Charles Sanders Peirce

Charles Sanders Peirce
Era	19th/20th century philosophy
Region	Western Philosophy
School	Pragmaticism (Pragmatism)
Main interests	Metaphysics, Logic, Epistemology, Mathematics, Science

Charles Sanders Peirce (pronounced purse), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. Although Peirce was educated as a chemist and was employed as a scientist for 30 years, it is for his contributions to logic, mathematics, philosophy, and the theory of signs, or semiotics, 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).

Peirce was largely ignored during his lifetime, and the secondary literature was scant until after World War II. Much of his huge output is still unpublished. Although he wrote mostly in English, he published some popular articles in French as well. An innovator in fields such as mathematics, research methodology, the philosophy of science, epistemology, and metaphysics, he considered himself a logician first and foremost. While he made major contributions to formal logic, "logic" for him encompassed much of what is now called the philosophy of science and epistemology. He, in turn, saw logic as a branch of semiotics, of which he is a founder. In 1886, he saw that logical operations could be carried out by electrical switching circuits, an idea used decades later to produce digital computers.

Life

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.

Peirce suffered all his life from what was then known as "facial neuralgia," a very painful nervous/facial condition. The Brent biography says that when in the throes of its pain "he was, at first, almost stupefied, and then aloof, cold, depressed, extremely suspicious, impatient of the slightest crossing, and subject to violent outbursts of temper." His condition would today be diagnosed as trigeminal neuralgia. Its consequences may have led to the social isolation which made the later years of his life so tragic.

United States Coast Survey

Between 1859 and 1891, Charles was intermittently employed in various scientific capacities by the United States Coast Survey, where he enjoyed the protection of his highly influential father until the latter's death in 1880. This employment exempted Charles from having to take part in the Civil War. It would have been very awkward for him to do so, as the Boston Brahmin Peirces sympathized with the Confederacy. At the Survey, he worked mainly in geodesy and in gravimetry, refining the use of pendulums to determine small local variations in the strength of the earth's gravity. The Survey sent him to Europe five times, the first in 1871, as part of a group dispatched to observe a solar eclipse. While in Europe, he sought out Augustus De Morgan, William Stanley Jevons, and William Kingdon Clifford, British mathematicians and logicians whose turn of mind resembled his own. From 1869 to 1872, he was employed as an Assistant in Harvard's astronomical observatory, doing important work on determining the brightness of stars and the shape of the Milky Way. (On Peirce the astronomer, see Lenzen's chapter in Moore and Robin, 1964.) In 1876 he was elected a member of the National Academy of Sciences. In 1878, he was the first to define the meter as so many wavelengths of light of a certain frequency, the definition employed until 1983 (Taylor 2001: 5).

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 him, 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. Brent conjectures that Peirce may have been manic-depressive, claiming that Peirce experienced eight nervous breakdowns between 1876 and 1911. Brent also believes that Peirce tried to alleviate his symptoms with ether, morphine, and cocaine.

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-Madison, 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.

Poverty

In 1887 Peirce spent part of his inheritance from his parents to purchase 2,000 acres (8 km²) rural 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 1998: 315–16, 374).

Peirce died destitute in Milford, Pennsylvania, twenty years before his widow.

Reception

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 times". 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 (1931–35), 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 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 (1902–2000) 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 (1900–1995) emerged as an authority on Peirce; Fisch (1986) reprints many of the relevant articles, including a wide-ranging survey (Fisch 1986: 422-48) 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, Franceand Spain. His writings have been translated into several languages, including German, French, Finnish, and Swedish. Since 1950, there have been French, Italian, and British Peirceans of note. 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.

Robert Burch has commented on Peirce's current influence as follows:

Currently, considerable interest is being taken in Peirce's ideas from outside the arena of academic philosophy. The interest comes from industry, business, technology, and the military; and it has resulted in the existence of a number of agencies, institutes, and laboratories in which ongoing research into and development of Peircean concepts is being undertaken. (Burch 2001/2005.)

Works

Peirce's reputation rests largely on a number of academic papers published in American scholarly and scientific journals. These papers, along with a selection of Peirce's previously unpublished work and a smattering of his correspondence, fill the eight volumes of the Collected Papers of Charles Sanders Peirce, published between 1931 and 1958. An important recent sampler of Peirce's philosophical writings is the two volume The Essential Peirce (Houser and Kloesel (eds.) 1992, Peirce Edition Project (eds.) 1998).

The only book Peirce published in his lifetime was Photometric Researches (1878), a monograph on the applications of spectrographic methods to astronomy. While at Johns Hopkins, he edited Studies in Logic (1883), containing chapters by himself and his graduate students. He was a frequent book reviewer and contributor to The Nation, work reprinted in Ketner and Cook (1975–87).

Hardwick (2001) published Peirce's entire correspondence with Victoria, Lady Welby. Peirce's other published correspondence is largely limited to the 14 letters included in volume 8 of the Collected Papers, and the 20-odd pre-1890 items included in the Writings.

Harvard University acquired the papers found in Peirce's study soon after his death, but did not microfilm them until 1964. Only after Richard Robin (1967) catalogued this Nachlass did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totalling 80,000 pages. Eisele (1976, 1985) published some of this work, but most of it remains unpublished. For more on the vicissitudes of Peirce's papers, see (Houser 1989).

The limited coverage, and defective editing and organization, of the Collected Papers led Max Fisch and others in the 1970s to found the Peirce Edition Project, whose mission is to prepare a more complete critical chronological edition, known as the Writings. Only 6 out of a planned 31 volumes have appeared to date, but they cover the period from 1859–1890, when Peirce carried out much of his best-known work.

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)

By 1870, the drive that Peirce exhibited to understand the character of knowledge, starting with our partly innate and partly inured models of the world and working up to the conduct of our scientific inquiries into it, having led him to inquire into the three-roled relationship of objects, signs, and impressions of the mind, now brought him to the pass of needing more power in a theory of relations than the available logical formalisms were up to providing. His first concerted effort to supply the gap was rolled out in his paper "Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic". But the nameplate "LOR of 1870" will do for ease of identification.

Logic of Relatives (1883)

Main article: Logic of Relatives (1883)

The Simplest Mathematics (1902)

Main article: The Simplest Mathematics

Kaina Stoicheia (1904)

Main article: Kaina Stoicheia

Mathematics

Mathematics of logic

It may be added that algebra was formerly called Cossic, in English, or the Rule of Cos; and the first algebra published in England was called "The Whetstone of Wit", because the author supposed that the word cos was the Latin word so spelled, which means a whetstone. But in fact, cos was derived from the Italian, cosa, thing, the thing you want to find, the unknown quantity whose value is sought. It is the Latin caussa, a thing aimed at, a cause. ("Elements of Mathematics", MS 165 (c. 1895), NEM 2, 50.)

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

• Showed how what is now called Boolean algebra could be expressed by means of a single binary operation, either NAND or its dual, NOR. (See also De Morgan's Laws). This discovery anticipated Sheffer by 33 years.

• In Peirce (1885), set out what can be read as the first (primitive) axiomatic set theory, anticipating Zermelo by about two decades.

• Discovered the now-classic axiomatization of natural number arithmetic, a few years before Dedekind and Peano did so.

• Discovered, independently of Dedekind, an important formal definition of an infinite set, namely, as a set that can be put into a one-to-one correspondence with one of its proper subsets.

Beginning with his first paper on the "Logic of Relatives" (1870), Peirce extended the theory of relations that Augustus De Morgan had just recently woken from its Cinderella slumbers. 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, allusively titled The New Elements of Mathematics, that presented mathematics from a decidedly novel, if not revolutionary standpoint.

In 1902 Peirce applied to the newly established Carnegie Institution for aid "in accomplishing certain scientific work", presenting an "explanation of what work is proposed" plus an "appendix containing a fuller statement". These parts of the letter, along with excerpts from earlier drafts, can be found in NEM 4 (Eisele 1976). The appendix is organized as a "List of Proposed Memoirs on Logic", and No. 12 among the 36 proposals is titled "On the Definition of Logic", the earlier draft of which is quoted in full above.

On Peirce and his contemporaries Ernst Schröder and Frege, Hilary Putnam (1982) wrote:

When I started to trace the later development of logic, the first thing I did was to look at Schröder's Vorlesungen über die Algebra der Logik. This book … has a third volume on the logic of relations (Algebra und Logik der Relative, 1895). [These] three volumes were the best-known logic text in the world among advanced students, and they can safely be taken to represent what any mathematician interested in the study of logic would have had to know, or at least become acquainted with in the 1890s.

While, to my knowledge, no one except Frege ever published a single paper in Frege's notation, many famous logicians adopted Peirce–Schröder notation, and famous results and systems were published in it. Löwenheim stated and proved the Löwenheim–Skolem theorem … in Peirce's notation. In fact, there is no reference in Löwenheim's paper to any logic other than Peirce's. To cite another example, Zermelo presented his axioms for set theory in Peirce–Schröder notation, and not, as one might have expected, in Russell–Whitehead notation.

One can sum up these simple facts (which anyone can quickly verify) as follows: Frege certainly discovered the quantifier first (four years before O. H. Mitchell did so, going by publication dates, which are all we have as far as I know). But Leif Ericson probably discovered America 'first' (forgive me for not counting the native Americans, who of course really discovered it 'first'). If the effective discoverer, from a European point of view, is Christopher Columbus, that is because he discovered it so that it stayed discovered (by Europeans, that is), so that the discovery became known (by Europeans). Frege did 'discover' the quantifier in the sense of having the rightful claim to priority; but Peirce and his students discovered it in the effective sense. The fact is that until Russell appreciated what he had done, Frege was relatively obscure, and it was Peirce who seems to have been known to the entire world logical community. How many of the people who think that 'Frege invented [formal] logic' are aware of these facts?

The main evidence for Putnam's claims is Peirce (1885), published in the premier American mathematical journal of the day. Peano, Ernst Schröder, among others, cited this article. Peirce was apparently ignorant of Frege's work, despite their rival achievements in logic, philosophy of language, and the foundations of mathematics.

Peirce's other major discoveries in formal logic include:

• Distinguishing (Peirce, 1885) between first-order and second-order quantification.

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

• Devising the existential graphs, a diagrammatic notation for the predicate calculus. These graphs form the basis of the conceptual graphs of John F. Sowa, and of Sun-Joo Shin's diagrammatic reasoning.

A philosophy of logic, grounded in his categories and semeiotic, can be extracted from Peirce's writings. This philosophy, as well as Peirce's logical work more generally, is exposited and defended in, and in Hilary Putnam (1982), the Introduction to Houser et al (1997), and Dipert's chapter in Misak (2004). Jean Van Heijenoort (1967), Jaakko Hintikka in his chapter in Brunning and Forster (1997), and Brady (2000) divide those who study formal (and natural) languages into two camps: the model-theorists / semanticists, and the proof theorists / universalists. Hintikka and Brady view Peirce as a pioneer model theorist. On how the young Bertrand Russell, especially his Principles of Mathematics and Principia Mathematica, did not do Peirce justice, see Anellis (1995).

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

• The philosophical algebraist William Kingdon Clifford and the logician William Ernest Johnson, both British;

• The Polish school of logic and foundational mathematics, including Alfred Tarski;

• Arthur Prior, whose Formal Logic and chapter in Moore and Robin (1964) praised and studied Peirce's logical work.

Logical graphs

Main article: Logical graph

Logic of information

Main article: Logic of information

Let us now return to the information. The information of a term is the measure of its superfluous comprehension. That is to say that the proper office of the comprehension is to determine the extension of the term. For instance, you and I are men because we possess those attributes — having two legs, being rational, &tc. — which make up the comprehension of man. Every addition to the comprehension of a term lessens its extension up to a certain point, after that further additions increase the information instead. (C.S. Peirce, "The Logic of Science, or, Induction and Hypothesis" (1866), CE 1, 467.)

Probability theory

Peirce held that science achieves statistical probabilities, not certainties, and that chance, a veering from law, is very real. In probability theory itself he held with the frequency interpretation (objective ratios of cases) rather than probability as a measure of confidence or belief, and he assigned probability to an argument’s conclusion rather than to a proposition, event, etc., as such.

Other areas of mathematics

Peirce produced a quincuncial projection of a sphere which kept angles true and resulted in less distortion of area than did other projections.

Peirce developed ideas about mathematical continuity. Continuity, or synechism, is important, even crucial, in his philosophy.

Philosophy

It is not sufficiently recognized that Peirce’s career was that of a scientist, not a philosopher; and that during his lifetime he was known and valued chiefly as a scientist, only secondarily as a logician, and scarcely at all as a philosopher. Even his work in philosophy and logic will not be understood until this fact becomes a standing premise of Peircian studies. (Max Fisch, in (Moore and Robin 1964, 486).

Peirce was a working scientist for 30 years, and arguably was a professional philosopher only during the five years he lectured at Johns Hopkins. He learned philosophy mainly by reading, each day, a few pages of Kant's Critique of Pure Reason, in the original German, while a Harvard undergraduate. His writings bear on a wide array of disciplines, including astronomy, metrology, geodesy, mathematics, logic, philosophy, the history and philosophy of science, linguistics, economics, and psychology. This work has become the subject of renewed interest and approval, resulting in a revival inspired not only by his anticipations of recent scientific developments but also by his demonstration of how philosophy can be applied effectively 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 initiated the philosophical tendency known as pragmatism, a variant of which his life-long friend William James made popular. Peirce believed that any truth is provisional, and that the truth of any proposition cannot be certain but only probable. The name he gave to this state of affairs was "fallibilism". This fallibilism and pragmatism may be seen as playing roles in his work similar to those of skepticism and positivism, respectively, in the work of others.

Theory of categories

Main article: Categories (Peirce)

In Aristotle's logic, categories are adjuncts to reasoning that are designed to resolve equivocations and thus to prepare ambiguous signs, that are otherwise recalcitrant to being ruled by logic, for the application of logical laws. An equivocation is a variation in meaning, or a manifold of sign senses, such that, as Aristotle put it about names in the opening of Categories (1.1^a1–12.), "Things are said to be named ‘equivocally’ when, though they have a common name, the definition corresponding with the name differs for each". So Peirce's claim that three categories are sufficient amounts to an assertion that all manifolds of meaning can be unified in just three steps.

Peirce introduces his Categories and their theory in "On a New List of Categories" (1867), a work cast as a Kantian deduction, a work which is short but dense and difficult to summarize. The following table is compiled from that and later works.

Peirce's Categories (technical name: the cenopythagorean categories)

Name:	Typical characterizaton:	As universe of experience:	As quantity:	Technical definition:	Valence, "adicity":
Firstness.	Quality of feeling.	Ideas, chance, possibility.	Vagueness, "some".	Reference to a ground (a ground is a pure abstraction of a quality).	Essentially monadic (the quale, in the sense of the thing with the quality).
Secondness.	Reaction, resistance, (dyadic) relation.	Brute facts, actuality.	Singularity, discreteness.	Reference to a correlate (by its relate).	Essentially dyadic (the relate and the correlate).
Thirdness.	Representation.	Habits, laws, necessity.	Generality, continuity.	Reference to an interpretant*.	Essentially triadic (sign, object, interpretant*).

 *Note: An interpretant is the product of an interpretive process, or the content of an interpretation.

Esthetics and ethics

Peirce did not write extensively in esthetics and ethics, but held that, together with logic in the broad sense, those studies constituted the normative sciences. He defined esthetics as the study of good and bad; and characterized the good as "the admirable". He held that, as the study of good and bad, esthetics is the study of the ends governing all conduct and comes ahead of other normative studies.

Peirce reserved the spelling "aesthetics" for the study of artistic beauty.

Philosophy: Logic, or semiotic

On the Definition of Logic. Logic is formal semiotic. A sign is something, A, which brings something, B, its interpretant sign, determined or created by it, into the same sort of correspondence (or a lower implied sort) with something, C, its object, as that in which itself stands to C. This definition no more involves any reference to human thought than does the definition of a line as the place within which a particle lies during a lapse of time. It is from this definition that I deduce the principles of logic by mathematical reasoning, and by mathematical reasoning that, I aver, will support criticism of Weierstrassian severity, and that is perfectly evident. The word "formal" in the definition is also defined. (Peirce, "Carnegie Application", NEM 4, 54).

Peirce referred to his general study of signs, based on the concept of a triadic sign relation, as semiotic or semeiotic, either of which terms are currently used in either singular of plural form. Peirce began writing on semiotic in the 1860s, around the time that he devised his system of three categories. He eventually defined 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". (Houser 1998: 411, written 1907). This triadic relation grounds the semeiotic.

Peirce's semiotic is philosophical logic studied in terms of signs and sign processes. When Peirce discusses things like assertions and interpretations, it is important to remember that he conceives of and defines them in terms of philosophical logic (which he called simply "logic"), rather than primarily in terms of psychology.

Every mind which passes from doubt to belief must have ideas which follow after one another in time. Every mind which reasons must have ideas which not only follow after others but are caused by them. Every mind which is capable of logical criticism of its inferences, must be aware of this determination of its ideas by previous ideas. (Peirce, "On Time and Thought", CE 3, 68–69.)

All through the 1860s, the young but rapidly maturing Charles Peirce was busy establishing a conceptual base camp and a technical supply line for the intellectual adventures of a lifetime. Taking the long view of this activity and trying to choose the best titles for the story, it all seems to have something to do with the dynamics of inquiry. This broad subject area has a part that is given by nature and a part that is ruled by nurture. On first approach, it is possible to see a question of articulation and a question of explanation:

• What is needed to articulate the workings of the active form of representation that is known as conscious experience?

• What is needed to account for the workings of the reflective discipline of inquiry that is known as science?

The pursuit of answers to these questions finds them to be so entangled with each other that it's ultimately impossible to comprehend them apart from each other, but for the sake of exposition it's convenient to organize our study of Peirce's assault on the summa by following first the trails of thought that led him to develop a theory of signs, one that has come to be known as 'semiotic', and tracking next the ways of thinking that led him to develop a theory of inquiry, one that would be up to the task of saying 'how science works'.

Opportune points of departure for exploring the dynamics of representation, such as led to Peirce's theories of inference and information, inquiry and signs, are those that he took for his own springboards. Perhaps the most significant influences radiate from points on parallel lines of inquiry in Aristotle's work, points where the intellectual forerunner focused on many of the same issues and even came to strikingly similar conclusions, at least about the best ways to begin. Staying within the bounds of what will give us a more solid basis for understanding Peirce, it serves to consider the following loci in Aristotle:

• The basic terminology of psychology, in On the Soul.

• The founding description of sign relations, in On Interpretation;

• The differentiation of the genus of reasoning into three species of inference that are commonly translated into English as abduction, deduction, and induction, in the Prior Analytics.

In addition to the three elements of inference, that Peirce would assay to be irreducible, Aristotle analyzed several types of compound inference, most importantly the type known as 'reasoning by analogy' or 'reasoning from example', employing for the latter description the Greek word 'paradeigma', from which we get our word 'paradigm'.

Inquiry is a form of reasoning process, in effect, a particular way of conducting thought, and thus it can be said to institute a specialized manner, style, or turn of thinking. Philosophers of the school that is commonly called 'pragmatic' hold that all thought takes place in signs, where 'sign' is the word they use for the broadest conceivable variety of characters, expressions, formulas, messages, signals, texts, and so on up the line, that might be imagined. Even intellectual concepts and mental ideas are held to be a special class of signs, corresponding to internal states of the thinking agent that both issue in and result from the interpretation of external signs.

The subsumption of inquiry within reasoning in general and the inclusion of thinking within the class of sign processes allows us to approach the subject of inquiry from two different perspectives:

• The syllogistic approach treats inquiry as a species of logical process, and is limited to those of its aspects that can be related to the most basic laws of inference.

• The sign-theoretic approach views inquiry as a genus of semiosis, an activity taking place within the more general setting of sign relations and sign processes.

The distinction between signs denoting and objects denoted is critical to the discussion of Peirce's theory of signs.

Signs

Sign relations

Main article: Sign relations

In order to understand what a sign is we need to understand what a sign relation is, for signhood is a way of being in relation, not a way of being in itself. In order to understand what a sign relation is we need to understand what a triadic relation is, for the role of a sign is constituted as one among three, where roles in general are distinct even when the things that fill them are not. In order to understand what a triadic relation is we need to understand what a relation is, and here there are traditionally two ways of understanding what a relation is, both of which are necessary if not sufficient to complete understanding, namely, the way of extension and the way of intension. To these traditional approximations, Peirce adds a third way, the way of information, in order to integrate the other two approaches in a unified whole. For discussion of Peirce's approach to comprehension, denotation, correspondence, semiotic determination, and other important sign relations, see the main article Sign relations.

Semiotic elements

Main article: Semiotic elements and classes of signs (Peirce)

Also see Sign relations for discussion of sign, object, and interpretant in terms of denotation, comprehension, correspondence, determination, and so forth.

Peirce held there are exactly three basic elements in semiosis (sign action):

1. A sign (or representamen) represents, in the broadest possible sense of "represents". It is something interpretable as saying something about something. It is not necessarily symbolic, linguistic, or artificial.
2. An object (or semiotic object) is a subject matter of a sign and an interpretant. It can be anything discussable or thinkable, a thing, event, relationship, quality, law, argument, etc., and can even be fictional, for instance Hamlet. All of those are special or partial objects. The object most accurately is the universe of discourse to which the partial or special object belongs. For instance, a perturbation of Pluto's orbit is a sign about Pluto but ultimately not only about Pluto.
3. An interpretant (or 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 or undeceptive 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, a state of agitation, a conduct, etc. Such is what is meant in saying that the sign stands for the object to the interpretant.

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

The object determines (not in the deterministic sense, but in a sense of "specializes," bestimmt) the sign to determine another sign -- the interpretant -- to be related to the object as the sign is related to the object, hence the interpretant, fulfilling its function as sign of the object, determines a further interpretant sign. The process is logically structured to perpetuate itself.

For further discussion of sign, object, and interpretant, see Sign relations and the main article Semiotic elements and classes of signs (Peirce).

Classes of signs

Main article: Semiotic elements and classes of signs (Peirce)

Three sign typologies, among others, are most prominent in Peirce's work. They depend respectively on (I) the sign itself, (II) the sign's relation to its denoted object, and (III) the sign's relation to its interpretant. The sign typologies are filled out by embodiments of each of three phenomenological categories, a trio of embodiments by each of these: (I) the sign itself, (II) the sign's manner of denoting the object, and (III) the manner attributed by the interpretant to the sign's denoting of the object.

I. Qualisign, sinsign, legisign (also called tone, token, type, and also called potisign, actisign, famisign): This typology emphasizes the sign itself in terms of the phenomenological category which it embodies -- the qualisign is a quality, a possibility, a "First"; the sinsign is a reaction or resistance, a singular object, an actual event or fact, a "Second"; and the legisign is a habit, a rule, a semiotic relation, a "Third".

II. Icon, index, symbol: This typology, the best known one, emphasizes the different ways in which the sign refers to its object -- the icon (also called semblance or likeness) by a quality of its own, the index by real connection to its object, and the symbol by a habit or rule for its interpretant.

III. Rheme, dicisign, argument (also called sumisign, dicisign, suadisign, also seme, pheme, delome, and regarded as very broadened versions of the traditional term, proposition, argument): This typology emphasizes that which the interpretant represents to be the sign's way of referring to its object -- the rheme is a sign interpreted to represent its object in respect of quality; the dicisign is a sign interpreted to represent its object in respect of fact; and the argument is a sign interpreted to represent its object in respect of habit or law.

Every sign falls under one class or another within (I) and within (II) and within (III). Thus each of the three typologies is a three-valued parameter for every sign. The three parameters are not independent of each other; many co-classifications aren't found, for reasons pertaining to the lack of either habit-taking or singular reaction in a quality, and the lack of habit-taking in a singular reaction. The result is not 27 but instead ten classes of signs fully specified at this level of analysis.

Modes of inference

Main article: Inquiry

Borrowing a brace of concepts from Aristotle, Peirce examined three fundamental modes of reasoning that play a role in inquiry, processes that are currently known as abductive, deductive, and inductive inference.

In the roughest terms, abduction is what we use to generate a likely hypothesis or an initial diagnosis in response to a phenomenon of interest or a problem of concern, while deduction is used to clarify, to derive, and to explicate the relevant consequences of the selected hypothesis, and induction is used to test the sum of the predictions against the sum of the data.

Pragmatism

Main articles: Pragmaticism and Pragmatic maxim

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

Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object. (CP 5.438.)

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. He differed from William James and the early John Dewey, in some of their tangential enthusiasms, in being decidedly more rationalistic and realistic, in several senses of those terms, throughout the preponderance of his own philosophical moods.

Peirce's pragmatism may be understood as a method of sorting out conceptual confusions by equating the meaning of any concept with the conceivable operational or practical consequences of whatever it is which that concept portrays. This pragmatism bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavellian search for mercenary or political advantage. Rather, Peirce's Pragmatic Maxim is the heart of his pragmatism as a method of experimentational mental reflection arriving at conceptions in terms of conceivable confirmatory and disconfirmatory circumstances -- a method hospitable to the generation of explanatory hypotheses, and conducive to the employment and improvement of verification to test the truth of putative knowledge. As such a method, pragmatism leads beyond the usual duo of foundational alternatives, namely:

• Deduction from self-evident truths, or rationalism;

• Induction from experiential phenomena, or empiricism.

His approach is often confused with the latter form of foundationalism, but is distinct from it by virtue of the following three dimensions:

• Active process of theory generation, with no prior assurance of truth;

• Subsequent application of the contingent theory, aimed toward developing its logical and practical consequences;

• Evaluation of the provisional theory's utility for the anticipation of future experience, and that in dual senses of the word: prediction and control. Peirce's appreciation of these three dimensions serves to flesh out a physiognomy of inquiry far more solid than the flatter image of inductive generalization simpliciter, which is merely the relabeling of phenomenological patterns. Peirce's pragmatism was the first time the scientific method was proposed as an epistemology for philosophical questions.

A theory that proves itself more successful in predicting and controlling our world than its rivals is said to be nearer the truth. This is an operational notion of truth employed by scientists. Unlike the other pragmatists, Peirce never explicitly advanced a theory of truth. But his scattered comments about truth have proved influential to several epistemic truth theorists, and as a useful foil for deflationary and correspondence theories of truth.

Pragmatism is regarded as a distinctively American philosophy. As advocated by James, John Dewey, Ferdinand Canning Scott Schiller, George Herbert Mead, and others, it has proved durable and popular. But Peirce did not seize on this fact to enhance his reputation. While it is sometimes stated that James' and other philosophers' use of the word pragmatism so dismayed Peirce that he renamed his own variant pragmaticism, this was not the main reason (Haack, 55). This is revealed by the context in which Peirce introduced the latter term:

But at present, the word [pragmatism] begins to be met with occasionally in the literary journals, where it gets abused in the merciless way that words have to expect when they fall into literary clutches. … So then, the writer, finding his bantling "pragmatism" so promoted, feels that it is time to kiss his child good-by and relinquish it to its higher destiny; while to serve the precise purpose of expressing the original definition, he begs to announce the birth of the word "pragmaticism", which is ugly enough to be safe from kidnappers. (C. S. Peirce, CP 5.414.)

Peirce's pragmatism is a department of his theory of method of inquiry, which he variously called Methodeutic and Philosophical or Speculative Rhetoric. He applied his pragmatism as a method throughout his work.

Theory of inquiry

Main article: Inquiry

Upon this first, and in one sense this sole, rule of reason, that in order to learn you must desire to learn, and in so desiring not be satisfied with what you already incline to think, there follows one corollary which itself deserves to be inscribed upon every wall of the city of philosophy:

Do not block the way of inquiry.

Although it is better to be methodical in our investigations, and to consider the economics of research, yet there is no positive sin against logic in trying any theory which may come into our heads, so long as it is adopted in such a sense as to permit the investigation to go on unimpeded and undiscouraged. On the other hand, to set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning, as it is also the one to which metaphysicians have in all ages shown themselves the most addicted. (Peirce, "F.R.L." (c. 1899), CP 1.135–136.)

Peirce extracted the pragmatic model or theory of inquiry from its raw materials in classical logic and refined it in parallel with the early development of symbolic logic to address problems about the nature of scientific reasoning.

Abuction, deduction, and induction typically operate in a cyclic fashion, systematically operating to reduce the uncertainties and the difficulties that initiated the inquiry in question, and in this way, to the extent that inquiry is successful, leading to an increase in the knowledge or skills, in other words, an augmentation in the competence or performance, of the agent or community engaged in the inquiry.

In the pragmatic way of thinking every thing has a purpose, and the purpose of any thing is the first thing that we should try to note about it. The purpose of inquiry is to reduce doubt and lead to a state of belief, which a person in that state will usually call 'knowledge' or 'certainty'. It needs to be appreciated that the three kinds of inference, insofar as they contribute to the end of inquiry, describe a cycle that can be understood only as a whole, and none of the three makes complete sense in isolation from the others.

For instance, the purpose of abduction is to generate guesses of a kind that deduction can explicate and that induction can evaluate. This places a mild but meaningful constraint on the production of hypotheses, since it is not just any wild guess at explanation that submits itself to reason and bows out when defeated in a match with reality. In a similar fashion, each of the other types of inference realizes its purpose only in accord with its proper role in the whole cycle of inquiry. No matter how much it may be necessary to study these processes in abstraction from each other, the integrity of inquiry places strong limitations on the effective modularity of its principal components.

If we then think to inquire, 'What sort of constraint, exactly, does pragmatic thinking place on our guesses?', we have asked the question that is generally recognized as the problem of 'giving a rule to abduction'. Peirce's way of answering it is given in terms of the so-called 'pragmatic maxim', and this in turn gives us a clue as to the central role of abductive reasoning in Peirce's pragmatic philosophy.

Philosophy: Metaphysics

In ontology, Peirce declared himself Scholastic Realist about generals early on. Eventually he embraced Scholastic Realism about modalities (possibility, necessity, etc.) as well.

Peirce also argued for God, though not in God as an actual being, but rather as a real being. He elucidates the distinction which he makes between actuality and reality in his "A Neglected Argument For the Reality Of God".

In physical metaphysics, Peirce held with the reality of chance (tychism), continuity (synechism), and the view that matter is effete mind, increasingly hardened by habit and exhausted of its life.

Science of review

Main article: Classification of the sciences (Peirce)

Peirce did considerable work over a period of years on the classification of sciences (including mathematics).

In 1902, he divided science into Theoretical and Practical. Theoretical Science was comprised of Science of Discovery and Science of Review, the latter of which he also called "Synthetic Philosophy", a name taken from the title of the vast work, written over many years, by Herbert Spencer. Then, in 1903, he made it a three-way division: Science of Discovery, Science of Review, and Practical Science. In 1903 he characterized Science of Review as:

...arranging the results of discovery, beginning with digests, and going on to endeavor to form a philosophy of science. Such is the nature of Humboldt's Cosmos, of Comte's Philosophie positive, and of Spencer's Synthetic Philosophy. The classification of the sciences belongs to this department."

Peirce opens his 1903 classification (the "Syllabus" classification) with a concise statement of method and purpose:

This classification, which aims to base itself on the principal affinities of the objects classified, is concerned not with all possible sciences, nor with so many branches of knowledge, but with sciences in their present condition, as so many businesses of groups of living men. It borrows its idea from Comte's classification; namely, the idea that one science depends upon another for fundamental principles, but does not furnish such principles to that other. It turns out that in most cases the divisions are trichotomic; the First of the three members relating to universal elements or laws, the Second arranging classes of forms and seeking to bring them under universal laws, the Third going into the utmost detail, describing individual phenomena and endeavoring to explain them. But not all the divisions are of this character.."

For further discussion, see main article Classification of the sciences (Peirce).

References

• Anellis, I.H. (1995) "Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic," Eprint Modern Logic 5: 270–328.
• Aristotle, "The Categories," Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library. London: William Heinemann, 1938.
• Aristotle, "On Interpretation," Harold P. Cooke (trans.), pp. 111–179 in Aristotle, Volume 1, Loeb Classical Library. London: William Heinemann, 1938.
• Aristotle, "Prior Analytics," Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library. London: William Heinemann, 1938.
• Boole, George (1854) An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan. Reprinted 1958 with corrections, New York: Dover Publications.
• Stanford Encyclopedia of Philosophy:
  • Atkin, Albert (2006) "Peirce's Theory of Signs".
• Brent, Joseph (1998), Charles Sanders Peirce: A Life. Revised and enlarged edition, Indiana University Press, Bloomington, IN.
  • Burch, Robert (2001) "Charles Sanders Peirce,". Revised, Winter 2005.
• Dewey, John (1910) How We Think, Lexington MA: D.C. Heath. Reprinted 1991, Buffalo NY: Prometheus Books.
• Haack, Susan (1998) Manifesto of a Passionate Moderate. Chicago IL: University of Chicago Press.
• 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.
• Liddell, Henry George, and Scott, Robert (1889) An Intermediate Greek-English Lexicon, Oxford UK: Oxford University Press. Reprinted 1991.
• Mac Lane, Saunders (1971) Categories for the Working Mathematician, New York: Springer-Verlag. Second edition, 1998.
• Peirce, C.S. (1877) "The Fixation of Belief," Popular Science Monthly 12: 1–15. Reprinted CP 5.358-387.
• Peirce, C.S. (1878) "How to Make Our Ideas Clear," Popular Science Monthly 12: 286–302. Reprinted CP 5.388-410.
• Peirce, C.S. (1897) "The Logic of Relatives," The Monist, vol. 7, pp. 161-217 (via Google Books with registration not required). Reprinted CP3.456-552.
• Peirce, C.S. (1899) " F.R.L. (First Rule of Logic)," unpaginated manuscript. Reprinted CP 1.135–140.
• Peirce, C.S., "Application of C.S. Peirce to the Executive Committee of the Carnegie Institution, July 15, 1902." Published in Eisele, Carolyn, ed. (1976) "Parts of Carnegie Application (L75)" in The New Elements of Mathematics by Charles S. Peirce, Vol. 4, Mathematical Philosophy. The Hague, Netherlands: Mouton Publishers: 13–73. Eprint version edited by Joseph Ransdell
• Peirce, C.S. (1992) The Essential Peirce, Selected Philosophical Writings, Vol. 1 (1867–1893), Nathan Houser and Christian Kloesel, eds. Bloomington and Indianapolis, IN: Indiana University Press.
• Peirce, C.S. (1998) The Essential Peirce, Selected Philosophical Writings, Volume 2 (1893–1913), Peirce Edition Project, eds. Bloomington and Indianapolis, IN: Indiana University Press.
• Robin, Richard S. (1967) Annotated Catalogue of the Papers of Charles S. Peirce. Amherst MA: University of Massachusetts Press.
• Taylor, Barry N., ed. (2001) The International System of Units, NIST Special Publication 330. Washington DC: Superintendent of Documents.
• van Heijenoort, Jean (1967) "Logic as Language and Logic as Calculus," Synthese 17: 324–30.

Bibliography

Main article: Charles Sanders Peirce (Bibliography)

A bibliography of Peirce's works may be found at the above location.

See also

Abstraction

• Continuous predicate
• Hypostatic abstraction
• Hypostatic object
• Prescisive abstraction

Contemporaries

• John Dewey
• William James
• Ernst Schröder

Information, inquiry, logic, semiotics

• Ampheck
• Binary relations
• Comprehension
• Entitative graph
• Existential graph
• Inquiry
• Laws of form
• Logic of information
• Logic of relatives

• Logical graph
• Logical matrix
• Logical NAND
• Logical NOR
• Meaning
• Peirce's law
• Pragmatics
• Rhema, Rheme
• Semeiotic

• Semiosis
• Semiotics
• Semiotic information theory
• Semiotic triangle
• Sign
• Sign relation
• Sole sufficient operator
• Theory of relations
• Triadic relation

Mathematics

• Dyadic relation
• Kaina Stoicheia
• Quincuncial map

• Relation
• Relation composition
• Relation construction

• Relation reduction
• Theory of relations
• Triadic relation

Philosophy

• Pragmatism
• Pragmaticism
• Pragmatic maxim
• Pragmatic theory of truth

External links

• Arisbe: The Peirce Gateway, Joseph Ransdell (ed.)
• Charles S. Peirce Society

• Transactions

• Charles S. Peirce Studies
• Charles Sanders Peirce, MacTutor History of Mathematics, O'Connor & Robertson
• Commens: Virtual Centre for Peirce Studies, University of Helsinki, Bergman & Paavola (eds.)

• Dictionary of Peirce Terms
• Peirce's Writings Online

• Digital Encyclopedia of Charles S. Peirce
• Grupo de Estudios Peirceanos, Jaime Nubiola (ed.)
• His Glassy Essence: Autobiography of Charles S. Peirce, Kenneth Laine Ketner
• Internet Encyclopedia of Philosophy, Fieser & Dowden (eds.)

• Charles Sanders Peirce (1839-1914), Albert Atkin
• C.S. Peirce's Architectonic Philosophy, Albert Atkin
• C.S. Peirce's Pragmatism, Albert Atkin

• Peirce, Charles Sanders (1839-1914), Ralph Lichtensteiger
• Peirce Edition Project

• Introduction to Essential Peirce, vol. 1, Nathan Houser
• Introduction to Essential Peirce, vol. 2, Nathan Houser

• Pragmatism Cybrary, John R. Shook (ed.)

• Cambridge School of Pragmaticm

• Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.)

• Charles Sanders Peirce, Robert Burch
• Peirce's Logic, Eric Hammer

• Wikipédia, l’encyclopédie libre

• Philosophie et sémiotique de Peirce, Raymond Robert Tremblay.

An earlier version of this article, by Jaime Nubiola, was posted at Nupedia.