Peirce, Charles Sanders
PEIRCE, CHARLES SANDERS
(b. Cambridge, Massachusetts, 10 September 1839; d. Milford, Pennsylvania, 19 April 1914)
logic, geodesy, mathematics, philosophy, history of science.
Peirce frequently asserted that he was reared in a laboratory. His father, Benjamin Peirce, was professor of mathematics and natural philosophy at Harvard University at the time of Charles’s birth; he personally supervised his son’s early education and inculcated in him an analytic and scientific mode of thought. Peirce attended private schools in Cambridge and Boston; he was then sent to the Cambridge High School, and, for a term, to E. S. Dixwell’s School, to prepare for Harvard. While at college (1855–1859), Peirce studied Schiller’s Aesthetische Briefe and Kant’s Kritik der reinen Vernunft, both of which left an indelible mark on his thought. He took the M.A. at Harvard (1862) and the Sc.B. in chemistry, summa cum laude, in the first class to graduate from the Lawrence Scientific School (1863). Despite his father’s persistent efforts to encourage him to make a career of science, Peirce preferred the study of methodology and logic.
Upon graduation from Harvard, Peirce felt that he needed more experience in methods of scientific investigation, and he became a temporary aide in the U.S. Coast Survey (1859). For six months during the early 1860’s he also studied, under Louis Agassiz, the techniques of classification, a discipline that served him well in his logic research. Like Comte, Peirce later set up a hierarchy of the sciences in which the methods of one science might be adapted to the investigation of those under it on the ladder. Mathematics occupied the top rung, since its independence of the actualities in nature and its concern with the framing of hypotheses and the study of their consequences made its methodology a model for handling the problems of the real world and also supplied model transforms into which such problems might be cast and by means of which they might be resolved.
Peirce was appointed a regular aide in the U.S. Coast Survey on 1 July 1861 and was thereby exempted from military service. On 1 July 1867 he was appointed assistant in the Survey, a title he carried until his resignation on 31 December 1891. In the early days his assignments were diverse. He observed in the field the solar eclipse of 1869 in the United States and selected the site in Sicily from which an American expedition℄headed by his father and including both himself and his wife℄observed the solar eclipse of 22 December 1870. He was temporarily in charge of the Coast Survey Office in 1872, and on 30 November of that year his father appointed him to “take charge of the Pendulum Experiments of the Coast Survey.” Moreover he was to “investigate the law of deviations of the plumb line and of the azimuth from the spheroidal theory of the earth’s figure.” He was further directed to continue under Winlock the astronomical work that he had begun in 1869, while an assistant at the Harvard College Observatory; his observations, completed in 1875, were published in 1878 in the still important Photometric Researches. He was an assistant computer for the nautical almanac in 1873, and a special assistant in gravity research from 1884 to 1891. During the 1880’s however, Peirce found it increasingly difficult, under the changing administration of the Survey, to conform to the instructions issued him; in 1891 he tendered a forced resignation and left government service. (In 1962 a Coast and Geodetic Survey vessel was named for him, in somewhat belated recognition of his many contributions).
Peirce’s astronomical work, which he began in 1867, was characterized as “pioneer” by Solon I. Bailey, director of the Harvard Observatory in 1920. Peirce attempted to reform existing scales of magnitudes with the aid of instrumental photometry, and he investigated the form of the galactic cluster in which the sun is situated, the determination of which was “the chief end of the observations of the magnitude of the stars.”
From April 1875 to August 1876 Peirce was in Europe to learn the use of the new convertible pendulum, “to compare it with those of the European measure of a degree and the swiss Survey,” and to compare his “invariable pendulums in the manner which has been usual by swinging them in London and Paris.” In England he met Lockyer, Clifford, Stokes, and Airy; and in Berlin, Johann Jacob Baeyer, the director of the Prussian Geodetic Institute, where Peirce compared the two standards of the German instrument and the American one. He was invited to attend the meetings of the European Geodetic Association held in Paris during the summer of 1875, and there made a name as a research geodesist. His discovery of an error in European measurement, which was due to the flexure of the pendulum stand, led to the important twenty-three-page report that Plantamour read for him at Geneva on 27 October 1877. The first Peirce pendulum was invented in June 1878 and superseded the Repsold model used in the Coast and Geodetic Survey. Although the United States did not become a member of the International Geodetic Association until 1889, Peirce’s geodetic work was widely recognized. His paper on the value of gravity, read to the French Academy on 14 June 1880, was enthusiastically received, and he was invited to attend a conference on the pendulum of the Bureau des Longitudes.
In 1879 Peirce succeeded in determining the length of the meter from a wavelength of light. Benjamin Peirce described this feat, an adumbration of the work of Michelson, as “the only sure determination of the meter, by which it could be recovered if it were to be lost to science.” By 1882 Peirce was engaged in a mathematical study of the relation between the variation of gravity and the figure of the earth. He claimed that “divergencies from a spherical form can at once be detected in the earth’s figure by this means,” and that “this result puts a new face on the relation of pendulum work to geodesy.”
Peirce’s mathematical inventiveness was fostered by his researches for the Coast Survey. His theory of conformal map projections grew out of his studies of gravity and resulted in his quincuncial map projection of 1876, which has been revived by the Coast Survey in chart no. 3092 to depict international air routes. This invention represented the first application of elliptic functions and Jacobian elliptic integrals to conformal mapping for geographical purposes. Peirce was further concerned with topological mapping and with the “Geographical Problem of the Four Colors” set forth by A. B. Kempe. The existential graphs that he invented as a means of diagrammatic logical analysis (and which he considered his chef d’oeuvre) grew out of his experiments with topological graphic elements. These reflect the influence on his thought of Tait’s historic work on knots and the linkage problems of Kempe, as well as his own belief in the efficacy of diagrammatic thinking.
Peirce’s interest in the linkage problem is first documented in the report of a meeting of the Scientific Association at the John Hopkins University, where Peirce was, form 1879 to 1884, a lecturer in logic and was closely associated with members of the mathematics department directed by J. J. Sylvester. (It was Sylvester who arranged for the posthumous republication, with addenda and notes by Charles Peirce, of Benjamin Peirce’s Linear Associative Algebra.) Peirce had persuaded his father to write that work, and his father’s mathematics influenced his own. J. B. Shaw has pointed out that two other lines of linear associative had been followed besides the direct one of Benjamin Peirce, one by use of the continuous group first announced by Poincare and the other by use of the matrix theory first noted by Charles Peirce. Peirce was the first noted by Charles Peirce. Peirce was the first to recognize the quadrate linear associative algebras identical with matrices in which the units are letter pairs. He did not, however, regard this combination as a product, as did J. W. Gibbs in his “Elements of Vector Analysis” of 1884. Gibbs’s double-dot product, according to Percey F. Smith, “is exactly that of C. S. Peirce’s vids, and accordingly the algebra of dyadics based upon the double-dot law of multiplication is precisely the matricular algebra” of Peirce. In his History of Mathematics, Florian Cajori wrote that “C. S. Peirce showed that of all linear associative algebras there are only three in which division is unambiguous. These are ordinary single algebra, ordinary double algebra, and quaternions, from which the imaginary scalar is excluded. He showed that his father’s algebras are operational and matricular.” Peirce’s work on nonions was to lead to a priority dispute with Sylvester.
By the time Peirce left the Johns Hopkins University, he had taken up the problem of continuity, a pressing one since his logical analysis and philosophical interpretation required that he deal with the infinite. In his 1881 paper “Logic of Number,” Peirce claimed to have “distinguished between finite and infinite collections in substantially the same way that Dedekind did six years later.” He admired the logical ingenuity of Fermat’s method of “infinite descent” and used it consistently, in combination with an application of De Morgan’s syllogism of transposed quantity that does not apply to the multitude of positive integers. Peirce deduced the validity of the “Fermatian method” of reasoning about integers from the idea of correspondence; he also respected Bolzano’s work on this subject. He was strongly impressed by Georg Cantor’s contributions, especially by Cantor’s handling of the infinite in the second volume of the Acta Mathematica. Peirce explained that Cantor’s “class of Mächtigkeit afeph-null is distinguished from other infinite classes in that the Fermation inference is applicable to the former and not to the latter; and that generally, to any smaller class some mode of reasoning is applicable which is not applicable to a greater one.” In his development of the concept of the orders of infinity and their aleph representations, Peirce used a binary representation (which he called “secundal “secundal notation”) of numbers. He eventually developed a complete algorithm for handling fundamental operations on numbers so expressed. His ingenuity as an innovator of symbolic notation is apparent throughout this work.
Peirce’s analysis of Cantor’s Menge and Mächtigkeit led him to the concept of a supermultitudinous collection beyond all the alephs—a collection in which the elements are no longer discrete but have become “welded” together to represent a true continuum. In his theory of logical criticism, “the temporal succession of ideas is continuous and not by discrete steps,” and the flow of time is similarly continuous in the same sense as the nondiscrete superpostnumeral multitudes. Things that exist form an enumerable collection, while those in futuro form a denumerable collection (of multitude aleph-null). The possible different courses of the future have a first abnumeral multitude (two raised to the exponent aleph-null) and the possibilities of such possibilities will be of the second abnumeral multitude (two raised to the exponent “two raised to the exponent aleph-null”). This procedure may be continued to the infinitieth exponential, which is thoroughly potential and retains no relic of the arbitrary existential—the state of true continuity. Peirce’s research on continuity led him to make an exhaustive study of topology, especially as it had been developed by Listing.
Peirce’s philosophy of mathematics postulated that the study of the substance of hypotheses only reveals other consequences not explicitly stated in the original. Mathematical procedure therefore resolves itself into four parts: (1) the creation of a model that embodies the condition of the premise; (2) the mental modification of the diagram to obtain auxiliary information; (3) mental experimentation on the diagram to bring out a new relation between parts not mentioned in its construction; and (4) repetition of the experiment “to infer inductively, with a degree of probability practically amounting to certainty, that every diagram constructed according to the same precept would present the same relation of parts which has been observed in the diagram experimented upon.” The concern of the mathematician is to reach the conclusion, and his interest in the process is merely as a means to reach similar conclusions, whereas the logician desires merely to understand the process by which a result may be obtained. Peirce asserted that mathematics is a study of what is or is not logically possible and that the mathematician need not be concerned with what actually exists. Philosophy, on the other hand, discovers what it can from ordinary everyday experience.
Peirce characterized his work in the following words: “My philosophy may be described as the attempt of a physicist to make such conjecture as to the constitution of the universe as the methods of science may permit. . . The best that can be done is to supply a hypothesis, not devoid of all likelihood, in the general line of growth of scientific ideas, and capable of being verified or refuted by future observers.” Having postulated that every additional imporvement of knowledge comes from an exercise of the power of perception, Peirce held that the observation in a necessary inference is directed to a sort of diagram or image of the facts given in the premises. As in mathematics, it is possible to observe relations between parts of the diagram that were not norticed in its construction. Part of the business of logic is to construct such diagrams. In short, logical truth has the same source as mathematical truth, which is derived from the observation of diagrams. Mathematics uses the language of imagery to trace out results and the language of abstraction to make generalizations. It was Peirce’s claim to have opened up the subject of abstraction, where Boole and De Morgan had concentrated on studies of deductive logic.
In 1870 Peirce greatly enlarged Boolean algebra by the introduction of a new kind of abstraction, the dyadic relation called “inclusion”—“the connecting link between the general idea of logical dependence and the idea of sequence of a quantity.” The idea of quantity is important in that it is a linear arrangement whereby other linear arrangements (for example, cause and effect and reason and consequent) may be compared. The logic of relatives developed by Peirce treats of “systems” in which objects are brought together by any kind of relations, while ordinary logic deals with “classes” of objects brought together by the relation of similarity. General classes are composed of possibilities that the nominalist calls an abstraction. The influence of Peirce’s work in dyadic relations may be seen in Schroder’s Vorlesungen über die Algebra der Logik, and E. V. Huntington included Peirce’s proof of a fundamental theorem in his “Sets of Independent Postulates for the Algebra of Logic” and in The Continuum refered to a statement that Peirce had published in the Monist. Peirce’s contribution to the foundations of lattice theory is widely recognized.
In describing multitudes of systems within successive systems, Peirce reached a multitude so vast that the individuals lose their identity. The zero collection represents germinal possibility; the continuum is concrete-developed possibility; and “The whole universe of true and real possibilities forms a continuum upon which this universe of Actual Existence is a discontiuous mark like a point marked on a line.”
The question of nominalism and realism became for Peirce the question of the reality of continua. Nature syllogizes, making inductions and abductions—as, for example, in evolution, which becomes “one vast succession of generalizations by which matter is becoming subjected to ever higher and higher laws.” Laws of nature in the present form are products of an evolutionary process and logically require an explanation in such terms. In the light of the logic of relatives, Peirce maintained, the general is seen to be the continuous and coincides with that opinion the medieval Schoolmen called realism. Peirce’s Scotistic stance—in opposition to Berkeley’s nominalism—caused him to attack the nominalistic positions of Mach, Pearson, and Poincaré. Peirce accused the positivists of confusing psychology with logic in mistaking sense impressions, which are psychological inferences, for logical data. Joseph Jastrow tells of being introduced by Peirce “to the possiblity of an experimental study of a psychological problem,” and they published a joint paper, “On Small Differences in Sensation,” in the Memoirs of the National Academy of Sciences (1884).
William James was responsible for Peirce’s worldwide reputation as the father of the philosophical doctrine that he originally called pragmatism, and later pragmaticism. Peirce’s famous pragmatic maxim was enunciated in “How to Make Our Ideas Clear,” which he wrote (in French) on shipboard before reaching Plymouth on the way to the Stuttgart meetings of the European Geodetic Association in 1877. The paper contains his statement of a laboratory procedure valid in the search for “truth”—“Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.” In a letter to his former student Christine Ladd-Franklin, Peirce emphasized that “the meaning of a concept . . . lies in the manner in which it could conceivably modify purposive action, and in this alone.” Moreover “pragmatism is one of the results of my study of the formal laws of signs, a study guided by mathematics and by the familiar facts of everyday experience and by no other science whatever.” John Dewey pointed out that reality, in Peirce’s system, “means the object of those beliefs which have, after prolonged and cooperative inquiry, become stable, and ‘truth,’ the quality of these beliefs, is a logical consequence of this position.” The maxim underlies Peirce’s epistemology, wherein the first procedure is a guess or hypothesis (abductive inference) from which are set up subsidiary conclusions (deductive inference) that can be tested against experimental evidence (inductive inference).
The results of the inductive process are ratios and admit of a probability error, abnormal occurrences corresponding to a ratio of zero. This is valid for infinite classes, but for none larger than the denumeral. Consequently, induction must always admit the possibility of exception to the law, and absolute certainty is unobtainable. Every boundary of a figure that represents a possible experience ought therefore to be blurred, and herein lies the evidence for Peirce’s claim to priority in the enunciation of a triadic logic.
Morris Cohen has characterized Peirce’s thought as germinal in its initiation of new ideas and in its illumination of his own “groping for a systematic view of reason and nature.” Peirce held that chance, law, and continuity are basic to the explanation of the universe. Chance accounts for the origin of fruitful ideas, and if these meet allied ideas in a mind prepared for them, a welding process takes place—a process called the law of association. Peirce considered this to be the one law of intellectual development.
In his educational philosophy Peice said that the study of mathematics could develop the mind’s powers of imagination, abstraction, and generalization. Generalization, “the spilling out of continuous systems of ideas,” is the great aim of life. In the early 1890’s he was convinced that modern geometry was a rich source of “forms of conception,” and for that reason every educated man should have an acquaintance with projective geometry (to aid the power of generalization), topology (to fire the imagination), and the theory of numbers (to develop the power of exact reasoning). He kept these objectives in view in the mathematics textbooks that he wrote after his retirement from the Coast Survey; these works further reflect the influence of Arthur Cayley, A. F. Mobius, and C. F. Klein. Peirce’s adoption of Cayley’s mathematical “absolute” and his application of it to his metaphysical thought is especially revealing. “The Absolute in metaphysics fulfills the same function as the absolute in geometry. According as we suppose the infinitely distant beginning and end of the universe are distinct, indentical, or nonexisten we have three kinds of philosophy, hyperbolic, parabolic, or elliptic.” Again “the first question to be asked about a continuous quantity is whether the two points of its absolute coincide.” If not, are they in the real line of the scale?” The answers will have great bearing on philosophical and especially cosmogonical problems.” For a time Peirce leaned to a Lobachevskian interpretation of the character of space.
Peirce once wrote to Paul Carus, editor of the Monist, “Few philosophers, if any, have gone to their work as well equipped as 1, in the study of other systems and in the various branches of science.” In 1876, for example, Peirce’s thought on the “economy of research” was published in a Coast and Geodetic Survey report. It became a major consideration in his philosophy, for the art of discovery became for him a general problem in economics. It underlay his application of the pragmatic maxim and became an important objective in his approach to problems in political economy, in which his admiration of Ricardo was reflected in his referring to “the peculiar reasoning of political economy” as “Ricardian inference,” Peirce’s application of the calculus approach of Cournot predated that of Jevons and brought him recognition (according to W. J. Baumol and S. W. Goldfeld) as a “precursor in mathematical economics.”
Peirce also sought systems of logical methodology in the history of logic and of the sciences. He became known for his meticulous research in the scientific and logical writings of the ancients and the medieval Schoolmen, although he failed to complete the book on the history of science that he had contracted to write in 1898. For Peirce the history of science was an instance of how the law of growth applied to the human mind. He used his revised version of the Paris manuscript of Ptolemy’s catalogue of stars in his astronomical studies, and he included it for modern usage in Photometric Researches. He drew upon Galileo—indeed, his abductive inference is identical twin to Galileo’s il lume naturale—and found evidence of a “gigantic power of right reasoning” in Kepler’s work on Mars.
Peirce spent the latter part of his life in comparative isolation with his second wife, Juliette Froissy, in the house they had built near Milford, Pennsylvania, in 1888. (His second marriage, in 1883, followed his divorce from Harriet Melusina Fay, whom he had married in 1862). He wrote articles and book reviews for newspapers and journals, including the Monist, Open Court, and the Nation. As an editorial contributor to the new Century Dictionary, Peirce was responsbile for the terms in logic, metaphysics, mathematics, mechanics, astronomy, and weight and measures; he also contributed to the Dictionary of Philosophy and Psychology. He translated foreign scientific papers for the Smithsonian publications, served privately as scientific consultant, and prepared numerous papers for the National Academy of Sciences, to which he was elected in 1877 and of which he was a member of the Standing Committee on Weights and Measures. (Earlier, in 1867, he had been elected to the American Academy of Arts and Sciences). Peirce also lectured occasionally, notably at Harvard (where he spoke on the logic of science in 1865, on British logicians in 1869–1870, and on pragmatism in 1903) and at the Lowell Institute. None of his diverse activities was sufficient to relieve the abject poverty of his last years, however, and his very existence was made possible only by a fund created by a group of friends and admirers and administered by his lifelong friend William James.
I. Original Works. Bibliographies and works by Peirce include Carolyn Eisele, ed., The New Elements of Mathematics by Charles S. Peirce, 4 vols. (The Hague, 1974); Charles Hartshorne and Paul Weiss, eds., The Collected Papers of Charles Sanders Peirce, I–VI (Cambridge, Mass., 1931–1935); Arthur W. Burks, ed., VII–VIII (Cambridge, Mass., 1958), with a bibliography in vol. VIII—supp. 1 to this bibliography is by Max Fisch, in Philip Wiener, and Harold Young, eds., Studiesin the Philosophy of Charles Sanders Peirce, 2nd ser. (1964), 477–485, and supp. 2 is in Transactions of the Charles S. Peirce Society,2 , no. 1 (1966), 51–53. Also see Max Fisch,” A Draft of a Bibliography of Writings About C. S. Peirce, “ in Studies, 2nd ser., 486–514; supp. 1 is in Transactions of the Charles S. Peirce Society, 2 no. 1 (1966), 54–59. Papers in the Houghton Library at Harvard University are listed in Richard S. Robin, Annotated Catalogue of the Papers of Charles S. Peirce (Amherst, 1967). In addition, see Richard S. Robin, “The Peirce Papers: A Supplementary Catalogue,” in Transactions of the Charles S. Peirce Society, 7 no. 1 (1971), 37–58. Unpublished MSS are in the National Archives, the Library of Congress, the Smithsonian Archives, and in the Houghton Library, Harvard University.
For Peirce’s work during 1879–1884, see John Hopkins University Circlars, esp. “On a Class of Multiple Algebras,” 2 (1882), 3–4; “On the Relative Forms of Quaternions,” 13 (1882), 179; and “A Communication From Mr. Peirce [On nonions],” 22 (1883), 86–88.
In the period 1870–1885, Peirce published fourteen technical papers as appendices to Reports of the Superintendent of the United States Coast and Geodetic Survey. See “Notes on the Theory of Economy of Research,” 14 (1876), 197–201, repr. in W. E. Cushen, :C. S. Peirce on Benefit-Cost Analysis of Scientific Activity,” in Operations Research (July-Aug., 1867), 641–648; and “A Quincuncial Projection of the Sphere,” in 15 (1877), published also in American Journal of Mathematics, 2 (1879), and in Thomas Craig, A Treatise omn Projections (1882). See also “Photometric Researches,” in Annals of Harvard College Observatory (Leipzig, 1878); and preface: “A Theroy of Probable Inference,” note A: “Extension of the Aristotelian Syllogistic”; and note B: “The Logic of Relatives,” in Peirce, ed., Studies in Logic. By Members of the Johns Hopkins University (Boston, 1883).
See also Charles S. Peirce Über die Klaheit unserer Gedanken (How to Make Our Ideas Clear), ed., trans., and with commentary by Klaus Oehler (Frankfurt am Main, 1968); Edward C. Moore, ed., Charles S. Peirce; The Essential Writings (Vorlesungen über Pragmatismus), ed., trans., and annotatted by Elisabeth Walther (Hamburg, 1973); and Morris R. Cohen, ed., Chance, Love, and Logic (New York, 1923).
II. Secondary Literature. The Transactions of the Charles S. Peirce Society contain a large number of papers on Peirce and his work. There are also interesting biographical notices in a number of standard sources—see esp. those by N. Bosco. in Enciclopedia filosofica (Florences, 1967); Murray G. Murphey, in The Encyclopedia of Philosophy (New York–London, 1967); Paul Weiss, in Dictionary of American Biography (New York, 1934); and Philip P. Wiener, in International Encyclopedia of the Social Sciences (New York, 1968). See also Lamb’s Biographical Dictionary of the United States (Boston, 1903); and American Men of Science (1906), which contains Peirce’s own list of his fields of research.
Recent books, not necessarliy listed in the bibliographies cited above, include John F. Boler, Charles S. Peirce and Scholastic Realism (Seattle, 1963); Hanna Buczynska-Garewicz, Peirce (Warsaw, 1965); Douglas Greenlee, Peirce’s Concept of Sign (The Hague-Paris, 1973); Edward C. Moore and Richard S. Robin, eds., Studies in the Philosophy of Charles Sanders Peirce, 2nd ser. (Amherst, 1964); Murray G. Murphey, The Development of Peirce’s Philosophy (Cambridge, Mass, 1961); Francis E. Reilly, Charles S. Peirce’s Theory of Scientific Method (New York, 1970); Don D. Roberts, The Existential Graphs of Charles S. Peirce (The Hague-Paris, 1973); Elisabeth Walther, Die Festigung der Überzeugung and andere Schriften (Baden-Baden, 1965); Hjamer Wennerberg, The Pragmatism of C. S. Peirce (Uppsala, 1962); and Philip P. Wiener and Frederic H. Young, eds., Studies in the Philosophy of Charles Sanders Peirce (Cambridge, Mass., 1952).
Especially pertinent to this article are J. C. Abbott, Trends in Lattice Theory (New York, 1970); Oscar S. Adams, “Elliptic Functions Applied to Conformal World Maps,” in Department of Commerce Special Publication No. 112 (1925); and “The Rhombic Conformal Projection,” in Bulletin géodésique, 5 (1925), 1–26; Solon 1. Bailey, History and Work of the Harvard College Observatory (1931); W. J. Baumol and S. M. Goldfeld, Precursors in Mathematical Economics (London, 1968); Max Bense and Elisabeth Walter, Wörterbuch der Semiotk (Cologne, 1973); Garrett Birkhoff, Lattice Theory (New York, 1948); Rudolf Carnap, Logical Foundations of Probability (London, 1950); Clarence 1. Lewis, A Survey of Symbolic Logic (Berkeley, 1918); James Byrnie Shaw, Spnopsis of Linear Associative Algebra (Washington, D.C., 1907); Percey F. Smith, “Josiah Willard Gibbs,” in Bulletin of the American Mathematical Society (Oct. 1903), 34–39; and Albert A. Stanley, “Quincuncial Projection,” in Surveying and Mapping (Jan.–Mar., 1946).
See also the section “Charles Sanders Peirce,” in Journal of Philosophy, Psychology and Scientific Methods, 13 , no. 26 (1916), 701–737, which includes Morris R. Cohen, “Charles S. Peirce and a Tentative Bibliography of His Published Writings”; John Dewey, “The Pragmatism of Peirce”; Joseph Jastrow, “Charles Peirce as a Teacher”; Christine Ladd-Franklin, “Charles S. Peirce at the Johns Hopkins”; and Josiah Royce and Fergus Kernan, “Peirce as a Philosopher.”
More recently published essays by Carolyn Eisele, not necessarily listed above, include “The Liber abaci Through the Eyes of Charles S. Peirce,” in Scripta mathematica, 17 (1951), 236–259; “Charles S. Peirce and the History of Science,” in Yearbook. American Philosophical Society (Philadelphia, 1955), 353–358; “Charles S. Peirce, American Historian of Science,” in Actes du VIII Congres international d’histoire des sciences (Florence, 1956), 1196–1200; “The Charles S. Peirce-Simon Newcomb Correspondence,” in Proceedings of the American Philosophical Society, 101 , no. 5 (1957), 410–433; “The Scientist-Philosopher C. S. Peirce at the Smithsonian,” in Journal of the History of Ideas, 18 , no. 4 (1957), 537–547; “Some Remarks on the Logic of Science of the Seventeenth Century as Interpreted by Charles S. Peirce,” in Actes du 2eme Symposium d’histoire des sciences (Pisa-Vinci, 1958), 55–64; “Charles S. Peirce, Nineteeth-Century Man of Science,” in Scripta mathematica, 24 (1959), 305–324; “Poincare’s Positivism in the Light of C. S. Peirce’s Realism,” in Actes du IX’ Congrè’s international d’histoire des sciences (Barcelona-Madrid, 1959), 461–465; “The Quincuncial Map-Projection of Charles S. Peirce,” in Proceedings of the 10th International Congress of History of Science (Ithaca, 1962), 687; and “Charles S. Peirce and the Problem of Map-Projection,” in Proceedings of the American Philosophical Society, 107 , no. 4 (1963), 299–307.
Other articles by Carolyn Eisele are “Fermatian Inference and De Morgan’s Syllogism of Transposed Quantity in Peirce’s Logic of Science,” in Physis. Rivista di storia della scienza, 5 , fasc. 2 (1963), 120–128; “The Influence of Galileo on the Thought of Charles S. Peirce,” in Atti del Simposio su Galileo Galilei nella storia e nella filosofia della scienza (Florence-Pisa, 1964), 321–328; “Peirce’s Philosophy of Education in His Unpublished Mathematics Textbooks,” in Edward C. Moore and Richard S. Robin, eds., Studies in the Philosophy of Charles Sanders Peirce, 2nd ser., (1964), 51–75; “The Mathematics of Charles S. Peirce,” in Actes du XIe Congrè’s international d’histoire des sciences (Warsaw, 1965), 229–234; “C. S. Peirce and the Scientific Philosophy of Ernst Mach,” in Actes du XIIe Congrè’s international d’histoire des sciences (Paris, 1968), 33–40; and “Charles S. Peirce and the Mathematics of Economics,” in Actes du XIIIe Congrè’s international d’histoire des sciences (Moscow, 1974).
Essays by Max H. Fisch include “Peirce at the Johns Hopkins University,” in Philip P. Wiener and Frederic H. Young, eds., Studies in the Philosophy of Charles Sanders Peirce (Cambridge, 1952), 277–312, written with Jackson I. Cope; “Alexander Bain and the Genealogy of Pragmatism,” in Journal of the History of Ideas, 15 (1954), 413–444; “A Chronicle of Pragmaticism, 1865–1897,” in Monist, 48 (1964), 441–466; “Was There a Metaphysical Club in Cambridge?,” in Edward C. Moore and Richard S. Robin, eds., Studies in the Philosophy of Charles Sanders Peirce, 2nd ser. (Amherst, 1964), 3–32; “Peirce’s Triadic Logic,” in Transactions of the Charles S. Peirce Society, 2 (1966), 71–86, written with Atwell Turquette; “Peirce’s Progress from Nominalism Toward Realism,” in Monist, 51 (1967), 159–178; and “Peirce’s Ariste: The Greek Influence in His Later Philosophy,” in Transactions of the Charles S. Peirce Society, 7 (1971), 187–210.
Essays by Victor F. Lenzen include “Charles S. Peirce and Die Europaische Gradmessung,” in Proceedings of the XIIth International Congress of the History of Science (Ithaca, 1962), 781–783; “Charles S. Peirce as Astronomer,” in Edward C. Moore and Richard S. Robin, eds., Studies in the Philosophy of Charles Sanders Peirce, 2nd ser. (Amherst, 1964), 33–50; “The Contributions of Charles S. Peirce to Metrology,” in Proceedings of the American Philosophical Society, 109 , no. 1 (1965), 29–46; “Development of Gravity Pendulums in the 19th Century,” in United States Museum Bulletin 240: Contributions From the Museum of History and Technology, Smithsonian Institution, paper 44 (Washington, 1965), 301–348, written with Robert P. Multhauf; “Reminiscences of a Mission to Milford, Pennsylvania,” in Transactions of the Charles S. Peirce Society, 1 (1965), 3–11; “The Role of Science in the Philosophy of C. S. Peirce,” in Akten des XIV Internationalen Kongresses für Philosophie (Vienna, 1968), 371–376; “An Unpublished Scientific Monograph by C. S. Peirce,” in Transactions of the Charles S. Peirce Society, 5 (1969), 5–24; “Charles S. Peirce as Mathematical Geodesist,” ibid., 8 (1972), 90–105; and “The Contributions of C. S. Peirce to Linear Algebra,” in Dale Riepe, ed., Phenomenology and Natural Existence (Essays in Honor of Martin Farber) (New York, 1973), 239–254.
Peirce, Charles Sanders
Peirce, Charles Sanders
Charles Sanders Peirce (1839-1914), the greatest of America’s scientific philosophers, was born in Cambridge, Massachusetts, the second son of the famous Harvard mathematician and astronomer Benjamin Peirce (1809-1880). Peirce was coached by his father in mathematics, physics, and astronomy, and was later to revise his father’sLinear Associative Algebra of 1870. After receiving his bachelor’s degree from Harvard in 1859, and a master’s degree summa cum laude, he joined the United States Coast and Geodetic Survey in 1861. During the thirty years he worked there, he became internationally famous for his pendular measurements of gravity and of starlight intensity (1878a). Between 1879 and 1884, he taught at the Johns Hopkins University, his only university teaching position. He was elected a member of the National Academy of Sciences in 1877 and, even before that, to the American Academy of Arts and Sciences.
Peirce published an improvement of Boole’s logic (1867), which was later further developed by H. M. Sheffer in his work on the stroke function. He also improved on De Morgan’s notation (1870) and developed further the logic of propositions, classes, and relations (1883). This was Peirce’s chief contribution to logic and helped pave the way for twentieth-century developments in symbolic logic. Just as the work of Giuseppe Peano in Italy on the foundations of mathematics influenced such Italian philosophers as the “logical pragmatist” G. Vailati, so Peirce’s research in logic and critical philosophy (especially his studies of Kant, Reid, Bain, Schelling, and Hegel) led to his own formulation of the pragmatic theory that the meaning of a conception lies in the sum total of the conceivable consequences which the object of that conception can possibly have on the conduct of “an indefinite community of investigators” (1877-1878, vol. 12, pp. 286-302). The final opinion of that ideal community would constitute the truth, and the object of that ultimate opinion would be “reality.”
This social criterion of meaning and truth mistakenly has been thought by critics to reduce philosophy to mere public opinion and group prejudice. But Peirce clearly limited his ideal community to scientific investigators. He insisted, furthermore, on the fallibilism of all beliefs, even if common sense and science do require that some premises be taken tentatively as indubitable until experience or experiment shows that a disparity exists between the accepted consequences of these premises and observation. Applying the test of performing specifiable procedures for verifying the calculable consequences of hypotheses has become known as operationalism; Percy Bridgman advocated it in his study of the logic of physics, and John Dewey in his study of the methodology of the social sciences.
Peirce formulated his early statements of pragmatism in two essays, “The Fixation of Belief” and “How to Make Our Ideas Clear,” the first two of six essays in “Illustrations of the Logic of Science” (1877-1878). Although in these early publications he did not call his philosophy “pragmatism,” he did use the term in his discussions about it around Harvard. Many of these discussions (mainly on the significance of the Darwinian controversy for methods of reasoning in the physical and social sciences) took place in an informal club to which he belonged in the early 1870s and whose members also included William James, Chauncey Wright, John Fiske, Oliver Wendell Holmes, Jr., Nicholas St. John Green, and Joseph B. Warner—the last three being law students at the time (see Wiener 1949).
Peirce’s survey of methodological theories in the first of the two essays was a critical analysis of these theories based on social psychology and intellectual history. He listed the four chief methods used to settle “doubts” (by which he meant externally caused disturbances of mind rather than the more subjective kind of Cartesian doubts): tenacity, authority, apriorism, and the scientific method. The scientific method is the most satisfactory in the long run because it is the only one of the four that is not in principle inflexible; it is self-corrective, whereas proponents of the other three methods can claim “infallibility” only by resting on premises other than those encountered in experience or experimental situations. Peirce also rejected intuitionism as being a form of a priori rationalism.
He believed in a kind of metaphysical evolutionism. Originally there was chaos, but as man continually used reason to order his experience, there was a “growth of concrete reasonableness” (1891; 1893). His three main metaphysical categories (that is, modes of representing all that is known) are exemplified by chance qualities (firstness), brute existence (secondness), and generality or order (thirdness) (1877-1878, vol. 12, pp. 604615, 705-718; vol. 13, pp. 203-217). In his later works, Peirce insisted that generality is objectively real, that it exists independently of our beliefs, and that it is given in perception of the particular.
Although Peirce defended a frequency theory of inductive probability, he also proposed other meanings of probable hypotheses or likelihood (1883). He thought all reasoning processes could be divided into three types, depending on their consequences: purely explicative deduction (for example, mathematics and formal logic), ampliative induction (for example, empirical generalization), and conjectural abduction, or reasoning culminating in a probable hypothesis. This third type of reasoning (in his logic of hypothesis) is also called retroduction and is exemplified by cryptography, medical diagnosis, historical inference, and detective work. For all scientific theory he advocated (at the same time as Ernst Mach, but independently of him) a principle of economy, or practical simplicity in the consideration of hypotheses, and a statistical conception of the laws of nature as predictive, fallible, and subject to modification in time.
In social matters, Peirce was intensely opposed to the rugged individualism or “philosophy of greed” of the political economy of Simon Newcomb and of other social Darwinists of his day. He also deplored the lack of faith in the gospel of love on the part of those theologians who practiced the “higher criticism.” In general, Peirce was concerned with the neglect of humanistic ethics in social or political matters.
During the last thirty years of his life he continued his studies in the logic and philosophy of the sciences, although he lived almost like a hermit at Milford, Pennsylvania, with his second wife, a French widow who spoke little English. His contributions to logic, to the philosophy of science, and to the theory of signs were, nevertheless, very influential in the development of the views of people who participated more actively in academic or political affairs, for example, William James, John Dewey, George Herbert Mead, C. I. Lewis, Charles E. Morris, Morris R. Cohen, F. P. Ramsey, Ernest Nagel, Sidney Hook, and others who call themselves pragmatists.
Recent commentators (Feibleman 1946; Thompson 1953; Wiener & Young 1952; Goudge 1950; Murphey 1961) have examined Peirce’s philosophy “as a whole” and have discerned a latent system in his diverse writings, a system that, although incomplete, is architectonic in its professed aims. Kant built an architectonic system of categories that was based on what he regarded as a finished classical logic, but Peirce went far beyond the classical syllogistic logic in his “logic of relatives.”
Murray G. Murphey, in The Development of Peirce’s Philosophy (1961, p. 432) has outlined four major phases of Peirce’s philosophy: a Kantian phase, 1857-1865; the development of the irreducibility of the three syllogistic figures corresponding to deduction, abduction, and induction, 1866-1869; the logic of relations, 1870-1884; and quantification and set theory, 1884-1912. These phases are not actually sharply demarcated in Peirce’s work. Murphey is correct, nevertheless, in emphasizing the fact that Peirce’s philosophical categories of firstness, secondness, and thirdness underwent changes as his logical theories developed; for like Kant, Peirce believed one’s philosophy should follow one’s logic.
Philip P. Wiener
[For the historical context of Peirce’s work, seePositivism; Social Darwinism; Statistics, article onThe History of Statistical Method. For discussion of the subsequent development of his ideas, seeErrors, article onNonsampling Errors; Semantics and Semiotics; and the biographies ofCohen; Dewey; Holmes; James; Mead.]
The most complete bibliography of Peirce’s writings of works on Peirce is contained in Volume 8 of Peirc Collected Papers. The best commentary is in Murphey 1961. For Peirce’s posthumously published contributi to logic, see Volumes 2, 3, and 4 of the Collected Papers.
1867 On an Improvement in Boole’s Calculus of Logic. American Academy of Arts and Sciences, Proceedings 7:250-261.
(1870) 1933 Description of a Notation for the Logic of Relatives, Resulting From an Amplification of the Conceptions of Boole’s Calculus of Logic. Volume 3, pages 27-98 in Charles S. Peirce, Collected Papers. Cambridge, Mass.: Harvard Univ. Press.
1873 On the Theory of Errors of Observations. U.S. Coast and Geodetic Survey, Report of the Superintendent :200-224.
1877-1878 Illustrations of the Logic of Science. Popular Science Monthly 12:1-15, 286-302, 604-615, 705-718; 13:203-217, 470-482.
1878a Photometric Researches. Leipzig: Engelmann.
(1878b) 1956 The Probability of Induction. Volume 2, pages 1341-1354 in James R. Newman (editor), The World of Mathematics: A Small Library of the Literature of Mathematics From A f h-mose the Scribe to Albert Einstein. New York: Simon & Schuster.
(1878c) 1956 The Red and the Black. Volume 2, pages 1334-1340 in James R. Newman (editor), The World of Mathematics: A Small Library of the Literature of Mathematics From A f h-mose the Scribe to Albert Einstein. New York: Simon & Schuster.
1881 On the Logic of Number. American Journal of Mathematics 4:85-95.
1883 A Theory of Probable Inference. Pages 126-181 in Charles S. Peirce (editor), Studies in Logic. Boston: Little.
1884 The Numerical Measure of the Success of Predictions. Science 4:453-454.
1891 The Architecture of Theories. Monist 1:161-176.
1893 Evolutionary Love. Monist 3:176-200.
Collected Papers. Edited by Charles Hartshorne et al. 8 vols. Cambridge, Mass.: Harvard Univ. Press, 19311958. → Volume 1: Principles of Philosophy. Volume 2: Elements of Logic. Volume 3: Exact Logic. Volume 4: The Simplest Mathematics. Volume 5: Pragmatism and Pragmaticism. Volume 6: Scientific Metaphysics. Volume 7: Science and Philosophy. Volume 8: Reviews, Correspondence, and Bibliography.
Airy, G. B. 1856 [Letter From Professor Airy, Astronomer Royal, to the Editor.] Astronomical Journal 4: 137-138. → On the work of Benjamin Peirce.
Buchler, Justus 1939 Charles Peirce’s Empiricism. New York: Harcourt.
Feibleman, James 1946 An Introduction to Peirce’s Philosophy, Interpreted as a System. New York: Harper.
Goodman, Leo A.; and Kruskal, William H. 1959 Measures of Association for Cross Classifications: II. Further Discussion and References. Journal of the American Statistical Association 54:123-163. → See especially pages 127-132, “Doolittle, Peirce, and Contemporary Americans.”
Goudge, Thomas A. 1950 The Thought of C. S. Peirce. Univ. of Toronto Press.
Gould, B. A. JR. 1855 On Peirce’s Criterion for the Rejection of Doubtful Observations, With Tables for Facilitating Its Application. Astronomical Journal 4: 81-87. → On the work of Benjamin Peirce.
Lewis, C. I. 1918 A Survey of Symbolic Logic. Berkeley: Univ. of California Press.
Murphey, Murray G. 1961 The Development of Peirce’s Philosophy. Cambridge, Mass.: Harvard Univ. Press.
Newman, James R. 1956 Commentary on Charles Sanders Peirce. Volume 3, pages 1767-1772 in James R. Newman (editor), The World of Mathematics: A Small Library of the Literature of Mathematics From A’h-mose the Scribe to Albert Einstein. New York: Simon & Schuster.
Peirce, Benjamin 1852 Criterion for the Rejection of Doubtful Observations. Astronomical Journal 2:161-163.
Stewart, R. M. 1920a Peirce’s Criterion. Popular Astronomy 28:2-3. → On the work of Benjamin Peirce.
Stewart, R. M. 1920b The Treatment of Discordant Observations. Popular Astronomy 28:4-6. → On the work of Benjamin Peirce.
Thompson, Manley H. 1953 The Pragmatic Philosophy of C. S. Peirce. Univ. of Chicago Press.
Wiener, Philip P. 1949 Evolution and the Founders of Pragmatism. Cambridge, Mass.: Harvard Univ. Press.
Wiener, Philip P.; and Young, Frederic H. (editors) 1952 Studies in the Philosophy of Charles Sanders Peirce. Cambridge, Mass.: Harvard Univ. Press.
Wilson, Edwin B.; and Hilferty, Margaret M. 1929 Note on C. S. Peirce’s Experimental Discussion of the Law of Errors. National Academy of Sciences,Proceedings 15:120-125.
Winlock, Joseph 1856 On Professor Airy’s Objections to Peirce’s Criterion. Astronomical Journal 4:145-147. → On the work of Benjamin Peirce.
Charles Sanders Peirce
Charles Sanders Peirce
Charles Sanders Peirce (1839-1914) was one of America's most important philosophers. Many of his writings were not published until after his death, but he made important contributions in both philosophy and science. His work in logic helped establish the philosophical school of thought known as pragmatism.
Charles Sanders Peirce was born on September 10, 1839, to Benjamin Peirce and Sarah (Mills) Peirce. His father was a professor at Harvard University and a leading mathematician of his day, and his mother was the daughter of Elijah Mills, U.S. senator from Massachusetts. Peirce grew up in the academic environment of Harvard at a time when science was challenging traditional religious views. He attended local private schools and then Cambridge High School, but his father closely supervised his education, exercising him in games of concentration and complicated mathematical analyses. Peirce was later to comment that his father's educational influence on him was the most important one.
Peirce entered Harvard in 1855 and graduated in 1859, one of the youngest members of the class. His interests pointed in the direction of philosophy, but at the urging of his father he entered scientific work. In 1861 he secured a position with the United States Coast Survey, for which he conducted scientific statistical research, a position he held until 1887. He also continued his formal education. In 1863 Harvard awarded him the B.Sc. in chemistry, summa cum laude. Over the following years his work in science was of such note that in 1877 he was elected a fellow in the American Academy of Arts and Sciences and was made a member of the National Academy of Science. Peirce's interest in philosophy continued, however. From 1864 to 1871 he gave occasional lectures in logic and the philosophy of science at Harvard and was a member of a select intellectual circle that included such luminaries as Ralph Waldo Emerson and John Fiske.
Scholar and Author
Because of circumstances and temperament, Peirce did not make teaching his career. His most significant academic post was as a lecturer in logic at the Johns Hopkins University from 1879 to 1884. He also lectured occasionally at the Lowell Institute and at Bryn Mawr College. He was an inspiring teacher for advanced students, but his insistence on logical precision and his use of a highly technical vocabulary did not appeal to most students. He once described himself as vain and ill-tempered; certainly he was a proud person, conscious of his intellectual power, and often insensitive to the feelings of others. Peirce's temperament apparently affected his first marriage, to Harriet Melusina Fay in 1862, which ended in divorce in 1883. However, his second marriage, to Juliet Frossy, lasted until his death.
A creative and productive scholar, Peirce worked long hours and wrote voluminously. Yet his philosophical work remained obscure until 1898, when William James recognized him as one of the originators of philosophical pragmatism. This reputation grew out of several articles Peirce published in Popular Science Monthly, particularly "How To Make Our Ideas Clear" (1878). In this piece he quarrelled with the accepted view in logic, dating back to Rene Descartes, that a clear idea is defined as "one which is so apprehended that it will be recognized wherever it is met with, and so that no other will be mistaken for it." Peirce labeled this "a prodigious force of clearness of intellect as is seldom met with in this world" and held that it was really based on the subjectivism of familiarity and not on the merits of logic itself. Descartes' use of methodical doubt, set forth in the cogito ("I think; therefore, I am"), was intended to permit at least some skepticism and to reject the practice of appealing to authority for the source of truth; instead, it transformed the traditional appeal to authority into an appeal to subjective introspection.
Rather than seeking the foundation of logic in subjective introspection, Peirce maintained, it is necessary to look to experience in the objective world. The action of thought is excited or motivated by the irritation of doubt, and this activity ceases when a belief is attained. In other words, Peirce held, the production of belief is the sole function of thought. But we also want beliefs that are sound, and hence we need a conception of logical thought process which will lead to clear ideas upon which sound beliefs may follow. The essence of belief is the establishment of sound habits of conduct in the world of people, events, things, and ideas. For Peirce, it was inconceivable that we should have an idea in our minds which relates to anything but conceivable sensible effects. As he put it, "Consider what effects, that might conceivably have practical bearings, we conceive the objects of our conception to have. Then, our conception of these effects is the whole of our conception of the object." In other words, "Our idea of anything is our idea of its sensible effects. … ." Many people took this to be a skeptical and materialistic principle, but Peirce pointed out that it was only an application of the principle of logic recommended by Jesus: "'Ye may know them by their fruits. … "' Peirce was pleased with James's recognition of his work, but he came to disagree with the latter's rendition of the principle as "Truth is what works." This interpretation led Peirce, in 1905, to devise another name for his own views, and he settled on the term "pragmaticism, " allowing that it was "ugly enough to be safe from kidnappers."
Scientist and Philosopher
During his work with the United States Coast Survey, Peirce conducted astronomical research at the Harvard Observatory which resulted in the only complete book he published during his lifetime, Photometric Researches (1878). In 1884, while teaching at Johns Hopkins, he also published Studies in Logic, a collection of essays by himself and some of his students. He did, however, publish a number of articles in journals such as The Monist, North American Review, The Nation, Journal of Speculative Thought, Hibbert Journal, and Popular Science Monthly. He was a significant contributor to such standard reference works as Century Dictionary (1889-1891) and Dictionary of Philosophy and Psychology (1901-1905).
In his later years Peirce's philosophical reputation and fortune, never very extensive, suffered decline. When he retired from the Coast Survey in 1887, he and his wife Juliet moved to the countryside near Milford, Pennsylvania. Gradually indebtedness, advancing age, and ill health took their toll. He approached the end of his life in poverty and without the recognition his work deserved. He finally succumbed to cancer on April 20, 1914.
The greater part of his work was not published until after his death when his papers were purchased by Harvard University. Much of this collection was disorganized, with many parts undated and with important manuscripts in several drafts. Nevertheless, significant portions have been published and have afforded scholars easier access. The Collected Works of Charles Sanders Peirce, volumes 1 to 6 (1931-1935) and volumes 7 and 8 (1966), made most of his major writings available. More recently, Writings of Charles Sanders Peirce: A Chronological Edition, volume 1 (1982), helped show the evolution of his thought in the early years. Future volumes are expected.
Along with these publications has come a better appreciation of Peirce's many contributions. Not only did he provide valuable work in logic, but in several other fields of philosophy as well. He grew to intellectual maturity during the time when Darwin's theory of natural selection created significant changes in people's outlooks. Although Peirce was well grounded in science, Darwinian naturalism was not a major part of his philosophical outlook. Instead, his thrust was toward the Kantian philosophical tradition of seeking the philosophical foundations of science in metaphysics or first philosophy. Peirce developed an evolutionary cosmology, but it was based on objective idealism rather than naturalism, which helps account for his attempt to separate himself from James and other pragmatists. These undercurrents in Peirce's thought led him to explore a wide range of philosophical interests, including the history of philosophy, the theory of signs, phenomenology, and perception—explorations which are now being more thoroughly studied by contemporary scholars.
Biographical material on Charles Sanders Peirce, written by Paul Weiss, may be found in the Dictionary of American Biography, volume XIV (1934). The same material is reprinted in Perspectives on Peirce (1965), which also contains critical essays on Peirce's philosophical contributions. More recent is the biographical sketch of Peirce's early life by Max H. Fisch, "Introduction, " Writings of Charles Sanders Peirce, volume I (1982). The most complete edition of Peirce's writings is The Collected Papers of Charles Sanders Peirce, volumes I-VIII (1931-1935, 1966). Selected papers may be found in Essays in the Philosophy of Science (1967). A helpful analysis of the overall philosophy is Christopher Hooking, Peirce (1985), which also contains a biographical sketch in the introduction. A briefer treatment is Peter Turley, Peirce's Cosmology (1977). □
Peirce, Charles Sanders (1839-1914)
PEIRCE, CHARLES SANDERS (1839-1914)
Born in 1839 in Cambridge, Massachusetts, Charles Sanders Peirce was the second and favorite son of Benjamin Peirce, who was a professor of mathematics and astronomy at Harvard University and was superintendent of the U.S. Coast and Geodetic Survey. Along with Abraham Lincoln in 1863, Benjamin Peirce founded the National Academy of Sciences. Charles graduated with high honors in 1854 from Cambridge High School, where one of his favorite pastimes was the debating society, a source of his reputation as an engaging conversationalist and dynamic lecturer. He then graduated from Harvard with a B.A. in 1859 and an M.A. in 1862. In 1863, he graduated summa cum laude with a B.S. in chemistry from the Lawrence Scientific School at Harvard. He had an erratic and confrontational personality, largely preventing him from permanent employment in the academic world. He was a part-time lecturer in logic at Johns Hopkins University from 1879 to 1884. Despite the persistent efforts of William James, he never obtained a position at Harvard. His more periodic employment with the Coast Survey, and later with the U.S. Assay Commission, fared no better. He suffered seven mental breakdowns between 1876 and 1911 due to a condition now known as trigeminal neuralgia, associated with manic depression. With a small inheritance, he purchased a retirement home at Milford, Pennsylvania, and lived in extreme poverty. During the years between 1903 and 1908, he corresponded on logic and semiotics with Victoria Lady Welby in England. Peirce died of cancer on April 19, 1914.
Peirce comes closest to being America's only systematic philosopher, writing widely and in detail. His principal philosophic system draws from medieval learning focused on the semiotic trivium of grammar, logic, and rhetoric—the building blocks of modern communication theory and mathematical (information) exchange theory. But, the behaviorist division of semiotics, proposed by Charles Morris, is better known. For Morris, grammar is syntactics, or the study of sign structures (codes), whether animal, machine, or human. Logic is semantics, or the study of choices in meaning that govern intention in communication. Last, rhetoric is pragmatics, or the use of discourse to inform and convince. These three elements combine to create the world of human reference (named the "semiosphere" by Juri Lotman).
Peirce uses the covering term "semiotic" to include his major divisions of thought and communication process: (1) speculative grammar, or the study of beliefs independent of the structure of language (i.e., unstable beliefs); (2) exact logic, or the study of assertion in relation to reality (i.e., stable beliefs); and (3) speculative rhetoric, or the study of the general conditions under which a problem presents itself for solution (i.e., beliefs dependent on discourse). This division previews Peirce's famous triadic models of analysis. Peirce goes on to make the distinction between communication (a process) and signification (a system). Communication is the study of messages and the process of meaning, whereas signification is the study of codes and the system of referential signs used. Messages may contain codes (e.g., linguistics or computer programs) or codes may contain messages (e.g., cryptography or measurement). Messages constituting codes are Peirce's doctrine of "tychism," or the study of probabilities where absolute chance is real. What is probable can be understood as the distinction among type, token, and tone. A typology is a category Peirce called "firstness," the condition under which something exists. A token is an example illustrating the type and is a case of "secondness." The tone is "thirdness," a unique individual (a paradigm or prototype example) known by the connection between the type and token. In short, firstness and secondness are two categories held together, related, by thirdness. Thus, types are more probable than tokens; tokens are more probable than tones. For example, one's actual ability to drive a car is more probable than one's ability to own a car, but one's owning a car is more probable than one's buying a new Ford. The communication process of tychism for Peirce is the existential experience of learning how to learn in a general communication experience. When one learns, an object presents itself to the person's consciousness as a sign or "representamen" that "stands to somebody for something in some respect or capacity." An equivalent sign or "interpretant" is created in the mind and this new sign stands for the object. How this communication process of representation (phenomenology) works is the study of signification.
Signification or the doctrine of "synechism" is the analysis of possibilities where codes contain messages. This doctrine holds that all problems can be solved because there is an absolute continuity among things that can be generalized as such. This basic doctrine is applied in Peirce's classification of signs. He divides signs into three basic types, although there are sixty-four subtypes. First, an icon is a sign that has a similarity to its object. Second, an index is a sign that physically connects to its object. Third, a symbol is a sign that arbitrarily links to its object. For example, a statue of a person is an icon, a photograph taken of that person is an index, and the naming noun "person" is a symbol of that person. As Umberto Eco suggests, keep in mind that in complex communication systems the types of signs are often "overcoded" in one object; for example, a traffic stop sign is an icon (similar to a raised hand), an index (red color of danger, octagon shape of convergence), and a symbol (contains the word "stop" on the sign face). Film and television images have much the same overcoded effect. Undercoding occurs when one or more of the signs are taken away, such as when a stop sign does not have the word "stop" on it or when one suddenly loses the audio while watching a television set.
Peirce is noted for his philosophic realism, or the belief that probability and possibility are linked to the actual existence of things or that which can become actual. Hence, people inherit the association of "pragmatism" with a test of real-world application that Peirce called the doctrine of "fallibilism." This existential and phenomenological orientation made Peirce a polymath, according to his biographer Joseph Brent. Peirce was conversant with chemistry, geodesy, metrology, and astronomy. He was the first experimental psychologist in America, a mathematical economist, a logician and mathematician, a dramatist, an actor, a writer, and a book reviewer. He created the modern discipline of semiotics to include all the arts and sciences of communication, information (informatics), and exchange.
Brent, Joseph. (1998). Charles Sanders Peirce: A Life, revised edition. Bloomington: Indiana University Press.
Eco, Umberto. (1976). A Theory of Semiotics. Bloomington: Indiana University Press.
Freeman, Eugene, ed. (1983). The Relevance of Charles Peirce. La Salle, IL: The Hegeler Institute, Monist Library of Philosophy.
Lanigan, Richard Leo. (1992). The Human Science of Communicology. Pittsburgh, PA: Duquesne University Press.
Liszka, James Jakob. (1996). A General Introduction to the Semiotic of Charles Sanders Peirce. Bloomington: Indiana University Press.
Lotman, Juri. (1990). Universe of Mind: A Semiotic Theory of Culture. Bloomington: Indiana University Press.
Nöth, Winfried. (1990). Handbook of Semiotics. Bloomington: Indiana University Press. Peirce, Charles Sanders. (1931-1935, 1958). Collected
Peirce, Charles Sanders. (1976). The New Elements of Mathematics by Charles S. Peirce, 4 vols., ed. Carolyn Eisele. The Hague: Mouton Publishers.
Peirce, Charles Sanders. (1982-1999). Writings of Charles Sanders Peirce: A Chronological Edition, Vols. 1-6 (with 30 projected), ed. Christian J. W. Kloesel. Bloomington: Indiana University Press.
Richard L. Lanigan
Peirce, Charles Sanders
PEIRCE, CHARLES SANDERS
Charles Sanders Peirce (1839–1914), pronounced "purse," was born in Cambridge, Massachusetts on September 10, and died in Milford, Pennsylvania on April 19. In the year of his birth, the first electric clock was built, ozone was discovered, and the growth of cells was charted, while the year of his death saw Robert H. Goddard (1882–1945) inaugurate his rocket experiments and J. H. Jeans (1877–1946) publish a paper on "Radiation and Quantum Theory." Peirce graduated from Harvard College in 1859, the year English naturalist Charles Darwin's (1809–1882) On the Origin of Species appeared. Peirce's life was thus framed by significant scientific and technological developments; its fruits included a multifaceted contribution to early twenty-first century philosophical understanding of scientific investigation and other human achievements. Trained as an experimental scientist, Peirce worked in this capacity for both the Harvard College Observatory and the U.S. Coast and Geodesic Survey. His contribution, however, was far more that of a philosopher than a scientist.
Philosopher of Semiotics and of Science
Peirce is best known in philosophy as the founder of pragmatism and, outside that discipline, as the theorist who, at roughly the same time as the Swiss linguist Ferdinand de Saussure (1857–1913), envisioned a comprehensive study of signs. But Peirce did far more than envision the possibility of such an investigation: He systematically elaborated, yet left ultimately unfinished, a theory of signs designed to provide indispensable resources for a normative account of objective inquiry and, beyond this, for a systematic analysis of the myriad forms of meaning—not just those observable in the practices of experimental or objective investigators. Saussure coined the word semiologie to designate this study, whereas Peirce used the term semeiotics (now more commonly spelled semiotics).
But the scope of Peirce's concerns is inadequately conveyed by calling attention to his role in the founding of pragmatism and semiotics. He tended to identify himself as a logician, but he vastly expanded the scope of logic. Moreover, he devoted considerable energy to defending an evolutionary cosmology informed by the monumental achievements of such classical metaphysicians as Plato, Aristotle, and Friedrich Schelling as well as by what he judged to be the most important implications of the greatest scientific discoveries of his own day.
While Peirce devoted a great deal of his intellectual energy to an understanding of science, he tended to ignore questions specifically concerning technology. This might seem ironic, given his pragmatic commitments. He tended, however, to draw a sharp distinction between theory and practice. He believed in a strict division of intellectual labor and that the very best work required a steadfast concern with a more or less delimited object of investigation. However, he conceived theory itself to be a historically evolved and evolving practice (or, more accurately, a family of such practices). Indeed, Peirce was keenly interested in preserving the integrity of theoretical practices, defining them ultimately in terms of the objective of simply discovering truths not yet known. At the heart of his pragmatism, then, one finds not only a refusal to subordinate theoretical practices to other forms of practices but also an insistence that theory itself is a unique form of human practice.
Peirce's account of science is distinguished by a number of factors, but most importantly by the role he accords abduction in the conduct of inquirers and the attention he pays to the history of science as a resource for understanding science. He identified abduction as one of the three modes of inference (deduction and induction being the other two). Abduction is that mode by which hypotheses are formulated or initiated. In classifying it as a form of inference, Peirce was refusing to leave the formulation of hypotheses as a mysterious, psychological process. The work of scientists involves the complex interplay of all three modes of inference, but abduction is clearly central to this work. Long before Thomas Kuhn's The Structure of Scientific Revolutions (1962), Peirce was acutely aware of how an adequate conception of science must be based upon a detailed acquaintance with the actual development of diverse experimental practices. Such acquaintance reveals the intimate relationship between theoretical discoveries and technological innovations. Thus, whereas Peirce did not make technology in general a focal object of his theoretical concern, he did devote attention to how technology operates within science.
The Normative Sciences
Somewhat late in his life Peirce came to an appreciation of the importance of what he called the normative sciences (logic, ethics, and esthetics) and, within this cluster of sciences and his broader classification of human practices, an appreciation of the pivotal role of ethics as both a cultural inheritance and a normative science. He came to see logic as a species of ethics. Whereas ethics offers a normative account of self-controlled conduct, logic provides a normative account of a species of such conduct, namely, self-controlled thought or inquiry. Just as logic in this sense depends upon a more general theory of self-controlled action, so ethics depends upon a critical theory of the intrinsically admirable or worthwhile ends of action. Peirce proposed esthetics as the name for this theory of the ends of action. A critical determination of the ends one espouses is at least as important as a critical assessment of the variable means available for the realization of a given objective.
Peirce's historically informed understanding of experimental inquiry is, arguably, one of the most complete, nuanced, and adequate accounts of science yet articulated. The centrality he accords to abduction distinguishes his account of science from most others and, in addition, more intimately connects his theoretical understanding of scientific investigation to the actual practices of scientific investigators than do rival accounts. Though he did not specifically concern himself with technology, his philosophy of science and theory of signs provide resources for illuminating numerous aspects of the diverse phenomena studied by philosophers of technology and others interested in such phenomena. His classification of the theoretical sciences is, in fact, embedded in a more comprehensive classification of human practices; this classification offers important suggestions for how to understand the relationships between the theoretical and technological undertakings of humankind.
Finally, even though he did not explore ethics or esthetics as deeply as he studied logic, his general conception of the normative sciences and his specific treatments of ethics and esthetics are sites yet to be mined by contemporary inquirers, especially ones interested in the interconnections among science, technology, and ethics.
Anderson, Douglas R. (1995). Strands of System: The Philosophy of Charles Peirce. West Lafayette, IN: Purdue University Press.
Eisele, Carolyn, ed. (1985). Historical Perspectives on Peirce's Logic of Science: A History of Science. New York: Mouton.
Peirce, Charles S. (1957). Essays in the Philosophy of Science. New York: Liberal Arts Press.
Peirce, Charles S. (1998). Chance, Love, and Logic; Philosophical Essays, ed. Morris R. Cohen. Lincoln: University of Nebraska Press.
Peirce, Charles S. (1998). Charles S. Peirce: The Essential Writings, ed. Edward C. Moore.
Peirce, Charles S. (1998). His Glassy Essence: An Autobiography of Charles Sanders Pierce, ed. Kenneth Laine Ketner. Nashville: Vanderbilt University Press.
Peirce, Charles Sanders
PEIRCE, CHARLES SANDERS
American philosopher, pioneer in symbolic logic, originator of one version of pragmatism, outstanding neorealist; b. Cambridge, Mass., Sept. 10, 1839; d. Milford, Pa., April 19, 1914.
Life and Work. A close associate of Chauncey Wright, John Fiske, Josiah royce, and William james, Peirce studied at Harvard University and lectured there briefly in philosophy in 1864. Besides another brief teaching stint at Johns Hopkins University (1879–84), he worked as a physicist for the U.S. Coast Survey. Peirce
was known for his broader philosophical speculations by only a few contemporaries familiar with his articles, lectures, reviews, and correspondence. He wrote no single definitive philosophical work that clearly establishes the unity of his thought. The first presentation of a unified portion of his work appeared in M. R. Cohen's edition titled Chance, Love and Logic (New York 1923), containing the first Peirce bibliography. Between 1931 and 1953 appeared the first eight volumes of the Collected Papers of Charles Sanders Peirce (Cambridge, Mass.). Because of the lack of any certain order in Peirce's treatment of essential aspects of his philosophy, the extensive indexes in the Collected Papers are indispensable for the study of Peirce. (In references to Peirce, the general practice is to indicate the volume and paragraph number of this edition, e.g., 5.432.)
Teaching. Under the influence of his father, Benjamin Peirce, a Harvard University professor, Peirce became a complete mathematician. He made extensive and original contributions to the then-growing symbolic logic. I. kant was his first philosophical mentor, although he grew critical of Kant as he studied British empiricism, aristotle, and scholastic sources, especially Duns Scotus. He sums up his position thus: "I should call myself an Aristotelian of the scholastic wing, approaching Scotism, but going further in the direction of scholastic realism" (5.77).
Although this statement is arguable, Peirce tried to establish a complete system by relating all his conclusions to his three categories: firstness, secondness, and thirdness. He claimed that these are not only the categories of all experience as revealed in phenomenology, but that they are also the essential categories of thought, of sign relations, and of reality itself. Independent of, and perhaps prior to, E. husserl, Peirce determined the role of phenomenology (or phaneroscopy, as he called it) and worked out its details along lines remarkably similar to those of Husserl. This he related to a theory of meaning that embraced his metaphysical realism, asserting that things have meaning insofar as they embody triadic relations. It was in this sense that he maintained; "General principles are really operative in nature. This is the doctrine of scholastic realism" (5.101).
His teaching that general principles are signs operating in nature is essential to an understanding of his doctrine of pragmatism, which he called pragmaticism to distinguish it from William James's version. James, he contended, borrowed the idea of pragmatism from him and badly misinterpreted it. Peirce modified his conception of pragmatism several times, finally concluding that it is a method of determining the meaning of signs, completely in accord with his version of scholastic realism.
Moreover, Peirce incorporated into his system a thorough evolutionism, in which respect he compared with H. bergson and A. N. whitehead. Chance and law, he maintained, were two sides of evolution. The theory that chance is an objective reality operating in the universe he called tychism. The operation of law he called synechism, explaining it thus: "Synechism is founded on the notion that the coalescence, the becoming continuous, the becoming governed by laws, the becoming instinct with general ideas, are phases of one and the same process of the growth of reasonableness" (5.4). Metaphysics, taken as ontology and cosmology, is fundamentally concerned with this evolution of law as reality, which is the heart of his category of thirdness.
It is strongly debated as to whether Peirce was indeed a realist or an objective idealist. The complexity of his thought and its wide range make it unwise to offer any certain critique this early in the development of Peircean studies. He is generally considered to be far superior to his contemporary American philosophers and particularly relevant to the statement of present scholastic philosophy.
Bibliography: w. p. haas, The Conception of Law and the Unity of Peirce's Philosophy (Fribourg 1964). j. boler, Charles Peirce and Scholastic Realism (Seattle 1963). m. g. murphey, The Development of Peirce's Philosophy (Cambridge, Mass. 1961).
[w. p. haas]
Peirce, Charles Sanders (1839-1914)
Charles Sanders Peirce (1839-1914)
Geodesist, philosopher of science
Background. Charles Sanders Peirce, one of the greatest of American philosophers, was the son of Benjamin Peirce (1809-1880), superintendent of the U.S. Coast Survey in 1867-1874 and a professor of mathematics and astronomy at Harvard University. Charles Peirce, who used to say he was raised in a laboratory, received his bachelor’s degree in chemistry from Harvard in 1863, as a member of the first class to graduate from the Lawrence Scientific School. Having already joined the Coast Survey as a temporary aide in 1859, Peirce went to work for the Survey full-time in 1861 and as a result was exempted from military service during the Civil War. He remained a member of the Coast Survey until 1891. He specialized in gravity research, but the accuracy of his observations during the solar eclipses of 1869 and 1870 also identified him as a first-rate observational astronomer, and he went on to measure the magnitudes of the stars in the galactic cluster that includes the Sun.
Measuring Gravity. In 1875 Peirce learned how to use the new convertible pendulum to measure gravity. Comparing his results with those obtained in Europe, he found an error in European measurement caused by the pendulum stand. As a result the Repsold pendulum used by the Coast Survey was replaced by one Peirce invented in 1878. In 1879 Peirce determined the length of a meter from a wavelength of light, anticipating the later experiments of Albert Michelson. In 1882 he made a mathematical study of the relationship between the variation of gravity and the shape of the Earth.
Philosophy. From 1879 to 1884 Peirce was a lecturer in logic at Johns Hopkins University but devoted much of his time to mathematics, developing a philosophy of mathematics based on the notion that mathematicians are concerned with what is logically possible, but not with actual reality. During the 1880s and 1890s he devised a classification of knowledge. Mathematics was the first science, while normative science had three divisions: aestheticism, ethics, and logic. He called logic the science of how humans should obtain their objectives. After leaving the Coast and Geodetic Survey in 1891, Peirce devoted himself mainly to philosophy. He has been recognized as the founder of the distinctly American school of philosophy called pragmatism, whose adherents also included William James and John Dewey.
Evolution. Like virtually all other American scientists of his day, Peirce was an evolutionist and sought to formulate philosophical concepts in accord with evolutionary theories. He shared with the leading American scientists of his generation a belief in a theory first formulated by Jean-Baptiste Lamarck (1744-1829): the doctrine that characteristics acquired by an organism during its lifetime may be passed on genetically to its offspring. Peirce believed that humans were born with their minds already adapted to identify the laws of nature more readily than if they had attempted to guess them by chance. Thus, he believed that common sense would tell which scientific hypotheses are true and which are not. Because of these views, he was also convinced that the direction of evolution was toward ever-increasing order.
Carolyn Eisele, “Charles Sanders Peirce,” Dictionary of Scientific Biography, 18 volumes (New York: Scribners, 1970) X: 482-488;
Murray G. Murphey, The Development of Peirce’s Philosophy (Cambridge, Mass.: Harvard University Press, 1961).
Peirce, Charles Sanders
Charles Sanders Peirce
Charles Sanders Peirce
American mathematician who contributed to the study of associative algebras, mathematical logic, and set theory, extending the work of his father, Benjamin Peirce. Charles Peirce was born in Cambridge, Massachusetts, and attended Harvard University. He worked for many years on the Coast and Geodetic Survey. Between 1879 and 1884 he gave occasional courses on logic at Johns Hopkins University, though never held an academic post during his career.