Philosophy series was appearing. Her articles reappeared in book form in Edinburgh and London in 1870. She also took a leading part in the organization of the shortlived Cambridge Co-operative Housekeeping Society, which rented the old Meacham House on Bow Street for its meetings as well as for its laundry, store, and kitchen. For her second concern, she was active in the movement for a “Woman’s Parliament” and was elected president of its first convention in New York City, on 21 October 1869. That movement was still active under the name of “The Women’s Congress” at least as late as 1877. For her third concern, she was one of the organizers of the Woman’s Education Association of Boston, and her work in it was part of the pre-history of Radcliffe College.

Though Charles never became active in politics, he was an advocate of proportional representation. Zina made notes of his conversations with her about it, and published his views in two of her later books.

Though Zina was not a scientist, she did become a member of the international scientific community by serving, like Charles, as an observer near Catania in Sicily of the total eclipse of the sun on 22 December 1870 and by the inclusion of her excellent account of it in the annual report of the Coast Survey for that year.

Zina’s younger sister Amy Fay was a gifted pianist who, after the best training that could be had in New England, studied in Germany from 1869 to 1875 under several of its best teachers, including Tausig, Kullak, and Deppe in Berlin and Liszt in Weimar. By visiting her in Germany and by reading her long and frequent letters home, Zina and Charles became vicarious members of the international community of musicians. Zina published selections from the letters in the Atlantic Monthly for April and October 1874, and later a more comprehensive collection in book form, in a single chronological order, under the title Music-Study in Germany. It went through more than twenty editions, was translated into French and German, and is still in print. The first twelve chapters come within the period of the present volume. One of them contains a vivid account of the five days that Amy and Charles spent in Dresden in August 1870.

Within the period of the present volume Peirce became acquainted with modern German experimental psychology, as represented by Weber, Fechner, Wundt, and Helmholtz. By 1869 he was already contemplating experiments of the kind he carried out with Jastrow in 1884, which made him the first modern experimental psychologist on the American continent. He sent Wundt copies of his Journal of Speculative Philosophy papers and asked permission to translate Wundt’s Vorlesungen über die Menschen- und Thierseele, to which he refers in appreciative terms on page 307 below. Wundt’s reply thanking him for the papers and granting the permission was dated at Heidelberg 2 May 1869. No translation by Peirce was published, and no drafts have been found. A translation of the much revised edition of 1892 was published by J. E. Creighton and E. B. Titchener in 1894 and reviewed by Peirce in the Nation. When Helmholtz visited New York City in 1893, Peirce had a visit with him, and his long obituary of Helmholtz in 1894 was reprinted in Pollak’s 1915 anthology of the Nation’s first fifty years.

Back now to logic. In his Harvard University Lectures on the logic of science in the spring of 1865, a few months after the death of George Boole, Peirce had said that Boole’s 1854 Investigation of the Laws of Thought “is destined to mark a great epoch in logic; for it contains a conception which in point of fruitfulness will rival that of Aristotle’s Organon” (WI:224). In the first of his fifteen Harvard University Lectures of 1869–70 on “British Logicians,” before turning to medieval nominalism and realism, Peirce said, according to the notes of one of his students, that there was enough in Boole to “take the whole time” of the course. By 1877 the British mathematician and philosopher W. K. Clifford was ready to say that “Charles Peirce … is the greatest living logician, and the second man since Aristotle who has added to the subject something material, the other man being George Boole, author of The Laws of Thought.”¹⁰

What was the “something material” that Peirce had added? That takes us back once more to 1867, for it certainly included “On an Improvement in Boole’s Calculus of Logic.” What else? At the very least, and above everything else, the most difficult and, at least for logicians and for historians of logic, the most important paper in the present volume: “Description of a Notation for the Logic of Relatives, resulting from an Amplification of the Conceptions of Boole’s Calculus of Logic” (DNLR).¹¹ But is it not the case that, though the logic of relations can be traced back at least to Aristotle, De Morgan was the first logician to invent a notation for it? And was not that in 1860, a decade before Peirce’s memoir? Yes, but as soon as Peirce’s memoir began to circulate, there was room for the question whether De Morgan’s notation might be a dead end. In his obituary of De Morgan, Peirce said (p. 450 below) “it may at least be confidently predicted that the logic of relatives, which he was the first to investigate extensively, will eventually be recognized as a part of logic.” He did not predict, however, that it would be in De Morgan’s notation that it would achieve that recognition. But was not the Boole-Peirce-Schroder line in logic superseded by the Frege-Peano-Russell-Whitehead line? No; it was only eclipsed.

Even more intimately than with Boole and De Morgan, Peirce associated his DNLR with his father’s Linear Associative Algebra. The two appeared at almost the same time, midway between two total eclipses of the sun, but the connections between them did not become fully apparent until, after his father’s death in 1880, Peirce prepared a second edition of the LAA, with an addendum by his father and two addenda by himself, and with well over a hundred footnotes to the original text, in over sixty of which he supplied translations from the LAA formulas into DNLR formulas.

Peirce’s father had been one of the founding members of the National Academy of Sciences in 1863. Beginning in 1867, he presented instalments of the LAA at meetings of the Academy.¹² Charles’s focus on the logic of relations went back to his earliest work on his categories. A logician who had only three central categories —Quality, Relation, and Representation—was bound to return again and again to the logic of relations. Recall, for example, his remarks about equiparant and disquiparant relations in volume 1, and note what he says about mathematical syllogisms on 42 f. below. But his earliest published mention of De Morgan’s paper of 1860 was written late in 1868 (p. 245n2), and he may not have seen that paper more than a few weeks earlier. So the actual composing of the DNLR may have begun in 1869.

Then, on 7 August 1869, came the first of the two eclipses. It was observed by several teams at several points along the line of totality. Peirce and Shaler were stationed at Bardstown, Kentucky. Their report, one of the most vivid as well as detailed, was submitted by Peirce to Winlock, included in Winlock’s report to Superintendent Peirce, and published by him in the Survey’s Annual Report. It reappears on pages 290–93 below. A quarter of a century later, in an unpublished paper entitled “Argon, Helium, and Helium’s Partner,” Peirce gave an equally vivid retrospective account (Robin MS 1036).

I remember, as if it were yesterday, the first time I saw helium. It was in 1869. Astronomical spectroscopy was then in its earliest infancy. … It was impossible in those early days, for the same observer to point his telescope and to use the spectroscope; so I had brought along with me the Kentuckian geologist Shaler, a man of nerve and proved in war, to bring successively the different protuberances of the sun upon the slit of my spectroscope, while I examined the spectrum and recognized what I could.…

The observations of the sun’s corona and protuberances by the Peirce-Shaler and other teams prompted new theories as to the composition of the sun, but there was some skepticism about these theories among European astronomers. The earliest opportunity for a test of them would be the eclipse of 22 December 1870, whose path of totality was to pass through the Mediterranean. It was desirable that as many as possible of the American observers of the 1869 eclipse should be observers of the 1870 one also, and Peirce’s father began making plans to bring that about. One of these plans was to have Charles follow the path of totality from east to west several months in advance, inspecting possible sites for observation parties, reporting to his father and to Winlock, and making tentative preliminary arrangements. But if Charles was to be in Europe for six or more months and his father for two or more, those interruptions might be detrimental to the major works they had in progress. It would be advantageous to finish them before leaving, and even more advantageous to take published copies with them, each of the other’s work as well as his own, and get them that much sooner into the hands of the mathematicians and logicians they hoped to be meeting.

At the 616th meeting of the American Academy, on 26 January 1870, as reported by Chauncey Wright, its Recording Secretary, “The President… communicated by title … a paper ‘On the Extension of Boole’s System to the Logic of Relations by C. S. Peirce’.” Late in the spring, Peirce supplied final copy; it was set in type and he was given fifty copies in paperback quarto book form, dated Cambridge 1870, “Extracted from the Memoirs of the American Academy, Vol. IX,” though that volume did not appear until three years later.

Also late in the spring, since the National Academy, only seven years old, had as yet no funds for printing the papers or books its members presented, Julius E. Hilgard, a fellow member of the Academy, took Superintendent Peirce’s manuscript, had it copied in a more ornate and legible hand, and then had fifty copies lithographed from it.

When Charles sailed from New York on 18 June 1870, he took with him copies of the lithographed book and the printed memoir. In London on 11 July he delivered one of each, with a covering letter from his father, to De Morgan’s residence. On a later day he had a visit with De Morgan, who, unfortunately, was already in the final decline that ended in his death in the following March, eleven days after Charles’s return to Cambridge.

Charles presented another copy of the DNLR to W. S. Jevons, from whom he received a letter about it farther along on his eastward journey, to which he replied from Pest on 25 August (pp. 445–47 below).

Directly or indirectly, Robert Harley too received a copy. At the Liverpool meeting of the British Association for the Advancement of Science in September, Harley first presented “Observations on Boole’s ‘Laws of Thought’ by the late R. Leslie Ellis,” and then a paper by himself “On Boole’s ‘Laws of Thought’ “ (continuing one he had presented four years earlier), in which, after reviewing recent works by Jevons, Tait, and Brodie, he said: “But the most remarkable amplification of Boole’s conceptions which the author has hitherto met with is contained in a recent paper by Mr. C. S. Peirce, on the ‘Logic of Relatives’.” He proceeds to quote the passage on “the three grand classes” of logical terms that appears on pages 364–65 below, and then the sentence that appears on page 359: “Boole’s logical algebra has such singular beauty, so far as it goes, that it is interesting to inquire whether it cannot be extended over the whole realm of formal logic, instead of being restricted to that simplest and least useful part of the subject, the logic of absolute terms, which, when he wrote, was the only formal logic known.” “The object of Mr. Peirce’s paper,” he went on, “is to show that this extension is possible,” and he gave some account of the notation and processes employed.

So Clifford was not alone in thinking that Peirce was “the second man since Aristotle.” He was present at the meeting and spoke “On an Unexplained Contradiction in Geometry.” He and Peirce may have met in London in July, and he too may then have received a copy of DNLR. If not, they almost certainly met as eclipse observers near Catania in December. In any case, they became well acquainted not later than 1875.

Two brief examples now of Benjamin Peirce’s distribution of copies of LAA. In Berlin, on his way to Sicily in November, he gave two copies to our ambassador, his old friend and former colleague, the historian George Bancroft; one for himself and one to present to the Berlin Academy, of which he was a member. And in January, after the eclipse, he addressed the London Mathematical Society on the methods he had used in his LAA, and presented a copy to the Society. Clifford was present and proposed the name “quadrates” for the class of the algebras that includes quaternions, and the Peirces adopted the proposal.

From London in the last week of July 1870, shortly after the Vatican Council had declared the conditions of papal infallibility, and just as the Franco-Prussian War began, Charles journeyed eastward by way of Rotterdam, Berlin, Dresden, Prague, Vienna, Pest, the Danube, and the Black Sea, to Constantinople. Then he began moving westward along the path of totality in search of eligible sites. (He recommended sites in Sicily and southern Spain, and became himself a member of one of the Sicilian teams.) In Berlin he visited Amy Fay, and she accompanied him to Dresden, chiefly for visits to the great art museum there. In Vienna, the director of the Observatory was hospitable and helpful. From Pest, he wrote the letter to Jevons. In Constantinople he enjoyed the guidance of Edward H. Palmer, “the most charming man” he had so far known, and of Palmer’s friend Charles Drake; and he began the study of Arabic. In Thessaly he found the English consul most helpful, and the impressions he formed there he later worked up into “A Tale of Thessaly” of which he gave several readings. From Chambéry in Savoy, after his visit to Spain, he wrote to his mother on 16 November 1870, five weeks before the eclipse, that he had heard eighteen distinct languages spoken, seventeen of them (including Basque) in places where they were the languages of everyday speech.

On the whole, the American observations and inferences of the preceding year were vindicated. This was Peirce’s first experience of large-scale international scientific cooperation. He had already committed himself to the social theory of logic, but this experience and those of his four later European sojourns confirmed him in that commitment.

Julius E. Hilgard, the Assistant in Charge of the Survey’s Washington Office, which included the Office of Weights and Measures until the creation of the National Bureau of Standards in 1901, was to spend several months in Europe in mid-1872. Among other duties, he was to represent the United States at a Paris conference looking toward the international bureau of weights and measures which was finally established there in 1875. Peirce was to substitute for Hilgard in his absence, and that called for several weeks of previous training under Hilgard’s supervision. He spent most of December 1871 and part of January 1872 at the new quarters of the Survey in the elegant Richards Building on Capitol Hill, where the Longworth House Office Building now stands. Hilgard gave good reports of his progress.

Hilgard’s European sojourn would of course enhance his qualifications for succeeding Peirce’s father as Superintendent of the Survey. Peirce’s training and experience would qualify him to succeed Hilgard in case of Hilgard’s death or resignation or promotion to Superintendent. It would even qualify him, under conceivable future circumstances, to be considered for the superintendency.

The Philosophical Society of Washington (in whose name, as in that of the American Philosophical Society in Philadelphia, “philosophical” meant scientific) had held its first meeting on 13 March 1871. At its 17th meeting, on 16 December 1871, Charles presented the first of the six wide-ranging papers he presented to that Society. It was “On the Appearance of Encke’s Comet as Seen at Harvard College Observatory.”

Charles’s father was to address the Cambridge Scientific Club on 28 December 1871 on the application of mathematics to certain questions in political economy, such as price and amount of sale, and the conditions of a maximum. Charles undertook to prepare diagrams for his father to exhibit at that meeting, and these were mailed to Cambridge on or about the 19th.

Simon Newcomb, then at the Naval Observatory, called on Charles on the 17th and they conversed about these matters. (Fifteen years later Newcomb published a book entitled Principles of Political Economy on which Charles commented adversely.) In the evening after the visit Charles wrote Newcomb a letter explaining what he had meant by saying that the law of supply and demand holds only for unlimited competition, and concluded: “P.S. This is all in Cournot.” (On the strength of this letter, Baumol and Goldfeld recently included Peirce among their Precursors in Mathematical Economics.) In the same evening, Charles wrote to his wife Zina, who had remained in Cambridge, that he had been spending his evenings on political economy, and gave her some account of the questions he had been pursuing. On the 19th, he wrote a letter to his father, beginning: “There is one point on which I get a different result from Cournot, and it makes me suspect the truth of the proposition that the seller puts his price so as to make his profits a maximum.”¹³

Charles’s own principal contribution to economics, his 1877 “Note on the Theory of the Economy of Research,” will be included in our next volume, but these three letters are evidence that he brought to that particular topic a more general competence in economic theory.

But what, finally, of the Metaphysical Club at Cambridge, in which pragmatism was born? According to the best evidence we now have, it was founded not later than January 1872, after Peirce’s return from Washington. The introduction to volume 3 will resume the story at that point. But from a consecutive and careful reading of the present volume it will already be evident that pragmatism was the natural and logical next step.

II

The Journal of Speculative Philosophy Papers

C. F. DELANEY

The Journal of Speculative Philosophy papers of 1868–69 fall into two quite distinct groups. The first set is composed of a series of interchanges between C. S. Peirce and W. T. Harris (the editor of the journal) on issues of logic and speculative metaphysics that emerge from the philosophy of Hegel. The second set of papers, quite different in tone, consists of Peirce’s classic papers on cognition and reality, and the relatively neglected concluding paper of the series on the grounds of validity of the laws of logic.

1.

The Peirce-Harris exchange on Hegelian logic and metaphysics was occasioned by Harris’s review article entitled “Paul Janet and Hegel” which appeared in his own journal. This was a long critical review of Janet’s Etudes sur la dialectique dans Platon et dans Hegel, published in Paris in 1860. The exchange itself consists of letters from Peirce to Harris, two of which the latter transformed into dialectically structured discussion articles for his journal.

After some extensive preliminaries about the spread of Hegelianism, the original Harris article (like Janet’s book that it reviews) focuses on Hegel’s logic and follows Janet’s tripartite division into “The Beginning,” “The Becoming,” and “The Dialectic.” In the section labeled “The Becoming” Harris takes issue with Janet’s account of the relation of Being and Nothing and the consequent genesis of Becoming. This is the problem that interested Peirce, and in his initial letter (24 January 1868) he takes issue with Harris’s own account of the matter. These comments, together with his own replies, Harris published under the title “Nominalism versus Realism.”

Peirce’s criticisms take the form of five inquiries seeking clarification. Initially he raises some general questions about Harris’s doctrine of abstraction; then he raises three sets of questions about what he understands to be Harris’s three arguments for the identity of Being and Nothing; finally he suggests, contrary to what he takes to be Harris’s view, that the ordinary logical strictures against contradiction should at least have the presumption in their favor. Harris’s response to these criticisms is most interesting, particularly in the light of Peirce’s mature philosophy. He maintains that the tone of Peirce’s initial set of questions about abstraction suggests that Peirce is committed both to nominalism and to a doctrine of immediacy, and that Peirce’s consequent specific criticisms of his three arguments bear his suspicion out. Peirce’s specific objections draw on formal logic’s strictures against contradiction which, Harris maintains, are only adequate to the immediate world of independent things. But, Harris concludes, if one is to be a true speculative philosopher one must transcend this nominalism and become a realist.

Needless to say, Peirce thought that this response totally missed the point. In his follow-up letter, he makes the suggestion that a great deal of the misunderstanding between them may flow from certain unclarities with regard to the term “determined” as it functions in the discussion of Being and its determinations. He distinguishes several senses of “determine,” “abstract,” and “contradiction” in an attempt to move the discussion forward. Again, Harris published these comments together with his own terse responses, this time under the title “What Is Meant by ‘Determined’.”

One of the most obvious characteristics of this interchange on Hegel’s logic is the marked difference between Harris’s sympathy with the dialectical logic of the Hegelian tradition and Peirce’s employment of ordinary formal logic. Harris’s request that Peirce do something for his journal on the rationale of the objective validity of the laws of logic is a happy outgrowth of this basic difference between the two. In his letter of 9 April 1868 Peirce responds that he has already devoted considerable time to this subject and could not adequately treat the issue in less than three articles. He enclosed the first of his three classic 1868 papers on cognition.

2.

Peirce’s 1868 papers on cognition, reality, and logical validity bring up the questions that were to be central throughout his whole philosophical career. In these he articulates his many-faceted attack on the spirit of Cartesianism, a spirit which he sees dominating most of modern philosophy. The Cartesian concern with skeptical doubt, individual justification, immediate knowledge and certainty (which traits he also saw in the empiricists), he seeks to replace by a view of knowledge that was through and through mediate, that construed knowledge as both an historical and communal human activity. From this perspective on knowledge, he proceeds to work through a concept of intersubjectivity to a full-blown account of objectivity, truth, reality, and the basis of the validity of the laws of logic.

The first piece included here is MS 148, consisting of three separately titled sections listed as “Questions on Reality” in the Contents. The third section, entitled “Questions concerning Reality,” is an early version of the first published paper in the series, “Questions Concerning Certain Faculties Claimed for Man,” but it is most interesting in its own right. In the first place, it is an heroic attempt to handle in a unified way all the issues that would eventually be divided among the three published papers in the 1868–69 series. The unity of the overall project is brought out forcefully in the introductory paragraph of the piece. Here Peirce makes the point that the logician’s initial concern is with the forms of language but that he must inevitably push on from here to consider what we think, that is, the manner of reality itself; and, as a precondition for this inquiry, must get clear about the proper method for ascertaining how we think. His order of treatment, then, is, first, to give an account of cognition; secondly, to give an account of truth and reality; and, finally, to deal with some issues of formal logic. It is instructive to note that all three of these topics are treated under the general heading “Questions concerning Reality,” indicating a metaphysical thrust that might be overlooked given the final titles: “Questions Concerning Certain Faculties Claimed for Man,” “Some Consequences of Four Incapacities,” and “Grounds of Validity of the Laws of Logic: Further Consequences of Four Incapacities.”¹⁴ It is further instructive to glance over the twelve questions Peirce poses for himself in the outline given in the first section of MS 148 and observe how they reappear in the three published pieces.

The first six questions have to do with an account of thinking and with the methodology appropriate in generating such an account; and it is these six questions that make up the substance of the first published paper in the series, “Questions Concerning Certain Faculties Claimed for Man.” The central issue is whether we have any immediate knowledge at all (of ourselves, our mental states, or the external world) and Peirce answers in the negative. In the process he distinguishes between intuition (cognition not determined by a previous cognition) and introspection (internal cognition not determined by external cognition) and defends an account of knowledge construed as a thoroughly mediated inferential sign process. A linchpin of his argument is a methodological stance that favors any account of mental activity that abides by the normal conventions of theory construction, a stance which shifts the burden of proof to those accounts wherein some special faculties are claimed for man. Peirce concludes by adding as a novel seventh question some summary material that appears at the end of “Questions concerning Reality” dealing with some general arguments against the thesis that there is no cognition not determined by a previous cognition.

There are two short pieces entitled “Potentia ex Impotentia” also included here. These are early versions of beginnings of the second published paper, “Some Consequences of Four Incapacities,” and again are interesting in their own right because of some methodological points therein. First, Peirce makes the general comment that on the one hand we should begin our philosophizing simply with those beliefs we have no reason to call into question, but, on the other, we should not maintain an attitude of certainty on matters concerning which there is real disagreement among competent persons. In short, our philosophizing should be continuous with our commonsense ways of dealing with the world about us. Secondly, he makes a series of provocative statements about the present state of philosophy and the methods of explanation that should be employed in philosophy. The state of philosophy he likens to the state of dynamics before Galileo; namely, a theater of disputation and dialectics with little by way of established results. In this state, he maintains, what is called for is not conservative caution (as would have been called for in mechanics where much was truly established) but rather bold and sweeping theorizing to break new ground and put the area in order. Peirce does not mean that our metaphysical speculation should be uncontrolled and irresponsible but that it should be guided by the various different tangible facts we have at our disposal without any pretense to demonstration, certainty, or finality. We should content ourselves with the probable forms of reasoning that are so fruitful in physical science and congratulate ourselves if we thereby reduce the uncertainty in metaphysics to one hundred times that of these sciences. It is in this spirit of speculation that one should view the sweeping theory of mental activity he articulates in “Some Consequences of Four Incapacities.”

In the first published paper in this series Peirce had suggested, in opposition to the Cartesian account, that all knowing involved an inferential sign process. In the second paper in the series he takes up the task of articulating in some detail his own theory of the structure of mental activity, that is, the structure of the internal sign process that is involved in knowing. Constructing this account, he is guided by his methodological strictures to the effect that any account of the internal (mental activity) must be in terms of the external (publicly accessible objects) and that, given the postulation of one structure, another is not to be introduced into the theory unless there are facts impossible to explain on the basis of the first.

Focusing on our public sign system, that is, language, as the paradigmatic external manifestation of mental activity, Peirce proceeds to construct an account of mental activity in terms of “inner speech.” Furthermore, he develops an holistic form of this tradition in which the basic mental unit is not the concept (the mental word) or even the judgment (the mental sentence) but rather the process of reasoning itself (the mental syllogism). Since it is then the structure (rather than the matter) of the sign process that is of primary importance, Peirce accordingly construes the process as one of drawing inferences, as syllogistic in nature. Next, drawing on his formal accounts of deduction, induction, and hypothesis, he proceeds to give an account not only of thinking but also of the other forms of mental activity (sensation, emotion, and attention) in terms of his syllogistic model. His final extrapolation of the model enables him to give a speculative account of the mind itself.

The third paper in the published series, “Grounds of Validity of the Laws of Logic: Further Consequences of Four Incapacities,” picks up some of the remaining questions outlined in MS 148 and finally comes to grips with Harris’s original challenge which had been the impetus for all three papers, namely, how can Peirce account for the objective validity of the laws of logic? The theories of cognition and reality were developed for the sake of providing just such an account, an account which begins with a justification of deduction and then broadens out to encompass a philosophical grounding of the general logic of science.

The point of continuity with the previous pieces is Peirce’s claim that every cognition results from an inference and that the structure of all mental activity is inferential. Can’t the question be raised—what reason do we have to believe that the principles of inference are true or correspond to anything in the real world? While not purporting to take seriously the stance of the absolute skeptic, Peirce does think it incumbent upon him to provide an account of the objective validity of the logical principles of inference. He proceeds to give an account of the validity of deduction, induction, and hypothesis; and his proffered “justifications” invoke the characteristic Peircean concepts of truth (as the ultimate agreement of investigators), reality (as that which is represented in that agreement), and community (as the ultimate ground of both logic and reality).

It would be difficult indeed to overstate the importance of these three papers in the Peircean corpus. That Peirce himself saw them as central is clear from his designation of them as Chapters 4, 5, and 6 of one of his major projected works, the 1893 “Search for a Method.” Most later commentators have seen them as the key to his overall philosophical orientation.

III

The 1870 Logic of Relatives Memoir

DANIEL D. MERRILL

Peirce’s “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of Boole’s Calculus of Logic” (DNLR) is one of the most important works in the history of modern logic, for it is the first attempt to expand Boole’s algebra of logic to include the logic of relations. The complex mathematical analogies which govern parts of this work make it obscure in spots; but the main thrust of its important innovations may be seen by placing it in the context of Peirce’s earlier logical studies, and by relating it to the work of Boole, De Morgan, and Benjamin Peirce.

The logical substructure of DNLR is a modified version of Boole’s algebra of classes, in which Peirce had shown an early interest.¹⁵ One modification is the use of the “inclusive” sense of logical addition, which Peirce had introduced by 1867.¹⁶ The other main modification is the replacement of Boole’s equality or identity sign (=) by the sign of illation or inclusion () as the sign for the fundamental logical relation. While this replacement may have been primarily dictated by formal considerations, it was an important step on the road to a less algebraic approach to the logic of classes.

To this basically Boolean structure, Peirce adds a notation for relations and for operations upon relations, as well as laws governing those operations. Even then, though, the influence of Boole remains strong. While Peirce admits logical relations between relations, he most often considers logical relations that hold between class terms of which relation terms form a part.

Peirce’s interest in the logic of relations can be traced to several sources.¹⁷ Published and unpublished papers prepared around 1866 show a strong interest in the problems which relation terms present for the theory of categories.¹⁸ They are also concerned with different types of relations, such as the distinction between relations of equiparance and relations of disquiparance. His work at this time also shows an interest in arguments involving relations and multiple sub-sumptions. Such an argument is “Everyone loves him whom he treats kindly; James treats John kindly; hence, James loves John.” Peirce’s early treatment of these arguments is rather conservative, either reformulating them so as to apply the usual syllogistic forms, or using some principle of multiple subsumption which is construed as a natural generalization of the syllogism.

Unfortunately, the origins of the more powerful and, indeed, revolutionary techniques of DNLR are more obscure.¹⁹ Only two surviving documents provide a sustained insight into their origins. One is the so-called Logic Notebook (LN), which carries entries from 3 to 15 November 1868 in which several notations are devised and some basic identities are shown. Only the rudiments of DNLR may be found here. The same is true of the other source, a series of notes that Peirce wrote at about the same time to add to a projected republication of his American Academy papers of 1867. Note 4 in this set shows how an algebraic notation may be used to validate the following argument, which De Morgan had claimed could not be shown to be valid by syllogistic means:

Every man is an animal.

Therefore, any head of a man is a head of an animal.

Most unfortunately, the surviving parts of LN have no entries from 16 November 1868 through 5 October 1869, nor is there any other document which would allow us to trace the development of these techniques.

Peirce’s references to De Morgan in DNLR, as well as an undated comparison (in LN) between his notation and De Morgan’s, raise the question of De Morgan’s role in stimulating the work which led to DNLR.²⁰ It must be noted, though, that there is little direct biographical information on this issue, and that Peirce’s later recollections are contradictory and even inconsistent with known facts.

Peirce apparently initiated an exchange of papers with De Morgan in late 1867, as a result of which De Morgan received a copy of Peirce’s “Three Papers on Logic” (the first three American Academy papers) by May 1868. In a letter dated 14 April 1868, De Morgan had promised to send Peirce a copy of his classic paper of 1860 on the logic of relations,²¹ but there is no direct evidence that this was ever sent. Nevertheless, Peirce had seen De Morgan’s paper by late December 1868, since he refers to it in another paper sent to the printer at that time.²² It is thus very likely that Peirce had read De Morgan’s paper before he wrote the entries in LN dated November 1868, even though those entries carry no clear references to De Morgan and use quite different examples.

Biographical issues aside, Peirce’s initial work in the logic of relations is significantly different from De Morgan’s. The most important difference is that while De Morgan was interested primarily in the composition of relations with relations, Peirce is concerned with the composition of relations with classes. Thus, while De Morgan’s paradigm is an expression such as “X is a lover of a servant of Y,” Peirce is first concerned with such expressions as “lover of a woman.” A predilection for class expressions is found even in DNLR, though this is often combined with the composition of relations, as in “lover of a servant of a woman.” This emphasis upon class expressions seems to reflect the Boolean frame of reference in which Peirce was working.

De Morgan also considered two types of “quantified relations.” The first is “X is an L of every M of Y,” which is expressed by Peirce as “involution,” or exponentiation. Even here, the LN shows him more concerned with the composition of a relation and a class, as in “lover of every woman,” than with strictly relational composition. The other form of quantified relation is “X is an L of none but M of Y,” a form which Peirce only considers in the section on “backward involution” which he added to DNLR shortly before it was printed (pp. 400–408).

These comparisons between De Morgan and Peirce make their relationship problematic. It becomes more so in view of the fact that some of De Morgan’s most dramatic results involve the contrary and the converse of a relation. While Peirce deals with contraries throughout LN and DNLR, he did not consider converses in the 1868 portions of LN, and he only deals with them in that section of the DNLR which he added at the time of printing.

We may conclude that while Peirce probably knew of De Morgan’s memoir on relations when he was working out the full notation of DNLR, his own Boolean orientation meant that he was working on these topics in his own way.

While DNLR is primarily a contribution to logic, parts of it may also be related to the developments in algebra to which his father contributed. During the years 1867–69, Benjamin Peirce presented a series of papers to the National Academy of Sciences which resulted in a book entitled Linear Associative Algebra (LAA) which was privately published in 1870, and then republished with notes by C. S. Peirce in 1881.²³ In it Benjamin Peirce surveyed all the types of linear associative algebras which can be constructed with up to seven units, enormously generalizing such algebras as that of complex numbers (of the form a • 1 + bi) and Hamilton’s quaternions (a • 1 + bi + cj + dk). In the subsection on Elementary Relatives in DNLR, Peirce conjectured that all linear associative algebras could be expressed in terms of elementary relatives, which he then proved in 1875²⁴ and illustrated in his notes to his father’s book. This technique formed the foundation for the method of linear representation of matrices, which is now part of the standard treatment of the subject.

As in the case of the relationship of the DNLR to De Morgan’s paper, its relation to his father’s LAA is difficult to estimate accurately. Certainly they were working on these long papers at about the same time, so that some influence would not be surprising. In a short letter to his father that has been dated 9 January 1870, Peirce writes:

I think the following may possibly have some interest to you in connection with your algebras. I have been applying Boole’s Calculus to the Logic of Relative Terms & in doing so have got (among other operations) an associative non commutative multiplication. It is like this. Let k denote killer, w wife, m man. Then

kwm denotes the class of killers of wives of men

The letter then concludes with the colleague-and-teacher example which is found in the Elementary Relatives section of DNLR (pp. 408–11). While this letter shows that Peirce was thinking of his father’s work as he completed DNLR, it also suggests that the relationship between the two papers may not be very intimate.

DNLR was communicated to the American Academy of Arts and Sciences on 26 January 1870 and printed in the late spring. The exact time of its printing is uncertain, though it must have been printed by 17 June 1870 when Peirce left for Europe. He carried with him a letter of introduction from his father to De Morgan, to whom he apparently delivered copies of his memoir and his father’s book. Although there is no contemporary record of Peirce’s visiting De Morgan, he planned to do so and recalled such a meeting in later years. But the meeting could not have been a very happy one, since De Morgan was in very poor health by that time and incapable of sustained logical or mathematical discussion.

The Boolean substructure of DNLR consists of inclusion and the usual Boolean operations of addition (x + y), multiplication (x,y), and class complementation (1 —x), along with their standard laws. To illustrate the relational notation, let s = servant, l = lover, and w = woman. The most important notations are relative multiplication (sl, servant of a lover), relative involution (sl, servant of every lover), backward involution (sl, servant of none but a lover), and converse of a relation ( s, master). Invertible forms of several of these operations are also given. Relation expressions and class expressions may be combined, as in “s^w” (servant of every woman) and “s^(lw)” (servant of every lover of a woman). Boolean operations may be applied to relations as well as to classes, so that, for instance, “(s + l)” means “either a servant or a lover.”²⁵

While DNLR is largely devoted to the logic of two-place relations, Peirce also includes a rather confusing discussion of “conjugative terms,” which stand for three-place relations. This is a marked advance over De Morgan’s restriction to two-place relations, but Peirce’s attempts to deal with this topic within the framework of DNLR present many problems of interpretation.

In addition to outlining a notation, DNLR contains a great many principles which may be easily interpreted in the modern logic of relations. Some significant identities are

There are also a great many inclusions, such as

along with chains of inclusions involving combinations of operations, as in

The complement of a relation is treated not only in a Boolean way, but also as an operation upon a relation, as is the operation of forming the converse of a relation. De Morgan’s principles governing these operations are given in Peirce’s notation. The universal and null relations are introduced, and their laws are stated.

While Peirce does not attempt to develop the laws of his notation in a deductive manner, he does provide demonstrations of a sort for many of his laws, especially in the section entitled “General Method of Working with this Notation” (pp. 387–417). In the first subsection on Individual Terms, many intuitively valid laws are demonstrated by reducing inclusions between classes to individual instances. In addition to its discussion of backward involution and conversion, the subsection on Infinitesimal Relatives contains the most elaborate mathematical analogies in the memoir, with very puzzling applications of such mathematical techniques as functional differentiation and the summation of series. The subsection on Elementary Relatives relates his own work to Benjamin Peirce’s linear associative algebras.

For all its importance, the Logic of Relatives memoir presents many problems of interpretation. Perhaps the most serious issue is whether 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.