Information AboutCharles Peirce |
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Charles Sanders Peirce (pronounced ''purse''), ( 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, he is now mostly seen as a Philosopher . He is the greatest American builder of Architectonic systems, and his admirers deem him the most important systematizer since Kant and Hegel , who were major influences. 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 Much of his huge output is still unpublished. 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, thus anticipating the digital computer. LIFE
Brent (1998) is the only Peirce biography in English. 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 devoured an older brother's copy of Richard Whately 's ''Elements of Logic'', then the leading English language text of its kind. Thus began his lifelong fascination with logic and reasoning. He went on to obtain the BA and MA from Harvard, and in 1863 was awarded the Lawrence Scientific School 's first B.Sc. in chemistry. This last degree was awarded ''summa cum laude''; his academic record was otherwise 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 him; they clashed on later occasions. This was unfortunate, because Eliot was President of Harvard 1869-1909, a period encompassing nearly all of Peirce's working life, during which he repeatedly vetoed having Harvard employ Peirce in any capacity. United States Coast Survey Charles was employed as a scientist by the United States Coast Survey ( 1859 – 1891 ), 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 , sparing him a very awkward situation, as his Boston Brahmin family sympathized with the Confederacy . At the Survey, he worked mainly in Geodesy and in Gravimetry , refining the use of Pendulum s 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. During 1869-72, 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 1878, he was the first to define the Meter as so many Wavelength s of Light of a certain Frequency , the definition employed today. Over 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 required 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, he 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 John Dewey were students), 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. It is a fact that Clark, Wisconsin, Michigan, Cornell, Stanford, and Chicago all declined to hire him, although the precise reasons for their so doing can no longer be determined. 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 (1835-1909). 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 , further claiming that Peirce experienced 8 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), marrying her immediately upon divorcing Harriet 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, and to his being deemed morally unfit for academic employment anywhere in the USA. Peirce had no children by either marriage. Poverty In 1887 , Peirce used an 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. He insisted on living well beyond his means, which 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. His only food was bread donated by the local baker, and he wrote on the verso side of old manuscripts because he could not afford new stationery. For a while an outstanding warrant for assault and debt led to his becoming a fugitive in New York. A variety of people including his brother James Mills Peirce and his neighbors, relatives of Gifford Pinchot , paid his property taxes and mortgage, and settled other debts. During this long final twilight phase of Peirce’s life, he 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. Peirce tried his hand at inventing, and began but did not complete a number of books, all in the hope of making money. 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 this his hour of desperate need was his old friend William James , who helped arrange four series of lectures at or near Harvard, and dedicated his ''Will to Believe'' to Peirce. 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 showed his gratitude for these remarkable gestures of friendship 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 '' fails to mention Peirce.) While reading some of Peirce's unpublished manuscripts soon after arriving at Harvard in 1924, Alfred North Whitehead was struck by the extent to which 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 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 and Paul Weiss, did not become Peirce specialists. Early landmarks of the secondary literature include the monographs 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 the history of American philosophy, including pragmatism, 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 (pp. 422-48) a wide-ranging survey of the impact of Peirce's thought through 1983. Peirce has come to enjoy an international following. University research centers devoted to Peirce Studies and Pragmatism can be found in Brazil, Finland, Germany, and Spain. There have been French and Italian Peirceans of note since 1950. For many years, the University Of Toronto housed the North American philosophy department most devoted to Peirce. In recent years, Peirce scholars have clustered at Indiana University - Purdue University Indianapolis , the home of the Peirce Edition Project, and the Pennsylvania State University . WORKS Peirce's reputation is based in large part 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 corresondence, fill the eight volumes of the ''Collected Papers of Charles Sanders Peirce'', published between 1931 and 1958 . A first taste of Peirce's philosophical writings can be found in the two volumes of ''The Essential Peirce'' (Houser and Kloesel (eds.) 1992, Peirce Edition Project (eds.) 1998). The only book-length account of his own investigations that 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 '', the sum of which writing is reprinted in ''Contributions to 'The Nation' '' (Ketner and Cook, 1975-1987). 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) published his catalog of this legacy, did it become clear that Peirce had left approximately 1650 unpublished manuscripts, totalling 80,000 pages. A number of these works were published in Eisele (1976, 1985), but most of them remain as yet unpublished. For more on the vicissitudes of Peirce's papers, see (Houser 1989). The increasingly apparent limitations of the ''Collected Papers'', with respect to coverage and organization both, led Max Fisch and others in the 1970's to establish the Peirce Edition Project, whose mission is to prepare a more complete critical edition, known as the ''Writings'', organized chronologically. A mere half dozen of the anticipated 30-plus volumes have appeared to date, but they cover a period from 1859 to 1890 when Peirce carried out some of his most important work. Logic of Relatives (1870) See Also: 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) See Also: Logic of Relatives (1883) Logic of Relatives (1897) PEIRCE'S PHILOSOPHY
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 a few pages of Kant 's '' Critique Of Pure Reason '' in the original German, every day 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. PRAGMATISM 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:
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 Idea s 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 linking the meaning of concepts to their operational or practical consequences. This pragmatism bears no resemblance to "vulgar" pragmatism, which misleadingly connotes a ruthless and Machiavelli an search for mercenary or political advantage. Rather, Peirce sought an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond the usual duo of foundational alternatives, namely:
His approach is often confused with the latter form of Foundationalism , but is distinct from it by virtue of the following three dimensions:
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. Instead, what James and others called "pragmatism" so dismayed Peirce that he renamed his own variant Pragmaticism , joking that it was "ugly enough to be safe from kidnappers" (CP 5.414). SCHOLASTIC REALISM Peirce’s confession to being a “scholastic realist of a somewhat extreme stripe” (CP 5.470) is well known and baffles some. He has been described by careless writers as an Idealist (“ Reality ” = “the object of the final opinion of the scientific community”), but this description is inaccurate, since he believed that reality was best described 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). In his first remarks on the realist vs. nominalist debate, Peirce sided with nominalism:
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 two of the Chronological Edition of Peirce’s writings (1984). However, 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.” (6.605, italics mine) 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:
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, i.e., 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; it has no secondness). FORMAL PERSPECTIVE
Peirce did not live or work in a vacuum. No one who appreciates his use of phrases like 'laws of the symbol' in their historical context could fail to hear the echoes of Boole, nor indeed the background stirrings of the contemporary Zeitgeist in mathematics that went under the name of the 'symbolist movement', the clarion call to which is commonly attributed to George Peacock (1791-1858). If Peirce appears at times to march out of step, it is because he hears the beat of many different drummers, not just one. The main themes of the symbolist movement, though they may have presented novelties to the general understanding of mathematics in the 19th Century, are nowadays familiar to anyone who has had a brush with the 'art of the story problem' in an elementary algebra course. There one learns to approach the story problem, a roughly realistic representation of a concrete circumstance, with the aim to abstract or to 'tease out' a general formula from the concrete data that specify the situation. Next one proceeds to 'crank the formula', starting from a form that is true but problematically obscure in its implications, and, circumstances warranting, continuing until a logically equivalent or a lower implied form is reached, but one that is maximally clarified in its implications. That most clear result one dubs the 'abstract answer' or the 'general solution' to the story problem, leaving nothing more to do but 'plug in' the concrete data that came with the story problem to arrive at the 'concrete answer' or the 'specific solution'. The three-phase maneuver for solving a story problem, (1) teasing out, (2) cranking the crank, (3) plugging in, can be articulated in semiotic or sign-relational terms as follows: The first phase passes from the object domain to the sign domain, the second phase passes from the sign domain to the interpretant sign domain, continuing perhaps in a relay of successive passes, and the third phase passes from the last interpretant sign domain back to the object domain. There are a number of issues that typically arise with the continuing development of a symbolist perspective, in any field of endeavor, over the years of its natural life-cycle. We can see these issues illustrated clearly enough in our story problem paradigm, with its parsing of the problem-solving process into the three phases of abstraction, transformation, and application.
Returning to the formal sciences of logic and mathematics and focusing on the rise of symbolic logic in particular, all of the above issues were clearly recognized and widely discussed among the movers and shakers of the symbolist movement, with especial mention of George Boole , Augustus De Morgan , Benjamin Peirce , and Charles Peirce. The first symptoms of a crisis typically arise in connection with questions about the status of the abstract symbols that are 'manipulated' in the transformation phase, to express it in sign-relational terms, the sign-to-sign aspect of semiosis. In the beginning, while it is still evident to everyone concerned that these symbols are mined from the matrix of their usual interpretations, which are generally more diverse than unique, these abstracted symbols are commonly referred to as ' Uninterpreted Symbol s', the sense being that they are transiently detached from their interpretations simply for the sake of extra facility in processing the more general thrust of their meanings, after which intermediary process they will have their concrete meanings restored. When we start to hear these abstract, general, uninterpreted symbols being described as 'meaningless' symbols, then we can be sure that a certain line in our sand-reckoning has been crossed, and that the crossers thereof have hefted or sublimated ' Formalism ' to the status of a full-blown Weltanschauung rather than a simple Heuristic device. What we observe here is a familiar form of cyclic process, with the crest of excess followed by the slough of despond. The inflationary boom that raises 'formalism' beyond its formative sphere as one among a host of equally useful heuristic tricks to the status of a totalizing worldview leads perforce to the deflationary bust that makes of 'formalist' a pejorative term. The point of the foregoing discussion is this, that one of the main difficulties that we have in understanding what the whole complex of words rooted in 'form' meant to Peirce is that we find ourselves, historically speaking, on opposite sides of this cycle of ideas from him. And so we are required, as so often happens in trying to read a writer of another age, to lift the scales of the years from our eyes, to drop the reticles that have encrusted themselves on our 'reading glasses', our Hermeneutic scopes, due to the interpolant philosophical schemata that have managed to enscounce themselves in our unthinking culture over the years that separate us from the writer in question. Logic as formal semiotic
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:
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:
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). / 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 :
Relationships, relations, relatives The reader of Peirce needs to be aware of the distinction between ''relations'' and ''relatives''. Succinctly put, relations are objects and relatives are signs. The term "relative" is short for "relative term", and a relative term is a type of sign that forms the main study of the ''logic of relatives''. A relation, on the other hand, is a type of formal object that is treated in the mathematical ''theory of relations''. There is of course an intimate relationship between the two studies, but like most intimate relationships it has its fair share of intricacies. 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). To understand these definitions, as everywhere in Peirce's work, one needs to keep a close watch on the things that are meant as objects of discussion and thought and the things that are meant as signs and thoughts in which discussion and thought take place. Doing this is trickier than it seems at first, since many standard approaches to defining abstract, formal, or '' Hypostatic '' objects approach their objects by way of formal operations on the corresponding signs. Relatives See Also: Logic of relatives Relations See Also: Theory of relations A concept of relation that suffices to begin the study of Peirce's logic, mathematics, and semiotics, making use of analogous concepts of relation that have served well enough in other areas of experience to make further experience possible, can be set out as follows.
: x = (x1, …, xk) : x = x1 ''':''' … ''':''' xk It is critically important to understand that a relation in extension is a '' Set '', in other words, an aggregate entity or a collection of things. More to the point, a k-tuple is not a relation, it is only an '' Element '' of a relation, what Peirce quite naturally called an ''elementary relation'' or sometimes an ''individual relation''. In his time, Peirce found himself forced by the task of understanding the intertwined natures of science and signs to develop the logic of relations from the fairly primitive state in which he found it to a condition of readiness more qualified for the job. There was nothing very cut and dried about trying to do this from scratch, as will be evident in the appropriate Sections below when we sample the fits and starts forward, the culs-de-sac, and the many paths that had to be backtracked in order to arrive at an adequate theory of relations. For the purpose at hand, however, we can rely on the fact that few readers these days will have escaped some encounter with Relational Database s, and so we can draw on these resources of experience to speed the exposition of relations in general. Table 1 shows how the k-tuples of a k-adic relation might be conceived in tabular form, with the k-uple xi = For ease of exposition, Table 1 shows the generic form of a '' Discrete '' k-adic relation, one that contains a '' Countable '' number of k-tuples, indeed, it shows a '' Finite '' k-adic relation, one that contains a finite number of k-tuples. Generalizations to relations with an Infinite or even a Continuous Cardinality in respect of their numbers of elementary relations are possible. Indeed, it is possible to conceive of relations with infinite, continuous, or even no fixed numbers of components in their elementary relations, but finite k-adic relations are illustration enough for our immediate aims. Dyadic relations See Also: Binary relation Triadic relations See Also: Triadic relation : This completes the classification of dual relatives founded on the difference of the fundamental forms A : A and A : B. Similar considerations applied to triple relatives would give rise to a highly complicated development, inasmuch as here we have no less than five fundamental forms of individuals, namely: : (Peirce, CP 3.229, "On the Algebra of Logic", ''American Journal of Mathematics'', 3, 15-57 (1880), CP 3.154-251). Theory of categories
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:
In the logic of Aristotle 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, and 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. The following passage is critical to the understanding of Peirce's Categories:
The first thing that we need to extract from this text is the fact that Categories are predicates of predicates, in effect, types of relations. Logical graphs See Also: Logical graph Mathematics
Peirce made a number of striking discoveries in foundational mathematics, nearly all of which came to be appreciated only long after his death. He:
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 Database s. 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. DYNAMICS OF REPRESENTATION
All through the 1860's, the young but rapidly maturing Charles Peirce — our focus now being his coming of age in the sphere of intellect — was busy establishing a conceptual basecamp and a technical supply line for the intellectual adventures of a lifetime. Taking the longview 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 Representation , divided into the portion that we are given by Nature and the portion that we are given to Nurture . In this quest we may discern a question of Articulation and a question of Explanation :
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 Sign s, 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 :
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 distinction between signs denoting and objects denoted is critical to the discussion of Peirce's theory of signs. Wherever needed in the rest of this article, therefore, in order to mark this distinction a little more emphatically than usual, double quotation marks placed around a given sign, for example, a string of zero or more characters, will be used to create a new sign that denotes the given sign as its object. Theory of signs, or semiotic Peirce is one of the two founders of the general study of signs, the other being Ferdinand De Saussure . Peirce referred to his approach, based on Triadic Sign Relation s, as '' Semiotic '' or '' Semeiotic '', either of which terms are currently used in either singular of plural form. In contrast, Saussure referred to his approach, based on dyadic sign relations, as '' Semiology ''. Peirce began writing on semeiotic in the 1860s, around the time 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. 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 '', that integrates the other two approaches in a unified whole. Sign relations See Also: Sign relation With that hasty map of relations and relatives sketched above (§ 4.3.2), we may now trek into the terrain of '' Sign Relation s'', the main subject matter of Peirce's '' Semeiotic '', or theory of signs. Types of signs Theory of inquiry See Also: 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: : 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. 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. These three processes 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. Logic of information See Also: Logic of information
PARALLELS WITH LEIBNIZ Peirce was aware that the breadth and depth of his ideas resembled those of the ). Both were passionate about natural science and contributed thereto, dabbled in inventions, and worked on engineering projects. Both were fascinated by Semiotics and Mathematical Notation , and the interplay between philosophy and mathematics. Both were surprisingly friendly to some parts of Scholastic metaphysics as well as logic; e.g., Peirce frequently invoked the Scotistic notion of Haecceity . Both published few books, many articles, and died leaving a vast amount in manuscript. The ideas of both men underwent oversimplification in the hands of others, and were little appreciated for some time after their deaths. The critical editions of the works of both men are far from complete. The secondary literature on both men mostly dates from the end of WWII . Leibniz differs from Peirce in his greater range, vast correspondence, freedom from financial difficulties, and his passionate Christianity . REFERENCES
BIBLIOGRAPHY See Also: Charles Peirce (Bibliography) A bibliography of Peirce's works may be found at the above location. SEE ALSO Abstraction Contemporaries Information, inquiry, logic, semiotics
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