Introduction to Volume 5
The years 1884-1886 were a time of transition for Peirce. When the period began, he intended to make Baltimore his permanent home, confident that his connection with Johns Hopkins was secure. His main work in life would be logic. But he soon learned of the fateful resolution of the Johns Hopkins Executive Committee that his contract would not be renewed, and he knew that his days there were numbered. After his shock had subsided and he had reluctantly yielded to the inevitable, his focus shifted back to his scientific work for the Coast and Geodetic Survey. During these years he probably spent more time on science, either with pendulum observations or with the reduction of scientific data and the preparation of reports, than on all other activities combined. He was on location for the Survey much of the time; almost continuously between July 1884 and February 1886 he directed pendulum operations at a succession of sites extending from Washington, DC to Key West, Florida and Madison, Wisconsin. It might have been a time of passage to a long and influential career in science, but a scandal led to Peirce's estrangement from the Survey and considerably dampened his enthusiasm for government service. By 1886 his scientific interest shifted from gravity research and metrology to such subjects as the study of color and the history of science, which were outside his sphere of responsibility for the Survey, and after the brief resurgence of his enthusiasm for science, philosophy came again to dominate his thought.1
These years mark the end of what Max Fisch calls Peirce's "cosmopolitan period," a time devoted mainly to science and frequent travels in Europe and throughout the United States and Canada.2 That period began in June 1870, when Peirce sailed for Europe to arrange for scientific observations of the 22 December solar eclipse,3 and ended in April 1887, when he and his second wife, Juliette, moved to Milford, Pennsylvania, a Pocono Mountain resort town. The following year the Peirces settled on a farm on the Delaware River just outside Milford in the home they would soon name "Arisbe," and in the years that followed, except for frequent trips to New York City (some for extended intervals) and occasional trips to Cambridge, Peirce stayed in Pennsylvania.
From a different point of view, that of Peirce's intellectual growth, the years 1884-1886 mark a new beginning. According to Murray Murphey, this is the start of the fourth and final phase of Peirce's intellectual development, stemming from his discovery of quantification and set theory.4 In 1883 Peirce's Johns Hopkins student Oscar Howard Mitchell had introduced indices into algebraic logic in a way Peirce recognized as the key to quantification.5 Over the following months (see items 20-22), Peirce developed a theory of quantification that by 1885 (items 30-32) took a very modern form. At about the same time, he first came into contact with the work of Georg Cantor (see MS 530), which must have been a stimulus for the investigations he had already begun on number theory. He had probably also begun to reflect deeply on the nature of continuity, for by 1 April 1884, while working on the definition for the Century Dictionary, he lamented that "continuity" had never been adequately defined: "Kant's definition, to which I am ashamed to say I have hitherto given my adhesion, is ridiculous when you come to think of it" (MS 528).6 By that time Peirce had begun to formulate his unique theory of the continuum that would ground his anti-Cantorian set theory (and theory of number). His discovery of the quantifier and set theory marks the beginning of a major phase of his intellectual development because, as Murphey has shown, Peirce was forced to make major revisions to his theory of reality and to his categories. 7 The groundwork for this final period in Peirce's thought was laid in works included in the present volume.
Peirce wrote or published over one hundred papers and reports between 1884 and 1886, ranging in subject matter from the measurement of sensations and the price of sugar to the algebra of logic and philosophical categories. Most of the fifty-eight items included in the present volume belong to science, logic, or philosophy; the Study of Great Men, which fills eighty pages (items 2-19), was described by Peirce as comparative biography, and thirty-two pages (item 57) are devoted to definitions of words beginning with the letter "e" that Peirce drafted for the Century Dictionary. At least one paper (item 24) belongs most appropriately with psychology, and there are four private letters and several reviews.
For much of this three-year period the Peirces were
itinerant. They stayed in Baltimore for the first
half of 1884, where Peirce's contract with Johns Hopkins
ran until September, but spent the summer in Virginia,
where Peirce was conducting gravity experiments and
looking for sites for new pendulum stations. They
were in Washington for much of the latter part of 1884
and the first part of 1885, where from October to February
Peirce was in charge of the Office of Weights and Measures
and directed pendulum operations at the Smithsonian.
From March 1885 through February 1886 the Peirces
traveled for extended visits to Key West, Ann Arbor,
Madison, and Ithaca, all on Coast Survey business.
Finally in 1886, engaged only in local operations
and soon to be relieved of fieldwork so that he could
devote his time to preparing reports, he settled down
in New York City, where he and Juliette stayed until
their move to Pennsylvania the following year.
The year 1884 may have been the worst of Peirce's life (although Joseph Brent's biography reveals that there were bitter years still ahead). Peirce and Juliette had been married for only a few months and had hardly settled into their newly leased house when they learned of the decision by the Johns Hopkins trustees to let Peirce go.8 It is clear nowthough it was not thenthat Peirce's dismissal was a sign that society could not tolerate his disregard for its conventions. His unique and somewhat arrogant individuality was too much at odds with the tenor of the times, and especially the conservatism of Baltimore. (Ironically, in less than a decade Peirce would express grave reservations about the American propensity to regard one's character as an individual as more important than one's social character.) By mid-year Peirce and Juliette knew that they would have to give up their Baltimore house and dispose of the elegant home furnishings they had so painstakingly chosen. The shock and disappointment of this turn of events led to ill-health and despair. 9
It must have come as a relief when in July 1884 Peirce was assigned to Fort Monroe in Virginia to make gravity determinations, and then to reconnoiter for one or two more stations in the mountains of the Virginias and North Carolina. Traveling with Juliette, Peirce arrived at Fort Monroe at the bottom of Chesapeake Bay on 23 July and proceeded to set up a station. The Superintendent's Report for the fiscal year ending June 1885 (P 331) indicates that only Peirce Pendulum No. 3 was swung and that Peirce was pleased with the results. In addition to gravity measurements, Peirce experimented with the use of an instrument, called a noddy, for measuring the swaying of the pendulum support and worked up some theoretical results for the 1884 Report (item 42). In September Peirce looked for new mountain stations, but not finding any that met the Superintendent's specifications, he returned to Washington toward the end of the month and on 1 October was put in charge of the Office of Weights and Measures, an agency of the Coast Survey.
Peirce began his tenure with a great deal of energy and enthusiasm and even announced to Superintendent Julius Hilgard that he would write a book on the history of standards. Before year's end he had traveled to Boston, Providence, Hartford, New York, and Philadelphia and had met with electricians and manufacturers of gauges and other machinery in order to determine how best to meet the need for metrical standards as recommended by the U.S. Electrical Conference. In mid-October he attended the scientific session of the National Academy of Sciences in Newport, where he presented three papers: "On Gravitation Survey" (P 281), "On Minimum Differences of Sensibility," co-authored with Joseph Jastrow (P 282), and "On the Algebra of Logic" (P 283). His paper on logic must have been a preview, along the lines of items 20-22, of the paper he would soon finish for the American Journal of Mathematics (item 30). The paper on gravity surveys elaborated on a program for future gravity determinations that Peirce had proposed to Hilgard in his 1 October letter (item 23) and that was summarized in the 24 October issue of Science (pp. 396-97):
While in Newport he took time to investigate an old stone mill to try to determine what standard of length had been used for its construction, probably thinking that he might help settle a dispute about the mill's origin. He argued that the construction of such a building would have required a "drawing to scale" and therefore a unit of length, which he assumed was either the English or Norse foot. In December he published his findings in Science (item 26) and might have established himself in the popular mind as an authority in the field of measurementbut alas, his conclusions favored a Norse origin for the mill and it was soon revealed that it was English (which fact had already appeared in print).10 In fairness to Peirce it must be said that he stated his purpose as purely metrological and that he had deliberately declined to offer an archeological opinion.
On 30 December 1884 Peirce attended the meeting of the American Metrological Society at Columbia College in New York City. He read a paper on the determination of gravity (P 270) and gave an account of his measures of the Old Stone Mill. He also participated in a discussion of the adequacy of the standards of weight and measure in the United States and pointed out some of the deficiencies in the current system. As a result of his revelations, the Society passed a resolution recommending the appointment of a committee to advise Congress on the need for establishing an efficient bureau of standards.
Peirce had managed to finish this difficult year with a burst of energy. Perhaps he had resigned himself to a non-academic life and had readjusted to the idea of a life of science. Toward the end of the year, he began a series of five lengthy occupations that would continue to the end of January 1886, at stations in Washington, Key West, Ann Arbor, Madison, and Ithaca. The occupations began at the Smithsonian, where all four Peirce Pendulums were measured (compared to standards) in preparation for the elaborate fieldwork ahead, and continued there under his direction through February 1885.
Probably the most important of Peirce's scientific writings to appear in print in 1884 was his "Determinations of Gravity at Allegheny, Ebensburgh, and York, Pa., in 1879 and 1880" (item 1). It had been scheduled to appear in two previous Coast Survey Reports, but he had not been able to finish it because he was overextended with his dual appointment at Johns Hopkins. It is an important work, in part because it connects American geodetic methods and results with European geodesy. Another 1884 publication, Observations with the Meridian Photometer During the Years 1879-1882 (P 271), makes heavy use of Peirce's scientific findings, in particular his Photometric Researches (P 118).
When his Johns Hopkins classes ended in the spring of 1884, Peirce might have stopped his university related research, but a momentum had built up that carried him along for several months. In the fall of 1883 he had begun teaching a course on the psychology of great men, a subject he had found interesting since boyhood. As early as 1860, in his "Private Thoughts," he had reflected on greatness and had concluded that a great man should be revered "notwithstanding his mistakes" (W1:5). The subject of human character was a topic of general interest and was addressed on more than one occasion at the Johns Hopkins Metaphysical Club: the work of Francis Galton was discussed on at least two occasions, and William James's "Great Men, Great Thoughts, and the Environment" was the topic for one meeting. A special interest of Peirce while at Johns Hopkins was the application of statistics to different subjects, and comparative biography lent itself to the illustration of statistical investigations that depended largely on impressionistic data. Some years later Peirce wrote that he had "cast about for a subject that might afford valuable training in such inductive investigation [as] the members of my class might need in future life and which they would not be likely to acquire in their other classes" (CP 7.256). The course, although poorly enrolled (like many of Peirce's other courses), was an apparent success. A carefully thought out program was followed that involved reading standard biographies and extracting relevant information (the question of relevance having been settled beforehand), compiling impressionistic lists of great men (and a few women), and submitting the resulting data to statistical examination. The study was carried on informally by Peirce and his students after the course had ended, apparently up to the time of his final departure from Baltimore near the end of 1884. In the absence of a complete record of the research it is unclear how far the study had progressed by then, and it seems likely that results were spread among the papers of the participants. The parts that are published here (items 2-19) give only a sampling of the methods and results as preserved in pages that remain with the Peirce Papers, and it may appear that the study never achieved any considerable success. But later discussions in Peirce's writings11and references to the study made by Jastrow suggest otherwise. When in 1894 the American educator Albert Yoder asked G. Stanley Hall, then of Clark University, about the study of greatness, Hall referred him to Peirce. Some years after he had left Baltimore, possibly stimulated by the 1891 publication of The Man of Genius by Cesare Lombroso and the 1892 New Calendar of Great Men (based on Comte's positivist calendar),12 Peirce's interest in the old study was rekindled. An invitation to give the 1892 Lowell Lectures led Peirce to write to Augustus Lowell suggesting his "Comparative Biography of Great Men" as a topic for the series:
Peirce took up the study again at the turn of the century and in 1901 published a paper on "The Century's Great Men of Science." In a manuscript related to that paper (Harvard MS 1125), Peirce explained more fully his distinction between eminent men and truly great men:
When Peirce recalled the original course of study, it was always with the greatest fondness for his students: "It was one of those matchless classesthe very salt of the earth,which it was my privilege to enjoy in Baltimore."
Peirce taught two courses in the spring of 1884: one was the second half of his advanced logic course and the other a course on probabilities. His last two advanced logic students were Henry Taber and Joseph Jastrow. Taber had planned to write his dissertation on logic but after Peirce's dismissal had to give it up because, as he explained in a letter to Paul Weiss dated 3 September 1931, Peirce's successor "was quite ignorant of formal logic except the very rud[i]ments." Taber held Peirce in high esteem: "I have been told that James, or perhaps it was Royce, I have forgotten which, had said that Peirce impressed him as potentially the most powerful intellect he had ever known. I would certainly subscribe to this estimate of Peirce's powers."
Peirce's other advanced student, Jastrow, went on to become a respected psychologist and a well-known debunker of the paranormal.14 In addition to logic (and probability theoryboth Jastrow and Taber took the course on probabilities along with five other students, including William E. Story), Jastrow studied experimental psychology independently with Peirce. In his 1930 autobiography Jastrow said that "it was Charles S. Peirce, one of the most exceptional minds that America has produced, who stimulated me most directly." 15 Peirce suggested to Jastrow that they undertake an experiment to test Fechner's claim that human sensations are subject to a limitation he called a Differenzschwelle (the minimum perceptible difference of sensation). Below this threshold it was said to be impossible to discern differences of intensity. Peirce and Jastrow conducted elaborate experiments between 10 December 1883 and 7 April 1884 that constituted the first psychological investigation undertaken at Johns Hopkins and one of the earliest studies in experimental psychology in North America. 16 Peirce described the experiment in a letter to Simon Newcomb dated 7 January 1908:
They had good reason to be content. Their report (item 24), presented to the National Academy of Sciences on 17 October 1884 and published in the Academy's Memoirs in 1885, is described by Stephen M. Stigler as unexcelled in the nineteenth century and "a good example of a well-planned and well-documented experiment today.".18 Stigler points out that the study was the first to employ a "precise, mathematically sound randomization scheme," and also the first to require subjects to state their confidence in their choice (weight A is lighter or heavier than weight B) and to choose even when the level of confidence was zero. Ian Hacking, who also discusses the experiment, points out that Peirce's understanding of the importance of randomization was at least three decades ahead of his time. 19 Yet Peirce's idea was forcefully rejected by E. B. Titchener for being out of touch with psychological reality, and it was not reintroduced until R. A. Fisher's Design of Experiments appeared in 1935.20 Hacking also remarks on the interesting last paragraph of item 24 where Peirce and Jastrow indicate that their conclusion has important bearings on such questions as women's insight and telepathic phenomena. The word "telepathy" was less than two years old, according to Hacking. It is noteworthy that at about this time the American Society for Psychical Research was being formed (an organizational meeting was held in Boston on 23 September) to "ascertain the truth in regard to the alleged psychical phenomena" and to expose "charlatan spiritualism." 21
In addition to his gravimetric work, his Johns Hopkins classes and the study of great men, and his work with Jastrow, as well as other activities not yet considered, Peirce somehow managed to devote very productive time in 1884 to algebraic logic. In his 1880 paper in the American Journal of Mathematics (W4: item 19) he had given the first definitions of logical addition and multiplication suitable for modern Boolian algebra and, as Arthur Prior has shown, the system developed in that paper, with only slight enhancements, gives a complete basis for the classical propositional calculus.22 The paper was intended as the first part of a much longer work on formal logic, but, though Peirce started several continuations (see items 20-22), certain difficulties and discoveries held him back. The greatest difficulty concerned the problem of distribution, which had arisen as a result of his claim that he could easily prove the law of distribution but had omitted a proof because it was too tedious. Ernst Schröder rejoined that Peirce must be mistaken because the independence of one of the distribution principles could be demonstratedthus showing that the full law could not be proved. Peirce was convinced at first that Schröder was right but later reasserted that distribution could indeed be proved for his system. His position is often said to amount to the claim that every lattice is distributive, but that is almost certainly a misconstrual of Peirce's views.23
Between 1880 and 1885 Peirce developed a conception of truth values (a sentence has the value v if it is true or f if it is false) and created a semantics for his algebraic logic. Items 20-22 show him in the process of discovery. Stimulated no doubt by Schröder's 1883 paper to the British Association for the Advancement of Science, which argued against Peirce's distribution claim, but also by his 1882 edition of his father's Linear Associative Algebra and the recent publication of Studies in Logic, Peirce filled these short manuscripts with brilliant flashes of insight. In addition to the systematic introduction of truth values, we find an early statement of truth-function analysis ("it is clear that the truth of a general formula may be tested by trying whether it will always hold when either v or f is substituted throughout for each letter" [p. 112]), the development of quantifiers (following their anticipation in W4: item 66) and remarks about their significance for distinguishing logic from mathematics, the groundwork for "Peirce's law", matrix representations of universes of discourse, the idea that the elementary logical operations are insertion and deletion (item 20), and a great deal more. The idea that the copula of inclusion might be abandoned in favor of disjunction and conjunction with rules only for insertion (amplification) and deletion (simplification), an idea Peirce got from Mitchell, may be seen as the forerunner of the idea on which Gentzen based his system of natural deduction.24 As late as the summer of 1884 Peirce was still working on a continuation of his 1880 paper, but within a few months he would be ready to relegate reference to the earlier paper to a footnote in what would become his most influential work on logic.
Peirce had delivered his (and Jastrow's) paper on minimum sensibility to the National Academy in October. The success of that study may have encouraged him in his use of statistical methods, for it was soon followed by a paper on the "Success of Predictions" (item 25) in which, according to Stigler, he derived "a latent structure measure of association for 2 X 2 tables."25 In this work Peirce addresses the question whether meteorologists could successfully predict tornadoes. He finished the year with a discussion in the pages of the New York Evening Post and the Nation on the economics of the sugar trade with Cuba (items 27-28).
The year 1884 had been difficult, but by its end Peirce had reoriented himself to a life of science. He was ready to start the Smithsonian occupation, the beginning of more than a year mostly on locationaway from Baltimore! And he had his definitions to write for the Century Dictionary, something he had been working on for over a year. Perhaps the worst was over.
By a cruel turn of events, Peirce had hardly settled himself to the harsh reality of his dismissal from Johns Hopkins when he had to face a whole new episode of bitter and painful events. It began without much fanfare as a broad investigation of four federal scientific agencies which had outgrown their original charters: the Geological Survey, the Coast and Geodetic Survey, the Signal Service of the U.S. Army, and the Hydrographic Office of the U.S. Navy. The investigation was conducted by a joint commission of the U.S. Senate under the chairmanship of Senator William B. Allison of Iowa and was undertaken to examine the structure and operation of the four agencies for economy, efficiency, legality, and utility.26 The Commission heard testimony from more than fifty federal employees between 4 December 1884 and 28 February 1885 and in a subsequent session about a year later. Peirce was called to testify on 24 January, one of only ten Survey employees questioned by the Commission. Even though he had been in charge of the Gravimetric Survey for many years, he was questioned almost exclusively about the work of the Office of Weights and Measures, which he had directed only since October 1884. This may have had something to do with the 30 December 1884 resolution of the American Metrological Society, for the Commission's questioning and Peirce's testimony (item 29) bear a marked resemblance to the discussion at Columbia one month earlier. Peirce made it plain that many, if not most, of the standards in the United States were in great need of improvement. One example that caught the interest of the commissioners was that the hollow brass weights used to weigh out gold for coins minted at Philadelphia and Denver actually measured out different amounts of gold because of the buoyancy of air. The result was that coins minted at Denver contained too much gold. Peirce's testimony before the Allison Commission and the resolution of the American Metrological Society were the first two steps toward the creation of the National Bureau of Standards.27
In the course of about four months as head of the Office of Weights and Measures Peirce had established a noticeable momentum toward an improved agency. He had written to Superintendent Hilgard on 27 September with an impressive plan for his first six months of service, including the preparation of at least five reports on metrological research (including his long-awaited report on the spectrum meter), some new computations and comparisons, an inventory of instruments and records, the commencement of an index of results, the preparation of a history of instruments and standards, and the systematic collection of foreign publications on metrology for the library. Given Peirce's obvious enthusiasm, it is surprising that on 22 February 1885, less than five months after his appointment, Peirce declined further service as head of Weights and Measures. The reason for his action was revealed to Simon Newcomb in a letter dated 10 June 1899: "[I] only left because [Hilgard's] physical condition was such as to cause me embarrassment which I thought required me to quit Washington."28 Hilgard's condition would soon be revealed to the world.
It is not clear whether the findings of the Allison Commission directly damaged Peirce or the Coast Survey, but the mere fact that the investigation was conducted revealed that federal science in America was entering a new age, a time when the value of work would be judged by its immediate practical (economic) benefits. When Grover Cleveland took office in March as the 22nd president of the United States, and his Democratic Party took control of the government, anti-scientific sentiment had won the day. Dedicated to reducing the federal bureaucracy, Cleveland found a ready target in the Coast Survey.29
On 25 July 1885 the Washington Post broke a story with the headline, "Exhorbitant [sic] Expenditures. Coast Survey Officials Suffer Penalty for Extravagance. Superintendent Hilgard Suspended, Several Subordinates Dismissed and an Investigating Committee Appointed." The Post announced that the Treasury Department had for some time been dissatisfied with the Coast Survey accounts and, after an audit, had found them to be "entirely unsatisfactory." Cleveland had dismissed Hilgard and had appointed Frank M. Thorn, chief clerk of the Internal Revenue Bureau, to head a commission to take charge of the Coast Survey office and to conduct a full investigation. On 7 August the Post reported that "the actual condition of the office of [the] survey was one of demoralization, and its workings [were] inefficient, unjust, and to some extent disreputable." Hilgard was accused of misappropriating federal funds and was reported to be an alcoholic, which was widely known and probably contributed to the decision of the Treasury Department to investigate the Survey.30 In a paragraph dealing with Peirce, it was reported that for several years he had been performing pendulum experiments "without restriction or limitation" and that the "meager value" of his work was substantially destroyed by its cost. Peirce was shocked and indignant. He wrote a letter of protest and rebuttal from Ann Arbor on 10 August that was published four days later in the New York Evening Post (P 300) and later in Science (P 317). His chief concern, the main reason for his indignation, was that unscientific men had been permitted to judge the importance of his work and had judged it to be of "meager value." 31 He announced that he would resign if that estimate was accepted by the Survey. It is to Peirce's credit that the scientific community, even within the Survey, immediately came to his defense. Charles A. Schott wrote to Benjamin A. Colonna: "I trust you will be able to induce Mr P. to reconsider his action and for the sake of the scientific reputation of the Survey, continue the work, now that we are on the eve of reaping the practical benefit of his researches." And at the 28 August 1885 executive meeting of the American Association for the Advancement of Science a resolution was passed on Peirce's behalf which chastised the Treasury Department for referring the question of the value of scientific work to non-scientists. The Association recognized that an ominous note had been sounded by the Cleveland administration and perhaps foresaw that the shift of power from scientists to bureaucrats would bring about a period of decline for pure science in America. Its resolution urged that the head of the Coast Survey "should be appointed by the President, with the advice and consent of the Senate," and "should have the highest possible standing among scientific men and should command their entire confidence." Peirce's scientific reputation had been vindicated. Still the scandal was a great strain on him. In October he wrote to William James that
About six months later, the Allison Commission found that the Geological Survey, headed by John W. Powell, was extravagant in its operations and sought passage of a congressional bill to restrict its work and limit its publications. Again the scientific community was outraged and none more than Peirce. He wrote to Powell assuring him of strong support within the Coast Survey and proposed a plan of attack: "Let the congressmen hear of science, no longer as merely giving reasons, but as an interest, saying We want so and so.... There are a hundred votes in the house to be commanded in this way."32
Tumultuous though it was, 1885 was one of Peirce's most productive years in the field. On 1 March, after concluding the Smithsonian occupation and within a few days of his resignation from Weights and Measures, Peirce left for Key West. He set up a station in an Army barracks which he occupied until 1 May. Using only Peirce Pendulum No. 2, he discovered that the residual difference between gravity in Washington and Key West was smaller than he had expected. From the Superintendent's Report on Peirce's work for the year ending June 1885, it appears that the Key West results helped determine his next major assignment.
By this time Peirce should have been able to replace the somewhat defective American-made set of (Peirce) pendulums that he had designed a few years earlier. He had ordered new pendulums from Gautier in Paris during his final European assignment in 1883 but had been directed by Hilgard to return to Washington before they were finished. As a result of a series of inadvertencies, including possibly some disingenuousness on the part of Gautier, communications broke down between the Coast Survey and the Paris manufacturerand it became a matter of some dispute who if anyone was at fault. As it turned out, the Gautier pendulums were never acquired, and this became the cause of both regret and embitterment for Peirce.33
In July Peirce was directed to make a reconnaissance for an east-west line of three or four stations approximately along the forty-third parallel and as far west as the Mississippi River. Peirce chose Ann Arbor, Madison, and Ithaca and, in August, began operations in Ann Arbor. The American Association for the Advancement of Science held meetings in Ann Arbor while Peirce was stationed there, and it was then that the executive committee passed its resolution of support for him. Operations at the University of Wisconsin began early in October and continued throughout the month. The station was set up in Library Hall (today called Music Hall), which had a clock connected to the University's Washburn Observatory. Peirce's main contact at the University was Edward S. Holden, Director of the Observatory, with whom he became very friendly (and with whom he would correspond for many years). From Madison Peirce proceeded to Ithaca, where work began by early December. En route the Peirces passed through Niagara Falls, where because of a miscalculation on Peirce's part, compounded by the delay of a payment from Washington, they were "stranded" for fifteen days. Being stranded in Niagara was not altogether a bad thing, as is revealed in a letter to Holden dated 8 January 1885: "Mrs. Peirce doesn't progress very fast. We stayed a fortnight in Niagara & that did her ever so much good." Peirce spent some of that time working on mathematical problems related to "the effect of the air on the period of the pendulum" (Peirce to Thorn, 7 November 1885), a problem in hydrodynamics that had never been satisfactorily treated. He was impressed with the Falls and frequently referred to it in illustrations in subsequent writings (see especially item 54). Peirce arrived in Ithaca on 19 November 1885, where he found his foreman demoralized because of the delay. By the end of the month Peirce had discharged the man and had hired a Cornell graduate student to replace him. Peirce's host at Cornell was E. A. Fuertes, Dean of the Faculty of Engineering, who so greatly impressed Peirce that he worked behind the scenes to get him appointed as superintendent of the Survey. Operations in Ithaca continued to the end of January.
At each of these stations, and then again at the Smithsonian, Peirce swung Peirce Pendulums Nos. 2 and 3 (a meter and yard respectively). A description of the procedures employed for these operations appeared in the 1886 Report, which illustrates the laboriousness of gravity determinations (for which the data were hand-recorded for subsequent manual reduction and computation).
The paper that resulted from this series of occupations was Peirce's second major memoir on gravitythe first was his "Measurements of Gravity at Initial Stations in America and Europe" (P 161; W4: item 13)and, according to Victor Lenzen, would have been an influential work in geodesy had it appeared in 1890 when Peirce finally had it ready for publication.34 But on the advice of Newcomb, then Superintendent of the Coast Survey Thomas C. Mendenhall declined to print Peirce's memoir (P 285) and, having decided that Peirce's usefulness to the Survey had come to an end, asked for his resignation.
Two papers appeared in 1885 as appendices to the 1884 Coast Survey Report and both deal with Peirce's investigations of the flexure of pendulum stands. "On the Use of the Noddy" (item 42) describes a method he devised for measuring flexure, and "Note on the Effect of a Pendulum upon its Period of Oscillation" (item 43) discusses the degree of disturbance caused by flexure, an effect which he concluded must be considerable "for all the reversible pendulums which have ever been constructed." In the second paper Peirce introduced the expression "kinetic potency" to avoid using the more standard expression "potential energy," which he said "grates upon the ear of a student of Aristotelian philosophy."
Except for his scientific work and the Coast Survey scandal, logic dominated Peirce's life, at least until August. As a result of the stimulating insights of the summer of 1884 and the realization that he had moved too far from his 1880 paper (W4: item 19) to write a second part, he refocused his attention on a new formalization of logic, self-consciously motivated by his notational discoveries. In the new paper, "Algebra of Logic: A Contribution to the Philosophy of Notation" (item 30), Peirce considered the different kinds of signs necessary for a fully adequate logic system, and he concluded that it is necessary to have tokens (conventional or general signs, usually called symbols), indexes (demonstrative signs), and icons (signs of resemblance). This is the first published application of his revised theory of signs to algebraic logic, which he had begun to formulate in item 22.35
It is in this paper, appearing February 1885, that Peirce introduces truth-values in giving his decision procedure for theoremhood, and the first theorem proved by that method is his fourth icon, (((p< q) <p) < p), which marks the difference between classical and positive logic.36 The axioms for first-order logic are given in the first five icons, although the fourth (the negation principle) can be used to reduce Peirce's basis to the Tarski-Bernays axiomatic system for implicational logic.37 Here quantifiers are first introduced in their standard form and Peirce anticipates the modern distinction between first- and second-order logic. 38 Furthermore, he provides the basis for a complete quantification theory with identity 39 and in his discussion of procedures for working with his calculus shows remarkable insight into modern methods, even introducing something very much resembling what today is called Skolem normal form. The paper was widely read and had considerable influence on the development of symbolic logic. It is cited as a key work by many notable logicians, including Peano, Whitehead, Lewis, and Tarski; and through Schröder, Peirce's most influential follower, its results reached many others, including Löwenheim and Skolem. Lukasiewicz often quoted the first paragraph of Part II to show that Peirce was a precursor in conceiving of many-valued logics.40 Even Bertrand Russell read the paper (along with the 1880 paper) at the turn of the century,41 but how much he was influenced by Peirce, directly or indirectly, is far from clear. In addition to its place in the history of exact logic, for which it is justly acclaimed, item 30 represents an advance in semiotic theory and an important stage in Peirce's systematic thought.42
Throughout the early months of 1885 and into the summer, Peirce worked on a continuation of item 30, which he justly believed set the stage for a whole new era in logic. On 25 June he wrote to William James: "I have not sent out any copies of my new memoir ... because the paper is not yet completed & the most important part of it is to come. But I consider it as the beginning of a new life for Formal Logic." When he had finished the second part, which extended his theory of quantification and what he called his general algebra of logic, he submitted it to Newcomb, then editor of the American Journal of Mathematics. (J. J. Sylvester, who had agreed in principle to publish it, had returned to England to take up a chair at Oxford.) Newcomb read Peirce's paper and agreed to publish it only if Peirce said that it was mathematics, not logic. Peirce refused and the paper was rejected.43 He retold this incident to James in August 1905 and, as he often did, gave him a lesson in logic at the same time. In explaining how to draw certain inferences in his general algebra of logic, he made use of the principle [Pi]xlxx -< [Pi]x[Sigma]ylxy, which led him to reflect:
Item 31 appears to be part of the paper Newcomb rejected. Together with the related item 32logical investigations carried out over a six-day stretch in Mayit represents logic in its most advanced state until after the turn of the century.
Except for logic and the revision of his theory of signs, Peirce had not wrestled with philosophy for over a yearsince his lecture on design and chance. But sometime during the summer of 1885 he turned again to speculative philosophy. Several events and circumstances stand out as instrumental in Peirce's return to philosophy at that time. There was the Coast Survey scandal that thoroughly demoralized him and destroyed his commitment to federal service and a life of experimental science, and there was Newcomb's rejection of his pioneering logic paper, which dampened his enthusiasm for that most formal and technical branch of philosophy. These two events led Peirce to close off avenues he might otherwise have followed, which helped clear the way for his resumption of speculative philosophy. His travels to Michigan, Wisconsin, and Cornell may also have played a part; perhaps someone at one of the universities re-ignited his enthusiasm for philosophy, or perhaps Peirce deliberately turned to philosophy as the field most likely to secure him a teaching position. Brent speculates that Peirce may have had something like that in mind,45and certainly it is clear that he wanted a university post. He had written to James in June about giving a fall course at Harvard, and in October he wrote to his brother James Mills (usually called Jem) that teaching was the life he desired. He knew from his experience at Johns Hopkins (and with Newcomb) that logic was not very marketable, and may therefore have decided to recast his academic profile in the direction of traditional philosophy.
Possibly all these factors played a part in Peirce's shift of focus back to philosophy in the summer of 1885, but probably the most influential event was the publication of Josiah Royce's Religious Aspect of Philosophy, which appeared mid-year. In his book Royce argued for the existence of God from the possibility of error and, almost as a challenge to Peirce, defended his position against the "modern Thrasymachus" who held that all we can conclude from the possibility of error is the possibility of God. Peirce recognized himself as the modern Thrasymachus and took up the challengeand in doing so, according to Fisch, "turns some of the will-bes of his Popular Science Monthly series into would-bes, and thereby takes a short step from his earlier nominalistic pragmatism toward his later realistic pragmaticism."46 Peirce wrote a long review (item 33) for Edward L. Youmans's Popular Science Monthly, but, as he explained to William James in a letter of 28 October, it was never printed: "I wrote to Youmans,at his particular request,a notice of Royce's book. I was a long time over the book & wrote I thought something really very good, for me; but Youmans wouldn't print it, i.e. he made such a wry mouth that I relieved him of it." In the review, Peirce criticized Royce's idealism as being too much like that of Hegel, whose "capital error ... which permeates his whole system in every part of it is that he almost altogether ignores the Outward Clash." Peirce repeated the thesis of item 30, that three kinds of signs are indispensable in all reasoning, and emphasized the necessity for indexes to refer to individuals: "one such index must enter into every proposition, its function being to designate the subject of discourse." There is no doubt that Royce's book, in conjunction with his own recent discoveries in logic and his revised theory of signs, had a profound effect on Peirce. It was then that Peirce returned to his categories and to a reassessment of Kant.
In an unfinished draft of the review (MS 540), Peirce reflected that Kant's entire system of thought stood on his logic, in particular on his analysis of propositions. He then mused:
If we assume then that the logical distinctions of propositions are necessarily involved in reasoning and take their origin in the nature of the human mind, then so also do these conceptions, cause, reality, etc., which are essentially presupposed in those distinctions.... Thus, the whole system of Kant depends upon the truth and necessity of the system of formal logic which furnishes these distinctions of propositions. If the latter system is artificial, the Kantian philosophy must fall to the ground; yet even then it would seem that there must be in place of that a true system which would be based in a similar way upon the correct analysis of formal logic.
But, he concluded, Kant's system is artificial: "the traditional distinctions of propositions rest nearly all of them upon mere accidents of language." In Kant's wake, Peirce was ready to put forward "the correct analysis of formal logic" upon which "a true system" of thought might be founded: "there are three conceptions which enter necessarily into formal logic at every turn and under a thousand shapes,namely, the ideas of First, Second, and Third; or, more accurately expressed, An, Other, and Medium." Here we have a preview of what was to come, a new architectonic system of thought based on Peirce's categories to replace Kant's. In his finished review, but more intensely in items 34-37, Peirce worked out the revisions to his theories of categories and signs in his quest for "the correct analysis of formal logic." These papers constitute the spadework for his new system of thoughthis architectonic evolutionary philosophyand are the precursors of his book "One, Two, Three."
Three reviews from the latter part of 1885, which are included in the present volume, may have contributed toor resulted fromthe resumption of Peirce's interest in speculative philosophy. In November Peirce reviewed Raymond Perrin's Religion of Philosophy for the Nation (item 39). Even though he was thoroughly unimpressed with the book, it is interesting that Perrin's purpose, revealed in the paragraph-long full title, was to reduce "the categories of thought, or the most general terms of existence, to a single principle, thereby establishing a true conception of God." Around the same time Peirce reviewed Thomas K. Abbott's translation of Kant's Introduction to Logic (item 40) and John Fiske's The Idea of God (item 41). The review of Kant's Logic is unfinished, but there is enough to see that Peirce's reassessment of Kant occasioned by his response to Royce is uppermost in his mind. In his one-paragraph review of Fiske, unpublished and probably unfinished, he refocuses directly on the old "Design and Chance" conceptions of evolution and chance, but perhaps more importantly on what elements are necessary for explaining the "whole development of the world." Peirce mentions in particular Fiske's claim that the events of the universe are the result neither of chance nor of blind necessity, and he counters that "minds ... formed under the influence of physical science" hold that events are brought about by force and chance and that the place of freedom, if granted at all, is very limited as compared with that of necessity. Of course Peirce was one of the physical scientists who granted a small, though profoundly important, role for freedom. A fourth review in late 1885of Clifford's Common Sense of the Exact Sciences published in the Nation on 3 September (item 38)does not address architectonic or cosmological questions of the sort touched on above, but it does contain an early indication of Peirce's relativismabsolute position in space and absolute velocity have no meaning. Also in the review is an interesting reference to the ideas of Peirce's old school friend Francis Ellingwood Abbot, who was within a few days of finishing his Scientific Theism.
In the closing months of 1885, Peirce formulated the general outlines of the project that would grow into his 1887-88 "Guess at the Riddle." Although there is no full articulation of his guess to be found in the writings of 1885, it is clear from the final incomplete paragraph of item 35 that he had already made it. In his 25 October letter to Jem (quoted below), he spoke of the "momentous thing" he had to say and on its importance for molecular science and psychology. Three days later he wrote to William James (in the same letter in which he mentioned his review of Royce): "I have something very vast now.... It is ... an attempt to explain the laws of nature, to show their general characteristics and to trace them to their origin & predict new laws by the laws of the laws of nature."
Peirce spent the first month of 1886 swinging pendulums in Ithaca, but was back in New York by 1 February. On the 3rd his brother Jem held a reception for him in Cambridge. Abbot was there and wrote of the proceedings in his diary:
Peirce had written to Abbot from Ithaca (items 44 and 45) about his new book, Scientific Theism, and had probably already written the review that appeared in the 11 February issue of the Nation (item 46). Abbot, more the iconoclast than Peirce, had spun his own cobweb which, if not glistening, was at least alluring. Abbot's would be the second book of the period to exert a considerable influence on the course of Peirce's thought.
Having just returned from directing pendulum operations at three major universities and, as a matter of prudence, still planning for a life of science, Peirce might have held forth on a topic related to experimental science. But Abbot's diary reveals what purpose had taken hold of Peirce's mind. Three months earlier, on 25 October, Peirce had written to Jem:
Peirce was "straining at the bit" to get back to work on his neo-Kantian architectonic, but Survey work would keep him from it for a few months longer.
After his return from Ithaca Peirce took charge of pendulum operations at the Stevens Institute in Hoboken, where the British Kater pendulums had to be measured before their return to Herschel, and again at the Smithsonian to remeasure the pendulums he had used for the operations of the past year. But as Peirce had anticipated, the Survey was changing with Thorn in control, and it soon became apparent that leadership in geodetic science was being transferred to Schott.47 Thorn did make an effort to bring Peirce around to his own way of doing things, perhaps out of a genuine appreciation of his powers, but more likely because Peirce represented a great investment on the part of the Survey; however, he never grasped the full seriousness of Peirce's ordeal nor its disruptive effect on his capacities. Peirce, of course, wanted to proceed with his plan for gravity determinations as set out in his letters to Hilgard of 1 October 1884 (item 23) and 30 June 1885 (and reiterated in a letter of 27 October 1885 to Thorn), but he was swamped with volumes of unreduced data from years of work that had to be turned into publishable reportswhich was all Thorn seemed to want. He did manage to get three short papers into print in 1886 (items 51-53) which took some account of the 1885 work at Key West, but there was still an abundance of data on gravity and on flexure to be worked up for publication and, more importantly, a major unfinished paper on the spectrum meter which represented a great outlay of time and money. There was also the report on the 1882-83 gravity work in the Arctic, carried out for Peirce by the ill-fated Greely party. Lieutenant Greely returned from Lady Franklin Bay late in 1884 to a hero's welcome, and he made it known that the work he had carried out for Peirce was for him a matter of much satisfaction. Two years had passed since he had handed over the Arctic gravity records to Peirce, and he was anxious for results. 48 There was also a lot of unreduced data from various less extensive operations, some gravitational and others metrological, and to make matters worse, Peirce now had a mass of data from the just completed gravity operations in Washington, Ann Arbor, Madison, and Ithaca. 49
In the Survey scandal of the previous year, one of the main criticisms of Peirce had been that his work was of "meager value." It is true, of course, that however great its potential, his results were not of much use until the raw data were reduced and reports were written for publication. Thorn saw the risks and in August officially relieved Peirce of his field duties so that he might devote all his time to preparing his reports.50 He wrote to Peirce on 26 October: "It seems to us here that the feeling in Congress indicates that the whole future of the pendulum work of the Survey will depend upon your success in giving us some systematic work and adequate returns for the thousands of dollars already spent in pendulum research." Thus came the end of Peirce's long period of leadership in geodetic science for the Survey.
The year 1886 was a watershed in Peirce's intellectual life. It was the year when his guess at the riddle of the universe became fully articulated and then grew into the hypothesis that would guide the course of his thought for years to come. By the summer, when he began writing the book that was to set out his new system of thought (items 47-50), the guess was featured in his opening chapter:
On 20 August Peirce wrote to Holden at the University of Wisconsin that his "evolutionist speculation" had grown into "a great working hypothesis of science, destined to play a great part in the future." He said that the skeleton of his ideas had "filled itself out on the philosophical side, so that my book will be a real manual of philosophy, leaving no question untouched."
It is remarkable how many lines of thought came together at this pointhow many influences led Peirce to his guess. The story is too complex to be given here in fullthe best account so far is by Fisch51 but a sketch of some of the main factors will further illustrate the significance of the writings of the present volume.
With his 17 January 1884 lecture on design and chance Peirce had taken a stand on the question of determinism, declaring that absolute chance was a real agency in the evolution of the universe and even in the evolution of law itself. This thesis became a fundamental doctrine of his evolutionary cosmology and was a major factor in preparing him for his guess. It is important to remember, however, that the path to "Design and Chance" was itself very complex and that the roots of Peirce's tychist logic extend deep into his early thought.52
Although the general thesis of an evolving universe, a universe subject to the originating influence of absolute chance, was crucial to his guess, it was not in itself sufficient. It might be more accurate to say that the key was his theory of categories, which had virtually lain dormant since first expounded in 1867 (W2: item 4). Only after he had revived his theory of categories, stimulated by his study of Royce, was Peirce ready to make his guess. But what was also revived by the study of Royce was Peirce's Kant-inspired attraction for architectonic philosophy, for system building, and the belief that in his categories he could improve on Kant. By the end of 1885 Peirce knew that by combining his evolutionary speculations with his revived and revised categories he was on to something vast.
It is not clear exactly when he started thinking of his project as the elaboration of a guess or when he first conceived of his guess as solving the riddle of the universe in the fullest senseso that everything would be included within the scope of his solution. A number of factors have already been mentioned that probably led Peirce to think along those lines, including the books he reviewed in 1885. Another important factor was his work for the Century Dictionary, which led him to reconsider Greek philosophy. Fisch emphasizes that nearly all the Greek philosophers were evolutionary cosmologists and he flatly states that "it was by way of the Greeks, and especially by way of Empedocles, Aristotle, and Epicurus, ... that Peirce arrived at his own evolutionary cosmology."53 In his earliest sketch of the book that was to present his new system of thoughtin thirteen chapters, beginning with a chapter on fundamental conceptions and ending with one on theismPeirce related his purpose to that of pre-Socratic philosophy: "I am going ... to propound a hypothesis about the constitution of the universe," he began, and then pointed out that the "very first philosophical conception that appeared in early Greece was that of primal matter" (pp. 294, 295). He then defended the pre-Socratic approach to the problem of accounting for the world, which was to "first determine where their account was to begin." That called for a guess! "Now every intellectual undertaking must in its inception strike out with an original ejaculation of thought. A guess has always to be made" (p. 296). It may have been these reflections that led Peirce to cast his cosmological speculations as a guess at the riddle of the universe. Thus his great project had both a distinct Kantian characterits rigorous architectonic structure with its foundation in the categoriesand an equally distinct Greek characterits evolutionary and cosmological approach self-consciouly grounded on a guess.
In considering how Peirce reached the mature conception of his cosmological project, a factor not to be left out is the influence of Abbot. When Peirce had written to Abbot in December 1885 and again in early 1886 about Scientific Theism, he had said little to indicate that he was impressed with the scope of the book, which is in some respects suggestive of Peirce's own cosmological project. It was a sort of manifesto for a "scientific theism" and introduced the Scientific Method as the new deity: "the head has been too long sacrificed to the heart in religion."54
Abbot asserted that "the great principle of the Infinite Intelligibility of the Universe is the corner-stone of Scientific Theism" and that the key to philosophy and to the explanation of the universe lies in the conception of organic teleological evolution, not in the mechanistic ideas of Spencer and Haeckel.
In his letters and review Peirce appears to have been mainly interested in Abbot's theory of reality, especially as it concerned relations. Initially he opposed Abbot: "I am not only phenomenalist, but also idealist" (p. 280)two positions Abbot abhorred. But before long he had been converted to Abbot's view, and in his definition of "realism" for the Century Dictionary Peirce included a lengthy quotation from Scientific Theism as the primary illustration. In his first letter Peirce had indicated that he agreed with Abbot's "universal endocosmic teleology," although he showed little interest in his cosmology. But it is interesting that Abbot mentions "Sphinx-riddles" very near the time when Peirce began to conceive of his projected book as his "Guess at the Riddle" and not long before he decided that it should appear with a vignette of the Sphinx printed below the title. By 1887, or at the latest 1888, Peirce would succinctly express his guess by speculating that "three elements are active in the world: first, chance; second, law; and third, habit-taking," and then add that "Such is our guess of the secret of the sphynx" (EP 1: 277; CP 1.409-10).
But it was not only Abbot who reminded Peirce of cosmological riddles and the Sphinx. During his Johns Hopkins years he suffered two lossesone great and the other at least soberingwhich somehow may have primed him for his cosmological turn and which may also shed light on his understanding of the riddle that he supposed he had solved.
Peirce's father, Benjamin, the single greatest influence in his life, had died on 6 October 1880. Just eight months earlier, at the Peabody Institute of Johns Hopkins, he had delivered a series of six lectures on "Ideality in the Physical Sciences,"56 where he spoke of some ancient tablets, recently discovered in Nineveh, on which was recorded an account of Babylonian cosmogony.
Later in the lectures Benjamin remarked that "Nature's riddles are man's intellectual nourishment.... To shrink from them is cowardice and want of faith." Peirce had been deeply shaken by the loss of his father and had almost immediately become the vehicle for the continuation of Benjamin's mathematical thought. He may well have imagined that to some extent his father's mind could live in himand perhaps it was true that Benjamin's more metaphysical, more speculative thought found a place in his mind to rest and await a revival. In the coming years, as Peirce delved deeply into the primeval origins of the universe, he must have known that, were it possible, his father would have smiled on him.
There was another seer in Peirce's life, the old family friend Ralph Waldo Emerson. After Emerson's death in April 1882, Peirce often raised his ghost when expressing profound thoughts, especially the elusive connection between thinking and what is thought, between seeing and what is seen. "Of thine eye I am eyebeam," says Emerson's Sphinx. In Nature, which Peirce must have known from his youth, Emerson stated the riddle more preciselyand it might have stayed in the back of Peirce's mind as a motivation for later cosmological speculations:
That is the riddle. For Peirce, at the end of 1886, the universe was becoming transparent and the light of higher laws was shining throughthe laws of the laws of nature. An exciting path of thought lay open to him, and he had a clear conception of where it would lead. But the book that would found a new era in philosophy was barely started. It remained for Peirce to work up the details and consequences of his grand hypothesis into a systematic philosophy that would leave no question untouched.
It would be a mistake to suppose that, while Peirce delved into cosmology and system building, he discontinued his work in logic and the foundations of mathematics. He had a remarkable capacity for carrying out concurrent investigations, and his interest in those areas continued almost unabated for the rest of his life. His short paper on the properties of number (item 45), which he typed at Ithaca on 5 January 1886, seems rather more anomalous than most other work of the period in that it does not fit easily into the context of his other studies, and it is not mentioned anywhere in his correspondence. He did participate in the university's intellectual life while he was at Cornell, and he gave at least two lectures to engineers and mathematicians. An announcement in the 3 December 1885 Cornell Daily Sun, which introduced Peirce as "the son of one of the most eminent mathematicians of [the] century," encouraged anyone interested in the mathematical intricacies of pendulum operations to attend his lecture the following afternoon: "Professor Peirce's ready command of language, thorough acquaintance with the subject and pleasing delivery will make the occasion profitable and enjoyable." It is not unlikely that a mathematician at Cornell stimulated Peirce's interest in number theory and that item 45 was prepared for discussion or presentation. On the other hand, after his 1880-81 work on the axioms of arithmetic, Peirce always remained interested in further developing his theory of number and related conceptions of mathematical continua, and item 45 might have been part of this ongoing study.
After Newcomb had declined to publish the continuation of item 30, Peirce did not pursue other routes to publicationand seven years passed before he would again publish on symbolic logic. But his 1886 work in logic (items 54-56) shows that he continued to write with publication in mind. These items, all incomplete, appear to be continuations of his earlier work on a general logic book (see W4: items 30, 31, and 61) that would eventually turn into "How to Reason" (more commonly known as the "Grand Logic"). Items 55 and 56 may be more directly related to the continuation of item 30, although the set of papers that Peirce had planned for the American Journal of Mathematics was probably only a reconception of the plan for his book. On the other hand, by mid-1886 Peirce was beginning to wonder how he might supplement his income, and his 1886 work may have been part of a plan he was concocting to make logic pay.
Together, these items consolidate many important logical ideas from the years immediately past, and they anticipate some key ideas that Peirce would soon develop. This is especially true of item 54 which, although to some extent elementary, contains valuable discussions of modality and possible worlds, the importance of observation and the limitations of syllogistic reasoning for mathematics, the importance of temporality for logic, and some interesting spatial conceptions suggestive of his later Existential Graphs. Peirce points out explicitly (p. 331) that part of the business of logic is to teach useful ways of constructing diagrams, and he claims that "the ordinary business of life is best conducted without too much self-criticism" (p. 327) and that ordinary day-to-day reasonings are "better performed unconsciously than they would be if we were to try to interfere with them by a captious and hypochondriac logic" (p. 328). In some respects item 54 seems to be an expansion and development of the 1880 paper on the algebra of logic, while he might have intended to further develop the 1885 paper in a second book on quantitative logic. Item 56 expands somewhat on Peirce's revised theory of signs as set out in the 1885 paper.
Another endeavor that extended throughout the period of this volume was Peirce's lexicographical work for the Century Dictionary. He had been recruited in 1882 by Benjamin Eli Smith, a Johns Hopkins graduate assistant who soon became managing editor for the Century, and by 1883 Peirce had begun to write definitions. He was responsible for several subject areas and contributed over five thousand definitions (see W4: lvi). Edited by the great American linguist William Dwight Whitney, the Century Dictionary still stands as America's greatest single contribution to lexicography. Peirce worked diligently on the dictionary project until he left Johns Hopkins, but it is difficult to determine exactly how much he produced during the following two years. There seems to have been a hiatus in his dictionary work after his departure from Baltimore, although by 1886 he was again hard at work on his definitions.
The method employed in the preparation of the Century Dictionary was to distribute to its contributors relevant pages from the Imperial Dictionary, for which the Century Company held rights, to serve as a basis for the new work, and then to supply them with selections of quotations using new or difficult words. Item 57 illustrates how (at a fairly early stage) Peirce carried out his work for some words in "e"; he would continue in this vein for the rest of the alphabet, until the first edition appeared in 1889-91. But even then Peirce's dictionary work was not finished, for he set to work at once rewriting definitions for a supplement that appeared in 1909. (A fuller account of Peirce's lexicographical work will be given in W7, which will include a substantial selection of his published definitions.)
It is perhaps a fitting sign of Peirce's mind that at the close of 1886 he paused from his logical and cosmological speculations, and from his lexicographical work, to point out to his former student, Allan Marquand, the key to moving from one age of computing to the next. With his simple circuit diagrams (item 58) Peirce provided the clue that might have opened the way to modern electrical computing. But even though Marquand followed Peirce's advice and had elaborate wiring diagrams drawn up,59 and although reference to these diagrams was made in the article on logical machines in Baldwin's Dictionary, it was to no avail. Peirce probably should have pursued his idea, but he was not really very interested in computing, for he did not conceive of computers capable of effective inductive reasoningespecially weak inductive reasoningwhich he believed to be the foundation of human intelligence.
Looking back, we see that Peirce's stint at Johns Hopkins had been a time of great originality and remarkable accomplishments (recounted in the introduction to W4), accomplishments due in part to stimulation from brilliant colleagues and students. Yet in the short period of the present volume we see an even greater concentration of brilliance. There may not be a richer three-year stretch in Peirce's life, nor one that gave rise to so many critical turning points. It is true that many of his most remarkable advances were continuations of work begun earlier; for example, his 1885 contributions to logic were direct outgrowths of a creative surge that had begun as early as 1879 and should be regarded as fruits of his Johns Hopkins experience. But we cannot say the same for his philosophy, where his creative surge began with the "Design and Chance" lecture of January 1884. Although there were many influences that led to that lecture, the ideas expressed there stand out as a starting point for a new line of thought.
It is hard to tell what really set Peirce going in a new directionwhat actually moved him. Perhaps the shock of his dismissal from Johns Hopkins (and thus from university life) threw him into the state of disequilibriuma state soon intensified by his troubles at the Surveythat triggered his creative energy. The finality of his dismissal and the shocking discontinuity it forced on the course of his life must have brought a kind of freedom, a time when he could look forward without looking back. At such times, fresh ideas, either new or drawn from some reservoir of the past, are likely to have unusual impactespecially when they are in conflict with a present course of thought. So in early 1884, at the most pronounced moment of disruption and uncertainty in Peirce's life, he surrendered to his long-held attraction for the idea of the efficacy of chance. He opened his lecture on design and chance by remarking on a new element in intellectual history: the tendency to question the exact truth of axioms. By the summer of 1886 he would begin his book on the categories with the abrupt assertion: "This is the day for doubting axioms" (p. 292). In Peirce's own words we have a good summation of where he stood at the time.
To assess how the work in this volume contributes to the overall development of Peirce's thoughta task far too complex to be fully addressed hereit will be helpful to follow the guidance of Fisch and Murphey. The measure Fisch uses to gauge Peirce's general intellectual development is how far he had progressed from his early nominalism (some say his early weak realism) toward his ever more encompassing realism.60 In Fisch's broadest characterization Peirce can be classified as a one-, two-, or three-category realist, depending on whether he acknowledged the reality of Thirdness, of Thirdness and Secondness, or of all three categories. Peirce did not accept the reality of actuality, or Secondness, until about 1890, and it was seven years later, in 1897, when he finally accepted the reality of possibility, or Firstnessand only then became a three-category realist. Thus, during the period of the present volume, Peirce was still a one-category realist, accepting only the reality of Thirdness. However, his intellectual progress did not occur in two or three great leaps but in a series of many steps. Some of the most significant developments leading to his acceptance of the reality of Secondness are directly related to the work of this period. According to Fisch, these include
Murphey divides Peirce's intellectual development into four periods or systems, each characterized by a distinctive approach to the categories. Peirce's growth from his earliest to his latest system of thought was the result of successive discoveries in logic, each requiring revisions to the categories because of Peirce's architectonic approach to philosophy. Murphey and Fisch agree that it is how the categories stand in relation to Peirce's theory of reality that best measures his development.
When the period covered by the present volume began, Peirce was just entering the final and longest phase of his intellectual life, according to Murphey's account. The logical discoveries that led Peirce to this final phase were his discoveries of quantification and set theory. In particular it was Peirce's discovery of the index, following Mitchell, that led him to understand the importance of individuality and of reference to the individual.62 Fisch also emphasizes the importance of this discovery and points out that it forced Peirce to revise both his theory of signs and his theory of categories. It was at this time that Peirce began to stress that "the actual world cannot be distinguished from a world of imagination by any description. Hence the need of pronouns and indices" (p. 164). Toward the end of 1885, in his review of T. K. Abbott's translation of Kant's Logic (item 40), Peirce remarked that Kant's statement that no general description of existence is possible "is perhaps the most valuable proposition that the Critic contains."
According to Murphey, Peirce's new understanding of the fundamental importance of reference to the individual led him to abandon his definition of reality as "that which is thought in the final opinion to which inquiry will lead," which equates the real with the end of a series of cognitions.63 That theory of reality was a constitutive doctrine. Murphey says that sometime between 1880 and 1890 Peirce abandoned the constitutive principle for a weaker regulative principle, which held only that "in order to make certain that agreement will be pursued it is necessary to hope that ultimate agreement will come." Peirce's 1885 study of Royce may have played the essential role in leading him to this revision. There Peirce claimed that a skeptic (like himself) can fruitfully embrace God's omniscience "as a regulative but not a speculative conception" (p. 229). Christopher Hookway also points to that review as giving an early account of Peirce's "moderate fallibilism." 64
Other important doctrines and themes in Peirce's later thought seem also to be prefigured, if not directly grounded, in the writings of this volume. For example, in the Royce review just cited, Peirce briefly discusses his theory of the existence of God, which he says he hoped soon to get into print: "I think that the existence of God, as well as we can conceive of it, consists in this, that a tendency toward ends is so necessary a constituent of the universe that the mere action of chance upon innumerable atoms has an inevitable teleological result." We can see here the interplay of Peirce's theology with his methodology and cosmology and that his conception of chance had begun to spread throughout his thought. Earlier in this period, in April 1884, he had asked to teach a fall course at Johns Hopkins on the logic of religion, and in May he had delivered a paper on that subject to the Metaphysical Club, where he discussed proofs of the existence of God (see W4: p. lxvi). It was noted above that the final chapter of "One, Two, Three," Peirce's projected treatise on evolutionary cosmology, was entitled "Theism."
There are other "turning points," not mentioned above, that belong to this time. For example, Peirce's reading of Kempe's 1886 "Memoir on the Theory of Mathematical Form" (cf. MS 583) was an important stimulus in turning his thoughts to logical diagrams and the development of his Existential Graphs.65 And there are indications that his study of Abbot's Scientific Theism may have led him to investigate how relations are represented in thought and to reflect deeply on the importance of diagrams for understanding thinking as a process (see pp. 287-88). Also in the Abbot review there is an early statement of Peirce's vortex solution to the mind-body problem.
But while these years represent a new beginning in the development of Peirce's philosophy, they effectively mark the end of his life of science. It is true that he spent the next few years working up scientific results for publication and he sometimes attempted to revive the goodwill he once had in the Survey (until his forced resignation on 31 December 1891), but he was never again given the chance to work in the field as a professional geodesist. In 1899 he tried to reenter the world of professional science as head of the newly formed Bureau of Standards, but he was foiled again by Newcomb, his old nemesis.66 Occasionally Peirce would resume old investigations such as his study of colorhe began some color experiments in June of 1886 which continued until June of 1887but most later work in experimental science was sporadic and connected with some scheme or other in his (never successful) quest for prosperity. It is ironic that Peirce's geodetic work continued to contribute and even to bring great credit to the Survey, though without acknowledgment or benefit to him.67
For his life in general, these years were a time of dislocation and uncertaintya mid-life crisis of massive proportions and in the most literal sense. This is reflected early in the period in a 1 May 1884 letter from his mother: "I am longing to hear of your cologne water, your lectures, your Actuaryship & whatever other schemes you may have thought of & trust they will not all die out 'like the baseless fabric of a vision.'" (Peirce had concocted a cologne water that he hoped to market.) Was his mother paraphrasing her late husband, Charles's father: "how can we be sure that our intellectual picture of the external world is not a human creation, and the fabric of a vision?"68 She wrote again the following month, on 6 June:
As the years progressed, Peirce's attention shifted, often abruptly and erratically, between science and philosophy. When 1886 came to an end, his mind must have been a swirl of ideas about logic and categories and evolutionary cosmologyand about the various scientific reports he was working hard to finish. But prominent in his consciousness was the realization that somehow he had to make a living. For the life he wantedthe life he had promised Juliettehe needed more money than he could make at the Survey, and even that source of income was tenuous. Perhaps Juliette could go on stageit was said that she had great talent. In 1886 she began to study acting with Steele MacKaye, New York playwright and theater manager, and Peirce toyed with the idea that she might become a great success: "then a difficult question will arise for me between my duty to Humanity in the abstract, and my duty to this Lady in the concrete."69 But Peirce knew that this was not the solution to his financial problems. Was there not a way to make a living from what he knew best: logic? He finished the period making plans. On 4 January 1887 he wrote to his cousin, Henry Cabot Lodge, asking for a short-term loan to fund a new venture:
Peirce did not get the loan, but his circular was already written and would soon appear in The Century Magazine and other popular publications. If he could not live his life teaching logic at a university, he would make his living teaching logic in some other way.70 So he thought.
1 In writing this introduction, I have depended a great deal on the results of Max H. Fisch's many years of research, contained in his files at the Peirce Edition Project. The best accounts of Peirce's intellectual development are in Fisch, Peirce, Semiotic, and Pragmatism, eds. Kenneth L. Ketner and Christian J. W. Kloesel (Bloomington: Indiana University Press, 1986) and Murray G. Murphey, The Development of Peirce's Philosophy (Cambridge: Harvard University Press, 1961). For a general account of Peirce's life, see Joseph Brent, Charles Sanders Peirce: A Life (Bloomington: Indiana University Press, 1993).
To reduce the number of footnotes, I do not give references for items that can be easily located by keeping the following in mind: all manuscript references (according to either the Peirce Edition Project or Harvard arrangement) are to the Peirce Papers at Harvard University which also contain the correspondence between Peirce and the members of his family; correspondence with employees of the Coast Survey is in Record Group 23 in the National Archives. NEM refers to The New Elements of Mathematics, ed. Carolyn Eisele (The Hague: Mouton, 1976), and EP to The Essential Peirce, eds. Nathan Houser and Christian Kloesel (Bloomington: Indiana University Press, 1992).
2See Fisch, p. 227.
3Discussed in W2 Introduction, pp. xxxi-xxxiv.
4See Murphey, p. 3.
5See Oscar Howard Mitchell, "On a New Algebra of Logic," in Studies in Logic, ed. C. S. Peirce (Boston: Little, Brown, & Co., 1883), pp. 72-106.
6Quoted in Fisch, p. 233.
7See Murphey, ch. 15.
8For more on Peirce's life during the early months of 1884, see W4: xxxv-xxxvi and lxii-lxx.
9For a fuller account of the impact of Peirce's dismissal on his life, see Brent, ch. 3.
10See also the note for 139-43.
11See, for example, CP 7.256-66, where the study is described in some detail.
12The New Calendar of Great Men: Biographies of the 558 Worthies of all ages and countries in the Positivist Calendar of August Comte, ed. Frederick Harrison (London: Macmillan, 1892).
13Peirce to Lowell, 6 December 1891. Quoted in Carolyn Eisele, Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce, ed. R. M. Martin (The Hague: Mouton, 1979), pp. 141-42.
14See Thomas A. Sebeok, Semiotics in the United States (Bloomington: Indiana University Press, 1991), pp. 114-15.
15"Joseph Jastrow," in A History of Psychology in Autobiography, ed. Carl Murchison (Worcester, MA: Clark University Press, 1930), vol. 1, pp. 135-62.
16See Thomas C. Cadwallader, "Charles S. Peirce (1839-1914): The First American Experimental Psychologist," Journal of the History of the Behavioral Sciences 10 (1974): 291-98.
17Quoted in Eisele (1979), p. 87.
18Stephen M. Stigler, "Mathematical Statistics in the Early States," Annals of Statistics 6 (1978): 248.
19See Ian Hacking, "Telepathy and Randomization," Isis 79 (1988): 427-51.
20R. A. Fisher, The Design of Experiments (Edinburgh: Oliver & Boyd, 1935).
21Science (17 October 1894): 370. References to the Society had appeared even earlier in the popular press.
22See Arthur N. Prior, "The Algebra of the Copula," in Studies in the Philosophy of Charles Sanders Peirce, eds. Edward C. Moore and Richard S. Robin (Amherst: University of Massachusetts Press, 1961), pp. 79-84.
23See W4: xlvi-xlvii and note 184.3 for further discussion of the 1880 "Algebra of Logic."
24See Irving Anellis, "Forty Years of 'Unnatural' Natural Deduction and Quantification," Modern Logic 2 (1991): 113-52, especially 115. For another discussion of Peirce's anticipation of Gentzen, see Don D. Roberts, "The Existential Graphs and Natural Deduction," in Moore and Robin, pp. 109-21.
25Stigler (1978), 249.
26See Thomas G. Manning, Government in Science (Lexington: University of Kentucky Press, 1967), pp. 122-23.
27See Fisch, p. 409.
28Quoted in Eisele (1979), p. 82.
29See Thomas G. Manning, "Peirce, the Coast Survey, and the Politics of Cleveland Democracy," Transactions of the Charles S. Peirce Society 11 (1975): 187-94. See also Brent, ch. 3.
30See Manning (1975), 188.
31The source of the "meager value" remark appears to be a disposition of B. A. Colonna on the condition of the Survey (see L91a: 127).
32Peirce to Powell, 2 May 1886; quoted in Manning (1967), pp. 138-39.
33For a fuller account of the Gautier pendulum episode, see W4: xxxiv and Brent, pp. 140-41, 164, and 177.
34See Victor F. Lenzen, "An Unpublished Scientific Monograph by C. S. Peirce," Transactions of the Charles S. Peirce Society 5 (1969): 5-24.
35See also item 62 in W4.
36This principle has been known since Lukasiewicz as Peirce's Law.
37See Atwell R. Turquette, "Peirce's Icons for Deductive Logic," in Moore and Robin, pp. 95-108, especially p. 101.
38See Richard Martin, Peirce's Logic of Relations and Other Studies (Dordrecht, Holland: Foris Publications, 1980), p. 63.
39See J. Jay Zeman, "Peirce's Philosophy of Logic," Transactions of the Charles S. Peirce Society 22 (1986): 1-22, especially 7.
40See Henry Hiz, "Peirce's Influence on Logic in Poland," forthcoming in Studies in the Logic of Charles Sanders Peirce, eds. Nathan Houser, Don D. Roberts, and James Van Evra (Bloomington: Indiana University Press, 1994).
41See Irving Anellis, Review of Volumes 1-4 Writings of Charles S. Peirce, Modern Logic 3 (1992): 77-92, especially 87.
42See item 56 for a related but somewhat fuller presentation of Peirce's revised theory of signs.
43In one recollection of this incident (cited in NEM 3: 1069), Peirce said that Newcomb rejected a proposal on the grounds that the planned work was not mathematics and that, as a result, the paper remained unwritten. If that was the case, items 31 and 32 may constitute Peirce's most finished results. But Peirce's earlier accounts tend to confirm that he submitted a finished paper for publication.
44NEM 3: 816-17.
45Brent, p. 174.
46Fisch, pp. 190-91.
47See Brent, p. 177.
48Peirce's report on the Arctic gravity work will be included in W6, and a more detailed account of the Peirce-Greely interaction will be given in the introduction to that volume.
49See Brent, pp. 196-201.
50Victor F. Lenzen, "Charles S. Peirce as Mathematical Geodesist," Transactions of the Charles S. Peirce Society 8 (1972): 90-105, especially 98.
51See Fisch, ch. 12.
52See W4: lxvii-lxix; Fisch, ch. 12; and Brent 171-73. An excellent account of Peirce's early indeterminism, especially as developed in his 1866 Lowell Lectures, was given by Paul D. Forster in Toronto on 9 October 1992: "The Logical Foundations of Peirce's Indeterminism" will be published in the proceedings of the conference, entitled "New Topics in the Philosophy of C. S. Peirce" and held at Trinity College, University of Toronto.
53Fisch, p. 233.
54Francis Ellingwood Abbot, Scientific Theism (London: Macmillan, 1885), p. 217.
55Ibid., pp. 121-22.
56These lectures were first given at the Lowell Institute in Boston in 1879. They were edited by Jem after Benjamin's death and published in 1881.
57This and the immediately following quotation are from Benjamin Peirce's Ideality in the Physical Sciences (Boston: Little, Brown, and Co., 1881), pp. 43-44 and 183.
58This quotation, and the idea that it may be connected with Peirce's guess, appears in an unpublished manuscript by John Sheriff.
59See Kenneth Laine Ketner, "The Early History of Computer Design," Princeton University Library Chronicle 45 (1984): 187-224.
60See Fisch, ch. 10.
61Fisch, p. 189.
62Indices do appear in Peirce's earlier work, especially in his "New List" (W2: item 4), but not as signs that refer directly to individuals. See Murphey, pp. 299-300.
63Murphey, p. 301.
64Christopher Hookway, Peirce (London: Routledge & Kegan Paul, 1985), p. 73.
65See Don D. Roberts, The Existential Graphs of Charles S. Peirce (The Hague: Mouton, 1973), pp. 20ff.
66See Brent, pp. 152 and 266-67.
67Ibid., p. 198.
68B. Peirce (1881), p. 23.
69Peirce to E. S. Holden, 20 August 1886.
70 Selections from Peirce's correspondence course in logic will be included in the next volume of the present edition.
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