Introduction to Volume 4

The years 1879-84 were perhaps the most fulfilling and disappointing in the life of Charles Sanders Peirce. He saw the promise of a long hoped for academic career, established important academic contacts and had remarkable successes as a teacher, and gained international prominence as a scientist. But in 1884 his academic career ended in disgrace, and his scientific reputation was soon to suffer a serious assault. His purpose and sense of direction would be so battered that he would retreat to the seclusion of a country house to spend the rest of his life with his second wife, Juliette. However, during these years, amid the turmoil of personal victories and private calamities, Peirce worked at a fever pitch and produced some of his most important writings. 1

The most momentous and consequential event during these years was the death of his father on 6 October 1880. Born in 1809, Benjamin Peirce was Harvard's Perkins Professor of Astronomy and Mathematics for nearly 40 years, and America's leading mathematician. He was largely responsible for introducing mathematics as a subject for research in American institutions, and he is known especially for his contributions to analytic mechanics and linear associative algebra. He helped organize the Smithsonian Institution, and from 1867 to 1874 served as superintendent of the United States Coast Survey. Benjamin Peirce was generally regarded as the most powerful mind so far produced in the United States. 2

At the time of Benjamin's death, it was thought that of his four surviving children (Benjamin Mills had died in 1870) the one most endowed with his intellectual powers was Charles, who was expected to carry on his father's work. Benjamin himself appears to have expected as much, for at the close of his remarks on the impossible in mathematics before the Boston Radical Club near the end of his life, he "observed that his son Charles was now engaged in carrying on his investigations in the same line to which he had specially applied himself; and it was a great gratification to him to know that his son would prosecute the work to which he had devoted the latter part of his own life." 3

There is no doubt that his father had greater influence on Charles's intellectual development than did anyone else. Early on he had recognized his son's powers and had taken a regular and ongoing interest in his education and career. He got Charles started with the Coast Survey, giving him a salaried position in 1867, and put him in charge of pendulum operations, and in so doing, set the course for Charles's scientific work for the remainder of his career with the Survey. When in 1870 they traveled home to Cambridge from Michigan with the body of Benjamin Mills, he advised Charles against trying to make a career of logic; it would be better, he said, to stick with science. When his father died in 1880, Charles may well have remembered this advice, for he soon announced that he would quit logic and philosophy.

The full impact on Charles of his father's final illness and death can only be guessed at. The emotional toll is manifested in his impulsive decision to quit logic and philosophy and sell his library, a decision he soon came to regret, and in a general malaise that settled over him. Upon returning to Baltimore after the funeral in Cambridge, Peirce wrote to his mother in late October: "I have had a fog resting on my spirit ever since I have been back, so that I have not been working very successfully but I hope it is clearing up. It has been just like a steamer forging through a fog." That image may well have been vivid for Peirce. Because of his father's grave condition a few months earlier, in late July, he had been called home from Europe where he had been on assignment for the Coast Survey, and it is likely that he returned aboard the French steamer St. Laurent which arrived in New York on 4 August "after a passage in which it had strong W. gales and fog most of the time." 4

The effect of his father's death on the direction of Peirce's work was immediate. Along with his brother, James Mills, Charles turned to Benjamin's writings, hoping to get more of them into print. He spent much of the next year editing and annotating his father's privately printed Linear Associative Algebra of 1870. Mathematical topics began to occupy him more frequently than ever before, although this was also due to the influence of the mathematical community in which he found himself at the Johns Hopkins University. But Peirce was already a talented mathematician who had accomplished enough to be included in the small group of scientific men in America who were capable of contributing to sciences that were laden with mathematical theory. Other men in this group, mainly mathematical astronomers, included Simon Newcomb, Asaph Hall, and George William Hill. 5

Probably the greatest effect of Benjamin's death on Charles was the loss of the influence and protection that his father's reputation had provided. Benjamin had been so highly regarded in scientific and academic circles, and his opinions and interests had carried such weight, that Charles almost always received special consideration. After his father's death this protective influence ended and Charles was left to make his own way.

The loss of his father was soon followed by the death of Carlile P. Patterson, who in 1874 had succeeded Benjamin Peirce as superintendent of the Coast Survey. Patterson's death on 15 August 1881 brought to an end the golden age of the Coast Survey, a time when pure research was much esteemed and the daily course of activity was governed by a desire to learn and discover as much as by the need to achieve practical results for a technologically oriented and sometimes shortsighted Congress. Patterson had been an ideal employer and it appears from Peirce's eulogy (P 264) that he feared a change for the worse:

"His superintendency was marked by . . . great practical achievements. . . . Yet, although he was not professedly a scientific man, under none of the eminent geodesists who had preceded him was more stress laid upon the scientific branches of the work—to their extension, and to the precision of their execution.

"No one was so earnest as he to secure to the Survey the labors of men of purely scientific, and especially mathematical, attainments and abilities.

". . . I feel that in Patterson's death the science of the country has lost a staunch ally."

As it turned out, Peirce had good reason to fear the worst. No sooner had Julius Hilgard taken over as superintendent, something Benjamin had sought to prevent, than Peirce was put on notice that his reports would have to be more timely. In this way Hilgard let it be known that he did not have Patterson's patience for Peirce's exacting and time-consuming methods nor, perhaps, for delays caused by his recent commitment to the Johns Hopkins. So began a period of disaffection that in 1891, after thirty-one years of service, led to Peirce's forced resignation. In the meantime Hilgard had led the Survey into a public scandal and, after his dismissal in 1885, the Survey fell for the first time into the hands of F. M. Thorn, a bureaucrat with no training in science.

Nearly as consequential for Peirce as his father's death was his divorce from his first wife, Harriet Melusina (Zina) Fay Peirce, on 24 April 1883, and his marriage to Juliette Annette Froissy Pourtalai (or de Pourtalès) just six days later. Peirce and Zina had married on 16 October 1862 and they lived together until Zina refused to accompany Peirce when he moved from Cambridge in October 1876. Although her reasons have never been fully disclosed, it is clear that Zina was unwilling to live the itinerant life that Peirce thought essential for his work with the Survey. She never remarried and in later years expressed regret that she had not stayed with Peirce.

Sometime during his separation from Zina, perhaps within the first year, Peirce met Juliette, who was thought to be the widow of a Count Pourtalai and the sister of a diplomat brother who had, it seems, been known to George Bancroft while he was ambassador to Prussia. Bancroft is said to have recognized Juliette in America from her resemblance to her brother. She was generally thought to be a Frenchwoman, but she actively suppressed all accounts of her origin and her identity remains uncertain.

Peirce probably met her at the Brevoort House, a European-styled hotel located on Fifth Avenue near Washington Square, where he usually stayed when in New York City. He was well known to the manager of the Brevoort, who reportedly introduced Peirce and Juliette on the occasion of a great ball. 6 Thus began an affair conducted far less discreetly than the times demanded, an affair for which Peirce and Juliette would suffer greatly. Rumors of their romantic indiscretions would ultimately cut Peirce off from university life and Juliette from society.

Of those outside Baltimore who knew of Peirce during the period covered by the present volume, most thought of him as a scientist in the service of the Coast Survey. 7 His association with the Survey began in 1859 and in July 1861 he was appointed a regular aide. In 1867, less than five months after Benjamin had become superintendent, Charles was promoted to a salaried position and began his rise to prominence in science. His primary field of scientific endeavor became geodesy, a field he led after 1872 when his father promoted him to assistant, the rank immediately below that of superintendent, and put him in charge of pendulum experiments. The two main aims of Peirce's geodetic operations were to determine the force of gravity at various locations in the United States and abroad and, from these results, determine the figure of the earth.

But Peirce's scientific work extended far beyond geodetic operations. He made notable contributions to metrology, for example. Precise determinations of gravity require exact measurements of the length of the pendulums employed, and exact measurements demand that precise relations to standards of length be determined. Consequently, Peirce spent a good deal of time comparing the lengths of Coast Survey pendulums with recognized standards of length throughout Europe, and with each other, under controlled conditions. This work led to a more generalized interest in standards, and for several months in 1884-85 he was in charge of the U.S. Office of Weights and Measures.

It seems natural that extensive work with pendulums should have led an inquiring mind like Peirce's to reflect on the methodology of pendulum experimentation and on the adequacy of the instruments themselves. To some extent such reflection was part of the job, for it was essential that the data of observations be "corrected" to eliminate the effect of systematic sources of error. Peirce was adept at this work and in addition to establishing that the flexure of the stand of a popular pendulum (the Repsold compound pendulum) was an important source of error, which demonstrated the need for corrections to many of the gravity determinations of leading European scientists, Peirce conducted numerous experiments to determine additional sources of error. These included the effect of the wearing of the knife-edge (the thin blade on which the compound pendulum oscillates), the effect of using steel cylinders instead of knives, the effect of the oscillation of the walls of the receiver (the container in which the pendulum swings), and the effect of temperature on the length of the pendulum. Peirce also invented two styles of pendulum (only one of which was constructed) as well as a new kind of pendulum stand.

At the beginning of the period 1879-84 Peirce was involved with the U.S. Treasury Department in a matter that may have planted seeds of disaffection with the Survey. Late in 1878 he had requested an increase in his salary, from $2870 to $3500 and was so determined to have his raise that he was prepared to submit his resignation should it be refused. "I prefer working for somebody who will consider the character of my work," he wrote to his father on 14 January 1879. (Peirce may have had Daniel C. Gilman in mind, the president of the Johns Hopkins University, with whom he had been in correspondence for more than a year about the possibility of an academic appointment.) By 8 July Superintendent Patterson sent the request to John Sherman, Secretary of the Treasury, with the following supporting argument:

"Mr. Peirce is forty years of age, has been employed on the Survey for eighteen years, and on account of his exceptional ability for special investigations, was during eleven years service rapidly advanced to his present pay in 1873. Since that date Mr. Peirce has made extraordinary advances in Pendulum observations of a very original character, exciting the deepest interest in this important scientific subject on the part of all physicists, both in this country and abroad, and leading to a complete revision of all past observations at the main initial points for Pendulum observations in Europe. In fact Mr. Peirce is the first person in this country who has with any success attacked this problem, the subject having remained in abeyance for many years, awaiting a truly scientific observer. Mr. Peirce has also succeeded in comparing the accepted standard unit of length (the meter) with a permanent (so far as now known) length in nature, a wave length of light, a task hitherto never attempted on account of the inherent difficulties of the case, over which after many discouragements and failures he has at last triumphed. These results of Mr. Peirce's work have greatly advanced the science of Geodesy, the scientific reputation of the Survey, and therefore that of the Country.

"The enclosed extracts from letters of eminent American Scientists offer the best evidence of the value of Mr. Peirce's work." 8

The eminent scientists were Alfred M. Mayer, professor of physics at Stevens Institute of Technology; Wolcott Gibbs, Rumford Professor at Harvard University; Ogden N. Rood, professor of physics at Columbia College; and Benjamin Peirce.

Mayer reported that the results of Peirce's work already "are of the highest importance to the advancement of science and to the interest of the U.S. Coast Survey. Mr. Peirce's methods are original, and of an accuracy and refinement which are unsurpassed"; he added that "Mr. Peirce deserves well of his countrymen, for his work has added much to the scientific reputation of the U.S. Coast Survey among European nations." Gibbs discussed the spectroscopic apparatus that Peirce used in his experiments with light waves. "I have carefully examined the apparatus," he said, "and am of opinion that it is admirable both in design and in workmanship. In fact I do not hesitate to say that both the spectroscope and spectrometer are the most perfect instruments of the kind in existence, and I have been both delighted and instructed by a critical examination of the refinements introduced in their construction." Rood addressed Peirce's general merit and the "very high estimation in which Mr. Peirce's contributions are held by the scientific men of this country and of Europe," and he claimed that "it would be difficult to find another scientist having similar qualifications with Mr. Peirce either in the special education required, or in natural ability. I certainly know of no one in this country who would be at all qualified to take the position which he now holds in your Survey." Finally, Benjamin Peirce, whose relation to Charles may have somewhat diluted the impact of his remarks, wrote of his son's work in establishing a wave-length of light as a standard of length:

"It is a most remarkable achievement to have thus determined the length of the meter from the wave-length of light, which is the shortest length which has ever been measured; and the only sure determination of the meter, by which it could be recovered if it were lost to science. It will certainly secure for the Survey the applause of all scientific men.

"When combined with Mr. Peirce's admirable measures of the pendulum, which have justly been regarded by the savans of Europe as adding a new era to this most difficult branch of observation, it places him among the great masters of astronomical and geodetic research, and it would be most unfortunate, i[f] such grand strides in science were not suitably acknowledged."

But Peirce did not get his raise. In his letter conveying Sherman's decision, Patterson regretfully assured Peirce that he would do anything in his power to advance his interests outside the Survey, but said that it would be difficult to replace him. By the time Peirce heard of Sherman's denial he had received his part-time appointment at the Johns Hopkins and he concluded that with his combined salaries he was sufficiently well off. Besides, he felt that Patterson, who had admitted that he was not adequately paid, might be "more or less indulgent" of his connection with the Johns Hopkins—a recognition of the potential difficulty of pursuing two careers at once.

William James had recommended Peirce to Gilman for the professorship of logic and mental science in 1875, and Benjamin Peirce had later recommended him for the professorship of physics. By 13 January 1878 Peirce had informed Gilman of his strong interest in being "called" to the Johns Hopkins and had set out in detail his projected program for the physics department. Peirce emphasized that he was a logician and had learned physics as part of his study of logic; for "the data for the generalizations of logic are the special methods of the different sciences. To penetrate these methods the logician has to study various sciences rather profoundly." He then described his view of logic and remarked on the importance of his work:

"In Logic, I am the exponent of a particular tendency, that of physical sciences. I make the pretension to being the most thorough going and fundamental representative of that element who has yet appeared. I believe that my system of logic (which is a philosophical method to which mathematical algebra only affords aid in a particular part of it) must stand, or else the whole spirit of the physical sciences must be revolutionized. If this is to happen, it cannot be brought about in any way so quickly as by the philosophical formularization of it and the carrying of it to its furthest logical consequences. If on the other hand it is to abide, its general statement will be of consequence for mankind. I have measured my powers against those of other men; I know what they are. It is my part to announce with modest confidence what I can do. My system has been sketched out but not so that its bearings can be appreciated. If the world thinks it worth developing, they have only to give me the means of doing it. But if not, I shall follow another path, with perfect contentment."

Gilman inquired on 23 January whether Peirce would accept a half-time appointment as lecturer of logic, while retaining his position with the Survey. Peirce replied on 12 March that he would.

"The truth is that the great difficulty I had in reaching a decision was that if I were to be your professor of logic, my whole energy and being would be absorbed in that occupation. Right reasoning is in my opinion the next thing in practical importance to right feeling; and the man who has to teach it to young minds has such a tremendous responsibility, that the idea of giving 1/2 his activity to such a business seems shocking. All the more so, that students have hitherto been fed with such wretched bran under the name of logic. That name now rests under a just opprobrium from which, if I should become your professor, it would be the purpose of my life to redeem it, first in the eyes of those who had been my pupils, and next before the world; for I should think that I had failed if my pupils did not carry into after-life a more distinct idea of what they had learned from me than of most of the subjects of their study and did not feel that the study of reasoning had been of great advantage to them."

But the trustees had already decided not to make any further appointments that year.

Gilman inquired again the following year, and though Peirce now set certain conditions, he again replied affirmatively (on 6 June 1879). He wanted to have sole charge of instruction in logic and the assurance that the position would eventually be full-time. Furthermore, he advised Gilman that he would be on Coast Survey business in Europe until after the beginning of the fall term. As for the teaching of logic, Peirce's views were much the same as he had expressed the previous year.

"There are two things to be done; one, to communicate the logica utens, and to make expert reasoners of the pupils, able to form clear ideas, to avoid fallacies & to see in what quarters to look for evidence; the other, to familiarize them with the logical ideas which have percolated through all our language & common sense, & to show their significance & what they are worth. Special branches of logic may of course be taught in special cases; such as logical algebra, the history of logic, etc. etc."

On 13 June 1879 Gilman made an offer which Peirce accepted on 20 June, the day after he received it.

So it happened that for most of the period 1879-84 Peirce pursued two careers: as a scientist in the most prestigious scientific agency in America and as a teacher and scholar in the most advanced American school for graduate studies. Peirce was a regular commuter on the B & O railroad between Washington and Baltimore during these years. He tried to do well in both jobs, but that was a formidable predicament and, as it turned out, a near impossibility. Given the demands of his position of leadership in the Coast Survey, which included frequent travel and sustained periods of research and experimentation, and the pressures of a new career in teaching with the excitement of his longed-for interaction with brilliant students, it is not surprising that Peirce's health began to break. He struck an alarming note toward the end of his first term of teaching when in a curious letter to Gilman, written on Christmas Day 1879, he wrote:

"I have an odd thing to say to you which is to be perfectly confidential unless something unexpected should occur. In consequence of certain symptoms, I yesterday went to see my physician in New York, & he after calling in an eminent practitioner in consultation, informed me that he considered the state of my brain rather alarming. Not that he particularly feared regular insanity, but he did fear something of that sort; and he must insist on my being some little time in New York and he could not promise that I should go back on January 5th. For my own part, I do not think the matter so serious as he thinks. The intense interest I have had in the University and in my lectures, combined with my solitary life there, & with the state of my physical health, has undoubtedly thrown me into a state of dangerous cerebral activity & excitement. But I feel convinced that I shall surprise the doctors with the rapidity with which I regain my balance. I don't think the matter of any particular importance. However, I think it best to say to you as much as I do say; both that you may understand why I may possibly not be on hand Jan 5, and also because the matter might turn out worse than I anticipate, and I might do some absurd thing. I have said nothing to anybody else than you; & I beg you will not let me see that it is in your mind when I go back; for I shall not go back until it is quite over."

The matter was apparently no more serious than Peirce had thought, but it is true that for the next several years he suffered from ill health.

It is amid the events and circumstances so far described that Peirce's writings of this period were created. Although much of his work exhibits his dual preoccupations—his scientific work is reflected in his academic work, and vice versa—his writings generally concern one or the other of his pursuits. These pursuits are distinct enough to be treated separately, though it is well to keep in mind the parallel unfolding of the events described in the following two sections.

The Coast and Geodetic Survey

Although the decade preceding 1879-84 has sometimes been regarded as Peirce's most "intensely scientific period," he seems to have lost little intensity during the present period. A review of his scientific undertakings and accomplishments reveals that his productivity remained on a par with that of the previous decade. However, his reliability, especially with regard to the preparation of his field reports, did decline somewhat. With his part-time employment at the Johns Hopkins Peirce could not be so single-mindedly directed toward scientific undertakings as he had been during the 1870s. But Peirce's commitment to teaching did not keep him from carrying on a full life of science.

From 1879 to 1884 Peirce was in charge of half a dozen major pendulum observation parties at several sites in Pennsylvania and at St. Augustine, Savannah, Fortress Monroe in Virginia, and the Smithsonian. Extensive experiments were also conducted in Baltimore and Cambridge and at the Stevens Institute in Hoboken, New Jersey. Besides these domestic occupations Peirce led an observation party to Montreal in 1882, and in the summers of 1880 and 1883 he made the final two of his five sojourns to Europe on assignment for the Coast Survey. The fieldwork for these assignments resulted in one to two hundred field books of experimental data, and it generated over a linear foot of detailed correspondence (most of which is deposited in Record Group 23 in the National Archives). In addition to these major assignments Peirce performed the regular functions of his office and he carried out a number of other experiments at the Washington headquarters. He conducted experiments with his spectrum meter in his attempt to establish a wave of sodium light as a unit of length and he oversaw the construction of four pendulums of his own design (Peirce Pendulums 1 - 4). Throughout these years Peirce was always at work on the reduction of the data of his field notes and on the preparation of reports for publication, primarily for the superintendent's annual reports. He saw more than a dozen scientific papers into print and he contributed at least as many papers and reports to scientific associations, most notably the National Academy of Sciences.

In 1879 Peirce's initial concern was to get fieldwork underway in accordance with his assignment to determine the disturbing effect of the Appalachian mountains on geodetic operations. Early in January he occupied the Allegheny Observatory in Pennsylvania 9 and began to take measurements of gravity. Peirce had coordinated the pendulum operations there so that he could supervise the Observatory for its director, Samuel P. Langley, while he was off to Mt. Etna during the first part of the year. Before Langley's departure Peirce had visited the Observatory to "get the hang of it." (In later years, when he was director of the Smithsonian Institution, Langley provided much-needed employment for Peirce as a translator of French and German scientific publications).

Peirce's fieldwork was completed at Allegheny in March and resumed at Cresson in July and at Ebensburgh in mid-August. Field operations at these Pennsylvania stations were concerned with the determination of gravity but also with sources of error resulting from the nature of the pendulum apparatus itself. Peirce had worked on the latter since 1875 when he had surprised Europe's leading geodesists at a Paris conference where he proclaimed that the stand of the Repsold pendulum was unstable and thus a systematic source of error.

Peirce had acquired a Repsold pendulum during his second European assignment in 1875, and had made a series of determinations at selected European locations (or "initial stations") in order to relate American to European results. In his report on these determinations he emphasized that "The value of gravity-determinations depends upon their being bound together, each with all the others which have been made anywhere upon the earth." He had made determinations in Berlin, Geneva, Paris, and Kew, and had met such leading figures as James Clark Maxwell of Cambridge, Johann Jakob Baeyer of Berlin, and Emile Plantamour of Geneva.

It appears that General Baeyer had first raised the suspicion that the Repsold stand might be unstable. Peirce examined the stand in Geneva and worked out an approximate value of the error due to its swaying, which he presented at the Paris conference. If Peirce was right, all of the results published in Europe during the previous ten years would be vitiated. Although Peirce's claim drew little response, Hervé Faye suggested that such an error might be overcome by setting up two pendulums on the same stand and by swinging them simultaneously in opposite directions. The following year at a meeting in Brussels, which Peirce did not attend, it was concluded that he was mistaken. Peirce resolved to defend his claim at the next meeting of the European Geodetic Association in 1877 in Stuttgart. With abundant experimental data in hand and with the mathematical theory well worked out, Peirce won the day. He later reported that "from that time I was acknowledged as the head of that small branch or twig of science." 10

The results of Peirce's geodetic work in Europe, and some subsequent work in the United States, were set forth in the extensive monograph entitled "Measurements of Gravity at Initial Stations in America and Europe" (item 13), which is regarded as one of the classics of geodesy and the first notable American contribution to gravity research. It was specially noted at the Munich meetings of the International Geodetical Association in 1880 and it is listed as a basic monograph on the pendulum in the 1904 Encyklopädie der mathematischen Wissenschaften. The results of Peirce's work on flexure were presented in April 1879 at a meeting of the National Academy of Sciences (P 152) and appeared not long after in the American Journal of Science and Arts as "On a method of swinging Pendulums for the determination of Gravity, proposed by M. Faye" (item 5), which shows the theoretical soundness of Faye's method for avoiding error due to flexure.

Three more papers that Peirce read to the Academy in April indicate his other scientific endeavors. His "Comparison of the meter with wave lengths" (P 154) detailed his efforts to establish wave-lengths of light as a standard of length, a different version of which (P 133) was presented by his father to the American Academy of Arts and Sciences in Boston. Although summary reports of this work were published in various scientific journals—as in items 2 and 4, or in his "Mutual Attraction of Spectral Lines" in Nature (P 156)—no major study was ever published. By 1886 Peirce had several times revised his report on the spectrum meter but the finished monograph has been lost. Item 37 is what remains of an 1882 version.

In his spectrum meter experiments, Peirce compared wave-lengths of light with the breadth of a diffraction plate. He used a machine called a comparator, a spectrometer he himself designed, and a diffraction plate designed by Lewis M. Rutherfurd. These experiments led him to the discovery of hitherto unknown diffraction phenomena called "ghosts," which provided the topic for his third paper to the National Academy (P 153) and the published paper "On the Ghosts in Rutherfurd's Diffraction-Spectra" (item 10).

Peirce's fourth paper, "On the projections of the sphere which preserve the angles" (P 151), was the first public presentation of his quincuncial projection; it was later published in the American Journal of Mathematics (item 11) and in the 1876 Coast Survey Report (P 138; see also P 238). The quincuncial projection allowed for repetition of the whole sphere in transposed positions on the map so that any location might be viewed as occupying a central position relative to the rest of the earth. It was used during World War II for charting international air routes. Peirce had completed most of the work on the projection by 1879 and the first quincuncial map appeared in May 1879 in an appendix to the Proceedings of the American Metrological Society, but there it was only a convenient map for showing the date-line from pole to pole, not a new projection with supporting mathematical theory.

Another classic paper in the 1876 Report (in addition to item 13) is Peirce's "Note on the Theory of the Economy of Research" (item 12). The theory developed in this paper was intended to guide scientific researchers in their efforts to balance the benefit of advancing knowledge against the costs of the research. The main problem of the doctrine of economy is "how, with a given expenditure of money, time, and energy, to obtain the most valuable addition to our knowledge," a problem that concerned Peirce even in his later years. This paper has been reprinted as recently as 1967 in Operations Research.

Two other papers published in 1879 illustrate the scope of Peirce's scientific interests during the period 1879-84. The 16 October issue of the Nation contained his review of Ogden Rood's Modern Chromatics (item 9), which makes several references to Peirce's own experimental work on color, and the 1876 Coast Survey Report contained yet a third paper, entitled "A Catalogue of Stars for observation of latitude" (P 159). This catalogue, which was intended to supersede the list published in the 1873 Report (P 95), does not appear under Peirce's name, but J. E. Hilgard's preface indicates that "the list was selected under the direction of Assistant C. S. Peirce, and the names of the stars were assigned by him."

Peirce concluded his fieldwork for the determination of the disturbing effects of the Allegheny mountains with a three-month occupation of a station at York, Pennsylvania, in 1880. Henry Farquhar conducted the operations, which continued until mid-June, under Peirce's direction. In addition to measurements of gravity, observations were made for the detection of flexure and experiments were conducted in which the standard pendulum knife was replaced by small steel cylinders that acted as bearings. This method had been proposed by both Peirce and Yvon Villarceau in order to avoid the effects of the blunting of the knife-edge, but Peirce eventually showed that the cylinders increased rather than reduced friction.

Peirce sailed on his fourth Coast Survey assignment to Europe in April. Although his previous gravity determinations in Paris varied significantly from the accepted measures of Borda and Biot, he demonstrated that, when corrected for errors not suspected at the time of their observations, their work came into line with his. His paper "On the Value of Gravity at Paris" (item 15) is a translation of the paper he presented to the French Academy of Science and published in the Academy's Comptes Rendus (P 171). Peirce intended to report on his pendulum work and his spectrum meter at the International Geodetic Association meeting in September in Munich but, as mentioned earlier, he was called home when his father became seriously ill. He sent an abbreviated report in the form of a letter to Hervé Faye, which was published in the Association's proceedings (item 17).

After his return from Europe in 1880, for his father's final illness and death, Peirce does not appear to have taken up any new projects right away. He provisionally completed his comparison of the meter with a wave-length (although he soon resumed that study), pursued his investigations of the effect of the walls of the receiver on the period of oscillation, and labored to improve the related mathematical theory. In mid-November he read a paper "On the ellipticity of the earth as deduced from pendulum experiments" to the National Academy of Sciences in New York City; it was later published in the 1881 Coast Survey Report (item 76).

Several more of Peirce's scientific writings appeared in print in 1880. In July, Nature published "On the Colours of Double Stars" (item 18), and "The quincuncial projection" was reprinted in the 1876 Coast Survey Report. A summary of the "Measurements of Gravity at Initial Stations" appeared as "Results of Pendulum Experiments" in the October issue of the American Journal of Science and Arts (item 21, which was reprinted in the November issue of The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science), and a report of his pendulum operations was included in the 1879 report of the Commission der Europæischen Gradmessung (P 184).

Much of Peirce's Coast Survey work during the first half of 1881 focused on the construction of his four invariable reversible pendulums which, according to Hilgard, had their surfaces "as nearly as convenient in the form of an elongated ellipsoid." Peirce had invented the pendulums so that the effects of viscosity could be theoretically ascertained. Three of them (Nos. 1, 2, and 4) were meter pendulums, and one (No. 3) was a yard pendulum. Peirce No. 1 was used in the Arctic, in Franklin Bay above the 80th Parallel, by an expeditionary party led by Lieutenant Adolphus W. Greely later in the year. Greely's party was one of two U.S. parties assembled as a result of a meeting in Hamburg in 1879 where eleven nations 11 had agreed to man polar stations for one year (1882-83) to conduct scientific observations and pool their results. Included in Greely's assignment was pendulum work for the determination of gravity, which Peirce had carefully planned. He had personally instructed Greely's astronomer, Sergeant Edward Israel, in the conduct of the experiments. Unhappily, Greely's party suffered terrible hardships and eighteen of his twenty-five men died during the course of the next three years, including Israel. Although he and Greely had meticulously recorded and maintained the records of their pendulum experiments, Peirce at first concluded from the data that some accident must have befallen the pendulum. When he recorded this opinion in his official report of the experiments (P 369), it occasioned a mild dispute. But it ended amicably when Peirce assured Greely that "there has been no failure, but this determination is far more reliable than any other which has ever been made within the arctic circle, and this will be take my assurance of it the ultimate judgment of experts".12

In mid-April 1881, Peirce delivered a report "On the progress of pendulum work" to the National Academy of Sciences (P 199), and in June he made gravity determinations at Washington, in late July and August at Baltimore, and in September at Cambridge. He continued his investigations of error due to the flexure of the stand and the receiver and he experimented with the Faye/Peirce plan of swinging two pendulums from the same support. In July he sent his letter to Faye (item 17) and saw the publication of his "Width of Mr. Rutherfurd's Rulings" in Nature (item 29), and in August he attended the thirtieth meeting of the American Association for the Advancement of Science in Cincinnati where he read a paper entitled "Comparison Between the Yard and Metre by Means of the Reversible Pendulum" (P 186). On 30 August he was elected to membership in the Association and was appointed to the standing committee on weights and measures.

Although Peirce's reputation as a geodesist was strong as 1882 got underway, he was beginning to be a source of irritation inside the Survey, primarily because of his growing tendency toward tardiness in reducing the results of his fieldwork and the preparation of reports for publication. In April he was urged by Richard D. Cutts, assistant in charge of the Survey office, to send in his appendices for the 1881 Report and, on 6 July, Superintendent Hilgard informed him that it had gone to press without the four appendices ("Determination of Force of Gravity at points in Penn.," "Variation of Gravity with the Latitude," "Flexure of Pendulum Supports," and "Oscillation Period of the Walls of the Receiver"). He implored Peirce to concentrate on what could be finished by 20 July, the final day for submission, and to let him know at once which papers could not be finished so that reference to them might be struck from the report. Surprisingly, the 1881 Report appeared with four appendices by Peirce, although the first of the four listed above was not included. Because of its bulkiness it was also absent from the 1882 Report, but it finally appeared as Appendix 19 in the 1883 Report (P 290).

In April 1882 Major John Herschel of the India Survey arrived in the United States to conduct gravity operations at selected stations in order to connect British with American pendulum work. Peirce helped him get set up at Hoboken and frequently assisted him during his year-long stay. In May Herschel was invited to participate in an informal conference on the future of pendulum work and the efficiency and accuracy of the methods employed, a conference no doubt occasioned by his presence in the United States and by his prominence in the field of pendulum operations. Those in attendance besides Peirce and Herschel were Simon Newcomb of the Nautical Almanac and Superintendent J. E. Hilgard, as well as George Davidson and C. A. Schott of the Coast Survey. J. W. Powell, director of the United States Geological Survey, was unable to attend. Peirce edited the proceedings of the conference, which were published in the 1882 Report (items 48-55).

In addition to the considerable attention he gave to Herschel's pendulum operations throughout the year and to his supervision of the construction of the Peirce pendulums (work on No. 4 was still underway in May), Peirce conducted extensive fieldwork of his own. From May through September he made gravity determinations and other pendulum observations in Washington, Baltimore, Hoboken, Montreal, and Albany. Although he continued to swing the Repsold pendulum in order to coordinate his operations with those of Herschel and others, he also made observations with his new invariable reversible pendulums. By the end of 1883, Peirce Pendulums 2 and 3 had been swung at Washington, Hoboken, Montreal, Albany, and St. Augustine.

Peirce traveled to Montreal in August to make a series of pendulum experiments at the McGill College Observatory and to attend the thirty-first meeting of the American Association for the Advancement of Science. The work was very demanding and beset with complications due to equipment problems. Peirce was beginning to feel the strain of overcommitment. On 29 August he wrote to his mother:

"For a long time I have been so driven with work that I have had no time to write the smallest line except in the way of business. . . . I have prepared an enormous quantity of matter for the press of late,—almost enough to make a volume of the Coast Survey Reports. . . . I have also been very active in the line of experiments, frequently working all night. Hilgard is a regular task-master. My assistants and I have been nearly killed with overwork."

Yet Peirce managed, somehow, to take in some of his surroundings. His letter continues: "I am charmed with Montreal. It is a most lovely site, much of the architecture is fine, there is very little that is utterly dreary, and the admixture of the French element contributes something very pleasing."

Peirce had not traveled to Montreal alone. Juliette had accompanied him on the train and may have stayed with him for a short time in Montreal before traveling with her maid to Quebec City. When Peirce left on 10 September after completing his work in Montreal, Juliette again accompanied him. They stopped over in Albany, where Peirce visited the Dudley Observatory, and they stayed at the same hotel. Peirce's brazenness in his relations with Juliette, whether from innocence or arrogance, did not go unnoticed, especially by Superintendent Hilgard.

Operations at the Fort Marion station in St. Augustine were occasioned by a field party sent by the French government to observe the 6 December transit of Venus. Peirce was assigned to assist the French party by determining the longitude of the station, which he did with the assistance of E. D. Preston, at a station in Savannah, Georgia, and Captain Desforges at Fort Marion. Although he does not seem to have spent much time in Florida in December, he did oversee the setting-up of the station, and he wrote the 21 December letter to Mitchell with a graphical notation for the logic of relatives (item 60) from St. Augustine.

Peirce read four papers to the National Academy of Sciences in 1882, two based on his work at the Johns Hopkins and two on his work for the Survey. The practice of reading papers based on his work at the Johns Hopkins seems to have begun in November 1881 when he read a version of his "Logic of Number" (item 38). In April he presented "On a fallacy of induction" (P 233), which he had read five months earlier to the Johns Hopkins Scientific Association (P 211). At the November meetings, he presented "On the logic of relatives" (P 235), which was probably a version of his soon to be published "Note B" in Studies in Logic (item 66). He also read two papers resulting from his Coast Survey work, "On the determination of the figure of the earth by the variations of gravity" (P 234) and "On Ptolemy's catalogue of stars" (P 236). The first paper may have been a version of what he had read to the Johns Hopkins Scientific Association in 1881 (P 210) and had published in 1883 as "On the Deduction of the Ellipticity of the Earth from Pendulum Experiments" (item 76).

Three of Peirce's scientific papers appeared in print in 1882. In October "On Irregularities in the Amplitude of Oscillation of Pendulums" was published in the American Journal of Science and Arts (item 58), which is a response to remarks made by O. T. Sherman in an earlier issue of the Journal (24:176). Volume 13 of the Annals of the Astronomical Observatory of Harvard College, entitled Micrometric Measurements and published in 1882, contains the results of extensive observations made under the direction of Joseph Winlock and Edward C. Pickering during the years 1866-81. Peirce was one of the principal observers during many of those years and much of his work is represented in the volume (P 219). The third publication (P 238) is in Thomas Craig's A Treatise on Projections, which contains an extract from the "Quincuncial Projection" first published in 1879 (item 11).

Peirce's Coast Survey work for the first four months of 1883 consisted primarily of fieldwork at the Smithsonian and at Hoboken. In late December 1882 and continuing through most of January 1883 he was at the Smithsonian, and in February he reoccupied the Stevens Institute at Hoboken, where Peirce Pendulums 2 and 3 were swung for the purpose of comparing the yard with the meter. In March and April he was back at the Smithsonian.

April 1883 was an important month in Peirce's personal life. Emotions were running high in a dispute about a reference Peirce had inserted into a paper by J. J. Sylvester. Yet probably of greater concern to Peirce was the fact that his divorce from Zina was drawing near. The final decree was issued on 24 April and six days later he married Juliette. On the day of his divorce he had written to Gilman that something had gone wrong at the Survey, that he could not make his afternoon class and that it might be best to bring his lectures that term to a close. It was surely not coincidental that Superintendent Hilgard had issued instructions on the 23rd directing him to go to Europe to help connect English and American pendulum work and to obtain additional, specially constructed pendulum apparatus. Peirce's fifth, and last, European assignment must have come as a great relief, for it gave him and Juliette the opportunity to honeymoon away from the reproachful societies of Baltimore and Washington. Yet Peirce was diligent in executing his duties during his four months in Europe. He compared the Survey's standard yard No. 57 with the imperial yard No. 1 and with the iron yard No. 58 at the British Standards Office in London (where he also visited the library of the Royal Society). At the Kew Observatory in Surrey he measured the flexure of the pendulum base used for his 1878 experiments, which he had been unable to measure in 1878, and in Geneva he measured the flexure of the table he had used for the pendulum base in his 1875 experiments.

Part of Peirce's European assignment was to obtain special pendulum apparatus from Gautier, world-renowned manufacturer of precision instruments in Paris (where, at the Bibliotheque Nationale, he made a thorough study of Paris MS. No. 7378, the Epistle of Petrus Peregrinus on the lodestone). He had known for some time that the four pendulums made at the Coast Survey Office were sufficiently defective to diminish the accuracy of measurements and he was much pleased with the prospect of having Gautier construct new pendulums, which he intended to take back with him in September. But during some preliminary experiments at the Gautier workshop he discovered a new source of error, the result of the flexure of the pendulum staff due to cuts about the knife-edges. He designed an improved staff to eliminate this flexure and he received permission to have the pendulums redesigned. Unfortunately, manufacturing delays and the necessity for continued experimentation during the manufacturing process resulted in Peirce's return to America without the new pendulums. He unsuccessfully sought to obtain them after his return but was forced to continue using the old Peirce pendulums, thus depending on theoretically derived correction formulas. His failure with the Gautier pendulums no doubt contributed to Peirce's embitterment and growing estrangement from the Survey.

Having settled in Baltimore with Juliette after his return from Europe in September 1883, Peirce resumed the direction of pendulum work for the Survey and was soon conducting experiments at the Washington Office and at the Smithsonian Institution. Probably due to his lengthy stay in Europe, Peirce did not make any presentations to scientific associations during the year, although a number of his scientific papers appeared in print. Nature published his "Note on Peirce's comparison of U. S. Yard No. 57 with British Yard No. 1" (P 249), and the 1881 Coast Survey Report, published in 1883, contained his "Flexure of Pendulum Supports" (item 75), "Deduction of the Ellipticity of the Earth" (item 76), "Method of Observing the Coincidence of Vibration of Two Pendulums" (item 77), and "Value of Gravity at Paris" (item 15). Peirce's fieldwork was, as usual, detailed in the Report's "Pendulum observations" (P 252). The 1882 Report was also published in 1883 and it contained the "Report of a Conference on Gravity Determinations, held at Washington, D. C., in May 1882" (items 48-55), which Peirce had edited and to which he contributed his "Six Reasons for the Prosecution of Pendulum Experiments" (item 51) and the "Opinions" section (item 54).

1884 was probably the worst year of Peirce's life. On 26 January he was informed of a resolution of the Executive Committee of the Johns Hopkins that led to his dismissal a few months later. For several weeks, even months, Peirce was in a state of shock over the realization that his life's ambition had been shattered. Except for pendulum operations at the Smithsonian that continued under his direction through April, Peirce seems to have taken up no new Survey work until July when he received instructions from Hilgard to proceed to Fortress Monroe, Virginia, for gravity determinations and then to reconnoiter for one or two more stations in the mountains of Virginia, West Virginia, and North Carolina. Peirce was pleased with the results of his work at Fortress Monroe but he did not succeed in finding any new gravity stations. When Peirce returned to Washington he was put in charge of the Office of Weights and Measures.

Peirce finished the year with what seems to have been a burst of energy. Having resolved himself to a non-academic life, perhaps he was settling into his life as a scientist. He occupied the Smithsonian through February 1885 and measured (by comparing with standards) all four of the Peirce pendulums. As head of the Office of Weights and Measures, he traveled to Boston, Providence, Hartford, New York, and Philadelphia and met with electricians and manufacturers of gauges and machinery to determine how to meet the need for standards of measure as set out in resolutions passed at the United States Electric Conference. At the October meetings of the National Academy of Sciences in Newport he read three papers: "On Gravitation Survey" (P 281), "On Minimum Differences of Sensibility" (P 282), co-authored with Joseph Jastrow, and "On the Algebra of Logic" (P 283). He also discussed Wolcott Gibbs's paper "On the Theory of Atomic Volumes" and R. Pumpelly's paper "On an Experimental Composite Photograph of the Members of the Academy."

On 30 December he attended the American Metrological Society meeting at Columbia College, where he read a paper on the determination of gravity (P 270) and gave an account of his measures of the Old Stone Mill at Newport. A short article on the Mill had appeared in the 5 December issue of Science (P 293). In a discussion of the adequacy of the standards of weights and measures in the United States, Peirce informed the Society of some of the deficiencies of the current system. As a consequence, the Society passed a resolution calling for the appointment of a committee to persuade Congress and the Secretary of the Treasury of the need for establishing an efficient national bureau of weights and measures.

Possibly the most important of Peirce's scientific writings of 1884 was his "Determinations of Gravity at Allegheny, Ebensburgh, and York, Pa., in 1879 and 1880" (P 290), which appeared as Appendix 19 of the 1883 Report. His Photometric Researches of 1878 (W3: item 69) figured prominently in volume 14 of the Annals of the Astronomical Observatory of Harvard College, entitled Observations with the Meridian Photometer, by Edward C. Pickering (P 271). And in November 1884, he published a paper on "The Numerical Measure of the Success of Predictions" (P 292) in Science, which illustrates that his interest in finding suitable means for quantifying even the evaluative elements of scientific work continued after his earlier work on the economy of research.

In bringing the picture of Peirce's scientific activities to the end of 1884 we have gone somewhat beyond the period of the present volume. Yet it should be noted that as the present period ends and as Peirce came to accept the end of his academic career, he experienced something of a resurgence of his enthusiasm for experimental science. For a few months, until scandal shook the Survey, he may have thought that goodwill toward him might be restored. But, as will be seen in the introduction to the next volume, that was not to be.

The Johns Hopkins

Though Peirce's decision to teach logic at the Johns Hopkins was a diversion from the scientific path he had been following so successfully, it did not set him on a new path of inquiry. As he had clearly shown in his January 1878 letter where he had set down his views on how the physics department should be organized, logic had long been his abiding research interest. Some of his earliest writings were about logic, broadly conceived to include the study of scientific method as well as the more formal investigations of the syllogism and the algebra of logic. His first major series of lectures, the Harvard Lectures of 1865, was on the logic of science, and by the following year he had begun chapter 1 of a treatise on logic where he had pointed out that, although formal logic may seem trivial, it has in fact such a deep significance that "the commonest and most indispensible conceptions are nothing but objectifications of logical forms" (W1:351). Six years later, spurred on by the seminal deliberations of the Cambridge Metaphysical Club, Peirce was at work on his Logic of 1872-73, with "logic" now defined as "the doctrine of truth, its nature and the manner in which it is to be discovered" (W3:14). Although his focus had shifted somewhat from the formal to the pragmatic aspects of inquiry, his general interest still was logic. There is good reason to believe that his famous "Illustrations of the Logic of Science" of 1877-78 was the fruition of the 1872-73 work. Peirce expected to finish the "Illustrations" as the period of the present volume got underway and to publish them in book form in the International Scientific Series. The sixth paper had appeared in the Popular Science Monthly in August 1878 and the French version of the second paper appeared in January 1879. As late as 1881 he wrote to his mother that he was thinking of writing more papers for the series and in early 1882 he wrote, in the front of a diary listing his expectations for the year, that he intended "to write my book on logic." With this in mind, and remembering his 1867 American Academy Series (W2: items 2-6) and his pioneering 1870 "Description of a Notation for the Logic of Relatives" (W2: item 39), it is clear that when Peirce took up logic at the Johns Hopkins, he was continuing a well-established line of research. Already, W. K. Clifford had declared Peirce to be "the greatest living logician, and the second man since Aristotle who has added to the subject something material." 13

But in January 1879, even with the "Illustrations" still underway, neither logic nor philosophy in general was much on Peirce's mind. He was hard at work on his spectrum meter experiments and plans for his extensive Pennsylvania fieldwork for the Survey, and he was under considerable pressure to finish his report on gravity at initial stations (item 13) and some other field reports. Almost all of Peirce's 1879 writings, until he took up his position at the Johns Hopkins in the fall, reflect these scientific interests. The only exceptions are his short review of Read's Theory of Logic (item 1) and his lecture on logic and philosophy (item 3) which he may have delivered to the Harvard Philosophical Club in May. But this soon changed. On 27 July, he wrote to President Gilman that he was preparing his first lectures—"You would be amused if I were to say that they were very fine"—and soon afterwards he was deeply engaged in some of his most original logical researches. Not for several years—not until after his dismissal from the Johns Hopkins—did his philosophical research extend once again beyond logic to phenomenology and metaphysics.

Before turning to a chronological account of Peirce's life at the Johns Hopkins, a few general historical remarks should be made. The Johns Hopkins University opened in 1876, financed by a bequest of the Baltimore philanthropist who gave the university its name. On the advice of the presidents of some leading universities, the trustees decided to focus on the establishment of professional schools and to emphasize research and graduate education. Daniel C. Gilman had been appointed president the year before, and he began to put together his faculty according to the trustees' plan. He was so successful that Peirce could announce, in his Fourth of July address to Americans in Paris in 1880 (item 16), that the Johns Hopkins was unique among American universities in that "it has here alone been recognized that the function of a university is the production of knowledge, and that teaching is only a necessary means to that end." In its first four years, the published results of research done at the Johns Hopkins nearly equaled the total research output of all American universities for the preceding twenty years.

Eighty-nine students were enrolled in 1876 and, three years later, when Peirce took up his appointment, enrollment reached 159. Many of the early students had already taken degrees from other universities, and at Hopkins they sought advanced degrees. Johns Hopkins was the first university in America to offer the doctorate. Many brilliant students made their way to the university during the early years, and some of the fifty or so who studied with Peirce who stand out include John Dewey, Fabian Franklin, Benjamin Ives Gilman, Joseph Jastrow, Christine Ladd (Franklin), Allan Marquand, Oscar Howard Mitchell, and Thorstein Veblen. Christine Ladd, with whom Peirce kept in touch throughout his life, was among the most gifted of his students. The admission of a woman for an advanced degree was remarkable for the times, although Ladd had been admitted under some pressure from James Joseph Sylvester, professor of mathematics and one of the university's chief luminaries, and on the recommendation of Benjamin Peirce. But when time came to confer Ladd's degree, the trustees broke the promise implicit in her admission; her doctorate was not conferred until many years later.

The Johns Hopkins was an intimate community during this period, for besides the students, the number of professors, lecturers, associates, and instructors ran to only about forty. Peirce stood out in these circumstances. In his life of Gilman, Fabian Franklin remarks that "the singular genius of Charles S. Peirce was made a source of remarkable intellectual stimulation in the University", 14 and Christine Ladd reported that in the classroom "Peirce . . . had all the air . . . of the typical philosopher who is engaged, at the moment, in bringing fresh truth by divination out of some inexhaustible well." 15 When Sylvester asked one of his students to tell him about Peirce's lectures, he was informed that they "were always substantial, often very subtle, never trite, not easy to follow, frequently so lacking in clearness that the hearers were quite unable to understand"; but the student added that "there can be no question that Mr. Peirce is a man of genius." "Well," Sylvester replied, "if he is a genius, isn't that enough? Isn't it men of genius that we want here?" 16

Sylvester too, was a man of genius and the most distinguished professor during the university's early years. Although he had been shut out of university life in England, his reputation as a mathematician was of the first order. He had once held a post at the University of Virginia but had been forced to resign after an unfortunate incident with a violent student. Benjamin Peirce, perhaps the only mathematician in America who truly comprehended Sylvester's greatness, had urged Gilman to appoint him. Gilman had hesitated because he thought that Sylvester might be "hard to get on with" 17 but came to realize that he was precisely the kind of stimulating intellect needed to ignite the minds of advanced students. Sylvester was on the faculty when classes began in 1876. When he left seven years later to become Savilian Professor at Oxford, Gilman was probably beginning to reach his limit with the difficult natures of men of genius. He had just seen Sylvester and Peirce through a troublesome public quarrel and he now had to deal with the revelations and deliberations that would lead to Peirce's dismissal not long after.

Sylvester fully lived up to Gilman's expectations. Under his leadership Hopkins became the center of mathematical research in America; in fact, it might be said that American mathematics, as a true contender on the world stage, was born there during Sylvester's tenure. (Earlier, perhaps only the work of Benjamin Peirce had gained international respect.) Although it may have been in the classroom that Sylvester sowed the seeds for the mathematical harvest that would follow, it was his founding of the American Journal of Mathematics (again with the help of Benjamin Peirce) that quickly put the Johns Hopkins at the center of mathematical thought. With the very first issue in 1878 the Journal became the forum for original mathematical research in America, and it served to connect American work with work from abroad.

Although it was Sylvester who galvanized the mathematical community at Hopkins, he was by no means the only creative force. Sylvester had helped persuade Peirce and Thomas Craig to stay on at Hopkins—as Coast Survey employees they were finding it difficult to fulfill the duties of two offices—and in March 1881 he wrote to Gilman:

"Allow me to express the great satisfaction I feel in the interest of the University at the measures adopted by the Trustees to secure the continuance of Craig and Peirce. We now form a corps of no less than eight working mathematicians—actual producers and investigators—real working men: Story, Craig, Sylvester, Franklin, Mitchell, Ladd, Rowland, Peirce; which I think all the world must admit to be a pretty strong team."

And when Professor Arthur Cayley of Cambridge University came as a visiting lecturer from January to June 1882, it is doubtful that as much sheer mathematical power was so concentrated anywhere else.

The other Hopkins professors during Peirce's time were Basil L. Gildersleeve (Greek), Newell Martin (biology), Charles D. Morris (Latin and Greek), Ira Remsen (chemistry), and Henry A. Rowland (physics). Peirce seems to have had little interaction with Gildersleeve, Martin, Morris, and Remsen, although all except Morris read papers to the Metaphysical Club, which Peirce presided over for several terms. In the spring of 1880, Gildersleeve travelled to Europe with Sylvester and Peirce, and on 15 July wrote to Gilman from Paris that he had been seeing a good deal of Peirce, who "has been kind to me in his way, and if he were always as he can be sometimes, he would be a charming companion." But apparently no regular friendship developed. Relations were much closer with Rowland, chairman of the Physics Department, the position Peirce had sought in January 1878. Peirce often saw Rowland at the meetings of the Johns Hopkins Scientific Association and the Mathematical Seminary and he frequented and probably used Rowland's laboratory. When Rowland undertook to map the solar spectrum he used the results of Peirce's work on the absolute wave-length of light, which, combined with the results of Ångström and Louis Bell (Rowland's assistant), gave him his table of solar spectrum wave-lengths that served as the world standard for a generation. 18

Three lecturers at the Johns Hopkins must be mentioned as influential in Peirce's career: G. Stanley Hall, George S. Morris, and Simon Newcomb. The first two were on the philosophy faculty and taught in alternate half years. Morris taught ethics and the history of philosophy and Hall taught courses in psychology and developed the psychological laboratory. Although Morris, Hall, and Peirce were rivals for the philosophy professorship, there seems to have been no animosity among them, and Peirce's relations with Hall, who for a time lived just across the street from him, were quite friendly. They both had an active interest in experimental psychology and they appreciated each other's work. In an 1879 article in Mind on "Philosophy in the United States," Hall had praised Peirce as "a distinguished mathematician" whose Popular Science Monthly "Illustrations" promised to be "one of the most important of American contributions to philosophy." 19 In 1884, when Hall was chosen over Peirce and Morris (and also William James) for the philosophy professorship, he expressed surprise: "Each of the three was older and abler than I. Why the appointment, for which all of them had been considered, fell to me I was never able to understand unless it was because my standpoint was thought to be a little more accordant with the ideals which then prevailed there." 20 Hall went on, in 1889, to become president of Clark University which he modeled after the Johns Hopkins. Peirce visited him there at least twice.

Simon Newcomb, a protégé and friend of Benjamin Peirce, was well-known to Charles. Their paths had often crossed, in and out of the Peirce home, and would continue to cross for years. They corresponded for over thirty years, with Peirce's last letter to Newcomb dated 7 January 1908. 21 But more often than one might expect of a presumed friend, and more often than anyone realized, Newcomb took actions that damaged Peirce. Three incidents stand out. The first concerns Newcomb's role in the events leading to Peirce's dismissal which will be discussed later. The second occurred after Peirce's dismissal when Newcomb had succeeded Sylvester as editor of the American Journal of Mathematics. The first part of Peirce's "Algebra of Logic" (P 296), which had been accepted for publication by Sylvester, appeared in the Journal in 1885, and part 2 was to follow in the next issue. Confident that it would be published, Peirce had duly submitted it, but Newcomb rejected it on the ground that its subject was not mathematics. Given that in the first part Peirce had introduced quantifiers into his system of logic, as well as truth function analysis, Newcomb's rejection can only be seen as a great misfortune for Peirce and for logic. The third incident occurred years later when Newcomb was asked to review a scientific monograph that Peirce had prepared for publication for the Coast Survey—the report on gravity at the pendulum stations Peirce began occupying in 1885. He had spent years reducing his data and writing this report and he expected it to be a major contribution. But two of three reviewers recommended that it not be published, with Newcomb's negative appraisal perhaps the deciding one. The rejection of Peirce's report contributed to the decision to ask for his resignation from the Coast Survey. It is ironic that in his last letter to Newcomb, Peirce asked that he put in a good word for him at the Nation, which had long been an important source of income for Peirce, "if you are disposed to do me such a good turn."

In his five years at the Johns Hopkins, Peirce taught logic courses each semester, often both elementary and advanced courses. He also taught special courses on the logic of relatives, medieval logic, philosophical terminology, and probabilities, as well as a course on the psychology of great men. Never before in America—nor anywhere else, save perhaps at Aristotle's Academy in Athens—had a logician of such power developed a program of research with such capable students. It seemed certain that Gilman would see the results he had hoped for when he took a chance with Peirce. The expectation was widespread. According to John Venn:

"Mr. C. S. Peirce's name is so well known to those who take an interest in the development of the Boolian or symbolic treatment of Logic that the knowledge that he was engaged in lecturing upon the subject to advanced classes at the Johns Hopkins University will have been an assurance that some interesting contributions to the subject might soon be looked for." 22

Venn was reviewing the 1883 Studies in Logic, of which he said that "such assurance is justified in the volume under notice, which seems to me to contain a greater quantity of novel and suggestive matter than any other recent work on the same or allied subjects which has happened to come under my notice."

Peirce's involvement in the life of the university extended far beyond the classroom. He attended the meetings of the Mathematical Seminary and the Scientific Association and occasionally contributed papers. Not long after he had arrived at the Johns Hopkins, he instigated the founding of the Metaphysical Club, perhaps inspired by his memory of the old Cambridge Metaphysical Club. He had conceived it, according to Christine Ladd, in this way: "So devious and unpredictable was his course that he once, to the delight of his students, proposed at the end of his lecture, that we should form (for greater freedom of discussion) a Metaphysical Club, though he had begun the lecture by defining metaphysics to be 'the science of unclear thinking'." 23 At the first meeting, on 28 October 1879, Peirce was elected president and Allan Marquand secretary, and six papers were read and discussed. According to the minutes of the second meeting, the club was to meet each month during the academic year, and the standard order of business was to be as follows:

"1. Reading of Minutes.
2. Reading & discussion of a Principal Paper, the delivery of which shall not exceed forty-five (45) minutes.
3. Papers deferred from previous meetings.
4. Reading & discussion of Minor Communications, the delivery of which shall not exceed twenty (20) minutes.
5. Reviews of books & magazines.
6. Transaction of business.
7. Adjournment"

Peirce served as president for about half the club's life, the other half being divided between Hall and Morris. He attended nearly two-thirds of the meetings and as late as 13 May 1884, long after it was known that his contract would not be renewed, he presided over the thirty-ninth meeting in the absence of Hall. He delivered his final paper to the club at its 40th meeting on 18 November. By this time Hall had been appointed to fill the philosophy position as professor of psychology and pedagogy, and he recommended at the 40th meeting that the Metaphysical Club should be reorganized to reflect the changes in the philosophy program. The club met only three more times, expiring with the 43rd meeting of 3 March 1885, not long after Peirce's departure.

It is not surprising that most of Peirce's research during the period of this volume, except for science, closely follows the paths marked out by his Hopkins courses and activities. Even the impact of his father's death on his program of research was influenced by Sylvester, who urged him to edit Linear Associative Algebra for publication in the Journal. Peirce's interest in carrying on some of his father's mathematical work became much intertwined with interests related to the mathematical community at Hopkins, which included some of his best logic students.

During his first semester he taught a general logic course that met three times a week for three months and a course in medieval logic which met only once a week. Fourteen students took general logic, including three who would make contributions to Studies in Logic: B. I. Gilman, Ladd, and Marquand. It was the lectures for this course that Peirce was preparing when on 27 July he wrote to Gilman that "you would be amused if I were to say that they were very fine." Earlier in the letter, Peirce had expressed some anxiety about the coming term:

"I have a good deal of confidence & a good deal of diffidence about my instruction in Logic. The former about the ultimate result if I succeed in pleasing you the first year, the latter about the first year. Logic is peculiar in this respect that it is not so much a body of information as it is knowing how to use the mind. That is why the Socratic method ought to be followed as much as possible. But then it is extremely difficult to make that method work right."

From lecture notes and course descriptions, and from class notes taken by Allan Marquand and other students, we can get a fairly clear picture of what Peirce's courses were like and what he was like as a teacher. Christine Ladd-Franklin speaks of the eagerness of Peirce's students for intellectual adventure and their receptiveness "to the inspiration to be had from one more master mind."

"He sat when he addressed his handful of students (who turned out afterwards, however, to be a not unimportant handful) and he had all the air . . . of the typical philosopher who is engaged, at the moment, in bringing fresh truth by divination out of some inexhaustible well. He got his effect not by anything that could be called an inspiring personality, in the usual sense of the term, but rather by creating the impression that we had before us a profound, original, dispassionate and impassioned seeker of truth." 24

Joseph Jastrow reports that "Peirce's courses in logic gave me my first real experience of intellectual muscle." He goes on to speak of Peirce's "fertile suggestiveness" and then of his personality.

"Mr. Peirce's personality was affected by a superficial reticence often associated with the scientific temperament. He readily gave the impression of being unsocial, possibly cold, more truly retiring. At bottom the trait was in the nature of a refined shyness, an embarrassment in the presence of the small talk and introductory salutations intruded by convention to start one's mind. His nature was generously hospitable; he was an intellectual host. In that respect he was eminently fitted to become the leader of a select band of disciples. Under more fortunate circumstances, his academic usefulness might have been vastly extended. For he had the pedagogic gift to an unusual degree. . . .

"The young men in my group who were admitted to his circle found him a most agreeable companion. The terms of equality upon which he met us were not in the way of flattery, for they were too spontaneous and sincere. We were members of his "scientific" fraternity; greetings were brief, and we proceeded to the business that brought us together, in which he and we found more pleasure than in anything else." 25

In reflecting on the courses she had taken with Peirce, Christine Ladd-Franklin remarked that "His lectures on philosophical logic we should doubtless have followed to much greater advantage if he had recommended to us to read his masterly series of articles on the subject which had already appeared in the Popular Science Monthly." 26 But Marquand's notes of Peirce's first classes show that, even if his "Illustrations" were not required reading, he often referred to them and spent his first three lectures discussing such topics as doubt and belief, methods of fixing belief, and degrees of clearness of ideas. This was the early part of the course Peirce called prolegomena, which continued through the eleventh class on 3 November. The final four paragraphs of Marquand's notes on lecture 11 show Peirce's concluding emphasis for this part of the course:

"Various forms of investigation of the same subject converge to one result. Eg on velocity of light. This gives a real significance—a finality to truth. It is no (made up) figment, but a reality.

"We do not make Reality independent of thought altogether, but only of the opinion of you I or any other man. We may adopt a false opinion, this only delays the approach of the true.

"Truth we may call a predestinate opinion—sure to come true. Fatalism proper assumes events as sure to come to pass, no matter what we do about it. But our reaching this opinion tomorrow or next year does depend upon what we do. Its characters nevertheless are independent of our opinion.

"To say that real things influence our minds & that opinion will finally become settled—one & same. No explanation to say we come to same conclusion because real things influence our minds. We come to this final opinion by a process. What is that process, is the problem of Logic which we now consider."

Peirce continued the course with a lecture and a half on his theory of signs, taken mainly from hisJournal of Speculative Philosophy series of 1868 (W2), and then he took up formal logic, which he divided into syllogistic, the theory of logical extension and comprehension, the quantification of the predicate, and the algebra of logic. The first three topics took Peirce to the end of the term (of thirty lectures). The algebra of logic was reserved for the second term.

Peirce's lectures on formal logic were based in part on his 1867 American Academy series (W2), but many new issues were developed which helped set the course for future work. For example, in order to examine reasoning in the theory of numbers, Peirce developed an axiomatic treatment of elementary number theory. In his 17 December lecture he gave the following seven premises:

"1. Every number by process of increase by 1 produces a number.
2. The no. 1 is not so produced.
3. Every other number is so produced.
4. The producing & produced nos. are different.
5. In whatever transitive relation every no. so produced stands to that which produces it, in that relation every no. other than 1 stands to 1.
6. What is so produced from any individual no. is an individual no.
7. What so produces any individual no. is an individual no."

Then, after specifying his notation and defining the relations "greater than" and "not greater than," he went on to develop examples. Items 24 and 38 show that Peirce continued to refine his basis for natural numbers.

Marquand's notes illustrate that Peirce used his classes to work through material that he was preparing for publication—or that what he prepared for his courses ended up in print. Several of Peirce's important writings on logic from this period correspond to the content of his courses. This is true of "On the Logic of Number" (item 38) as well as of "On the Algebra of Logic" (item 19). When Peirce began the second half of his first logic course on 12 January 1880, he indicated that he would be dealing with Boole's and Schröder's work and with his improvements on Boole. He also mentioned work by Leslie Ellis and his own "Logic of Relatives" and De Morgan's 1860 paper on the syllogism. But the material Peirce discussed in his winter 1880 classes was developed quite beyond his algebras of 1867 and 1870. In the fall or winter of 1879, Peirce worked out a systematic treatment of the algebra of logic entitled "On the Algebraic Principles of Formal Logic" (item 6). Although this work is fragmentary, it suggests a systematic presentation of the algebra of logic that may have served both as an outline for his class lectures and for item 19. Even though item 6 is no doubt an early version of item 19, it is of interest to look at some of the differences. In item 6 Peirce still employed his 1870 notation, using the claw (–<) as his sign for general inclusion, "+," for logical addition, and "," for logical multiplication. In item 19, however, he has replaced the "+," with the simpler "+" and the "," (for logical multiplication) with "x" (or mere conjunction) though he retains his claw, as he will for the rest of his life (except in his graphical notations). The most powerful rule in the earlier system is a principle of duality that permits the assertion of a dual form for every well-formed expression. This rule is not present in the item 19 system but in its place is a new, more powerful (and considerably more important) rule, related to the deduction theorem, that permits the assertion of inferences as inclusions and vice versa. As a general expression of this powerful rule Peirce asserted the identity of the relation expressed by the copula with that of illation, and said that this identification gives us the principle of identity (x –< x) and shows that the two inferences

                  y      and                         x
[therefore]z                  [therefore] y –<z

are of the same validity. By this rule modus ponens and conditional proofs are legitimized in item 19, but they are no part of the earlier work. Otherwise the systems bear marked similarities.

Item 19 did not appear in print until September 1880, though Peirce had completed it by April when he left for Europe on assignment for the Coast Survey. Thus within a few months' time, six at most, his system had evolved in the ways indicated above. Notably, what came in between was his first course in logic. We know from Marquand's notes that as early as 12 November 1879 Peirce had asserted that "the Copula expresses a transitive relation" and that on 3 December he pointed out that "later in theory than Syllogistic—springs also as all Logic, from transitiveness of Copula" and "we have already identified the illative sign with the transitiveness of the copula. A [therefore] B & A –<B. The resemblance more important than the difference." Although it is impossible to say how much Peirce's interaction with his students influenced his writings, the above case (which is one of several that could have been given) is very suggestive of the sort of synergism that one might expect between a good teacher and good students.

Another topic that occupied Peirce during the winter of 1879 was the relationship between thinking and cerebration (or logic and physiology in his first logic course). Two versions of a paper on the subject, included in the present volume, are first chapters of a work on logic, perhaps the book he was preparing from his "Illustrations." This is suggested by the fact that one version of the paper (item 7) moves into a discussion of the settlement of opinion that is taken almost verbatim from the first "Illustration" (W3:242-57), even as both papers appear to be early versions of the first section of item 19. Perhaps Peirce had it in mind to somehow combine his "Illustrations" with his 1879-80 work on the algebra of logic and to make that his logic book in the International Scientific Series. 27 It should also be noted that Peirce began his first logic course with a discussion of the connection between logic and physiology.

Five students were enrolled in Peirce's course in medieval logic, described in the Hopkins Circulars as "A course of lectures on Medieval Logic, designed to show the spirit and leading doctrines of the logic of the Middle Ages." Peirce had made a thorough study of the history of logic and was probably the most knowledgeable American in medieval logic, and his collection of medieval logic texts was unsurpassed in America. While he was teaching medieval logic, he also directed Marquand's study of Epicurean logic, especially of the Herculaneum papyrus of Philodemus's "On Methods of Inference." On Peirce's recommendation Marquand made the first English translation which he submitted along with a commentary as his doctoral dissertation. A paper by Marquand on Epicurean logic, possibly the commentary part of his dissertation, was included in Studies in Logic. Peirce's own study of Epicureanism, in guiding Marquand, may have planted the seed that a few years later, fed by his developing evolutionism, grew into the paper on "Design and Chance," the seed being the Epicurean doctrine of absolute chance, the view that a place for freedom was afforded by the uncaused swerve of atoms. 28

During the same term Peirce gave a paper to the Metaphysical Club on 11 November on "Questions Concerning Certain Faculties Claimed for Man" and, on 3 December he spoke to the Scientific Association on the four color problem (he is reported to have suggested improvements to the method of demonstration employed by A. B. Kempe). 29 Before the year was out, he reviewed Vol. 2, No. 3, of the American Journal of Mathematics for the Nation. He remarked that Hall's discovery (at the Johns Hopkins) of the effect of magnets on electric current (the Hall effect) could hardly be overestimated, and he took special note of Sylvester's stress on the importance of observation for the discovery of mathematical laws by saying that "there has been, perhaps, no other great mathematician in whose works this is so continually illustrated."

At the end of his first term Peirce wrote the 25 December letter to Gilman about his "state of dangerous cerebral activity & excitement." He returned in January to begin a very unsettling year, albeit one of remarkable achievement. While confined to his quarters with bronchitis during the first months of 1880, that he wrote "On the Algebra of Logic (item 19)", in which he produced a system of logic that with only slight augmentation provides a complete basis for logic. 30 This paper is part of a series in which Peirce set out his logic of relatives and as Tarski noticed, "laid the foundation for the theory of relations as a deductive discipline." 31 It is in this paper that Peirce begins to loosen the ties between his logic of relatives and mathematical analysis. Item 19 also gives Peirce a place in the development of the mathematical theory of lattices, although his rôle in the foundation of lattice theory is somewhat controversial (and it cannot even be said unequivocally that Peirce ever fully comprehended the idea of a lattice). The controversy stems from Peirce's claim that the full law of distribution could be proved within his 1880 system with the implication that all lattices are distributive. Peirce declined to give his proof in on the ground that it was too "tedious." Schröder and others (Vogt, Lüroth, Korselt, and Dedekind) 32 countered with proofs of the independence of the law of distribution but, after at first conceding, Peirce came back in 1903-04 in support of his original claim. His distributivity proof, first written out in his logic notebook (Robin MS 339, p. 437) on 31 January 1902, was published by Edward V. Huntington in 1904 33 and later by C. I. Lewis in his Survey of Symbolic Logic. 34 There is disagreement about the desirability of modifying the basis of Boolian algebra as Peirce did in order for his proof to go through. 35 An earlier proof given in Peirce's 1879 "Algebraic Principles" (item 6) has not yet been examined by mathematicians.

Also in 1880 he wrote his short "A Boolian Algebra with One Constant" (item 23), in which he anticipated H. M. Sheffer's paper of 1913 that introduced the stroke function. 36 He also continued his work on number theory and in the winter following his father's death began working in earnest on associative algebras. By the end of the year Peirce had sketched out his proof that, in the words of Eric Bell, "the only linear associative algebra in which the coordinates are real numbers, and in which a product vanishes if and only if one factor is zero, are the field of real numbers, the field of ordinary complex numbers, and the algebra of quaternions with real coefficients." 37 The proof appeared as an appendix to his edition of Linear Associative Algebra (item 42).

The Metaphysical Club was especially active during the first half of 1880 with about twenty presentations, and a special meeting was called in May for Josiah Royce's "On Purpose in Thought," read in his absence. On 9 March Peirce had presented "On Kant's Critique of the Pure Reason in the light of modern logic," which appears to be one of the few papers in this period focussing directly on the fundamental philosophical questions which Peirce had developed in his 1867 American Academy Series but which he would not take up again for several years. The following abstract of the paper appeared in the April Circular:

"Mr. Peirce compared Kant's solution of the problem "How are synthetical judgments à priori possible?" with the solution given by modern logic of the problem "How are synthetical judgments in general possible?" He showed that the reply which Kant makes to the former question has its analogue with reference to the latter. This analogous answer to the second question is true, indeed, but is far from being a complete solution of the problem. On the other hand, the solution which modern logic gives of its question may be successfully applied to Kant's problem; but this does not enable us to discover the origin of the conceptions of space and time. The categories of Kant were next considered. The list given by him is built upon the basis of a formal logic which subsequent criticism has undermined and carried away. Nevertheless there really do exist relationships between some of those conceptions and logic on the one hand and time on the other. The explanation of these relationships in conformity with modern logic, though far more definite than that of Kant, is not altogether dissimilar to it."

An impressive record of the fertility of Peirce's mind in 1880 can be found in a notebook, probably written during the summer while he was in Paris. Entitled "Logic of Relatives," MS 364 contains a remarkable set of ideas and developments, including notes on alternative copulas where Peirce first set out the idea for his single connective Boolian algebra, some suggestive moves toward his quantifier notation, a new set of seven axioms of number based on the "greater than" relation, and notes on his relative of simple correspondence that he used for his treatment of finite collections (see item 38). It is possible that, like items 20 and 22, these are notes toward a continuation of item 19, a continuation that was sidetracked by his father's death and by Schröder's criticisms of his distribution claims. As might be expected, the ideas Peirce developed in the summer made their way into his logic classes in the fall.

Peirce had begun 1880 teaching the second half of his first general course on logic, as well as a two-month course in probabilities. In connection with the latter he probably wrote his notes entitled "A large number of repetitions of similar trials" (item 14). But his courses appear to have been cut short by the illness that gave him the opportunity to finish item 19 before leaving for Europe in April.

Peirce had returned by 5 August and remained in Cambridge until after his father's death on 6 October. Although he had originally thought to skip the fall term at the Johns Hopkins (he had been authorized to stay in Europe until January), he now prepared for the full academic year. On 19 August he wrote to Gilman about his upcoming lectures:

"I wish to extend them through the whole year if possible, & if Patterson consents. I expect to make two courses, one very elementary and practical, the other to take up first the algebra of logic, then probabilities, and finally inductive logic. I have this summer made a discovery in logic which seems to me to be really important. I shall develop it in an early number of the Journal of mathematics; and shall explain it in my lectures."

The "Logic of Relatives" notebook (MS 364) provides clues as to what this discovery might have been: his successful axiomatization of the natural numbers or his definition of finite sets (item 38); his "A Boolian Algebra with One Constant" (item 23); or it might have involved quantification or truth values. Peirce continued his letter with a remark about "On the Algebra of Logic," which would soon be in print. "This paper which is appearing in the Journal will probably be in 3 parts and will cover over 100 pages. The first part appears in the number which is nearly ready. I think it would be well for me to put some of my copies on sale at Cushing & Baily's for the convenience of my students."

Although Peirce was despondent when he returned to Baltimore after his father's death, he pulled himself together for his two fall semester courses: elementary logic, which met twice a week with an enrollment of five, and advanced logic, which met three times a week with an enrollment of seven. Among the seven were all the contributors to Studies in Logic as well as Sylvester's favorite student, Fabian Franklin. The text for the first part of the advanced course (item 19) had been issued in September. One of Peirce's assignments appears to have been the preparation of class notes, or notes on the text, to be handed in for his scrutiny and comments. Christine Ladd's notes reveal an intensive study of item 19, especially with regard to his extension of De Morgan's eight propositional forms. Peirce had remarked that if we admit "particularly of the predicate," the system of propositions must be enlarged; but he did not say how many propositional forms there would be in the completed system. In one of the early classes in the fall term he showed that there are fifteen states of the universe for two terms; he did not yet consider the empty universe as a sixteenth state. Ladd made an elaborate study of this matter and struggled with the problematic empty universe. Taking a hint from Fabian Franklin's application of binary notation to logical formulae, she worked out binary numbers for all the value combinations for two terms. Though reluctant, she felt compelled for reasons of symmetry to include the null case. It was not until she read an early version of her Studies in Logic paper to the Metaphysical Club in January 1881 that she had overcome her reluctance to imagine an empty universe. A table in that paper gives "the sixteen possible constitutions of the universe with respect to two terms," which is in effect the second order truth-table for the sixteen binary connectives (probably making its first appearance in print). 38

Peirce had resigned the presidency of the Metaphysical Club before leaving for Europe, thinking he would be away until January, but he was reelected in the fall when he returned early. On 14 December 1880 he suffered from a severe headache and sent a note to be read in his absence at the meeting that evening. He reported that he had made contact with the secretary of the Leipzig Academical Philosophical Club, which sought to establish a "better acquaintance between the Clubs" and that he had "lately received papers from professors Wundt, Schröder, J. J. Murphy, Venn, Jevons, MacColl, and others on various logical and psychological subjects." With his fellows club members, Peirce was in the inner circle of logic.

Yet at the height of his success as a logician he had not settled on a career in logic. His success as a scientist, combined with the pressures of his duties for the Coast Survey, had something to do with his hesitation to commit himself to logic, as did his father's advice that he stick with science, but probably the main reason was his unhappiness with his part-time status at the Johns Hopkins. On 18 December he wrote to Gilman that he intended to leave the university in the spring because of the difficulty with conducting two careers at once and that, given his "subordinate position" at the Johns Hopkins, he was unwilling to modify his connection with the Coast Survey. He intended to abandon the study of logic and philosophy and offered to sell his library (on those subjects) to the University for $550. Before the week was out Gilman accepted Peirce's offer and, in his commencement day address on 22 February, he lauded Peirce and remarked on the importance of his collection. 39 But Peirce did not quit logic and philosophy and he soon deeply regretted the loss of his books. By November 1883 his efforts to secure special volumes for his research and his courses—most notably the Berlin Aristotle—and his attempt to buy back some of the books he had sold to the library had become a source of irritation to the library committee and of personal offense to Gilman.

When Peirce resumed teaching in January 1881 for his fourth term he expected it to be his last; for by 7 February the trustees had accepted his decision to leave. Had his elementary logic course with three students and his advanced course with six (including, again, B. I. Gilman, Ladd, and Marquand) been his last, he might have avoided the erosion of his welcome at the Johns Hopkins as well as the scandal of his dismissal, which closed academic doors later on. But by the end of March, Sylvester had prevailed on Gilman to keep Peirce (and Craig) and the trustees had agreed to raise his salary from $1500 to $2500. Peirce agreed to stay on, and soon he was again deeply engaged in his logical researches.

1881 was a very productive year for Peirce, especially in logic. Probably in the spring, in connection with his advanced logic class, he wrote his paper on the theory of probable inference, which would later be included in Studies in Logic (item 64), and in the summer he wrote "On the Logic of Number" (item 38) where, several years before the equivalent axiomatizations of Dedekind and Peano,40 he gave his successful axiomatization of the natural numbers. Near the end of the year he composed his "Proof of the Fundamental Proposition of Arithmetic" (item 36) in which he proved, using De Morgan's syllogism of transposed quantity to define a finite collection (as he had in item 38), that the sequential order of objects counted does not affect the count (the outcome of the counting). In November he read "On the logic of number" (P 200) before the National Academy of Sciences. In the meantime, he had continued work on his father's Linear Associative Algebra, with commentary and further developments of his own (items 26 and 27), including his proof that there are only three linear associative algebras in which division is unambiguous, which he presented to the Mathematical Seminary in January. He also continued his "Logic," in which he probably intended to include his "Illustrations," the papers on thinking as cerebration (items 7 and 8), and "On the Algebra of Logic" (item 19) and its projected continuation. Two other papers included here seem also to belong in this group: "Logic; and the Methods of Science" (item 30) and "Methods of Reasoning" (item 31), which provide an important link between item 19 and the 1885 article "On the Algebra of Logic."

An examination of the early volumes of the American Journal of Mathematics reveals that many of the contributions are entitled "Note on . . . " or simply "On . . . " and it is quite probable that many of Peirce's short manuscripts of this period that have such titles were written with the Journal in mind. A number of these pieces did appear there (items 10, 19, 38, 41, and 42) although at least three of them are more substantial than ordinary notes, and several others (items 5, 15, 18, and 44) appear elsewhere, though they too in may originally have been written for Sylvester's Journal. Even Notes A and B in Studies in Logic may have been intended at first for the Journal, along with items 6, 32, 33. But it is also possible that some of these papers were written for presentation at one or another of the Johns Hopkins clubs, for many of their presentations had such titles, including Peirce's "On Relations between Sensations" in April 1881 and Joseph Jastrow's "A Note on Mechanical Light" in April 1883.

Peirce was president of the Metaphysical Club for all of 1881 but was absent for two of its six meetings. At the meetings he attended he heard ten papers by among others, Ladd, Franklin, Davis, Marquand, B. I. Gilman, and G. S. Morris. These were mainly on logic (three were on induction) and psychology, but one by Burt was on Hegel's Philosophical Propaedeutic and Morris's was on "English Deism and the Philosophy of Religion." In November Peirce gave a paper entitled "A Fallacy of Induction" before the Scientific Association in which he examined some of Priestley's inferences concerning atomic weights and specific heats. 41

Peirce's courses in the fall of 1881 had unusually low enrollment with only three students both in his elementary and his advanced logic course. (Thorstein Veblen was in the elementary course, and Davis, B. I. Gilman, and Mitchell in the advanced.) The courses were described in the July Circular as follows :

"1. An elementary course on General Logic, deductive and inductive, including probabilities. This course will be designed to teach the main principles upon which correct and fruitful reasoning must proceed; and special attention will be paid to the discussion of the significance and validity of those logical conceptions and maxims which are current in literature and in law.
  2. A course upon the methods of science. A sketch of deductive logic and the theory of relative terms will lead to the study of the methods of Mathematics. The theory of chances and errors will next be expounded. Lastly, after the development of the general doctrine of induction and hypothesis, the methods of reasoning in several of the physical and moral sciences will be examined in detail."

By the end of 1881 Peirce was again fully committed to logic both as investigator and teacher, and his reputation was now such that his work was noticed almost as soon as it appeared. To his Preface in his Studies in Deductive Logic, dated 3 October 1880, W. Stanley Jevons added the following paragraph:

"To the imperfect list of the most recent writings on Symbolical Logic, given in this preface, I am enabled to add at the last moment the important new memoir of Professor C. S. Peirce on the Algebra of Logic, the first part of which is printed in the American Journal of Mathematics, vol. iii (15th September, 1880). Professor Peirce adopts the relation of inclusion, instead of that of equation, as the basis of his system." 42

Peirce's paper (item 19) had been out less than three weeks. John Venn noticed the same paper at the 6 December 1880 meeting of the Cambridge Philosophical Society, in particular Peirce's notation (which appeared just before Frege's). 43 But perhaps the most satisfying notice came in the 24 March 1881 issue of Nature where, in a piece entitled "Recent Mathematico-Logical Memoirs," Jevons claimed that: "The most elaborate recent contributions to mathematico-logical science, at least in the English language, are the memoirs of Prof. C. S. Peirce, the distinguished mathematician, now of the Johns Hopkins University, Baltimore."

Peirce's classes in the spring of 1882 were better enrolled, for he had five students in each of his two regular classes, elementary and advanced logic. (Mitchell took both, and B. I. Gilman and Ladd repeated the advanced course.) Peirce also taught a short course on the logic of relatives, where items 45 and 46 may have originated (as well as Note B of Studies in Logic). Perhaps the best indication of what Peirce covered in his short course is his "Brief Description of the Algebra of Relatives" (item 43) which he composed in very short order at the beginning of the term, inspired by what he heard from his advanced logic students who were taking Sylvester's new course of lectures on universal multiple algebra. Peirce was convinced that Sylvester's universal algebra was only a case, or interpretation, of his own logic of relatives, and he decided to write out his system in a way that would demonstrate the identity. He especially wanted to present his logic of relatives in a manner that would interest Sylvester. Peirce's "Brief Description" is dated 7 January and he had proof sheets in hand by the middle of the month. Even as he was writing his brochure he was in correspondence with Sylvester about some of the points he hoped to demonstrate. But Sylvester seems not to have been convinced—and he was not anxious to see the paper in print, as is evident from Peirce's 6 January 1882 letter:

"I lay no more claim to your umbral notation than I do to the conception of a square block of quantities! What I lay claim to is the mode of multiplication by which as it appears to me this system of algebra is characterized. This claim I am quite sure that your own sense of justice will compel you sooner or later to acknowledge. Since you do not acknowledge it now, I shall avail myself of your recommendation to go into print with it. I have no doubt that your discoveries will give the algebra all the notice which I have always thought it merited and therefore I hope my new statement of its principles will be timely. I cannot see why I should wait until after the termination of your lectures before appearing with this, in which I have no intention of doing more than explaining my own system & of saying that so far as I am informed it appears to be substantially identical with your new algebra, & that it ought to be, for the reason that mine embraces every associative algebra, together with a large class—perhaps all—of those which are not entirely associative. I am sorry you seem to be vexed with me."

Just the day before Peirce had written to Sylvester trying to explain the "precise relationship of your algebra of matrices to my algebra of relatives." He concluded that "It, thus, appears to me just to say that the two algebras are identical, except that mine also extends to triple & other relatives which transcend two dimensions."

Arthur Cayley had arrived at the Johns Hopkins in December and in January began his half-year tenure as visiting lecturer. On 18 January he, Sylvester, and Peirce had delivered a special program of lectures to the Mathematical Seminary in celebration of Cayley's visit. Peirce's paper, "On the Relative Forms of Quaternions" (item 44), was commented on favorably by Sylvester. On 16 January Peirce had added a note to his brochure, which was then in press, stating that on that day, for the first time, he had read Cayley's 1858 Memoir on Matrices and had discovered that his algebra of dual relatives had been substantially anticipated by Cayley although, he pointed out, "many of his results are limited to the very exceptional cases in which division is a determinative process." Peirce was beginning to fear that his brochure might somehow offend Sylvester, perhaps even Cayley. So on 7 February, when his printed copies arrived, Peirce sent one to President Gilman along with the following note:

"It occurs to me that it is possible that (although I am unable to see it at all) there may be some just cause of offense in my references on the last page to Professors Sylvester and Cayley. Of course, you will see none at first glance; but will you see them and find out 1st whether they think they see anything out of the way and 2nd whether if so it is merely the systematic arrogance of these Britishers or whether it is just. I will keep back the issue until I hear from you."

There must have been some objection, for Peirce never did distribute his brochure. But he no doubt taught its content in his course on the logic of relatives, and he used it in his logic class in the fall.

However frustrated Peirce may have been—on 7 January he wrote "Sylvester is a cad" in his diary, and in later years he remembered that he had "felt squelched" 44—his relations with Sylvester continued seemingly undamaged. On 5 March he again wrote to him: "I have a purely algebraical proof that any associative algebra of order n can be represented by a matrix of order n + 1 having one row of zeros, together with a rule for instantaneously writing down such a matrix." About the same time, Sylvester was seeing Peirce's "On the Logic of Number" and his edition ofLinear Associative Algebra through the press. They appeared in the fourth volume of Sylvester's Journal with the Linear Associative Algebra stretching over two issues. In the second addendum to LAA, "On the Relative Forms of the Algebras" (item 41), Peirce inserted a reference to his problematic brochure, which suggests that he may have completed this addendum between 7 January, when he finished the brochure, and the middle of February, by which time he had decided not to distribute it.

Peirce's summer was almost completely taken up with his scientific endeavors, especially his work with John Herschel and the construction of his new pendulums but also with his spectrum meter experiments and with his reports for the Superintendent. He was occupied, as well, with the legal preparations for his divorce from Zina. He commuted frequently Baltimore, Washington, and New York, and took occasional side trips on Coast Survey business including the ill-fated trip to Montreal and Albany.

Charles Darwin's death in April had rekindled discussions of the question of evolution. On 27 April T. H. Huxley had written for Nature:

"He found a great truth, trodden under foot, reviled by bigots, and ridiculed by all the world; he lived long enough to see it, chiefly by his own efforts, irrefragably established in science, inseparably incorporated with the common thought of men, and only hated and feared by those who would revile, but dare not." 45

When Peirce returned to Baltimore in September to begin his fall classes, he gave a public lecture (item 56) designed to convey "the purpose of the study of logic" and "remove some prejudices." He gave a general outline of his fall course (to meet four times a week) and made a strong pitch for liberal education:

"But when new paths have to be struck out, a spinal cord is not enough; a brain is needed, and that brain an organ of mind, and that mind perfected by a liberal education. And a liberal education—so far as its relation to the understanding goes—means logic. That is indispensible to it, and no other one thing is."

Reflecting on Darwin's achievements, he attributed them largely to his method:

"The scientific specialists—pendulum swingers and the like—are doing a great and useful work; each one very little, but altogether something vast. But the higher places in science in the coming years are for those who succeed in adapting the methods of one science to the investigation of another. That is what the greatest progress of the passing generation has consisted in. Darwin adapted to biology the methods of Malthus and the economists. . . ."

After several other examples of men who had adapted the methods of one science to the investigation of another, Peirce went on:

"in order to adapt to his own science the method of another with which he is less familiar, and to properly modify it so as to suit it to its new use, an acquaintance with the principles upon which it depends will be of the greatest benefit. For that sort of work a man needs to be more than a mere specialist; he needs such a general training of his mind, and such knowledge as shall show him how to make his powers most effective in a new direction. That knowledge is logic."

Peirce was beginning to see his task as that of applying the methods of logic, especially induction and hypothesis, to philosophy and science. Over the coming months he would reflect on the statistical method that had been so fruitful for Darwin and would make the bold surmise that chance is an active player in the evolution of the universe and its laws. The Epicurean seed would bear fruit.

Peirce's logic class for the fall of 1882 (with fourteen students!) and the spring of 1883 (with seven) was remarkable. Jastrow stayed for both terms, and it is probably this course he was thinking of when he said that Peirce had given him his first real experience of intellectual muscle. Peirce considered the foundations and philosophy of logic, using his "Illustrations" as his text, and then took up modern formal logic and the algebra of logic, using as texts De Morgan's Syllabus of Logic and Schröder's Operationskreis des Logikkalkuls, with examples from many other sources. He then took up (1) the logic of relatives, using as texts his "Logic of Relatives" (item 39 in W2), "Algebra of Logic" (item 19), "Algebra of Relatives" (item 43), and his paper on the logic of relatives that would become Note B in the Studies in Logic (item 66); (2) mathematical reasoning, where he examined the nature of mathematical demonstration and studied "the methods of mathematical research" using the history of multiple algebra as his example; (3) the theory of probabilities, with Liagre's Calcul des Probabilités, Boole's Calculus of Finite Differences, and Ferrero's Metodo dei Minimi Quadrati as texts; (4) inductive reasoning, to which he devoted a large part of the course and for which he used his "Theory of Probable Inference" (item 64); (5) the nature of scientific reasoning, with Kepler's De motibus stellae Martis; (6) an inquiry into the validity of modern conceptions of the constitution of matter, with Meyer's Kinetische Theorie der Gase; and (7) in conclusion, he considered the relation of the new theory of logic to philosophical questions. This course was Peirce's most ambitious bid for a permanent position as Professor of Logic.

Peirce continued his active participation in the Johns Hopkins clubs. He presided over the Metaphysical Club until November and gave a paper on Mill's logic and a response (item 47) to B. I. Gilman's "On Propositions and the Syllogism." In October he read "On a Class of Multiple Algebras" (item 57) to the Mathematical Seminary. He also presented two papers on logic to the National Academy of Sciences, one in April "On a fallacy of induction" (P 233) and another in November "On the logic of relatives" (P 235). The first may be the paper he had presented to the Johns Hopkins Scientific Association in November 1881, and the second is probably what became Note B in Studies in Logic.

By the end of 1882 Peirce was experimenting with graphical systems of logic. He may have been stimulated by Sylvester's 1878 paper "On an Application of the New Atomic Theory to the Graphical Representation of the Invariants and Covariants of Binary Quantics," perhaps in conjunction with his study of the atomic theory of matter for his logic class. In this paper, in what Peirce saw as an anticipation of his reduction thesis (see item 20), Sylvester had put forward "one simple, clear and unifying hypothesis, which will in no wise interfere with any actually existing chemical constructions. It is this: leaving undisturbed the univalent atoms, let every other n-valent atom be regarded as constituted of an n-ad of trivalent atomicules arranged along the apices of a polygon of n sides." After explaining his theory further, and giving numerous diagrammatic examples, Sylvester remarked: "The beautiful theory of atomicity has its home in the attractive but somewhat misty border land lying between fancy and reality and cannot, I think, suffer from any not absolutely irrational guess which may assist the chemical enquirer to rise to a higher level of contemplation of the possibilities of his subject." Peirce's paper on junctures and fractures (item 59) and his 21 December letter to O. H. Mitchell (item 60) suggest that he may have been trying to apply some of the methods of chemistry, and perhaps the theory of atomicity, to logic.

Also in 1882, though perhaps already in the latter part of 1881, Peirce met Benjamin Eli Smith, who had come to the Johns Hopkins as a graduate assistant. Although he seems not to have been a student in any of Peirce's courses, he presented two papers to the Metaphysical Club, one on "Wundt's Theory of Volition" in February 1882 and the other "On Brown's 'Metaphysics'" the following month. Smith was a member of the staff of the Century Dictionary (and soon became its managing editor) and he recruited Peirce to be a contributor. Peirce was given principal responsibility for terms in logic and philosophy, mathematics, mechanics and astronomy, weights and measures, and all words relating to universities. By 1883 Peirce had already begun working on definitions (see MSS 496 and 497) and in the fall of that year, with the dictionary project in mind, he added a new course on philosophical terminology. From this time onward—for after the first edition of 1889-91 he immediately set to work on a revised edition—Peirce had definitions, etymologies, and language groups (and other lexicographical matters) on his mind. This was a monumental project and Peirce's contribution was massive. Its impact on the evolution of his thought was surely very significant, though it has yet to be seriously examined. Peirce's difficulties with Sylvester had not ended with his decision to withhold his 1882 brochure. In the early weeks of 1883 a more severe and consequential dispute broke out. In August 1882 one of Sylvester's papers (an abstract of a paper on nonions which he had read in May to the Mathematical Society) appeared in the Circulars with the following sentence: "These forms can be derived from an algebra given by Mr. Charles S. Peirce (Logic of Relatives, 1870)." The sentence, as it turned out, had been written by Peirce. Apparently, Sylvester had entrusted Peirce with checking the proof-sheet of his paper for adequate reference to his own work. Peirce had expected that Sylvester would look over his changes before releasing the proof-sheet to the printer but, according to Sylvester, that did not happen. In reflecting on the episode in later years, 46 Peirce remembered that he had not made the insertion mark for the printer, but had only written out the sentence he thought Sylvester would want to insert. The February 1883 Circular carried an Erratum by Sylvester correcting the troublesome sentence to read "Mr. C. S. Peirce informs me that these forms can be derived from his Logic of Relatives, 1870." He went on to say:

"I know nothing whatever of the fact of my own personal knowledge. I have not read the paper referred to, and am not acquainted with its contents. The mistake originated in my having left instructions for Mr. Peirce to be invited to supply in my final copy for the press, such references as he might think called for."

Peirce was incensed. Not only had he engaged in lengthy discussions with Sylvester about his logic of relatives and carried on at least a limited correspondence with him, but in April 1882 Sylvester had discussed Peirce's logic of relatives before the Mathematical Seminary and in the same month had stated specifically before the Scientific Association that Peirce's logic was tantamount to his Nonions. His remarks had been reported in the Circulars as follows:

"Mr. Sylvester mentioned . . . that in his recent researches in Multiple Algebra he had come upon a system of Nonions, the exact analogues of the Hamiltonian Quaternions. . . .

"Mr. Charles S. Peirce, it should be stated, had to the certain knowledge of Mr. Sylvester arrived at the same result many years ago in connexion with his theory of the logic of relatives." 47

And only a year earlier, in Sylvester's own journal, Peirce had published the addendum to his father's Linear Associative Algebra (item 41) in which he proved "that any associative algebra can be put into relative form, i.e. . . . that every such algebra may be represented by a matrix."

Peirce wrote out a full reply to the Erratum and sent it to Gilman. There followed much correspondence between Gilman, Peirce, and Sylvester and there were drafts of responses and responses to responses. At one point, on 29 March, Peirce wrote to Gilman:

"I cannot consent to my statement being modified unless Professor Sylvester will say that my conduct was correct in regard to the proof-sheets. I have no objection to this being qualified by his saying that it was correct if the oral message was delivered to me as I say it was; but clearly if such a qualification is to be inserted, everything depends upon how it is put."

Peirce continued with detailed recommendations for emendation. At some point Gilman sent drafts of Peirce's reply and Sylvester's note to Peirce's reply to G. W. Brown, one of the trustees, to ask for advice. Brown replied on 17 April: "After thinking over this annoying matter it appears to me that nothing is to be done but to publish the articles as they stand. This should however be the last of it and would it not be well to say so to both in advance." Earlier there had been a suggestion, apparently from Brown, to publish Peirce's reply without Sylvester's note. But Sylvester had responded heatedly to Gilman:

"I am astonished at the proposition contained in your note of the 18th that it should be proposed to allow Mr. Peirce's virulent and disingenuous statements to be made in the circular without giving me an opportunity of replying thereto. If that course is adopted, self-respect will render it imperative for me to withdraw from all future participation in the circulars."

Peirce's "Communication" (item 67) finally appeared in the April Circular, preceded by this "Note" from Sylvester:

"I wished (as I still wish) it to be understood that it is Mr. Peirce's statement and not mine that the "forms" in question can be derived from his Logic of Relatives. I certainly know what he has told me and should attach implicit credit to any statement emanating from him, but have not the knowledge which would come from having myself found in his Logic of Relatives the forms referred to; as previously stated I have not read his Logic of Relatives and am not acquainted with its contents."

Many years later, when Peirce recounted these events, he wrote of Sylvester's character:

"Sylvester was a man whose imagination and enthusiasm were incessantly running away with him: he was given to harboring the most ridiculous suspicions and to making rasher assertions than became so great a man. His power of distinct recollection was most phenomenally weak, almost incredibly so; while his subconscious memory was not at all wanting in retentiveness. . . . I suppose, as he said, that he "came across" the system of novenions . . . and remembered, or thought he remembered, that I had pointed out these forms. Subsequently, he got a suspicion that I was about to charge him with plagiarizing my "Description of a Notation &c," and was anxious to declare that he had never read it, and knew nothing about it. He seems to have fancied that I had some deep-laid plot against him." 48

Peirce must have felt some relief from the tension of his conflict with Sylvester toward the end of March 1883 when his long-awaited Studies in Logic, which had been "in the works" for over two years, finally appeared. Peirce had written to Gilman about it as early as 9 February 1881, and on 8 December 1881 he had said to Christine Ladd that "after a long delay from various causes, I have everything arranged to go on with the publication of our essays except one thing—about $300 is still needed. I shall probably supply this myself, but am not prepared to do so now, so that the matter may rest idle till spring." Although the matter lay idle much longer, when it finally did come Studies in Logic the book was immediately recognized as an important contribution. The book as a whole covered a vast part of the field of symbolic logic and dealt with the work of the major contributors. Even Frege's Begriffsschrift appeared in Ladd's bibliography although it is not mentioned in the paper. In his review for Mind, Venn said that the most interesting paper philosophically, was the concluding one by Peirce which dealt with the nature and foundations of statistical reasoning and the connection between probability and induction. This was, of course, "A Theory of Probable Inference" (item 64) about which Peirce wrote to Paul Carus: "In my humble opinion you are never likely to say again anything so false as that writings lose their freshness by being worked over. The first page or two of my Theory of Probable Inference was put into more than 90 forms very varied before I was satisfied; yet nobody would suspect any elaborate work on it." 49

Peirce was pleased with Studies in Logic. He sent out many inscribed copies as gifts and for the remainder of his days he often referred to one or another of its papers as an authoritative source. Probably with a complimentary copy, he wrote to T. S. Perry: "If you are going to read any of my papers—which seems inconceivable—I hope you will try note B in the bound book." 50 In 1904 Peirce remarked about Note B to Lady Victoria Welby: "My friend Schröder fell in love with my algebra of dyadic relations. The few pages I gave to it in my Note B in the 'Studies in Logic by Members of the Johns Hopkins University' were proportionate to its importance." 51 It seems doubtful that Peirce was fully of this opinion in 1883 but he embraced it more and more fully as time went by.

Studies in Logic is a landmark not only for logic, but also for education in America. It was a work on the leading edge of research in its field by a team of researchers composed mainly of graduate students. Certainly they were led by a seasoned scholar but he neither demanded nor wanted credit for their work. Even though Peirce edited the book his name did not appear on the title page; it was by MEMBERS of the the Johns Hopkins University. This was in the spirit of Johns Hopkins in its first decade.

Peirce had a great deal on his mind in the winter and spring of 1883. There was his demanding logic course, the trouble with Sylvester and, as always during these years, he had several Coast Survey projects going at once: pendulum operations at the Smithsonian and the Stevens Institute, testing of the new Peirce pendulums, preparations for an eclipse expedition, continuation of spectrum meter experiments and other metrological work, plans (which would fall through) to go to Point Barrow in the Arctic, and the constant pressure to finish overdue reports. He participated in the first three meetings of the Metaphysical Club and remarked on papers by G. S. Morris, A. H. Tolman, and W. T. Sedgwick. On May he wrote to Hilgard to say that he had "written for Science a careful review of Dr. Craig's work on projections—a job upon which I have spent a great deal of time"; but apparently it was never published and only one manuscript page (MS 442) has been found. Looming over all this, casting its shadow, was Peirce's coming divorce and remarriage.

Peirce's divorce from Zina became final on 24 April. Six days later he married Juliette and by 2 May they were sailing to Europe. Peirce had made plans to visit with Hugh MacColl in Boulogne, which he probably did near the beginning of his stay. On 16 May he sent Gilman a general plan for his 1883-84 course of lectures based, as he said, on his "forthcoming book." From the plan, Gilman had the following notice printed in the June Circular:

"Mr. C. S. Peirce. 1. Will give forty lectures to graduate and special students upon General Logic. The course will follow the contents of Mr. Peirce's forthcoming treatise on logic. At least one lecture will be devoted to each chapter, but the preferences of the class will be consulted in deciding upon the topics of nine of the lectures. The distribution of topics in the chapters is as follows:

"Generalities (5 chapters)

Deductive Logic:
 Non-mathematical (3 chapters)

Algebraic (4 chapters)

Otherwise mathematical (4 chapters)

Inductive Logic:
 Theory (9 chapters)

Illustrations (6 chapters)

"2. Will give special courses or private lessons upon any branch of the subject in which any of the graduates or special students may desire instruction."

As the summer progressed Peirce expanded his plan into a full-fledged syllabus and, as it grew, so did the planned number of lectures. There are two manuscript versions of the syllabus, one with fifty lectures (MS 458) and a more finished one with sixty lectures (item 69). A few features of the syllabus stand out. Peirce has definitely introduced truth values into his system of logic by this time and he is using quantifiers as he will in his 1885 "Algebra of Logic." Most of the topics he had written about while at the Johns Hopkins are covered in one way or another. Possibly the best general outline we have of his logic of relatives is given in lectures X through XIV. Some lectures treat topics he had not yet written about but soon would. For example, part of lecture XIX is devoted to the nature of geometrical axioms and the last part of lectures XXXIII-XXXVI is devoted to the problem of the duration of play, applied to the theory of natural selection and to philosophy. Peirce's thoughts were turning toward "Design and Chance" (item 79). There is even a provocative reference in lecture XXV to the harmfulness of logic too narrowly studied. Overall, the syllabus provides a detailed account of Peirce's well thought out design for an advanced general course in logic.

There are four lectures or fragments of lectures that Peirce probably composed before classes began in the fall: items 70-73. In them he continues the discussion of the constitution of the universe begun in item 19 and in his class lectures (which Christine Ladd had developed in her Studies In Logic paper). Peirce's theory of quantification is also much in evidence. At least the first three lectures were probably written while Peirce was still in Europe, though it is possible that all of them were written out class by class.

When Peirce and Juliette returned from Europe in mid-September 1883, they took a two-year lease on a house in Baltimore and began to furnish it. Peirce had sought and had been given Gilman's assurance that his position with the philosophy department was secure, so he and Juliette were eager to make Baltimore their home. When Peirce began teaching in the fall he may well have supposed that it was just the next of many teaching years ahead of him. It turned out that enrollment in his courses dropped dramatically from the previous year. Only four students took the advanced logic class in the fall—John Dewey, Jastrow, C. W. E. Miller, and Henry Taber—and only Jastrow and Taber were left for the second term. Dewey had dropped out because the course was too mathematical. But he and Jastrow enrolled in Peirce's new course on philosophical terminology. The course met once a week and apparently lasted for only a few weeks. Beginning in early October, Peirce sought special privileges with the University Library. On 10 October he requested permission, for special reasons, to take out twelve books at a time. The special reason was that he was engaged in a "piece of work" that "requires me to make use of a great many books." He explained that his research required the regular consultation—in some cases many times a day—of certain books. "Such for instance is the Berlin Aristotle in 5 volumes." Probably the "piece of work" was his set of definitions for the Century Dictionary, but soon he was also stymied in his related course on philosophical terminology. Although he tried as best he could to work out a suitable arrangement with the library, he met with no success. Finally on 8 November he wrote to Gilman: "I find my work brought to a complete stand-still for the want of books. I have been obliged to suspend my lectures on Philosophical Terminology until I can obtain the Berlin Aristotle. My application to you to have the University add another Aristotle to the library I understand to be refused." Peirce went on to ask if he could buy back his books listed under Ancient Authors which he had sold three years earlier. Gilman must have taken offense for a week later Peirce wrote to him again: "I deeply regret having said anything which seems to offend you, since I am bound to you by every bond of official respect, personal esteem, gratitude, and if you will permit me to say so even affection." But Peirce continued in a less conciliatory way:

"Then, let me say with candour, my dear Mr. President, that although I believe I have never complained of it to anybody, I have not thought that any heed at all had been given to any of the suggestions which I have made in regard to wants in the Library, although I considered them important. . . . I think, without of course comparing you to the jailer of the Peabody Library, that Cambridge is a trifle ahead of Baltimore in its appreciation of the wants of its students in the way of books. You have always permitted me to express myself with great freedom to you, and I always think a misunderstanding should be seized as an occasion to have a mutual understanding. There[fore], I beg you will not find offence in what I am saying. I have lately been offending people everywhere by my speeches."

Peirce then withdrew his request, admitting that it had not been "in good taste or temper." Although it is not clear how the whole matter was finally settled, it does appear that the course on philosophical terminology had come to an end.

Peirce taught a third course in the fall of 1883, described very briefly in the Circulars: "He also guided a company of students in studying the psychology of great men." 52 He had invited a group of students to join him in this study, and they worked out an elaborate program that involved reading the chief biographies of the day, extracting data of specified sorts, compiling impressionistic lists of great men and finally, submitting the lot to statistical analysis. Peirce wanted to demonstrate that statistical analysis could be fruitfully applied even in situations where the primary data are impressionistic (based on impressions). This study may have been the first extended application of statistical methods to comparative biography. Although Peirce continued the study with his group of students through the summer and fall of 1884, and even into the winter, it was never completed. Sometime after his move to Milford in 1888 Peirce took up the study again, probably stimulated by the publication of The Comtist Calendar. His 1901 paper on "The Century's Great Men of Science" was an offspring of the earlier study, and shortly after Peirce's death one of the members of Peirce's group, Joseph Jastrow, remarked in a memorial article 53 that he had been permitted to publish two rather simple conclusions, one relating to "Longevity," and the other to "Precocity." 54 Although many of the manuscripts related to the study of great men were composed in the period of the present volume, the study as a whole went beyond the period and will therefore be included in the next volume.

Peirce attended all the meetings of the Metaphysical Club for the fall term and gave one paper, a reply to G. S. Morris's paper on "The Philosophical Conception of Life." Among several others, he heard Jastrow read a paper on "Galton's 'Inquiry into Human Faculty'," Dewey on "The Psychology of Consciousness," and A. T. Bruce on "The Design Argument." Bruce's paper was read on 11 December and the Club's minute book shows that Peirce remarked on it. Just over one month later Peirce would read his "Design and Chance" to the Club.

Looking through the correspondence of this period for clues to Peirce's life and work, one letter stands out as signalling the end of his fortunes at the Johns Hopkins. On 22 December 1883 Simon Newcomb wrote to Gilman: "I felt and probably expressed some uneasiness in the course of our conversation the other evening, lest I might have been the occasion of doing injustice to persons whose only wrong had been lack of prudence. I have therefore taken occasion to inquire diligently of my informant, and am by him assured that everything I had said was fully justified." Newcomb was referring to Peirce as the one he might have injured and his informant was Julius Hilgard. Although it is not known for sure what "wrong" Peirce had committed beyond a "lack of prudence," we do know that Newcomb's revelations led to a resolution, of the Johns Hopkins Executive Committee that effectively ended Peirce's connection with the university. The resolution passed on 26 January 1884, was not to renew the contracts of lecturers in philosophy and logic "after the present engagements expire" and to replace the three lecturers (Peirce, Morris, and Hall) with one Professor and an assistant. But only Peirce's appointment expired at the end of the 1883-84 academic year, and he soon realized that the resolution was aimed at him. At first he appealed to the sense of fairness of the university administration. On 8 February he wrote to Gilman and asked that his letter be laid before the Executive Committee:

"On returning to Baltimore last September, I was unable to obtain a suitable house for one year. Therefore, as soon as the President returned I went to him and explained my difficulty and asked whether in his judgment it would be prudent for me to take a house for two years. To this important inquiry he replied that he knew of no disposition to disturb me in my place. The Treasurer suggested my purchasing a house. In view of these encouragements, I did take a house for two years. I have never heard the smallest whisper of dissatisfaction or suggestion of a possible change until I yesterday received your resolutions. My lectures have been much better than hitherto. There has been more coöperation between the different branches of philosophical instruction. There has, in short, been no reason for a change which did not exist before. I, therefore, appeal to your sense of fairness, gentlemen, with great confidence; for to cut short my lectureship at the end of this year, though it be perfectly within the letter of the contract, is not one of the things which it is open to you under the circumstances to do. I have no doubt that President Gilman spoke truly and sincerely in encouraging me to take my house. He now tells me he has for a long time seen this crisis coming; this long time must however have been altogether subsequent to last October."

The final paragraph of Peirce's letter suggests that he thought religion was somehow at issue:

"I also desire to address you briefly upon the present state of philosophy, and to show you that the difficulty of finding a modus vivendi between philosophy, science, and religion, is now much less than it has been for a very long period; so that you have only to make the philosophical department really true to the actual condition of thought, and you will bring it into a state of warm sympathy and friendship with science on the one hand and with Christianity on the other."

Peirce was probably right on two counts. The immediate and official cause of the decision to let him go was something subsequent to October 1883, and probably something else, like his attitude about religion, had helped bring on the crisis. When Gilman had candidly told Peirce that he had "for a long time seen this crisis coming" he may have revealed a truth he would decline to make official. Certainly Peirce had given Gilman many reasons to be concerned about his long-term continuation at the Johns Hopkins beginning with his December 1879 letter about the alarming state of his brain. Peirce's work for the Survey had resulted in a number of conflicts and absences and, perhaps partly because of the pressures of two jobs, his ill health had been a source of inconvenience. His aborted resignation in 1880 and the events following the sale of his books, and the cancellation of his course in philosophical terminology, had been irritating and perhaps even embarrassing for Gilman, who surely also noticed that Peirce's courses often had low enrollments. And then there was the question of religion. Charles W. Nichols, who was in Peirce's first course in logic and who presented the first paper to the Metaphysical Club, recorded some telling remarks in his "Johns Hopkins University Note Book":

"I read by invitation from the university, before the Johns Hopkins Philosophical Association, a thesis on "Illustrations from Grecian philosophy of the fallacy that differences in nature must correspond to received verbal and grammatical distinctions." Professor Charles S. Peirce, the scientist who presided, was an agnostic, and heartily seconded the sophomoric flaying I administered to old father Aristotle and the Schoolmen." 55

If Nichols's perception of Peirce was common among his students, it probably would have come to Gilman's attention and would have disturbed him. He had worked hard to alleviate the fears of conservative Baltimorians who imagined that the University was encouraging agnosticism.

But the official cause of the decision to let Peirce go, and clearly the provocation, was Newcomb's revelation. This is evident in the record of the Johns Hopkins Executive Committee. On 1 December 1884, Committee Chairman William Brown made the following statement:

"The undersigned having read Mr. Peirce's recent letters to Judge Brown, & having refreshed their recollection by reference to the records of the Executive Committee, & the official correspondence, make the following statement so that if there should be any subsequent reference to this affair, their understanding of [it] may be on record.

"The change of attitude toward Mr. Peirce on the part of President Gilman, which is the cause of complaint, occurred near the beginning of January 1884 in consequence of information first brought to his knowledge in December 1883, several weeks subsequent to his remark that he "knew of no disposition to disturb Mr. Peirce in his relations to the university"; and from that time onward Mr. Gilman's communications to Mr. Peirce were governed by the action of the Executive Committee and were taken in consultation with two members of that body."

Newcomb's revelation never became part of the official record. The most explicit reference appeared in a 15 November 1884 letter from Gilman to the Executive Committee in which he summarized the events surrounding Peirce's dismissal:

"It is true that [at] the beginning of the academic year 1883-4, I knew of no disposition to disturb Mr. Peirce in his relations to this university. It was not until several weeks later that one of the Trustees made known to the Executive Committee & to me certain facts which had been brought to his knowledge quite derogatory to the standing of Mr. Peirce as a member of an academic staff. These facts & their bearing upon the philosophical instruction in this university were considered by the Executive Committee, at their meeting, January 26, 1884."

Further light is shed on the matter by Newcomb himself in a letter of 30 December 1883 to his wife:

"I have been somewhat exercised at being the unintended means of making known some of the points of C. Peirce's marital history at Baltimore. When last going to N. Y. I went from Balt. to Phil. in the same seat with Dr. Thomas, a J. H. U. Trustee, and supposing they all knew more or less of the affair got talking of it, and let several cats out of the bag. What I gave as reports, Dr. Th., I suspect, told Gilman as facts, and troubled the latter greatly, as it seems Mrs P (2) had begun to cultivate Mrs G's acquaintance. The supposition is, that the marriage last summer made no change in the relations of the parties. Mr. Hilgard assures me that it is all true, they having occupied the same apartments in N. Y. some years ago. It is sad to think of the weaknesses which may accompany genius." 56

An examination of the exchange of letters between Peirce and Gilman and other members of the Executive Committee, which began with Peirce's notification of the 26 January resolution and continued at least into December, reveals that Peirce's initial concern was to keep his position and to defend his honor as an instructor. But as he became aware of the unyielding resolve of Gilman and the Committee, his concern shifted to an interest in reimbursement for damages resulting from his dismissal. If anything beneficial came of that lengthy exchange of letters, it was at most some measure of compensation for his loss in setting up a home in Baltimore. But the loss of an academic career, both to Peirce and to the world, could not be compensated.

During that painful year Peirce must have suspected that his academic life was over. Although he made some attempts to find another teaching position, it was less than four years after his dismissal that he and Juliette moved to Milford, Pennsylvania, to live the rest of their lives in seclusion and relative obscurity. Peirce was never again offered a regular teaching position, and his dismissal from the Johns Hopkins was at least partly the reason. In dropping Peirce from consideration for a position in philosophy at the University of Chicago in 1892, William R. Harper relied on the advice of George H. Palmer of Harvard University, who had written on 4 June 1892:

"I am astonished at James's recommendation of Peirce. Of course my impressions may be erroneous, and I have no personal acquaintance with Peirce. I know, too, very well his eminence as a logician. But from so many sources I have heard of his broken and dissolute character that I should advise you to make most careful inquiries before engaging him. I am sure it is suspicions of this sort which have prevented his appointment here, and I suppose the same causes procured his dismissal from the Johns Hopkins." 57

It is remarkable that James, certainly a man of judgment and discrimination, never gave up on Peirce but continued to recommend him as both teacher and scholar. It is disturbing that others were so blind to what James saw in Peirce.

Peirce's appointment at the Johns Hopkins ran until 1 September 1884, so he labored under the cloud, even disgrace, of his dismissal for about seven months. Yet he persevered with his classes and managed to keep up a steady flow of manuscript pages. In addition to his advanced logic course that continued in the second term with only two students (Jastrow and Taber), he taught a course on probabilities that met twice a week with an enrollment of seven (Davis, Julius J. Faerber, Arthur S. Hathaway, Jastrow, Henry B. Nixon, William E. Story, and Taber). He also gave several papers during the year including one to the Mathematical Seminary and three to the Metaphysical Club. On 16 January he delivered "On the Mode of Representing Negative Quantity in the Logic of Relatives" to the Mathematical Seminary. However, he could not have hoped to enlighten Sylvester about the generality and power of his logic, for Sylvester had departed for England the previous month to take up his chair at Oxford. He did not find out about Peirce's dismissal right away and several years later (on 28 March 1888) he wrote to Gilman: "What was the cause of C. Peirce's leaving? I am truly sorry on his account. I regret the differences which sprang up between him and me for which I was primarily to blame. I fear that he may not have acted with entire prudence in some personal matters."

On 17 January, the night after his talk at the Mathematical Seminary, Peirce gave what may be his most important philosophical paper of the Johns Hopkins period. On that night he presented "Design and Chance" (item 79) to nine members of the Metaphysical Club. The following remarks appear in the Club's minute book: "President Morris in the Chair . . . Principal paper was read by Mr. Peirce. Subject: Chance and Design. Mr. Peirce, Dr. Franklin, Prof. Remsen, Mr. Dewey and Mr. Jastrow as well as the President took part in the discussion." The paper is not such a substantial work in itself, but it represents an important turning point in the evolution of his thought. It is curious that it was written at such a turning point in his life. We shall quickly survey the rest of Peirce's non-scientific papers for the remainder of the year and then return to "Design and Chance."

Peirce delivered his second paper of 1884 to the Metaphysical Club on 13 May. It was entitled "Logic of Religion." On 7 April he had written to Gilman to seek permission to give six lectures on the logic of religion in the fall "with the purpose of stating some things on the credibility of various religious beliefs." Although it is difficult to make out the text of this letter, Peirce seems to be saying that if the trustees would not sanction his lectures he would give them at his house. No such lectures seem to have been given, though his 13 May paper was probably a preview of what he had in mind. The Club's minute book only reports that "it had special reference to the proofs of the existence of a God," and the June 1884 Circular that it was "on the logic of religious life."

One of the manuscripts from this period (MS 505) is evidently an outline for an oral presentation and it may be the outline for the Metaphysical Club paper. There are no references, however, to existence proofs. It has "reading times" marked at the left margin which indicate that the first three pages took twenty-one minutes. It begins:

"Religion must be subject to good sense. It is always in danger of being carried to excess. . . . Morality cannot be carried to excess. Logic cannot be carried to excess; and it is not subject to good sense, but on the contrary gives good sense its law. But religion if not taken in moderation leads to insanity and that not as is sometimes said, because it is adulterated, but because of the element of it that is most essential,—the mystical element."

A fourth page, perhaps an outline for a separate talk, begins by asserting that "Scientists have faith in science" and "religionists want faith in religion." Peirce then mentions the prayer test which he says, is "also a test of faith." He goes on to say that if religionists really had faith they would not be afraid of science but would encourage it, "sure that it would ultimately be found on their side." Peirce ends with the following outlined remarks, the Cayley references supporting the supposition that they were intended for a talk at the Johns Hopkins:

"Reality. True nature given by me. Opposed to conception which makes it origin of force. True philosophy adequate to govern the science of the XIX Century, develops itself from my conception alone.

"Passage of Cayley's address. 58 Appears at first sight an anachronism. A man like Cayley had better not be rashly accused of anachronism. Really what distinguishes this XIX above all is the force of √-.

"How this came about.

"To the businessman—gold alone is real. To the physicist force alone. To the mathematician relations alone; √- more real than gold."

Peirce presented his final paper to the Metaphysical Club on 18 November, two and a half months after his appointment had ended. He discussed Petrus Peregrinus's De magnete which he had transcribed from a manuscript in the Bibliothèque Nationale the previous summer and which, because he thought it held a significant place in the history of scientific method, 59 he hoped to publish with an English translation. At the club's fortieth meeting president Hall recommended that it be reconstituted to reflect the reorganization of the Johns Hopkins philosophy program. According to the minute book there were only three more meetings, the last on 3 March 1885. Even in Peirce's absence, for he did not attend again and had left Baltimore by the new year, his influence continued. On 27 January Jastrow gave a demonstration of logic machines including the Stanhope Demonstrator, Marquand's machine for syllogistic variations, and two machines of his own. At the previous meeting, on 16 December, A. T. Bruce had read a paper on "Final Causes" arguing that "natural selection was a process, not consistent with the notion of a designer but more akin to the action of chance." This suggests the influence of Peirce's "Design and Chance." At the club's last meeting, M. I. Swift also spoke on "Final Causes."

In the spring of 1884 Hall, now Professor of Psychology and Pedagogy, had organized a program of lectures for about eighty graduate students planning to become teachers, with lectures by President Gilman, Gildersleeve, Remsen, Martin, Hall, Adams, Wood, and Peirce. In Hall's original plan, Peirce was slated to give two lectures, one on "The Observational Element in Mathematics" and another on "The a priori Element in Physics." Although no manuscripts with these titles remain, it is likely that item 80 is the first part of a lecture for Hall's special course.

According to a notice in the May issue of Science Peirce read two papers at the spring meeting of the National Academy of Sciences, one on the study of comparative biography and the other (with Jastrow) on whether there is a minimum perceptible difference of sensation. 60 But it is doubtful that Peirce attended that meeting, and the paper with Jastrow was first read at the October meeting of the Academy and published in its Memoirs (P 303). He read two other papers at the Academy meetings in Newport : "On Gravitation Survey," and "On the Algebra of Logic," the latter probably from what would soon appear in the American Journal of Mathematics (P 296).

It is remarkable that despite what must have been a great tragedy for Peirce—the loss of his academic position (and $2500 salary), the disappointment of having to prepare to leave the home he and his new bride had only a few months before begun to furnish, and the growing awareness that he and Juliette were now personae non gratae, especially in the home of President Gilman—he was able to remain productive as a scholar (and as a scientist).

But such a stunning blow would inevitably affect the course of his work. At first Peirce shifted much of his attention to science and his work for the Coast Survey. In October he had taken charge of the Office of Weights and Measures and had sought to convince Congress of the need for an efficient bureau of standards. And 1885 was largely devoted to pendulum swinging at Key West, Ann Arbor, Madison, and Cornell. But in July the Coast Survey was rocked by scandal; Hilgard was fired and the value of Peirce's work was impugned. Although Peirce's reputation was soon restored, the allegation that his work was of "meagre value" had greatly wounded him. When the Survey was placed in the hands of the chief clerk of the Internal Revenue Bureau, F. M. Thorn, who was a lawyer and not a man of science, Peirce knew that his days there were numbered. The enthusiasm that had been rekindled after his dismissal from the Johns Hopkins began to wane.

Another change in Peirce can be traced to his separation from teaching. Although he did not immediately give up the idea of teaching but in June 1885 proposed a course of twelve lectures on advanced logic at Harvard 61 and also developed a correspondence course that he offered for a while, the intense and fruitful interaction he had enjoyed with his logic students at the Johns Hopkins was over. Peirce now had time for the more solitary speculations that would lead to his grand architectonic schemes of the late '80s and '90s ("Guess at the Riddle" and the first Monist series). The most obvious beginning of this new philosophy was his Metaphysical Club lecture on "Design and Chance."

The lecture draws together a number of ideas that had become prominent in Peirce's writings and lectures. He had long been interested in the Darwinian controversy which had swept America after the first copies of Origin of the Species arrived in the fall of 1859, and as early as the following summer he was convinced that Darwin's theory, "which was nourished by positive observation," was destined to play a major rôle in the development of thought for years to come. 62 Philip Wiener has suggested that Peirce saw in evolutionism, when welded to his "rigorous scientific logic," a way to "make room for freedom of the individual will and religious values," 63and Max Fisch has suggested that "Peirce had an ulterior interest in the logic of evolution as a weapon in his lifelong war against nominalism." 64 But Peirce was also driven by the desire of the scientific philosopher to find things out and to bring whatever he could within the scope of explanatory hypotheses, and he was committed to the economy of explanation—he was a wielder of Ockham's razor—and always sought theories that represented the universe as parsimoniously as its richness would allow. In evolutionism he saw the prospect for a theory he could generalize and develop into a cosmological principle of the highest order.

Perhaps the key Darwinian idea that so attracted Peirce was that of the long run: "Darwin, while unable to say what the operation of variation and natural selection in any individual case will be, demonstrates that in the long run they will adapt animals to their circumstances" (W3:244). But Peirce had made a special study of induction and probability and was well acquainted with sampling techniques and the tendency of random events, when sufficiently multiplied in controlled experiments, to assume as a group a determinate character. His understanding of statistics led him to his view of induction as a self-corrective process. If we add to these ideas his conception of habit as a tendency to act in ways that have not met with (or that have over time met with the least) resistance (the irritation of doubt is a kind of resistance), so that a habit is a statistical result of sorts, then we have most of the ingredients for the bold thesis of "Design and Chance." Perhaps it was the suggestive Epicurean vision of the uncaused swerve of atoms that drew together these conceptions in such an original way. What we find in this paper for the first time is Peirce's hypothesis that chance is really operative in the universe, even in the realm of laws. 65

His main line of argument is that the fundamental postulate of logic, that everything is explicable, cannot be absolutely true—or at least, that there are good reasons for doubting its absoluteness. One of these reasons is that the operation of absolute chance, which is allowed for if the absoluteness of the postulate is rejected, provides the basis for a theory of cosmic evolution that promises both "the possibility of an indefinite approximation to a complete explanation of nature" and general guidelines for further scientific research. The hypotheses of absolute chance and universal evolution provide the means, perhaps the only means, of satisfying the non-absolute version of the postulate, which asserts that "everything is explicable . . . in a general way." So even though Peirce is challenging the absolute truth of the claim that everything is explicable, his motive is to explain, or to make possible the explanation of, facts which had hitherto remained inexplicable—the laws of nature, similarities among those laws, the general fact that there are laws, and so on and thus, by introducing the hypotheses of absolute chance, habit-taking, and universal evolution, to extend rather than reduce the range of explicability.

The introduction of absolute chance provides for the possibility of an indefinitely close approximation to a complete explanation of nature by allowing for the origin and growth of a tendency to habit-taking. On this view the laws of nature become both "statistical results" and "habits gradually acquired by systems." A kind of natural selection can take place among various systems, according to whether they develop "good" habits, "bad" habits, or no habits. Selection, in the form of elimination, takes place when a system disintegrates and also when entities move beyond the limits of the perceptible universe.

Peirce has generalized Darwinism, since what Darwin had done was to apply the "statistical method" (or probability theory) to the explanation of species, which had commonly been considered absolute and immutable. Peirce applies the same statistical method to the explanation of all regularities, including laws of nature, which still were generally assumed to be absolute and immutable. Add to this the sort of natural selection among habit-systems mentioned above, and the analogy between Darwinism and Peirce's evolutionism is very strong.

Despite its relative brevity and its incompleteness in the extant manuscript, the argument of "Design and Chance" is sufficiently strong and suggestive to stand as a major statement of Peirce's evolutionary explanation of the laws of nature—one worthy of close study and comparison with his later, more detailed presentations of the hypothesis. The paper records his rejection of his earlier necessitarianism in favor of tychism, and sets forth significant new developments in his views on the logic of explanation and the problem of induction. It is an important early attempt to advance his view that Nature performs not only deductions, but inductions and retroductions (abductions) as well.

Relieved of the duty to prepare regular lectures, Peirce could now take time to ponder his cosmological speculations. In the coming months his commitment to the Survey would wane, as his methods became less appreciated and his duties became fewer, and he could take even more time for deep reflections. He would soon be ready to make his guess at the riddle of the universe.



1 I thank Professor Max H. Fisch, without whose advice and extensive files this introduction could not have been written. For further information about Peirce's time in Baltimore, see his "Peirce at the Johns Hopkins," included in the invaluable collection of some of his papers: Peirce, Semeiotic, and Pragmatism, ed. Kenneth L. Ketner and Christian J. W. Kloesel, (Bloomington: Indiana University Press, 1986); for information about Peirce's scientific work, see the published writings of Victor Lenzen and Carolyn Eisele.
 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 are to the Peirce Papers at Harvard University which also contain the correspondence between Peirce and his parents; Daniel C. Gilman's correspondence, as well as the Metaphysical Club minute book, is in the Milton S. Eisenhower Library at the Johns Hopkins University; Allan Marquand's lecture notes are in the Princeton University Library; all correspondence with employees of the Coast Survey are in Record Group 23 in the National Archives; Max Fisch's correspondence is in the Peirce Edition Project in Indianapolis.

2 See "Reminiscences of Peirce," in Benjamin Peirce 1809-1880; Biographical Sketch and Bibliography, ed. Raymond Clare Archibald (Oberlin, OH: Mathematical Association of America, 1925; reprinted New York: Arno Press, 1980).

3Sketches and Reminiscences of the Radical Club, ed. Mrs. John T. Sargent (Boston: James R. Osgood & Co. 1880), pp. 379-80.

4 Victor Lenzen to Max H. Fisch, 3 March 1963.

5 John W. Servos, "Mathematics and the Physical Sciences in America, 1880-1930," Isis 77 (1986): 611-29. These men had all been students of Benjamin Peirce.

6 Henry James to Henry S. Leonard, 2 Oct. 1936.

7 The Coast Survey became the Coast and Geodetic Survey in 1878, thereby signifying official recognition that geodesy was now the regular business of the Survey. Peirce's father had played an important rôle in bringing about this expansion of its responsibilities. For conveniences sake, I use the older and shorter name.

8 This extract from Patterson's letter to Sherman, and the extracts referred to therein, are included in Patterson's 8 August 1879 letter to Peirce (L 91).

9 Allegheny was a city in Allegheny County, Pennsylvania, which later amalgamated with Pittsburgh.

10Peirce to J. H. Kehler, 22 June 1911 (L 231).

11 Austria, Denmark, England, Finland, France, Germany, Holland, Norway, Russia, Sweden, and the United States.

12 Peirce to Greely, 27 November 1888 (L 174).

13Quoted in Fisch (1986), p. 129.

14Life of Daniel Coit Gilman (New York: Dodd, Mead & Co., 1910), p. 239.

15 "Charles S. Peirce at the Johns Hopkins," Journal of Philosophy 26 (1916): 716.

16Reported by Cassius J. Keyser in "Charles Sanders Peirce as a Pioneer," Galois Lectures (Scripta Mathematica Library: No. 5, 1941), p. 94.

17 Daniel C. Gilman, The Launching of a University (New York: Dodd, Mead & Co., 1906), p. 66.

18 Fisch (1986), pp. 63-64.

19 Review of "Philosophy in the United States," Mind 4 (1879): 101f.

20 Life and Confessions of a Psychologist (New York: D. Appleton Co., 1923), p. 226.

21 See "The Correspondence with Simon Newcomb," in Studies in the Scientific and Mathematical Philosophy of Charles S. Peirce, ed. R. M. Martin (The Hague, Paris, New York: Mouton Publishers, 1979). For Peirce's last letter to Newcomb see pp. 86-88.

22 Mind 8 (1883): 594-603.

23 "Charles S. Peirce at the Johns Hopkins," 717.

24 Ibid., 716.

25 Joseph Jastrow, "Charles S. Peirce as a Teacher," Journal of Philosophy 26 (1916): 724-25.

26 "Charles S. Peirce at the Johns Hopkins," 717.

27 Edward L. Youmans, editor of the Popular Science Monthly, where Peirce's six "Illustrations" appeared, hoped to combine them with additional "Illustrations" in a book for his International Scientific Series.

28 Fisch (1986), pp. 235-37.

29 Johns Hopkins University Circulars 1 (1880): 16.

30 See Arthur N. Prior, "The Algebra of the Copula," in Studies in the Philosophy of Charles Sanders Peirce, 2nd series, ed. Edward C. Moore and Richard S. Robin (Amherst: University of Massachusetts Press, 1964), pp. 79-94; especially pp. 88-92.

31 Alfred Tarski, "On the Calculus of Relations," Journal of Symbolic Logic 6 (1941): 73.

32 V. N. Salii, Lattices with Unique Complements, tr. G. A. Kandall (Providence, RI: American Mathematical Society, 1988), p. vii.

33"Sets of Independent Postulates for the Algebra of Logic," Transactions of the American Mathematical Society 5 (1904): 288-309.

34Survey of Symbolic Logic (Berkeley: University of California Press, 1918).

35 See Salii (1988), pp. 36ff.

36 "A Set of Five Independent Postulates for Boolean Algebras, with application to logical constants," Transactions of the American Mathematical Society 14 (1913): 481-88.

37 The Development of Mathematics, 2nd ed. (New York: McGraw-Hill, 1945), p. 250.

38 See also, however, Mitchell's table on p. 75 of his paper in Studies in Logic ("On a New Algebra of Logic") and Peirce's table on p. 442 of his principal contribution ("A Theory of Probable Inference," item 64).

39 See Fisch (1986), pp. 52-53.

40 Paul Shields, "Charles S. Peirce on the Logic of Number," Diss. Fordham 1981.

41 Ellery W. Davis, "Charles Peirce at Johns Hopkins," Mid-West Quarterly 2 (1914): 48-56.

42 Studies in Deductive Logic (London: Macmillan, 1880), p. xxiii.

43 "On the various notations adopted for expressing the common propositions of Logic," Proceedings of the Cambridge Philosophical Society 4 (1883): 36-47. Reprinted in Symbolic Logic (London: MacMillan and Co., 1881).

44 Robin MS 302.

45 Nature 25 (1882): 597.

46 Robin MS 431.

47 Johns Hopkins University Circulars1 (1882): 203. Reprinted in James J. Sylvester, Mathematical Papers (Cambridge: University Press, 1909), 3:643.

48 Robin MS 431.

49 Peirce to Carus, 3 March 1893 (L 77).

50 Peirce to Perry, 24 March 1883 (L 344).

51 Semiotics and Significs, ed. Charles S. Hardwick (Bloomington and London: Indiana University Press, 1977), p. 29.

52 Johns Hopkins University Circulars 3 (1884): 119.

53"Charles S. Peirce as a Teacher," 725.

54 "The Longevity of Great Men," Science 8 (1886): 294-96 (also in Nature of 4 Nov. 1886); "Genius and Precocity," Christian Union 37 (1888): 264-66; a related paper with the same title appeared in the Journal of Education (July 1888): 326-28.

55Charles Wilbur de Lyon Nicholls, "Annals of a Remarkable Salon," unpublished brochure, deposited in the Johns Hopkins University Library.

56Newcomb's wife, Mary Hassler Newcomb, was the granddaughter of Ferdinand Hassler, first superintendent of the Coast Survey. She appears to have taken a special interest in finding out the worst about Peirce. See Josiah L. Auspitz, Commentary 52 (1983): 51-64.

57Darnell Rucker, The Chicago Pragmatists (Minneapolis: University of Minnesota Press, 1969), p. 10.

58Peirce may have had the following passage in mind: "I would myself say that the purely imaginary objects are the only realities, the ontwV onta , in regard to which the corresponding physical objects are as the shadows in the cave." The quotation is from the "Inaugural Address by Arthur Cayley," Nature 28 (1883): 492.

59Historical Perspectives on Peirce's Logic of Science, ed. Carolyn Eisele (Berlin: New York, Amsterdam: Mouton, 1985), 1:4 15-95.

60See also Nature 30 (1884): 40.

61Peirce to James, 20 June 1885 (Wm. James Papers, Harvard University).

62Fisch (1986), p. 23.

63 Philip P. Wiener, "Peirce's Evolutionary Interpretations of the History of Science," in Studies in the Philosophy of Charles Sanders Peirce, ed. Wiener and Young (Cambridge: Harvard University Press, 1952), p. 143.

64Fisch (1986), p. 29.

65The next four paragraphs are a slight recasting of a summary statement about "Design and Chance" prepared by William Davenport.

Copyright of the Peirce Edition Project 1998