Introduction to Volume 2
MAX H. FISCH
The most decisive year of Peirce's professional life, and one of the
most eventful, was 1867.
Superintendent Bache of the Coast Survey had
been incapacitated by a stroke in the summer of 1864. He died on 17
February 1867. Benjamin Peirce became the third Superintendent on 26
February and continued in that position into 1874. He retained his
professorship at Harvard and, except for short stays in Washington, he
conducted the business of Superintendent from Cambridge. Julius E.
Hilgard served as Assistant in Charge of the Survey's Washington office.
On 1 July 1867 Charles was promoted from Aide to Assistant, the rank
next under that of Superintendent. He continued in that rank for
twenty-four and a half years, through 31 December 1891.
National and
international awareness of the Survey was extended by two related
episodes beginning in 1867. A treaty with Russia for the purchase of
Alaska, negotiated by Secretary of State William Henry Seward, was
approved by the Senate on 9 April, but the House delayed action on the
appropriation necessary to complete the transaction. Superintendent
Peirce was asked to have a reconnaissance made of the coast of Alaska,
and a compilation of the most reliable information obtainable concerning
its natural resources. A party led by Assistant George Davidson sailed
from San Francisco on 21 July 1867 and returned 18 November 1867.
Davidson's report of 30 November was received by Superintendent Peirce
in January, reached President Johnson early in February, and was a
principal document in his message of 17 February to the House of
Representatives, recommending the appropriation. The bill was finally
enacted and signed by the President in July.
Charles's younger brother,
Benjamin Mills Peirce, returned in the summer of 1867 from two years at
the School of Mines in Paris. Seward wished to explore the possibility
of purchasing Iceland and Greenland from Denmark. His expansionist
supporter Robert J. Walker consulted Superintendent Peirce, who had his
son Ben compile A Report on the Resources of Iceland and Greenland which
he submitted on 14 December 1867, and which his father submitted to
Seward on the 16th. With a foreword by Walker, it was published in book
form next year by the Department of State. But congressional interest in
acquiring the islands was insufficient and no action was taken.
1
Joseph
Winlock had become the third Director of the Harvard College Observatory
in 1866, and working relations between the Survey and the Observatory
became closer than they had previously been. (Winlock had been
associated with the American Ephemeris and Nautical Almanac from its
beginning in 1852, and for the last several years had been its
Superintendent, residing in Cambridge. Benjamin Peirce had been its
Consulting Astronomer from the beginning. Charles had done some work for
it in recent years. Assistant William Ferrel and he had observed the
annular eclipse of the sun at St. Joseph, Missouri, 19 October 1865, and
both had submitted written reports to Winlock which are still
preserved.) By arrangement with Winlock, Charles began in 1867 to make
observations at the Observatory that were reported in subsequent volumes
of its Annals. In 1869 he was appointed an Assistant in the Observatory,
where, as in the Survey, the rank of Assistant was next to that of
Director.
In 1867 the Observatory received its first spectroscope. Among
the most immediately interesting of the observations it made possible
were those of the auroral light. In volume 8 of the Annals it was
reported that "On April 15, 1869, the positions of seven bright lines
were measured in the spectrum of the remarkable aurora seen that
evening; the observer being Mr. C. S. Peirce."
By that time, Peirce had
begun reviewing scientific, mathematical and philosophical books for the
Nation. His second review was of Roscoe's Spectrum Analysis, on 22 July
1869, and it was both as chemist and as astronomer that he reviewed it.
With Winlock's permission, he reported that
"In addition to the green line usually seen in the aurora, six others
were discovered and measured at the Harvard College Observatory during
the brilliant display of last spring, and four of these lines were seen
again on another occasion. On the 29th of June last, a single narrow
band of auroral light extended from east to west, clear over the
heavens, at Cambridge, moving from north to south. This was found to
have a continuous spectrum; while the fainter auroral light in the north
showed the usual green line."2
Peirce was a contributor to the Atlantic Almanac for several years,
beginning with the volume for 1868. In that for 1870 he had, among other
things, an article on "The Spectroscope," the last paragraph of which
was devoted to the spectrum of the aurora borealis and the newly
discovered lines.
As an Assistant both in the Survey and in the
Observatory, Peirce was an observer of two total eclipses of the sun, at
Bardstown, Kentucky, 7 August 1869, and near Catania, Sicily, 22
December 1870. And as late as 1894 he would write: "Of all the phenomena
of nature, a total solar eclipse is incomparably the most sublime. The
greatest ocean storm is as nothing to it; and as for an annular eclipse,
however close it may come to totality, it approaches a complete eclipse
not half so near as a hurdy-gurdy a cathedral organ."
In 1871 the
Observatory acquired a Zšllner astrophotometer and Winlock made Peirce
responsible for planning its use. More of that in our next volume. And
in 1871 Peirce's father obtained authorization from Congress for a
transcontinental geodetic survey along the 39th parallel, to connect the
Atlantic and Pacific coastal surveys. This led to Charles's becoming a
professional geodesist and metrologist; but that too is matter for the
third and later volumes. Back now to 1867.
One of the most famous cases
that ever came to trial was the Sylvia Ann Howland will case, and the
most famous of the many famous things about it was the testimony of the
Peirces, 5 and 6 June 1867. The questions at issue were (1) whether Miss
Howland's signatures to the two copies of the "second page" codicil of
an earlier will were genuine, or were forged by tracing her signature to
the will itself, and (2) whether, supposing them genuine, the codicil
invalidated a later will much less favorable to her niece, Hetty H.
Robinson. The Peirces addressed themselves to the first of these
questions. Under his father's direction, Charles examined photographic
enlargements of forty-two genuine signatures for coincidences of
position in their thirty downstrokes. In 25,830 different comparisons of
downstrokes, he found 5,325 coincidences, so that the relative frequency
of coincidence was about a fifth. Applying the theory of probabilities,
his father calculated that a coincidence of genuine signatures as
complete as that between the signatures to the codicil, or between
either of them and that to the will in question, would occur only once
in five-to-the-thirtieth-power times. The judge was not prepared to base
his decision on the theory of probabilities, but he decided against Miss
Robinson on the second issue.3 In the
Nation for 19 September 1867,
under the title "Mathematics in Court," there appeared a letter to the
editor criticizing Benjamin Peirce's testimony, and a long reply signed
"Ed. Nation" but written by Chauncey Wright, concluding that "The value
of the present testimony depends wholly on the judgment of his son in
estimating coincidences, and does not depend on the judgment of either
father or son as mathematical experts." In a long article on "The
Howland Will Case" in the American Law Review for July 1870 it was said
that: "Hereafter, the curious stories of Poe will be thought the
paltriest imitations."
Through 1867 (and on beyond) Peirce made frequent
additions to his library in the history of logic. In March and April he
acquired early editions of Duns Scotus. On 1 January 1868 he compiled a
"Catalogue of Books on Mediaeval Logic which are available in
Cambndge"more of them in his own library than at Harvard's or anywhere
else.
Charles W. Eliot became President of the University on 19 May
1869. Two days later he wrote to George Brush of Yale: "what to build on
top of the American college. . . . This is what we have all got to think
about." His first thought was to try turning the University Lectures
into sequences running through the academic year, with optional
comprehensive examinations on each sequence at the end of the year. He
arranged two such sequences for 1869-70; one in philosophy, the other in
modern literature. For philosophy he enlisted Francis Bowen, John Fiske,
Peirce, F. H. Hedge, J. Elliott Cabot, Emerson, and G. P. Fisher, in
that order. Peirce's fifteen lectures, from 14 December to 15 January,
were on the history of logic in Great Britain from Duns Scotus to Mill.
William James attended at least his seventh, on nominalism from Ockham
to Mill, and wrote next day to his friend Henry P. Bowditch that "It was
delivered without notes, and was admirable in matter, manner and
clearness of statement.... I never saw a man go into things so intensely
and thoroughly." The Graduate School was not established until 1890,
with James Mills ("Jem") Peirce, Charles's older brother, as Dean; but
the experiment of 1869-70 was later called "The Germ of the Graduate
School."4
Back again to 1867. On 30 January Peirce was elected a
Resident Fellow of the American Academy of Arts and Sciences. He
presented three papers to the Academy at its meetings of 12 March, 9
April, and 14 May, and two further papers at those of 10 September (read
by title only) and 13 November. The volume of the Academy's Proceedings
which included all five of these papers did not appear until the
following year, but by November 1867 Peirce had obtained collective
offprints of the first three under the title "Three Papers on Logic" and
had begun distributing them. He began receiving responses early in
December.5
The first philosophical journal in the United Statesindeed
the first in English anywherewas the quarterly Journal of Speculative
Philosophy, published in St. Louis and edited by William Torrey Harris.
It began with the issue for January 1867. Peirce subscribed at first
anonymously through a bookseller. But as soon as the collective
offprints of "Three Papers on Logic" were ready, he sent Harris a copy.
Harris responded with a letter dated 10 December 1867. He was especially
interested in Peirce's third paper, "On a New List of Categories."
(Peirce himself as late as 1905 called it "my one contribution to
philosophy.") In response to Harris, Peirce wrote a long letter on Hegel
which he did not mail and a short letter dated 1 January 1868 which he
did mail. Thus began the correspondence that led to five contributions
by Peirce to the second volume of the Journal: two anonymous exchanges
with the editor, and three articles under his own name in response to
the editor's challenge to show how on his nominalistic principles "the
validity of the laws of logic can be other than inexplicable." (These
five contributions are examined in detail by C. F. Delaney in part II of
the present introduction.)
In giving the title "Nominalism versus
Realism" to the first exchange, Harris obviously meant to call Peirce a
nominalist and Hegel and himself (and other followers of Hegel)
realists. Peirce did not disclaim the nominalism. But was he a
professing nominalist, and did Harris know that he was? And, if so, how
did he know it?
That question takes us back again to 1867. At the end of
the first of his "Three Papers on Logic" Peirce advocated a theory of
probability for a fuller account of which he referred to his review of
Venn's Logic of Chance. In that review he called it the nominalistic
theory, as opposed to the realistic and conceptualistic theories. But
Venn, though he used the latter two terms, nowhere used the terms
nominalism, nominalistic, or nominalist. (The terms he did use are
"material" and "Phenomenalist.") Evidently, therefore, Peirce wished to
make his own commitment to nominalism unmistakable.
When did Peirce
become a professing nominalist? Probably in 1851, about the time of his
twelfth birthday, when he read Whately's Elements of Logic.
Where is the
evidence in volume 1 of the present edition that he was a professing
nominalist during the period of that volume? In what he says about the
falsity of scholastic realism on pages 307 and 312 and in other relevant
passages on pages 287, 306, and 360.6 And that he was still a professing
nominalist when he began drafting his Journal of Speculative Philosophy
articles, commonly called his cognition series," appears from what he
says on pages 175, 180 and 181 of the present volume: "Thus, we obtain a
theory of reality which, while it is nominalistic, inasmuch as it bases
universals upon signs, is yet quite opposed to that individualism which
is often supposed to be coextensive with nominalism." "Now the
nominalistic element of my theory is certainly an admission that nothing
out of cognition and signification generally, has any generality....""
If this seems a monstrous doctrine, remember that my nominalism saves me
from all absurdity."
But in the published form of the second article, in
the paragraph on page 239 of the present volume, Peirce unobtrusively
takes his first step from nominalism toward realism.
7 "But it follows
that since no cognition of ours is absolutely determinate, generals must
have a real existence. Now this scholastic realism is usually set down
as a belief in metaphysical fictions"as Peirce himself had set it down
on pages 287, 307, 311 and 312 of our first volume. It is the realism of
Scotus to which he now commits himself. He takes a second and much more
emphatic step in his Berkeley review three years later. He says there
(on page 467 below) that Scotus "was separated from nominalism only by
the division of a hair." What was the hair that Scotus split, we might
ask, and how did he split it? Instead, going back once more to 1867 and
taking the "New List of Categories" together with the three articles of
the cognition series (1868-1869) and the Berkeley review (1871), let us
ask what hairs Peirce split and how he split them.
As we remarked on
page xxvi of the introduction to volume 1, Peirce's "is the first list
of categories that opens the way to making the general theory of signs
fundamental in logic, epistemology, and metaphysics." We may add here
that the "New List" together with the cognition series and the Berkeley
reviewfive papers in all, and all five contained in the present
volumeare now recognized as constituting the modern founding of
semeiotic, the general theory of signs, for all the purposes of such a
theory.8
Now for the hairsplitting. The Berkeley review is much more
emphatic than the cognition series on the distinction between the
forward and the backward reference of the term "reality" and the
identification of nominalism with the backward and of realism with the
forward reference. Which amounts to a semeiotic resolution of the
controversy. Of the three central categories, quality is monadic,
relation dyadic, and representation irreducibly triadic. The sign
represents an object to or for an interpretant. But we may focus on the
sign-object or on the sign-interpretant. If the question is whether
there are real universals, the nominalists turn backward to the
sign-object and do not find them; the realists turn forward to the
sign-interpretant and find them (pp. 467 ff. below). That is primarily
because the backward reference to the object is more individualistic,
and the forward reference to the interpretant is more social. So realism
goes with what has been called the social theory of logic, or "logical
socialism."9 If we were selecting key sentences from the Peirce texts in
the present volume, they might well include these two: (1) "Thus, the
very origin of the conception of reality shows that this conception
essentially involves the notion of a COMMUNITY, without definite limits,
and capable of an indefinite increase of knowledge" (p. 239). (2)
"Whether men really have anything in common, so that the community is to
be considered as an end in itself, and if so, what the relative value of
the two factors is, is the most fundamental practical question in regard
to every public institution the constitution of which we have it in our
power to influence" (p. 487).
The forward reference and the community
emphasis owed something to Charles's wife Zina. By 1865 they were
settled in a home of their own at 2 Arrow Street in Cambridge, and it
remained their home throughout the period of the present volume. Arrow
Street shot eastward from Bow Street into what was then Main Street but
is now Massachusetts Avenue. The Arrow Street years were a period of
experimentation and productivity for Zina as well as for Charles. Her
major concerns were three: (1) reducing the burden of housekeeping
drudgery for married women, (2) creating institutions to give women a
voice in public affairs without their having to compete with men, and
(3) higher education for women. For the first she advocated
"Co-operative Housekeeping" in a series of five articles in the Atlantic
Monthly from November 1868 through March 1869, when Charles's Journal of
Speculative Philosophy series was appearing. Her articles reappeared in
book form in Edinburgh and London in 1870. She also took a leading part
in the organization of the short-lived Cambridge Co-operative
Housekeeping Society, which rented the old Meacham House on Bow Street
for its meetings as well as for its laundry, store, and kitchen. For her
second concern, she was active in the movement for a "Woman's
Parliament" and was elected president of its first convention in New
York City, on 21 October 1860. That movement was still active under the
name of "The Women's Congress" at least as late as 1877. For her third
concern, she was one of the organizers of the Woman's Education
Association of Boston, and her work in it was part of the pre-history of
Radcliffe College.
Though Charles never became active in politics, he
was an advocate of proportional representation. Zina made notes of his
conversations with her about it, and published his views in two of her
later books.
Though Zina was not a scientist, she did become a member of
the international scientific community by serving, like Charles, as an
observer near Catania in Sicily of the total eclipse of the sun on 22
December 1870 and by the inclusion of her excellent account of it in the
annual report of the Coast Survey for that year.
Zina's younger sister
Amy Fay was a gifted pianist who, after the best training that could be
had in New England, studied in Germany from 1869 to 1875 under several
of its best teachers, including Tausig, Kullak, and Deppe in Berlin and
Liszt in Weimar. By visiting her in Germany and by reading her long and
frequent letters home, Zina and Charles became vicarious members of the
international community of musicians. Zina published selections from the
letters in the Atlantic Monthly for April and October 1874, and later a
more comprehensive collection in book form, in a single chronological
order, under the title Music-Study in Germany. It went through more than
twenty editions, was translated into French and German, and is still in
print. The first twelve chapters come within the period of the present
volume. One of them contains a vivid account of the five days that Amy
and Charles spent in Dresden in August 1870.
Within the period of the
present volume Peirce became acquainted with modern German experimental
psychology, as represented by Weber, Fechner, Wundt, and Helmholtz. By
1869 he was already contemplating experiments of the kind he carried out
with Jastrow in 1884, which made him the first modern experimental
psychologist on the American continent. He sent Wundt copies of his
Journal of Speculative Philosophy papers and asked permission to
translate Wundt's Vorlesungen jiber die Menschen- und Thierseele,to
which he refers in appreciative terms on page 307 below. Wundt's reply
thanking him for the papers and granting the permission was dated at
Heidelberg 2 May 1869. No translation by Peirce was published, and no
drafts have been found. A translation of the much revised edition of
1892 was published by J. E. Creighton and E. B. Titchener in 1894 and
reviewed by Peirce in the Nation. When Helmholtz visited New York City
in 1893, Peirce had a visit with him, and his long obituary of Helmholtz
in 1894 was reprinted in Pollak's 1915 anthology of the Nation's first
fifty years.
Back now to logic. In his Harvard University Lectures on
the logic of science in the spring of 1865, a few months after the death
of George Boole, Peirce had said that Boole's 1854 Investigation of the
Laws of Thought "is destined to mark a great epoch in logic; for it
contains a conception which in point of fruitfulness will rival that of
Aristotle's Organon (W1:224). In the first of his fifteen Harvard
University Lectures of 1869-70 on "British Logicians," before turning to
medieval nominalism and realism, Peirce said, according to the notes of
one of his students, that there was enough in Boole to "take the whole
time" of the course. By 1877 the British mathematician and philosopher
W. K. Clifford was ready to say that "Charles Peirce. . . is the
greatest living logician, and the second man since Aristotle who has
added to the subject something material, the other man being George
Boole, author of The Laws of Thought."
10
What was the "something
material" that Peirce had added? That takes us back once more to 1867,
for it certainly included "On an Improvement in Boole's Calculus of
Logic." What else? At the very least, and above everything else, the
most difficult and, at least for logicians and for historians of logic,
the most important paper in the present volume: "Description of a
Notation for the Logic of Relatives, resulting from an Amplification of
the Conceptions of Boole's Calculus of Logic" (DNLR).
11 But is it not
the case that, though the logic of relations can be traced back at least
to Aristotle, De Morgan was the first logician to invent a notation for
it? And was not that in 1860, a decade before Peirce's memoir? Yes, but
as soon as Peirce's memoir began to circulate, there was room for the
question whether De Morgan's notation might be a dead end. In his
obituary of De Morgan, Peirce said (p. 450 below) "it may at least be
confidently predicted that the logic of relatives, which he was the
first to investigate extensively, will eventually be recognized as a
part of logic." He did not predict, however, that it would be in De
Morgan's notation that it would achieve that recognition. But was not
the Boole-Peirce-Schršder line in logic superseded by the
Frege-Peano-Russell-Whitehead line? No; it was only eclipsed.
Even more
intimately than with Boole and De Morgan, Peirce associated his DNLR
with his father's Linear Associative Algebra. The two appeared at almost
the same time, midway between two total eclipses of the sun, but the
connections between them did not become fully apparent until, after his
father's death in 1880, Peirce prepared a second edition of the LAA,
with an addendum by his father and two addenda by himself, and with well
over a hundred footnotes to the original text, in over sixty of which he
supplied translations from the LAA formulas into DNLR formulas.
Peirce's
father had been one of the founding members of the National Academy of
Sciences in 1863. Beginning in 1867, he presented instalments of the LAA
at meetings of the Academy.12 Charles's focus on the logic of relations
went back to his earliest work on his categories. A logician who had
only three central categoriesQuality, Relation, and Representationwas
bound to return again and again to the logic of relations. Recall, for
example, his remarks about equiparant and disquiparant relations in
volume 1, and note what he says about mathematical syllogisms on 42 f.
below. But his earliest published mention of De Morgan's paper of 1860
was written late in 1868 (p. 245n2), and he may not have seen that paper
more than a few weeks earlier. So the actual composing of the DNLR may
have begun in 1869.
Then, on 7 August 1869, came the first of the two
eclipses. It was observed by several teams at several points along the
line of totality. Peirce and Shaler were stationed at Bardstown,
Kentucky. Their report, one of the most vivid as well as detailed, was
submitted by Peirce to Winlock, included in Winlock's report to
Superintendent Peirce, and published by him in the Survey's Annual
Report. It reappears on pages 290-93 below. A quarter of a century
later, in an unpublished paper entitled "Argon, Helium, and Helium's
Partner," Peirce gave an equally vivid retrospective account (Robin MS
1036).
"I remember, as if it were yesterday, the first time I saw helium. It
was in 1869. Astronomical spectroscopy was then in its earliest infancy.
. . . It was impossible in those early days, for the same observer to
point his telescope and to use the spectroscope; so I had brought along
with me the Kentuckian geologist Shaler, a man of nerve and proved in
war, to bring successively the different protuberances of the sun upon
the slit of my spectroscope, while I examined the spectrum and
recognized what I could."
The observations of the sun's corona and protuberances by the
Peirce-Shaler and other teams prompted new theories as to the
composition of the sun, but there was some skepticism about these
theories among European astronomers. The earliest opportunity for a test
of them would be the eclipse of 22 December 1870, whose path of totality
was to pass through the Mediterranean. It was desirable that as many as
possible of the American observers of the 1869 eclipse should be
observers of the 1870 one also, and Peirce's father began making plans
to bring that about. One of these plans was to have Charles follow the
path of totality from east to west several months in advance, inspecting
possible sites for observation parties, reporting to his father and to
Winlock, and making tentative preliminary arrangements. But if Charles
was to be in Europe for six or more months and his father for two or
more, those interruptions might be detrimental to the major works they
had in progress. It would be advantageous to finish them before leaving,
and even more advantageous to take published copies with them, each of
the other's work as well as his own, and get them that much sooner into
the hands of the mathematicians and logicians they hoped to be meeting.
At the 616th meeting of the American Academy, on 26 January 1870, as
reported by Chauncey Wright, its Recording Secretary, "The President . .
. communicated by title . . . a paper 'On the Extension of Boole's
System to the Logic of Relations by C. S. Peirce'." Late in the spring,
Peirce supplied final copy; it was set in type and he was given fifty
copies in paperback quarto book form, dated Cambridge 1870, "Extracted
from the Memoirs of the American Academy, Vol. IX," though that volume
did not appear until three years later.
Also late in the spring, since
the National Academy, only seven years old, had as yet no funds for
printing the papers or books its members presented, Julius E. Hilgard, a
fellow member of the Academy, took Superintendent Peirce's manuscript,
had it copied in a more ornate and legible hand, and then had fifty
copies lithographed from it.
When Charles sailed from New York on 18
June 1870, he took with him copies of the lithographed book and the
printed memoir. In London on 11 July he delivered one of each, with a
covering letter from his father, to De Morgan's residence. On a later
day he had a visit with De Morgan, who, unfortunately, was already in
the final decline that ended in his death in the following March, eleven
days after Charles's return to Cambridge.
Charles presented another copy
of the DNLR to W. S. Jevons, from whom he received a letter about it
farther along on his eastward journey, to which he replied from Pest on
25 August (pp. 445-47 below).
Directly or indirectly, Robert Harley too
received a copy. At the Liverpool meeting of the British Association for
the Advancement of Science in September, Harley first presented
"Observations on Boole's 'Laws of Thought' by the late R. Leslie Ellis,"
and then a paper by himself "On Boole's 'Laws of Thought'" (continuing
one he had presented four years earlier), in which, after reviewing
recent works by Jevons, Tait, and Brodie, he said: "But the most
remarkable amplification of Boole's conceptions which the author has
hitherto met with is contained in a recent paper by Mr. C. S. Peirce, on
the 'Logic of Relatives'." He proceeds to quote the passage on "the
three grand classes" of logical terms that appears on pages 364-65
below, and then the sentence that appears on page 359: "Boole's logical
algebra has such singular beauty, so far as it goes, that it is
interesting to inquire whether it cannot be extended over the whole
realm of formal logic, instead of being restricted to that simplest and
least useful part of the subject, the logic of absolute terms, which,
when he wrote, was the only formal logic known." "The object of Mr.
Peirce's paper," he went on, "is to show that this extension is
possible," and he gave some account of the notation and processes
employed.
So Clifford was not alone in thinking that Peirce was "the
second man since Aristotle." He was present at the meeting and spoke "On
an Unexplained Contradiction in Geometry." He and Peirce may have met in
London in July, and he too may then have received a copy of DNLR. If
not, they almost certainly met as eclipse observers near Catania in
December. In any case, they became well acquainted not later than 1875.
Two brief examples now of Benjamin Peirce's distribution of copies of
LAA. In Berlin, on his way to Sicily in November, he gave two copies to
our ambassador, his old friend and former colleague, the historian
George Bancroft; one for himself and one to present to the Berlin
Academy, of which he was a member. And in January, after the eclipse, he
addressed the London Mathematical Society on the methods he had used in
his LAA, and presented a copy to the Society. Clifford was present and
proposed the name "quadrates" for the class of the algebras that
includes quaternions, and the Peirces adopted the proposal.
From London
in the last week of July 1870, shortly after the Vatican Council had
declared the conditions of papal infallibility, and just as the
Franco-Prussian War began, Charles journeyed eastward by way of
Rotterdam, Berlin, Dresden, Prague, Vienna, Pest, the Danube, and the
Black Sea, to Constantinople. Then he began moving westward along the
path of totality in search of eligible sites. (He recommended sites in
Sicily and southern Spain, and became himself a member of one of the
Sicilian teams.) In Berlin he visited Amy Fay, and she accompanied him
to Dresden, chiefly for visits to the great art museum there. In Vienna,
the director of the Observatory was hospitable and helpful. From Pest,
he wrote the letter to Jevons. In Constantinople he enjoyed the guidance
of Edward H. Palmer, "the most charming man" he had so far known, and of
Palmer's friend Charles Drake; and he began the study of Arabic. In
Thessaly he found the English consul most helpful, and the impressions
he formed there he later worked up into "A Tale of Thessaly" of which he
gave several readings. From Chambery in Savoy, after his visit to Spain,
he wrote to his mother on 16 November 1870, five weeks before the
eclipse, that he had heard eighteen distinct languages spoken, seventeen
of them (including Basque) in places where they were the languages of
everyday speech.
On the whole, the American observations and inferences
of the preceding year were vindicated. This was Peirce's first
experience of large-scale international scientific cooperation. He had
already committed himself to the social theory of logic, but this
experience and those of his four later European sojourns confirmed him
in that commitment.
Julius E. Hilgard, the Assistant in Charge of the
Survey's Washington Office, which included the Office of Weights and
Measures until the creation of the National Bureau of Standards in 1901,
was to spend several months in Europe in mid-1872. Among other duties,
he was to represent the United States at a Paris conference looking
toward the international bureau of weights and measures which was
finally established there in 1875. Peirce was to substitute for Hilgard
in his absence, and that called for several weeks of previous training
under Hilgard's supervision. He spent most of December 1871 and part of
January 1872 at the new quarters of the Survey in the elegant Richards
Building on Capitol Hill, where the Longworth House Office Building now
stands. Hilgard gave good reports of his progress.
Hilgard's European
sojourn would of course enhance his qualifications for succeeding
Peirce's father as Superintendent of the Survey. Peirce's training and
experience would qualify him to succeed Hilgard in case of Hilgard's
death or resignation or promotion to Superintendent. It would even
qualify him, under conceivable future circumstances, to be considered
for the superintendency.
The Philosophical Society of Washington (in
whose name, as in that of the American Philosophical Society in
Philadelphia, "philosophical" meant scientific) had held its first
meeting on 13 March 1871. At its 17th meeting, on 16 December 1871,
Charles presented the first of the six wide-ranging papers he presented
to that Society. It was "On the Appearance of Encke's Comet as Seen at
Harvard College Observatory.''
Charles's father was to address the
Cambridge Scientific Club on 28 December 1871 on the application of
mathematics to certain questions in political economy, such as price and
amount of sale, and the conditions of a maximum. Charles undertook to
prepare diagrams for his father to exhibit at that meeting, and these
were mailed to Cambridge on or about the 19th.
Simon Newcomb, then at
the Naval Observatory, called on Charles on the 17th and they conversed
about these matters. (Fifteen years later Newcomb published a book
entitled Principles of Political Economy on which Charles commented
adversely.) In the evening after the visit Charles wrote Newcomb a
letter explaining what he had meant by saying that the law of supply and
demand holds only for unlimited competition, and concluded: "P.S. This
is all in Cournot." (On the strength of this letter, Baumol and Goldfeld
recently included Peirce among their Precursors in Mathematical
Economics.) In the same evening, Charles wrote to his wife Zina, who had
remained in Cambridge, that he had been spending his evenings on
political economy, and gave her some account of the questions he had
been pursuing. On the 19th, he wrote a letter to his father, beginning:
"There is one point on which I get a different result from Cournot, and
it makes me suspect the truth of the proposition that the seller puts
his price so as to make his profits a maximum."
13
Charles's own
principal contribution to economics, his 1877 "Note on the Theory of the
Economy of Research," will be included in our next volume, but these
three letters are evidence that he brought to that particular topic a
more general competence in economic theory.
But what, finally, of the
Metaphysical Club at Cambridge, in which pragmatism was born? According
to the best evidence we now have, it was founded not later than January
1872, after Peirce's return from Washington. The introduction to volume
3 will resume the story at that point. But from a consecutive and
careful reading of the present volume it will already be evident that
pragmatism was the natural and logical next step.
II
C. F. DELANEY
The Journal of Speculative Philosophy papers of 1868-69 fall into two
quite distinct groups. The first set is composed of a series of
interchanges between C. S. Peirce and W. T. Harris (the editor of the
journal) on issues of logic and speculative metaphysics that emerge from
the philosophy of Hegel. The second set of papers, quite different in
tone, consists of Peirce's classic papers on cognition and reality, and
the relatively neglected concluding paper of the series on the grounds
of validity of the laws of logic.
1.
The Peirce-Harris exchange on Hegelian logic and metaphysics was
occasioned by Harris's review article entitled "Paul Janet and Hegel"
which appeared in his own journal. This was a long critical review of
Janet's Etudes sur la dialectique dans Platon et dans Hegel, published
in Paris in 1860. The exchange itself consists of letters from Peirce to
Harris, two of which the latter transformed into dialectically
structured discussion articles for his journal.
After some extensive
preliminaries about the spread of Hegelianism, the original Harris
article (like Janet's book that it reviews) focuses on Hegel's logic and
follows Janet's tripartite division into "The Beginning," "The
Becoming," and "The Dialectic." In the section labeled "The Becoming"
Harris takes issue with Janet's account of the relation of Being and
Nothing and the consequent genesis of Becoming. This is the problem that
interested Peirce, and in his initial letter (24 January 1868) he takes
issue with Harris's own account of the matter. These comments, together
with his own replies, Harris published under the title "Nominalism
versus Realism."
Peirce's criticisms take the form of five inquiries
seeking clarification. Initially he raises some general questions about
Harris's doctrine of abstraction; then he raises three sets of questions
about what he understands to be Harris's three arguments for the
identity of Being and Nothing; finally he suggests, contrary to what he
takes to be Harris's view, that the ordinary logical strictures against
contradiction should at least have the presumption in their favor.
Harris's response to these criticisms is most interesting, particularly
in the light of Peirce's mature philosophy. He maintains that the tone
of Peirce's initial set of questions about abstraction suggests that
Peirce is committed both to nominalism and to a doctrine of immediacy,
and that Peirce's consequent specific criticisms of his three arguments
bear his suspicion out. Peirce's specific objections draw on formal
logic's strictures against contradiction which, Harris maintains, are
only adequate to the immediate world of independent things. But, Harris
concludes, if one is to be a true speculative philosopher one must
transcend this nominalism and become a realist.
Needless to say, Peirce
thought that this response totally missed the point. In his follow-up
letter, he makes the suggestion that a great deal of the
misunderstanding between them may flow from certain unclarities with
regard to the term "determined" as it functions in the discussion of
Being and its determinations. He distinguishes several senses of
"determine," "abstract," and "contradiction" in an attempt to move the
discussion forward. Again, Harris published these comments together with
his own terse responses, this time under the title "What Is Meant by
'Determined'."
One of the most obvious characteristics of this
interchange on Hegel's logic is the marked difference between Harris's
sympathy with the dialectical logic of the Hegelian tradition and
Peirce's employment of ordinary formal logic. Harris's request that
Peirce do something for his journal on the rationale of the objective
validity of the laws of logic is a happy outgrowth of this basic
difference between the two. In his letter of 9 April 1868 Peirce
responds that he has already devoted considerable time to this subject
and could not adequately treat the issue in less than three articles. He
enclosed the first of his three classic 1868 papers on cognition.
2.
Peirce's 1868 papers on cognition, reality, and logical validity bring
up the questions that were to be central throughout his whole
philosophical career. In these he articulates his many-faceted attack on
the spirit of Cartesianism, a spirit which he sees dominating most of
modern philosophy. The Cartesian concern with skeptical doubt,
individual justification, immediate knowledge and certainty (which
traits he also saw in the empiricists), he seeks to replace by a view of
knowledge that was through and through mediate, that construed knowledge
as both an historical and communal human activity. From this perspective
on knowledge, he proceeds to work through a concept of intersubjectivity
to a full-blown account of objectivity, truth, reality, and the basis of
the validity of the laws of logic.
The first piece included here is MS
148, consisting of three separately titled sections listed as "Questions
on Reality" in the Contents. The third section, entitled "Questions
concerning Reality," is an early version of the first published paper in
the series, "Questions Concerning Certain Faculties Claimed for Man,"
but it is most interesting in its own right. In the first place, it is
an heroic attempt to handle in a unified way all the issues that would
eventually be divided among the three published papers in the 1868-69
series. The unity of the overall project is brought out forcefully in
the introductory paragraph of the piece. Here Peirce makes the point
that the logician's initial concern is with the forms of language but
that he must inevitably push on from here to consider what we think,
that is, the manner of reality itself; and, as a precondition for this
inquiry, must get clear about the proper method for ascertaining how we
think. His order of treatment, then, is, first, to give an account of
cognition; secondly, to give an account of truth and reality; and,
finally, to deal with some issues of formal logic. It is instructive to
note that all three of these topics are treated under the general
heading "Questions concerning Reality," indicating a metaphysical thrust
that might be overlooked given the final titles: "Questions Concerning
Certain Faculties Claimed for Man," "Some Consequences of Four
Incapacities," and "Grounds of Validity of the Laws of Logic: Further
Consequences of Four Incapacities."14
It is further instructive to
glance over the twelve questions Peirce poses for himself in the outline
given in the first section of MS 148 and observe how they reappear in
the three published pieces.
The first six questions have to do with an
account of thinking and with the methodology appropriate in generating
such an account; and it is these six questions that make up the
substance of the first published paper in the series, "Questions
Concerning Certain Faculties Claimed for Man." The central issue is
whether we have any immediate knowledge at all (of ourselves, our mental
states, or the external world) and Peirce answers in the negative. In
the process he distinguishes between intuition (cognition not determined
by a previous cognition) and introspection (internal cognition not
determined by external cognition) and defends an account of knowledge
construed as a thoroughly mediated inferential sign process. A linchpin
of his argument is a methodological stance that favors any account of
mental activity that abides by the normal conventions of theory
construction, a stance which shifts the burden of proof to those
accounts wherein some special faculties are claimed for man. Peirce
concludes by adding as a novel seventh question some summary material
that appears at the end of "Questions concerning
Reality" dealing with some general arguments against the thesis
that there is no cognition not determined by a previous cognition.
There are two short pieces entitled "Potentia ex Impotentia"
also included here. These are early versions of beginnings of the second
published paper, "Some Consequences of Four Incapacities," and
again are interesting in their own right because of some methodological
points therein. First, Peirce makes the general comment that on the one
hand we should begin our philosophizing simply with those beliefs we
have no reason to call into question, but, on the other, we should not
maintain an attitude of certainty on matters concerning which there is
real disagreement among competent persons. In short, our philosophizing
should be continuous with our commonsense ways of dealing with the world
about us. Secondly, he makes a series of provocative statements about
the present state of philosophy and the methods of explanation that
should be employed in philosophy. The state of philosophy he likens to
the state of dynamics before Galileo; namely, a theater of disputation
and dialectics with little by way of established results. In this state,
he maintains, what is called for is not conservative caution (as would
have been called for in mechanics where much was truly established) but
rather bold and sweeping theorizing to break new ground and put the area
in order. Peirce does not mean that our metaphysical speculation should
be uncontrolled and irresponsible but that it should be guided by the
various different tangible facts we have at our disposal without any
pretense to demonstration, certainty, or finality. We should content
ourselves with the probable forms of reasoning that are so fruitful in
physical science and congratulate ourselves if we thereby reduce the
uncertainty in metaphysics to one hundred times that of these sciences.
It is in this spirit of speculation that one should view the sweeping
theory of mental activity he articulates in "Some Consequences of
Four Incapacities."
In the first published paper in this series Peirce had suggested, in
opposition to the Cartesian account, that all knowing involved an
inferential sign process. In the second paper in the series he takes up
the task of articulating in some detail his own theory of the structure
of mental activity, that is, the structure of the internal sign process
that is involved in knowing. Constructing this account, he is guided by
his methodological strictures to the effect that any account of the
internal (mental activity) must be in terms of the external (publicly
accessible objects) and that, given the postulation of one
structure,
another is not to be introduced into the theory unless there are facts
impossible to explain on the basis of the first.
Focusing on our
public sign system, that is, language, as the paradigmatic external
manifestation of mental activity, Peirce proceeds to construct an
account of mental activity in terms of "inner speech."
Furthermore, he develops an holistic form of this tradition in which the
basic mental unit is not the concept (the mental word) or even the
judgment (the mental sentence) but rather the process of reasoning
itself (the mental syllogism). Since it is then the structure (rather
than the matter) of the sign process that is of primary importance,
Peirce accordingly construes the process as one of drawing inferences,
as syllogistic in nature. Next, drawing on his formal accounts of
deduction, induction, and hypothesis, he proceeds to give an account not
only of thinking but also of the other forms of mental activity
(sensation, emotion, and attention) in terms of his syllogistic model.
His final extrapolation of the model enables him to give a speculative
account of the mind itself.
The third paper in the published
series, "Grounds of Validity of the Laws of Logic: Further
Consequences of Four Incapacities," picks up some of the remaining
questions outlined in MS 148 and finally comes to grips with Harris's
original challenge which had been the impetus for all three papers,
namely, how can Peirce account for the objective validity of the laws of
logic? The theories of cognition and reality were developed for the sake
of providing just such an account, an account which begins with a
justification of deduction and then broadens out to encompass a
philosophical grounding of the general logic of science.
The point
of continuity with the previous pieces is Peirce's claim that every
cognition results from an inference and that the structure of all mental
activity is inferential. Can't the question be raised-what reason do we
have to believe that the principles of inference are true or correspond
to anything in the real world? While not purporting to take seriously
the stance of the absolute skeptic, Peirce does think it incumbent upon
him to provide an account of the objective validity of the logical
principles of inference. He proceeds to give an account of the validity
of deduction, induction, and hypothesis; and his proffered
"justifications" invoke the characteristic Peircean concepts
of truth (as the ultimate agreement of investigators), reality (as
that which is represented in that agreement), and community (as the
ultimate ground of both logic and reality).
It would be
difficult indeed to overstate the importance of these
three papers in the Peircean corpus. That Peirce himself saw them as
central is clear from his designation of them as Chapters 4, 5, and 6 of
one of his major projected works, the 1893 "Search for a
Method." Most later commentators have seen them as the key to his
overall philosophical orientation.
III
DANIEL D. MERRILL
Peirce's "Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of Boole's Calculus of Logic"
(DNLR) is one of the most important works in the history of modern
logic, for it is the first attempt to expand Boole's algebra of logic to
include the logic of relations. The complex mathematical analogies which
govern parts of this work make it obscure in spots; but the main thrust
of its important innovations may be seen by placing it in the context of
Peirce's earlier logical studies, and by relating it to the work of
Boole, De Morgan, and Benjamin Peirce.
The logical substructure of
DNLR is a modified version of Boole's algebra of classes, in which
Peirce had shown an early interest.
15
One modification is the use of the
"inclusive" sense of logical addition, which Peirce had
introduced by 1867. 16
The other main modification is the replacement of
Boole's equality or identity sign (=) by the sign of illation or
inclusion ( -<) as the sign for the fundamental logical relation.
While this replacement may have been primarily dictated by formal
considerations, it was an important step on the road to a less algebraic
approach to the logic of classes.
To this basically Boolean
structure, Peirce adds a notation for relations and for operations upon
relations, as well as laws governing those operations. Even then,
though, the influence of Boole remains strong. While Peirce admits
logical relations between relations, he most often considers logical relations
that hold between class terms of
which relation terms form a part.
Peirce's interest in the logic of
relations can be traced to several sources.
17 Published and unpublished
papers prepared around 1866 show a strong interest in the problems which
relation terms present for the theory of categories.
18 They are also
concerned with different types of relations, such as the distinction
between relations of equiparance and relations of disquiparance. His
work at this time also shows an interest in arguments involving
relations and multiple subsumptions. Such an argument is "Everyone
loves him whom he treats kindly; James treats John kindly; hence, James
loves John." Peirce's early treatment of these arguments is rather
conservative, either reformulating them so as to apply the usual
syllogistic forms, or using some principle of multiple subsumption which
is construed as a natural generalization of the syllogism.
Unfortunately, the origins of the more powerful and, indeed,
revolutionary techniques of DNLR are more obscure.
19 Only two surviving
documents provide a sustained insight into their origins. One is the
so-called Logic Notebook (LN), which carries entries from 3 to 15
November 1868 in which several notations are devised and some basic
identities are shown. Only the rudiments of DNLR may be found here. The
same is true of the other source, a series of notes that Peirce wrote at
about the same time to add to a projected republication of his American
Academy papers of 1867. Note 4 in this set shows how an algebraic
notation may be used to validate the following argument, which De Morgan
had claimed could not be shown to be valid by syllogistic means:
Every man is an animal.
Therefore, any head of a man is a head of an animal.
Most unfortunately, the surviving parts of LN have no entries from 16
November 1868 through 5 October 1869, nor is there any other document
which would allow us to trace the development of these techniques.
Peirce's references to De Morgan in DNLR, as well as an undated
comparison (in LN) between his notation and De Morgan's, raise the
question of De Morgan's role in stimulating the work which led to
DNLR.20 It must be noted, though, that there is little direct
biographical information on this issue, and that Peirce's later
recollections are contradictory and even inconsistent with known
facts.
Peirce apparently initiated an exchange of papers with De
Morgan in late 1867, as a result of which De Morgan received a copy of
Peirce's "Three Papers on Logic" (the first three American
Academy papers) by May 1868. In a letter dated 14 April 1868, De Morgan
had promised to send Peirce a copy of his classic paper of 1860 on the
logic of relations,21 but there is no direct evidence that this was ever
sent. Nevertheless, Peirce had seen De Morgan's paper by late December
1868, since he refers to it in another paper sent to the printer at that
time.22 It is thus very likely that Peirce had read De Morgan's paper
before he wrote the entries in LN dated November 1868, even though those
entries carry no clear references to De Morgan and use quite different
examples.
Biographical issues aside, Peirce's initial work in the
logic of relations is significantly different from De Morgan's. The most
important difference is that while De Morgan was interested primarily in
the composition of relations with relations, Peirce is concerned with
the composition of relations with classes. Thus, while De Morgan's
paradigm is an expression such as "X is a lover of a servant of
Y," Peirce is first concerned with such expressions as
"lover of a woman." A predilection for class expressions is
found even in DNLR, though this is often combined with the composition
of relations, as in "lover of a servant of a woman." This
emphasis upon class expressions seems to reflect the Boolean frame of
reference in which Peirce was working.
De Morgan also considered
two types of "quantified relations." The first is "X is
an L of every M of Y," which is expressed by Peirce as
"involution," or exponentiation. Even here, the LN shows him
more concerned with the composition of a relation and a class, as
in "lover of every woman," than with strictly relational
composition. The other form of quantified relation is "X is an L of
none but M of Y," a form which Peirce only considers in the
section on "backward involution" which he added to DNLR
shortly before it was printed (pp. 400-408).
These comparisons
between De Morgan and Peirce make their relationship problematic. It
becomes more so in view of the fact that some of De Morgan's most
dramatic results involve the contrary and the converse of a relation.
While Peirce deals with contraries throughout LN and DNLR, he did not
consider converses in the 1868 portions of LN, and he only deals with
them in that section of the DNLR which he added at the time of
printing.
We may conclude that while Peirce probably knew of De
Morgan's memoir on relations when he was working out the full notation
of DNLR, his own Boolean orientation meant that he was working on these
topics in his own way.
While DNLR is primarily a contribution to
logic, parts of it may also be related to the developments in algebra to
which his father contributed. During the years 1867-69, Benjamin Peirce
presented a series of papers to the National Academy of Sciences which
resulted in a book entitled Linear Associative Algebra (LAA) which
was privately published in 1870, and then republished with notes by C.
S. Peirce in 1881.23 ln it Benjamin Peirce surveyed all the types of
linear associative algebras which can be constructed with up to seven
units, enormously generalizing such algebras as that of complex numbers
(of the form a 1 + bi) and Hamilton's quaternions (a 1 + bi + cj +
dk). ln the subsection on Elementary Relatives in DNLR, Peirce
conjectured that all linear associative algebras could be expressed in
terms of elementary relatives, which he then proved in 1875
24 and
illustrated in his notes to his father's book. This technique formed the
foundation for the method of linear representation of matrices, which is
now part of the standard treatment of the subject.
As in the
case of the relationship of the DNLR to De Morgan's paper, its relation
to his father's LAA is difficult to estimate accurately. Certainly they
were working on these long papers at about the same time, so that some influence would not be surprising. ln a short letter
to his father that has been dated 9 January 1870, Peirce writes:
"I think the following may possibly have some interest to you in
connection with your algebras. I have been applying Boole's Calculus to
the Logic of Relative Terms & in doing so have got (among
other operations) an associative non commutative multiplication. It is
like this. Let k denote killer, w wife, m man. Then
kwm denotes the class of killers of wives of men
The letter then concludes with the colleague-and-teacher example which
is found in the Elementary Relatives section of DNLR (pp. 4O8-11).
While this letter shows that Peirce was thinking of his father's work as
he completed DNLR, it also suggests that the relationship between the
two papers may not be very intimate.
DNLR was communicated to the
American Academy of Arts and Sciences on 26 January 1870 and printed in
the late spring. The exact time of its printing is uncertain, though it
must have been printed by 17 June 1870 when Peirce left for Europe. He
carried with him a letter of introduction from his father to De Morgan,
to whom he apparently delivered copies of his memoir and his father's
book. Although there is no contemporary record of Peirce's visiting De
Morgan, he planned to do so and recalled such a meeting in later years.
But the meeting could not have been a very happy one, since De Morgan
was in very poor health by that time and incapable of sustained logical
or mathematical discussion.
The Boolean substructure of DNLR
consists of inclusion and the usual Boolean operations of addition (x +
y), multiplication (x,y), and class complementation (1 - x), along with
their standard laws. To illustrate the relational notation, let s =
servant, l = lover, and w = woman. The most important notations are
relative multiplication (sl, servant of a lover), relative involution
(sl, servant of every lover), backward involution (sl,
servant of none
but a lover), and converse of a relation (Ks, master). Invertible forms
of several of these operations are also given. Relation expressions and
class expressions may be combined, as in "SW" (servant of
every woman) and "s(lw)" (servant of every lover of a woman).
Boolean operations may be applied to relations as well as to classes, so
that, for instance, "(S +, l)" means "either a servant or
a lover."25
While DNLR is largely devoted to the logic of two-place relations,
Peirce also includes a rather confusing discussion of "conjugative
terms," which stand for three-place relations. This is a marked
advance over De Morgan's restriction to two-place relations, but
Peirce's attempts to deal with this topic within the framework of DNLR
present many problems of interpretation.
ln addition to outlining a
notation, DNLR contains a great many principles which may be easily
interpreted in the modern logic of relations. Some significant
identities are
s(m +, w) = sm +, sw
(l +, s)w = lw +, sw
s,l = l,s
(sl)w - s(lw)
sm+,w - sm, sw
(s,l)w = sw,lw.
There are also a great many inclusions, such as
If a -< b then ca -< cb
If a -< b then cb -< ca,
along with chains of inclusions involving combinations of operations, as
in
sw -< sw
and (ls)w -< lsw.
The complement of a relation is treated not only in a Boolean way, but
also as an operation upon a relation, as is the operation of forming the
converse of a relation. De Morgan's principles governing these
operations are given in Peirce's notation. The universal and null
relations are introduced, and their laws are stated.
While Peirce
does not attempt to develop the laws of his notation in a deductive
manner, he does provide demonstrations of a sort for many of his laws,
especially in the section entitled "General Method of Working with
this Notation" (pp.387-417). In the first subsection
on Individual Terms, many intuitively valid laws are demonstrated by
reducing inclusions between classes to individual instances. ln addition
to its discussion of backward involution and conversion, the subsection
on Infinitesimal Relatives contains the most elaborate mathematical
analogies in the memoir, with very puzzling applications of such
mathematical techniques as functional differentiation and the summation
of series. The subsection on Elementary Relatives relates his own work
to Benjamin Peirce's linear associative algebras.
For all its
importance, the Logic of Relatives memoir presents many problems of
interpretation. Perhaps the most serious issue is whether Peirce is
dealing with relations or with relatives-that is, with the relation of
being a servant, or with such classes as the class of servants or the
class of servants of women. His choice of the term "relative"
suggests a desire to distinguish his project from De Morgan's, but in
some cases his terms clearly stand for relations. The situation is
complicated by the fact that many terms, such as "servant,"
can stand for either a relation or a relative, depending upon the
context. Perhaps it is safest to say that he deals with both relational
and relative terms, but that he usually treats relational terms within
the context of relative terms. While this seems true in general, the
interpretation of particular formulas still remains puzzling.
Other
serious issues concern his treatment of conjugative terms and his
elaborate and obscure mathematical analogies. More generally, one may
ask whether DNLR is best studied by translating it into standard
symbolic logic or by considering it in its own right. With the benefit
of hindsight, DNLR cries out for the modern theory of quantifiers, to
which Peirce was to make important contributions. Nevertheless, the core
of its notation is of considerable power and can be studied separately.
It remains of interest to those modern logicians and mathematicians who
have taken an algebraic approach to the study of logic.
26
1
Ben began a promising career as a mining engineer at Marquette, Michigan, but died near there at the early age of twenty-six, on 22 April 1870.
2 P. 288 below.
3Nevertheless, she married Edward H. Green later in 1867 and, as Hetty Green,
was on her way to becoming "the witch of Wall Street."
41n the interim, from 1872 to 1890, there had been a small "Graduate Department" and Jem, as secretary of the Academic Council, had been its administrator.
5He later obtained and distributed collective offprints of the fourth and fifth papers.
6This is a good point at which to remind our readers that even a twenty-volume
edition of Peirce's writings is only an anthology, and that statements about his views based on the anthology may be falsified (or at least may seem to be falsified) by writings it omits. Our first volume, for very good reasons, omits MS 52 (921). If it had been included, it would have come between pages 33 and 37. Past the middle of it there is a leaf whose recto was headed at first "Of Realism & Nominalism. 1859 July 25." The "& Nominalism" was later deleted. The recto continues:
"It is not that Realism is false; but only that the Realists did not advance in the spirit of the scientific age. Certainly our ideas are as real as our sensations. We talk of an unrealized idea. That idea has an existence as neumenon in our minds as certainly as its realization has such an existence out of our minds. They are in the same case. An idea I define to be the neumenon of a conception."
That is all. But on the verso there is a "List of Horrid Things I am." They are: Realist, Materialist, Transcendentalist, Idealist. Why did Peirce delete "& Nominalism"? We can only guess. He was not yet twenty. Perhaps he had confused the sense of realism in which it is opposed to idealism with that in which it is opposed to nominalism, but settled on the former.
7
For details see Max H. Fisch, "Peirce's Progress from Nominalism toward Realism," Monist 51(1967):159-78, at 160-65.
8For details see Max H. Fisch,
"Peirce's General Theory of Signs," in Sight, Sound, and Sense,
edited by Thomas A. Sebeok (Bloomington: Indiana University Press,
1978), pp. 31-70 at 33-38 and, for Berkeley, pp. 57, 63, 65. For
Peirce's early nominalism and its probable derivation from Whately, see
also pp. 60-63. (It is worth adding here that Boole in An Investigation
of the Laws of Thought after an introductory first chapter begins the
investigation with Chapter II "Of Signs in General, and of the Signs
appropriate to the science of Logic in particular; also of the Laws to
which that class of signs are Subject"; and that Chapter III is headed
"Derivation of the Laws of the Symbols of Logic from the Laws of the
Operations of the Human Mind.")
9Karl-Otto Apel,
Charles S. Peirce: From Pragmatism to Pragmaticism, translated by John
Michael Krois (Amherst: University of Massachusetts Press, 1981), pp.
53, 90, 153, 196, 213n107. Gerd Wartenberg, Logischer Sozialismus: Die Transformation der
Kantschen Transzendenta/philosophie durch Charles S. Peirce (Frankfurt: Suhrkamp,
1971).
10John Fiske, Edward Livingston Youmans (New York: D. Appleton and Co., 1894), p. 340. (From a letter of Youmans reporting a visit with Clifford.)
11See part three of the present introduction, by Daniel D. Merrill, and the literature there referred to.
12At a meeting of the much older American Academy of Arts and Sciences on 12 October 1869, "Professor Peirce made a communication on his investigations in Linear Algebra."
13Cf. Carolyn Eisele, Studies in the Scientific and Mathematical Philosophy of
Charles S. Peirce (The Hague: Mouton, 1979), pp. 58 f., 251 f., and The New Elements of Mathematics by Charles S. Peirce, edited by Carolyn Eisele (The Hague: Mouton, 1976), 3:xxiii-xxvii.
141t was probably Peirce's intention to use the title "Questions concerning Reality" for his first published article, but Harris advised against this in a letter of about 15 April 1868, and Peirce replied on 20 April: "Your remark upon my title is very just.
I will make it 'Questions concerning certain Faculties claimed for man'."
15 See Emily Michael, "An Examination of the Influence of Boole's
Algebra on Peirce's Development in Logic," Notre Dame Journal of
Formal Logic 20(1979): 801-6.
16 See "On an Improvement
in Boole's Calculus of Logic," item 2 below, pp.12-23.
17 See Emily Michael, "Peirce's Early Study of the Logic of
Relations, 1865-1867," Transactions of the Charles S. Peirce
Society 10(1974):63-75.
I8 This interest culminates in "On
a New List of Categories," item 4 below, pp.
49-59.
I9See Daniel D. Merrill, "De Morgan, Peirce and the
Logic of Relations" Transactions of the Charles S. Peirce
Society14(1978):247-84.
20Ibid. See also R. M. Martin, "Some Comments on De Morgan, Peirce,
and the Logic of Relations," Transactions of the Charles S.
Peirce Society12(1976):223-30.
21Augustus De Morgan, "On
the Syllogism, No. IV, and on the Logic of Relations,"
Transactions of the Cambridge Philosophical Society
10(1864):331-58.
22"Grounds of Validity of the Laws of
Logic: Further Consequences of Four Incapacities," item 23 below,
pp. 242-72.
23American Journal of Mathematics 4(1881):97-229, and as a separate
volume paged 1-133 (New York: D. Van Nostrand, 1882).
24"On
the Application of Logical Analysis to Multiple Algebra,"
Proceedings of the American Academy of Arts and Sciences n.s.
2(1874-75):392-94, which will be published in volume 3 of the present
edition.
25For analyses and interpretations of DNLR, see Chris Brink, "On
Peirce's Notation for the Logic of Relatives," Transactions of
the Charles S. Peirce Society 14(1978):
285-304; R. M. Martin, "Of Servants, Lovers and Benefactors:
Peirce's Algebra of Relatives of 1870," Journal of Philosophical
Logic 7(1978):27-48; Jacqueline Brunning, "Peirce's Development of
the Algebra of Relations," diss. Toronto 1981; and Hans G.
Herzberger, "Peirce's Remarkable Theorem," in Pragmatism and
Purpose: Essays Presented to Thomas A. Goudge Toronto:
University of Toronto Press, 1981), pp.41-58.
26Alfred Tarski, "On the Calculus of Relations," Journal of
Symbolic Logic 6(1941):73-89.
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