Difference between revisions of "Charles Sanders Peirce"

MyWikiBiz, Author Your Legacy — Wednesday September 22, 2021
Jump to navigationJump to search
(→‎See also: apply column templates)
(update wikinfo waybak)
(5 intermediate revisions by the same user not shown)
Line 1: Line 1:
<!-- Charles Sanders Peirce theb3558.jpg -->
'''Charles Sanders Peirce''' (10 September 1839 &ndash; 19 April 1914) was an American [[polymath]], born in [[Cambridge, Massachusetts]].  Although educated as a chemist and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or ''[[semeiotic]]'', that he is largely appreciated today.  The philosopher [[Paul Weiss (philosopher)|Paul Weiss]], writing in the ''[[Dictionary of American Biography]]'' for [[1934]], called Peirce "the most original and versatile of American philosophers and America's greatest logician" (Brent, 1).
'''Charles Sanders Peirce''' ([[September 10]], [[1839]] – [[April 19]], [[1914]]) was an American [[polymath]], born in [[Cambridge, Massachusetts]]. Although educated as a chemist and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or ''[[semeiotic]]'', that he is largely appreciated today.  The philosopher [[Paul Weiss (philosopher)|Paul Weiss]], writing in the ''[[Dictionary of American Biography]]'' for [[1934]], called Peirce "the most original and versatile of American philosophers and America's greatest logician" (Brent, 1).
The secondary literature on Peirce was scant until after [[World War II]].  Much of his huge output is still unpublished.  An innovator in fields such as logic, mathematics, [[philosophy of science]], research methodology, [[semiotics]], [[epistemology]], and [[metaphysics]], he considered himself a logician first and foremost.  While he made major contributions to the development of formal logic as it is known today, ''logic'' for him encompassed much of what is now studied under the philosophies of knowledge, language, and science.  Peirce saw logic as the formal branch of the theory of signs, or ''[[semiotics]]'', here using ''formal'' in the sense of ''[[normative]]'' or what he called ''quasi-necessary''.  In 1886 he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later in the development of [[electronic computer]]s.
Line 169: Line 167:
: ''Main article : [[Theory of relations]]''
: ''Main article : [[Relation theory]]''
Line 730: Line 728:
Portions of the above article were adapted from the following sources under the [[GNU Free Documentation License]], under other applicable licenses, or by permission of the copyright holders.
* [http://www.getwiki.net/-Charles_Sanders_Peirce "Charles Sanders Peirce"], [http://www.getwiki.net/ GetWiki].
* [http://www.getwiki.net/-Charles_Sanders_Peirce Charles Sanders Peirce], [http://www.getwiki.net/ GetWiki].
<!-- GetWiki: Charles Sanders Peirce
<!-- GetWiki: Charles Sanders Peirce
     version: 13:20, 28 Feb 2007
     version: 13:20, 28 Feb 2007
Line 737: Line 735:
* [http://www.wikinfo.org/index.php/Charles_Sanders_Peirce "Charles Sanders Peirce"], [http://wikinfo.org/index.php/Main_Page Wikinfo].
* [http://web.archive.org/web/20091209073359/http://www.wikinfo.org/index.php/Charles_Sanders_Peirce Charles Sanders Peirce], [http://web.archive.org/web/20091212091054/http://www.wikinfo.org/index.php/Main_Page Wikinfo].
<!-- Wikinfo: Charles Sanders Peirce
<!-- Wikinfo: Charles Sanders Peirce
     version: 16:34, 6 Dec 2006
     version: 16:34, 6 Dec 2006
Line 744: Line 742:
* [http://en.wikipedia.org/wiki/Charles_Sanders_Peirce "Charles Sanders Peirce"], [http://en.wikipedia.org/wiki/ Wikipedia].
* [http://en.wikipedia.org/w/index.php?title=Charles_Sanders_Peirce&oldid=74185526 Charles Sanders Peirce], [http://en.wikipedia.org/wiki/ Wikipedia].
<!-- Wikipedia: Charles Peirce
<!-- Wikipedia: Charles Peirce
     version: 02:25, 4 Sep 2006
     version: 19:20, 6 Sep 2006‎
     updater: Jon Awbrey
     updater: Jon Awbrey
     comment: /* Scholastic realism */ formats
     comment: /* Relations: cdots */
* Jaime Nubiola, [http://www.unav.es/users/Nupedia_Charles_S.html "Charles S. Peirce"], [http://web.archive.org/web/20030808013826/http://nupedia.com/ Nupedia].
* [http://www.unav.es/users/Nupedia_Charles_S.html Charles S. Peirce], Jaime Nubiola, [http://web.archive.org/web/20030808013826/http://nupedia.com/ Nupedia].
<br><sharethis />
[[Category:Charles Sanders Peirce]]

Latest revision as of 20:00, 28 July 2017

Charles Sanders Peirce (10 September 1839 – 19 April 1914) was an American polymath, born in Cambridge, Massachusetts. Although educated as a chemist and employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or semeiotic, that he is largely appreciated today. The philosopher Paul Weiss, writing in the Dictionary of American Biography for 1934, called Peirce "the most original and versatile of American philosophers and America's greatest logician" (Brent, 1).

The secondary literature on Peirce was scant until after World War II. Much of his huge output is still unpublished. An innovator in fields such as logic, mathematics, philosophy of science, research methodology, semiotics, epistemology, and metaphysics, he considered himself a logician first and foremost. While he made major contributions to the development of formal logic as it is known today, logic for him encompassed much of what is now studied under the philosophies of knowledge, language, and science. Peirce saw logic as the formal branch of the theory of signs, or semiotics, here using formal in the sense of normative or what he called quasi-necessary. In 1886 he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later in the development of electronic computers.


Charles Sanders Peirce was the son of Sarah Hunt Mills and Benjamin Peirce, a professor of astronomy and mathematics at Harvard University, perhaps the first serious research mathematician in America. At 12 years of age, Charles read an older brother's copy of Richard Whately's Elements of Logic, then the leading English language text on the subject. Thus began his lifelong fascination with logic and reasoning. He went on to obtain the BA and MA from Harvard, and in 1863 the Lawrence Scientific School awarded him its first M.Sc. in chemistry. This last degree was awarded summa cum laude; otherwise his academic record was undistinguished. At Harvard, he began lifelong friendships with Francis Ellingwood Abbot, Chauncey Wright, and William James. One of his Harvard instructors, Charles William Eliot, formed an unfavorable opinion of Peirce. This opinion proved fateful, because Eliot, while President of Harvard 1869–1909 — a period encompassing nearly all of Peirce's working life — repeatedly vetoed having Harvard employ Peirce in any capacity.

United States Coast Survey


During the 1880s Peirce's indifference to bureaucratic detail waxed while the quality and timeliness of his Survey work waned. Peirce took years to write reports that he should have completed in mere months. Meanwhile, he wrote hundreds of logic, philosophy, and science entries for the Century Dictionary. In 1885, an investigation by the Allison Commission exonerated Peirce, but led to the dismissal of Superintendent Julius Hilgard and several other Coast Survey employees for misuse of public funds. In 1891, Peirce resigned from the Coast Survey, at the request of Superintendent Thomas Corwin Mendenhall. He never again held regular employment.

Johns Hopkins University

In 1879, Peirce was appointed Lecturer in logic at the new Johns Hopkins University. That university was strong in a number of areas that interested Peirce, such as philosophy (Royce and Dewey did their PhDs at Hopkins), psychology (taught by G. Stanley Hall and studied by Joseph Jastrow, who coauthored a landmark empirical study with Peirce), and mathematics (taught by J.J. Sylvester, who came to admire Peirce's work on mathematics and logic). This untenured position proved to be the only academic appointment Peirce ever held.

Brent documents something Peirce never suspected, namely that his efforts to obtain academic employment, grants, and scientific respectability, were repeatedly frustrated by the covert opposition of a major American scientist of the day, Simon Newcomb. Peirce's ability to find academic employment may also have been frustrated by a difficult personality.

Peirce's personal life also proved a grave handicap. His first wife, Harriet Melusina Fay, left him in 1875. He soon took up with a woman whose maiden name and nationality remain uncertain to this day (the best guess is that her name was Juliette Froissy and that she was French), but did not marry her until his divorce with Harriet became final in 1883. That year, Newcomb pointed out to a Johns Hopkins trustee that Peirce, while a Hopkins employee, had lived and traveled with a woman to whom he was not married. The ensuing scandal led to his dismissal. Just why Peirce's later applications for academic employment at Clark University, University of Wisconsin, University of Michigan, Cornell University, Stanford University, and the University of Chicago were all unsuccessful can no longer be determined. Presumably, his having lived with Juliette for a number of years while still legally married to Harriet led him to be deemed morally unfit for academic employment anywhere in the USA. Peirce had no children by either marriage.


In 1887 Peirce spent part of his inheritance from his parents to purchase 2,000 rural acres near Milford, Pennsylvania, land which never yielded an economic return. On that land, he built a large house which he named Arisbe and where he spent the rest of his life, writing prolifically, much of it unpublished to this day. His insistence on living beyond his means soon led to grave financial and legal difficulties. Peirce spent much of the last two decades of his life so destitute that he could not afford heat in winter, and his only food was old bread kindly donated by the local baker. Unable to afford new stationery, he wrote on the verso side of old manuscripts. An outstanding warrant for assault and unpaid debts led to his being a fugitive in New York City for a while. Several people, including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot, settled his debts and paid his property taxes and mortgage.

Peirce did some scientific and engineering consulting and wrote a good deal for meager pay, primarily dictionary and encyclopedia entries, and reviews for The Nation (with whose editor, Wendell Phillips Garrison he became friendly). He did translations for the Smithsonian Institution, at the instigation of its director, Samuel Langley. Peirce also did substantial mathematical calculations for Langley's research on powered flight. Hoping to make money, Peirce tried his hand at inventing, and began but did not complete a number of books. In 1888, President Grover Cleveland appointed him to the Assay Commission. From 1890 onwards, he had a friend and admirer in Judge Francis C. Russell of Chicago, who introduced Peirce to Paul Carus and Edward Hegeler, the editor and owner, respectively, of the pioneering American philosophy journal The Monist, which eventually published a number of his articles. He applied to the newly formed Carnegie Institution for a grant to write a book summarizing his life's work. The application was doomed; his nemesis Newcomb served on the Institution's executive committee, and its President had been the President of Johns Hopkins at the time of Peirce's dismissal.

The one who did the most to help Peirce in these desperate times was his old friend William James, who dedicated his Will to Believe to Peirce, and who arranged for Peirce to be paid to give four series of lectures at or near Harvard. Most important, each year from 1898 until his death in 1910, James would write to his friends in the Boston intelligentsia, asking that they make a financial contribution to help support Peirce. Peirce reciprocated by designating James's eldest son as his heir should Juliette predecease him, and by adding "Santiago", "Saint James" in Spanish, to his full name (Brent, 315–316, 374).



Bertrand Russell opined, "Beyond doubt... he was one of the most original minds of the later nineteenth century, and certainly the greatest American thinker ever." (Yet his Principia Mathematica does not mention Peirce.) A.N. Whitehead, while reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, was struck by how Peirce had anticipated his own "process" thinking. (On Peirce and process metaphysics, see the chapter by Lowe in Moore and Robin, 1964.) Karl Popper viewed Peirce as "one of the greatest philosophers of all time". Nevertheless, Peirce's accomplishments were not immediately recognized. His imposing contemporaries William James and Josiah Royce admired him, and Cassius Jackson Keyser at Columbia and C.K. Ogden wrote about Peirce with respect, but to no immediate effect.

The first scholar to give Peirce his considered professional attention was Royce's student Morris Raphael Cohen, the editor of a 1923 anthology of Peirce's writings titled Chance, Love, and Logic and the author of the first bibliography of Peirce's scattered writings. John Dewey had had Peirce as an instructor at Johns Hopkins, and from 1916 onwards, Dewey's writings repeatedly mention Peirce with deference. His 1938 Logic: The Theory of Inquiry is Peircean through and through. The publication of the first six volumes of the Collected Papers (1931–1935), the most important event to date in Peirce studies and one Cohen made possible by raising the needed funds, did not lead to an immediate outpouring of secondary studies. The editors of those volumes, Charles Hartshorne and Paul Weiss, did not become Peirce specialists. Early landmarks of the secondary literature include the monographs by Buchler (1939), Feibleman (1946), and Goudge (1950), the 1941 Ph.D. thesis by Arthur Burks (who went on to edit volumes 7 and 8 of the Collected Papers), and the edited volume by Wiener and Young (1952). The Charles S. Peirce Society was founded in 1946. Its Transactions, an academic journal specializing in Peirce, pragmatism, and American philosophy, has appeared since 1965.

In 1949, while doing unrelated archival work, the historian of mathematics Carolyn Eisele chanced on an autograph letter by Peirce. Thus began her 40 years of research on Peirce the mathematician and scientist, culminating in Eisele (1976, 1979, 1985). Beginning around 1960, the philosopher and historian of ideas Max Fisch emerged as an authority on Peirce. Fisch (1986) reprints many of the relevant articles, including a wide-ranging survey of the impact of Peirce's thought through 1983.

Peirce has come to enjoy a significant international following. There are university research centers devoted to Peirce studies and pragmatism in Brazil, Finland, Germany, and Spain. For many years the North American philosophy department most devoted to Peirce was the University of Toronto's, thanks in good part to the leadership of Thomas Goudge and David Savan. In recent years, American Peirce scholars have clustered at Indiana University – Purdue University Indianapolis, the home of the Peirce Edition Project, and the Pennsylvania State University.

Peirce's philosophy


Peirce's lifelong work in science bears on a wide array of disciplines, including astronomy, economics, geodesy, linguistics, logic, mathematics, metrology, philosophy, psychology, and the history and philosophy of science. This work has become the subject of renewed interest, inspired not only by his anticipations of subsequent scientific developments but also by his articulation of the ways that philosophy applies to human problems.

Peirce's writings repeatedly refer to a system of three categories, named Firstness, Secondness, and Thirdness, devised early in his career in reaction to his reading of Aristotle, Kant, and Hegel. He later emphasized the principle of logic that he called the maxim of pragmatism, on which his lifelong friend William James based a popular philosophical movement known as pragmatism. Peirce believed that any truth is provisional, and that the truth of any proposition cannot be certain but only probable. The philosophical recognition of this fact he called fallibilism.


Main articles : Pragmatism, Pragmaticism, Pragmatic maxim

Peirce's recipe for pragmatic thinking, going under the label of pragmatism and also known as pragmaticism, is articulated in several versions of the maxim of logic that he called the pragmatic maxim. Here is one of his more emphatic statements of it:


William James, among others, regarded two of Peirce's papers, "The Fixation of Belief" (1877) and "How to Make Our Ideas Clear" (1878), as being the origin of pragmatism. Peirce conceived pragmatism to be a method for clarifying the meaning of difficult ideas through the application of the pragmatic maxim.

Peirce's pragmatism may be understood as a method for resolving conceptual confusions by linking the meanings of one's conceptions to one's conceptions of the operational or practical consequences of their use in practice. The concepts of belief, knowledge, and truth were some of the difficult ideas that Peirce sought to clarify by means of the pragmatic maxim. Doing this required a theory of inquiry that moderated the conventional dualism of foundational alternatives, namely:

His approach is distinguished from either coherentism or foundationalism by virtue of the following three dimensions:

  1. Active process of theory generation, with no prior assurance of truth.
  2. Subsequent application of the provisional theory, aimed toward developing its logical and practical consequences.




Scholastic realism

Peirce's at one point describes himself as a "scholastic realist of a somewhat extreme stripe" (CP 5.470). In contrast, some writers call him an idealist, apparently on account of his defining reality as "the object of the final opinion of the scientific community", but this label is based on a peculiar sense of the word idealist and is overall misleading in the case of Peirce, as he consistently and systematically argues that reality is best viewed as independent of mind, at least of minds in particular, if not necessarily of minds in general. The problem of interpretation appears to arise from at least three sources. First, Peirce's use of the word independent needs to be understood in a way that is analogous to its definition in mathematics, where it means orthogonal, or its definition in statistics, where it means uncorrelated. In these senses, independence is a particular kind of relation, not a lack of relation, and certainly not a form of disconnection or exclusion. Second, Peirce did in fact describe himself as being in favor of objective idealism, but what he meant by that is a far cry from ordinary idealism. Third, we need to recognize that scholastic realism is one side of the realist vs. nominalist debate over universals, and not a position in the realist vs. idealist debate about a mind-independent reality. Peirce's scholastic realism in fact supplies essential support for his own thesis of objective idealism regarding the relationship between matter and mind. Two early studies on Peirce's realism and the influence of Duns Scotus thereon, are the chapter by McKeon in Wiener and Young (1952), and that by Moore in Moore and Robin (1964).



Here Peirce is explicitly disparaging a position he is well-known for spending most of his life defending. How might we make sense of this apparent contradiction? The temptation is to simply say Peirce changed his mind. After all, since Peirce asserts nominalism in 1865 and scholastic realism in 1868, Peirce may have gone from denying the reality of universals to asserting it. This explanation is most famously given by Max Fisch in his "Peirce's Progress from Nominalism toward Realism" (1967) and then again in his introduction to Volume 2 of the Chronological Edition of Peirce's writings (1984). More recently this way of understanding Peirce has been indepenently challenged by Rosa Mayorga in her On Universals (2002) and by Robert Lane in his "Peirce's Early Realism" (2004). Both Mayorga and Lane are troubled by several instances where Peirce's self assessment of his own intellectual development contradicts Fisch's account of Peirce development. One of these statemesnts appears in 1893 when Peirce states that "never, during the thirty years in which I have been writing on philosophical questions, have I failed in my allegiance to realistic opinions and to certain Scotistic ideas" (CP 6.605). Remarks like these led Lane to conduct a re-evaluation of Peirce's 1865 declarations for nomianlism, whereupon Lane discovered significant evidence for the same conclusion Mayorga had already reached two years earlier (unbenownst to Lane). Both concluded that the correct way to understand Peirce's shift from outspoken nominalist to outspoken realist is not by reading into Peirce a change in his fundamental philosophical position, but instead to realize that Peirce merely changed his understanding and use of the terms scholastic realism and nominalism. The reason Peirce calls himself a nominalist in 1865 is because he believes realism to only come in the form offered by Plato:

It has been said that these 'abstract names' [blueness, hardness, and loudness] denote qualities and connote nothing. But it seems to me the phrase 'denoted object' is nothing but a roundabout expression for a thing. To say that a quality is denoted is to say it is a thing. [Such terms] were framed at a time when all men were realists in the scholastic sense and consequently things were meant by them, entities which had no quality but that expressed by the word. They, therefore, must denote these things and connote the qualities they relate to. (Peirce, CE 1, 311–312).

When Peirce goes on to call universals 'fictions', he is not condemning their truth; he is simply asserting that they do not exist as particulars. This becomes clearer when in the same paper Peirce argues against psychologism in logic, by establishing the same 'fictional' status for logic and mathematics that he claims for universals. Now by proving logic fictional, Peirce believes he does logic a favor, that is, by saving it from the psychologists. This suggests that Peirce employed fictional in a rather idiosyncratic way. Many things (including universals) covered by Peirce's pre-1868 use of fictional came under his post-1868 use of real. Peirce had been using 'fictional' to refer to things having no physical existence, and not to imply that something was merely the result of human imagination or fancy. By 1868 at least, Peirce had changed his mind about "reality", holding instead that "fictional" should be contrasted with "independent of what we think about it" (real). He no longer deemed existence as a physical object as a prerequisite for being real, so that a lack of physical existence no longer led Peirce to chatacterize universals as "fictional". That something has blueness can be true independent of what anyone thinks of it, and therefore it can be a part of reality despite the fact blueness never has a physical existence anywhere. Blueness is real independent of what anyone thinks, but it does not exist as an entity because it has no secondness.

Formal perspective
















Relationships, relations, relatives


The following collection of definitions is practically indispensable.

(Peirce, CP 3.466–467, "The Logic of Relatives", Monist, 7, 161–217 (1897), CP 3.456–552).



Main article : Logic of relatives


Main article : Relation theory


x = (x1, …, xk)
x = x1 :: xk



Table 1 shows how the k-tuples of a k-adic relation might be conceived in tabular form, with the k-tuple xi = <xi1, …, xik> = xi1 :: xik supplying the entries for the ith row of the Table.

Table 1. Relational Database
x11 x12 ... x1j ... x1k
x21 x22 ... x2j ... x2k
xi1 xi2 ... xij ... xik
xm1 xm2 ... xmj ... xmk


Dyadic relations

Main article : Binary relation

Triadic relations

Main article : Triadic relation
(Peirce, CP 3.229, "On the Algebra of Logic", American Journal of Mathematics 3, 15–57 (1880), CP 3.154–251).

Theory of categories


(Saunders Mac Lane, Categories for the Working Mathematician, 29–30).

Mac Lane did not mention Peirce among the objects of his sincerest flattery, but he might as well have, for his mention of Aristotle and Kant well enough credits his deep indebtedness to the pursers of them all. As Richard Feynman was fond of observing, "the same questions have the same answers", and the problem that a system of categories is aimed to beautify is the same sort of beast whether it's Aristotle, Kant, Peirce, Carnap, or Eilenberg and Mac Lane that bends the bow. What is that problem? To answer that, let's begin again at the source:


Things are univocally named, when not only they bear the same name but the name means the same in each case — has the same definition corresponding. Thus a man and an ox are called animals. The name is the same in both cases; so also the statement of essence. For if you are asked what is meant by their both of them being called animals, you give that particular name in both cases the same definition.

(Aristotle, Categories, 1.1a1–12).


The following passage is critical to the understanding of Peirce's Categories:






(Peirce, CP 4.549, "Prolegomena to an Apology for Pragmaticism", The Monist 16, 492–546 (1906), CP 4.530–572).


Peirce arrived at his own system of three categories after a thoroughgoing study of his predecessors, with special reference to the categories of Aristotle, Kant, and Hegel. The names that he used for his own categories varied with context and occasion, but ranged from moderately intuitive terms like quality, reaction, and symbolization to maximally abstract terms like firstness, secondness, and thirdness, respectively. Taken in full generality, k-ness may be understood as referring to those properties that all k-adic relations have in common. Peirce's distinctive claim is that a type hierarchy of three levels is generative of all that we need in logic.

Part of the justification for Peirce's claim that three categories are both necessary and sufficient appears to arise from mathematical facts about the reducibility of k-adic relations. With regard to necessity, triadic relations cannot be completely analyzed in terms or monadic and dyadic predicates. With regard to sufficiency, all higher arity k-adic relations can be analyzed in terms of triadic and lower arity relations.

Logic as formal semiotic



Peirce's major discoveries in formal logic include:

  • Seeing that Boolean calculations could be carried out by means of electrical switches (W5:421–24), anticipating Claude Shannon by more than 50 years.


Peirce's work on formal logic had admirers other than Ernst Schröder:


Dynamics of inquiry











Theory of signs, or semiotic

Main articles : Semeiotic, Semiotics, Sign relation

Peirce's efforts to articulate the logic of scientific inquiry forced him to examine the role of signs, including cognitive concepts, in the activities by which we inform ourselves about the world and make logical inferences on the basis of that information. The complexities of the possible relationships among signs, objects in the world, and ideas in the mind demanded that he develop a more powerful logic of relations. The hasty map of relations and relatives sketched above makes it possible to venture on the terrain of sign relations, the main subject matter of Peirce's semeiotic, or theory of signs.

Peirce referred to his theory of signs, based on a specific type of triadic relation called a sign relation, as semeiotic or semiotic, either of which terms are currently used in either singular of plural form. He described the corresponding process of semiosis as an "action, or influence, which is, or involves, a cooperation of three subjects, such as a sign, its object, and its interpretant, this tri-relative influence not being in any way resolvable into actions between pairs". (Peirce 1907, in Houser 1998, 411).

Sign relations

Here again is Peirce's definition of the triadic sign relation that formed the core of his definition of logic.


This definition, together with Peirce's definitions of correspondence and determination, is sufficient to derive all of the statements that are necessarily true all sign relations. There is a lot more to the theory of signs than simply proving universal theorems about generic sign relations, however. There is also the task of classifying the different species and subspecies of sign relations. As a practical matter, of course, familiarity with the full range of concrete examples is indispensable to theory and application both.

In Peirce's theory of signs, a sign is something that stands in a well-defined type of relation to two other things, its object and its interpretant sign. Although Peirce's definition of a sign is independent of psychological subject matter and his theory of signs covers more ground than linguistics alone, it is nevertheless the case that many of the more familiar examples and illustrations of sign relations will naturally be drawn from the descriptive sciences of linguistics and psychology, along with our ordinary experience of their subject matters.


For example, one way to approach the concept of an interpretant is to think of a psycholinguistic process. In this context, an interpretant can be understood as a sign's effect on the mind, or on anything that acts like a mind, what Peirce calls a quasi-mind. An interpretant is what results from a process of interpretation, one of the types of activity that falls under the heading of semiosis. One usually says that a sign stands for an object to an agent, an interpreter. In the upshot, however, it is the sign's effect on the agent that is paramount. This effect is what Peirce called the interpretant sign, or the interpretant for short. The interpretant may be regarded as one of the sign's roughly equivalent meanings, and especial interest attaches to the types of semiosis that proceed from obscure signs to relatively clear interpretants. In logic and mathematics the most clarified and most succinct signs for an object are called canonical forms or normal forms.

Some of the understanding needed by the mind depends on familiarity with the object. In order to know hat a given sign denotes, the mind needs some experience of that sign's object collaterally to that sign or sign system, and in this context Peirce speaks of collateral experience, collateral observation, and so on.

  • An interpretant (also called an interpretant sign) is the sign's more or less clarified meaning or ramification, a kind of form or idea of the difference which the sign's being true would make. (Peirce's sign theory concerns meaning in the broadest sense, including logical implication, not just the meanings of words as properly clarified by a dictionary.) The interpretant is a sign (a) of the object and (b) of the interpretant's "predecessor" (the interpreted sign) as being a sign of the same object. The interpretant is an interpretation in the sense of a product of an interpretive process or a content in which an interpretive relation culminates, though this product or content may itself be an act or conduct of some kind. Another way to say these things is that the sign stands for the object to the interpretant.

Object, sign, and interpretant are constrained by a relation of informational or logical determination which is more general than the special cases of causal or physical determination. In general terms, any information about one of the items in the sign relation tells you something about the others, although the actual ampont of this information may be nil in some species of sign relations. Moreover, when Peirce says that one thing determines some other things, he means determines in some measure, a measure that is not necessarily completely deterministic.


  1. Sign, always immediate to itself — that is, in a tautologous sense, present in or at itself, even if it is not immediate to a mind or immediately accomplished without processing or is a general apprehended only in its instances.
  2. Object
    1. Immediate object, the object as represented in the sign.
    2. Dynamic object, the object as it really is, on which the idea which is the immediate object is founded as on bedrock. Also called the dynamoid object, the dynamical object.
  3. Interpretant
    1. Immediate interpretant, the quality of the impression which a sign is fit to produce, not any actual reaction, and which the sign carries with it even before there is an interpreter or quasi-interpreter. It is what is ordinarily called the sign's meaning.
    2. Dynamic interpretant, the actual effect (apart from the feeling) of the sign on a mind or quasi-mind, for instance the agitation of the feeling.
    3. Final interpretant, the effect which the sign would have on any mind or quasi-mind if circumstances allowed that effect to be fully achieved. It is the sign's end or purpose. The final interpretant of one's inqury about the weather may consist in the effect which the true response would have on one's plans for the day which were the inquiry's purpose. The final interpretant of a line of investigation as such is truth and would be reached sooner or later but still inevitably by investigation adequately prolonged, though the truth remains independent of that which "you or I" or any finite community of investigators believe.


Signhood is a way of being in relation, not a way of being in itself. The role of sign is constituted as one role among three — object, sign, and interpretant sign — where the roles are distinct even when the things that fill them are not. In other words, the question of what a sign is depends on the concept of a sign relation, which depends on the concept of a triadic relation. This, in turn, depends on the concept of a relation itself. There are traditionally two ways of understanding what relations are, corresponding to definition by extension and definition by intension or comprehension. Peirce regards these aspects of relation as necessary but not sufficient, and he adds a third approach, the way of information — including the idea of change of information — in order to integrate the other two approaches into a unified whole.

Types of signs








Many variant descriptions of signs and their types appear throughout Peirce's writings, but one of the more canonical typologies classifies signs into icons, indices, and symbols (CP 2.228, CP 2.229, CP 5.473). A sign may compound these modes, for example, a roadside sign displaying a fork both (1) portrays and (2) indicates a rest stop, and (3) does so in keeping with some pronounced stylistic conventions which add something of a symbolic dimension.

  • An icon is a sign that denotes its object by virtue of a quality which is shared by them but which the icon has irrespectively of the object. The icon, for example, a portrait or a diagram, resembles or imitates its object. The icon has, of itself, a certain character or aspect, one which the object also has (or is supposed to have) and which lets the icon be interpreted as a sign even if the object does not exist. The icon signifies essentially on the basis of its ground. Peirce defined the ground as the pure abstraction of a quality, and the sign's ground as the respect in which it resembles its object.
  • An index is a sign that denotes its object by virtue of an actual connection to it, one that he also calls a real relation in virtue of its being irrespective of interpretation. If the indexical relation is a resistance or reaction physically or causally connecting an index to its object, then the index is a reagent, for example, smoke coming from a building is a reagent index of fire. Such an index refers to the object because that index is really affected or modified by the object, and is the only kind of index which can be used in order to ascertain facts about its object. Peirce held that an index does not have to be an actual individual fact or thing, but can be a general; a disease symptom is general, its occurrence singular; and he usually considered a designation to be an index, for example, a pronoun, a proper name, or a label on a diagram, actually directing or compelling the mind's attention toward the object just as a reagent does. (In 1903 Peirce said that only an individual is an index (EP 2.274) and called designations "subindices or hyposemes", classing them as symbols; he allowed of a "degenerate index" indicating a non-individual object, as exemplified by an individual thing indicating its own characteristics. But by 1904 he returned to allowing indices to be generals and to classing designations as indices.)
  • A symbol is a sign that denotes its object solely by virtue of the fact that it is interpreted to do so. The symbol does not depend on having any resemblance or actual connection to the denoted object but is fundamentally conventional, so that the signifying relationship must be learned and agreed upon, for example, the word cat. A symbol thus denotes, primarily, by virtue of its interpretant. Its sign-action (semeiosis) is ruled by a convention, a more or less systematic set of associations that ensures its interpretation.

These definitions are specific to Peirce's theory of signs and are not exactly equivalent to more general uses of the terms icon, index, or symbol.

Theory of inquiry

Main article : Inquiry
Do not block the way of inquiry.







Logic of information

Main article : Logic of information

Peirce was a pioneer in the study of information, lecturing on what he called the laws of information as early as 1865.


Logical graphs

Main article : Logical graph



Peirce made a number of discoveries in foundational mathematics, nearly all of which came to be appreciated only long after his death. Among other things, he:

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had recently revived after long years of neglect by logicians. Much of the actual mathematics of relations that is taken for granted today was borrowed from Peirce, not always with all due credit (Anellis 1995). Beginning in 1940, Alfred Tarski and his students rediscovered aspects of Peirce's larger vision of relational logic, developing the perspective of relational algebra. These theoretical resources gradually worked their way into applications, in large part instigated by the work of Edgar F. Codd, who happened to be a doctoral student of the Peirce editor and scholar Arthur W. Burks, on the relational model or the relational paradigm for implementing and using databases.

In the four volume work, The New Elements of Mathematics by Charles S. Peirce (1976), mathematician and Peirce scholar Carolyn Eisele published a large number of Peirce's previously unpublished manuscripts on mathematical subjects, including the drafts for an introductory textbook, titled The New Elements of Mathematics in allusion to Euclid's Elements, that presented mathematics from a novel standpoint.







On a New List of Categories (1867)

Main article: On a New List of Categories

Logic of Relatives (1870)

Main article: Logic of Relatives (1870)


Logic of Relatives (1883)

Main article: Logic of Relatives (1883)

Logic of Relatives (1897)

The Simplest Mathematics (1902)

Main article: The Simplest Mathematics

Kaina Stoicheia (1904)

Main article: Kaina Stoicheia


  • Abbreviations for frequently cited works:
CE n, m = Writings of Charles S. Peirce: A Chronological Edition, vol. n, page m.
CP n.m = Collected Papers of Charles Sanders Peirce, vol. n, paragraph m.
CTN n, m = Contributions to 'The Nation' , vol. n, page m.
EP n, m = The Essential Peirce: Selected Philosophical Writings, vol. n, page m.
NEM n, m = The New Elements of Mathematics by Charles S. Peirce, vol. n, page m.
SIL m = Studies in Logic by Members of the Johns Hopkins University, page m.
SS m = Semiotic and Significs … Charles S. Peirce and Lady Welby, page m.
SW m = Charles S. Peirce, Selected Writings, page m.

Works by Peirce

  • Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1981–. Cited as CE (volume), (page).
  • Peirce, C.S, The New Elements of Mathematics by Charles S. Peirce, 4 volumes in 5, Carolyn Eisele (ed.), Mouton Publishers, The Hague, Netherlands, 1976. Humanities Press, Atlantic Highlands, NJ, 1976. Cited as NEM (volume), (page).
  • Peirce, C.S., The Essential Peirce : Selected Philosophical Writings, Volume 1 (1867–1893), Nathan Houser and Christian Kloesel (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1992. Cited as EP 1, (page).
  • Peirce, C.S., The Essential Peirce : Selected Philosophical Writings, Volume 2 (1893–1913), Peirce Edition Project (eds.), Indiana University Press, Bloomington and Indianapolis, IN, 1998. Cited as EP 2, (page).
  • Peirce, C.S. (1865a), "On the Logic of Science", Harvard University Lectures, CE 1, 161–302.
  • Peirce, C.S. (1865b), "An Unpsychological View of Logic to which are appended some applications of the theory to Psychology and other subjects", MS 109 (Variant 1), May–Fall 1865, CE 1, 305–309.
  • Peirce, C.S. (1865c), "An Unpsychological View of Logic to which are appended some applications of the theory herein contained to Psychology and other subjects", MS 109 (Variant 2), May–Fall 1865, CE 1, 310–321.
  • Peirce, C.S. (1867), "On a New List of Categories", Proceedings of the American Academy of Arts and Sciences 7 (1868), 287–298. Presented, 14 May 1867. Reprinted (CP 1.545–559), (CE 2, 49–59), (EP 1, 1–10).
  • Peirce, C.S. (1877), "The Fixation of Belief", Popular Science Monthly 12, 1–15, 1877. Reprinted, CP 5.358–387. Eprint.
  • Peirce, C.S. (1878), "How to Make Our Ideas Clear", Popular Science Monthly 12, 286–302, 1878. Reprinted, CP 5.388–410. Eprint.
  • Peirce, C.S. (1899), "F.R.L." [First Rule of Logic], unpaginated manuscript, c. 1899. Reprinted, CP 1.135–140. Eprint.

Works by others

  • Awbrey, J.L., and Awbrey, S.M. (1995), "Interpretation as Action : The Risk of Inquiry", Inquiry : Critical Thinking Across the Disciplines 15, 40–52. Eprint.
  • Houser, Nathan (1989), "The Fortunes and Misfortunes of the Peirce Papers", Fourth Congress of the International Association for Semiotic Studies, Perpignan, France, 1989. Published, pp. 1259–1268 in Signs of Humanity, vol. 3, Michel Balat and Janice Deledalle–Rhodes (eds.), Gérard Deledalle (gen. ed.), Mouton de Gruyter, Berlin, Germany, 1992. Eprint.
  • Mac Lane, Saunders (1971), Categories for the Working Mathematician, Springer-Verlag, New York, NY, 1971. Second edition, 1998.
  • Taylor, Barry N. (ed.), The International System of Units (NIST Special Publication 330), Superintendent of Documents, Washington, DC, 2001. PDF text.


See Charles Sanders Peirce (Bibliography).

See also



Information, inquiry, logic, semiotics





External links

Document history
