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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. 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. 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 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." 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'." "1. Reading of Minutes. 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." 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. 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
x 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. 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, 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.
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." 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." 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:
Algebraic (4 chapters)
Otherwise mathematical (4 chapters) Inductive Logic:
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 Ã-.
"How this came about. "To the businessman—gold
alone is real. To the physicist force alone. To the mathematician
relations alone; Ã- 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.
NATHAN HOUSER
NOTES
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. 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 r™le 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.
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