written by John N. Warfield
His father, Benjamin Peirce, was head of the mathematics department at Harvard University, and was a well-known mathematician. He introduced Charles to philosophy, and urged Charles to study all the well-known philosophers, and show where they were wrong in their thinking.
Charles received two college degrees from Harvard.
His early career was scientific, working in precision measurements for the U. S. Coastal Survey. However he studied philosophy on the side. After being abused in several positions, he moved to Milford, PA, where he would spend the last third of his life largely in writing the results of his philosophical and logical investigations. From time to time, he would give lectures. A notable series was presented at Harvard in his last years.
While he published many articles, he also left much work unpublished. Since he died in poverty, the bulk of the unpublished work was purchased by Harvard University for a small amount, which helped his widow survive. Most of that material remained unread until the early 1930's, when funds were provided during the depression to occupy scholars. At that time much of his unpublished material was organized and published.
Following that, scholars began to take note of his work. Many scholars wrote books about Peirce or edited portions of his work, which were then published. The first thorough biography appeared in 1993, from Joseph Brent, a historian, who had done most of the work as early as 1960, but had not been able to get permission to publish it.
There are several centers at universities which specialize in the study of Peirce and which publish books or papers related to his work. I list them in the order of what I perceive to be the relative intensity and activity, most active first.
Texas Tech University maintains a center for the study of Peirce's work. Numerous publications have come from there, largely through the work of Ketner.
Fordham University has published interpretations of Peirce's work in its American Philosophy Series. Among the contributing scholars: the late Vincent G. Potter and his associate, Vincent M. Colapietro. Of special importance are the interpretations of "normative science", which connect esthetics, ethics, logic, and Peirce's views of God.
An early book on Peirce appeared under the editorship of Professor Goudge of the University of Toronto.
Harvard University seems to be doing relatively little in this area, but they did host (in conjunction with Texas Tech) a memorial week in 1989, 150 years after the birth of Peirce. Hundreds of philosophers attended the program, and many presented papers.
A thorough review of Peirce is presented in a book by Karl-Otto Apel, a contemporary German philosopher.
A few books present some of Peirce's most well-known articles. These two are relatively inexpensive, and give a good introduction:
"One singular deception of this sort, which often occurs, is to mistake the sensation produced by our own unclearness of thought for a character of the object we are thinking. Instead of perceiving that the obscurity is purely subjective, we fancy that we contemplate a quality of the object which is essentially mysterious...".
"...So long as this deception lasts, it obviously puts an impassable barrier in the way of perspicuous thinking; so that it equally interests the opponents of rational thought to perpetuate it, and its adherents to guard against it."
This idea can be paraphrased somewhat, and turned into a definition of "complexity". First of all, it is surely true that the vast majority of modern thought about complexity perceives it to be a property of what is being observed, instead of being a subjective response to the not-understood. The language itself clearly demonstrates this, in the common use of terms such as "complex system", and "complex problem".
Yet it is easy to imagine this: if the human being had the mental power to comprehend everything that was viewed of any interest, there would be no such thing as a complex system or complex problem in the usual sense, or of complexity in the sense discussed here.
Clearly then, the very existence of complexity is directly connected to human mental limitations. And just as clearly, every human being is involved in this connection, though not necessarily with equal results in all situations.
It is also easy to imagine this: what might be thought complex by person A might not be so conceived by person B. So not only is complexity human-specific, but in some respects it is individual-specific. The importance of the latter is not necessarily that some individuals are vastly less susceptible to the impact of complexity than others; but rather that even this noticeable distinction, sometimes encountered, testifies also that complexity is not a property of what is being observed, but rather is "a sensation" arising out of our own "unclearness of thought", when we are engaged with what we are observing. In summary,
While this definition may be thought surprising, one of its notable attributes is that it allows for the possibility that complexity may be reduced or even eliminated, at least for some human beings, by a process called "learning". This possibility may even be compatible with those who find the idea of a "learning organization" intriguing and valuable, even if they do not choose to pay any attention to the distinction between situations that are ordinary and situations described as complex, and to the implications thereof for methodology!
Harold D. Lasswell (1902-1978) was a political scientist. He was one of the foremost authorities in his field. He taught law and political science at the University of Chciago, Yale, and elsewhere. Author of many books, he also originated key ideas relating to the effective development and public understanding of public policy, most of which remain available for exploitation in the public domain.
Ralph Barton Perry (1876-1957) was an American philosopher, educator, and author. A professor of philosophy at Harvard University, he was a Pulitzer prize winner for his biography of his former teacher, William James. A staunch defender of freedom in academia, Perry also devoted considerable effort to illuminating desirable aims of education.
A graduate of Oxford, Vickers was knighted for his service in World War II. Educated as a solicitor, he held many high posts in England during that War. Author of several key books, he dealt insightfully with the institutional framework of society, and was a counselor to a number of respected scholars.
A strong scholar, manager, and leader, his interest in the human aspects of organizational behavior, and in the application of the highest quality of science in human affairs were unshakeable.
A graduate of the Sorbonne, Foucault worked as a writer and teacher of philosophy and French literature. He was chairman of the history of systems of thought at the College de France in the last fourteen years of his life.
His beliefs concerning knowledge have been described as follows: "Foucault believes that our own current intellectual life and systems of scientific thought are built on assumptions profoundly taken for granted and normally not exposed to conscious inspection, and yet likely in time...to be discarded." And, from another writer, "Foucault is one of the few social analysts whose work regularly unfits readers to continue looking at things or ideas or institutions in the same way...His archaeologies uncover architectures that make sensible order of what previously seemed sloppiness or incompetence or foolishness or malevolence."
The American philosopher, Peter Caws, wrote: "Foucault, turning over words with immense scholarship and erudition, reconstructs a group of intellectual activities collectively called in French the sciences humaines".
Critics of Foucault find him obscure, and others try to put him in the group of "deconstructionists", recently blasted in the Washington Post by George Will. But the fact is that Foucault is not a deconstructionist, but rather a "reconstructionist" or (in lay terms) he advocates the redesign of knowledge, to expand its comprehensiveness, and to correct its shallowness. His book The Archaeology of Knowledge, can be thought of as a call to upgrade knowledge in the liberal arts and sciences: a call which, so far, few of the appropriate people seem to be prepared to take up.
A mathematician, Harary received his doctorate at the University of California, Berkeley. Author of at least 6 books and over 500 publications, Harary is regarded as a specialist in graph theory, among the top group in the world in that field.
Spending most of his academic career at the University of Michigan, Harary was the lead author of a book titled Structural Modeling: The Theory of Directed Graphs, with Norman and Cartwright, social scientists affiliated with the University of Michigan Institute for Social Research. It is this book, and this book alone, that warrants the inclusion of Harary in the present document.
In this book, Harary spans several branches of mathematics to present the analytical basis for the mathematics of modeling, the mathematics of structure.
Taking that mathematics as a basis, John Warfield augmented it with the corresponding synthesis scheme, so that where Harary's approach analyzes structural models and shows how they are presentable symbolically; Warfield's approach offers the algorithmic basis for model construction; i.e., for construction of structural models that show patterns of understanding.
The subsequently-developed software, using Warfield's "Interpretive Structural Modeling process", basically applied Harary's fundamental mathematics and made it available to groups of people to work together in construction of high-quality models of situations found to be too complex for individuals acting alone to develop.
Born in India, of a British military father, De Morgan graduated from Cambridge University. He became Chair of mathematics at University College, London, at the age of 22.
He was the first president of the London Mathematical Society, and a prolific writer, contributing over 850 articles. His pupils included Todhunter, Routh, and Sylvester, all well known mathematicians.
He was the first logician to present a logic of relations. The extension of this idea was not adopted until, late in the 19th century, it reached the eyes of the Peirces at Harvard, where Charles Sanders Peirce lauded this work and extended it still further as part of his general archetectonic of science and human belief.
George Boole, inventor of Boolean algebra that underlies modern computational systems, acknowledged his debt to De Morgan in the preface to his first logical work, The Mathematical Analysis of Logic, published in 1847. In that same year, 1847, De Morgan published his foundational treatise on the logic of relations.
It is the logic of relations that underlies Harary's book, mentioned elsewhere in this section; and which underlies the Interpretive Structural Modeling process developed by Warfield.
De Morgan was almost certainly unknown to Michel Foucault, who did not know that De Morgan's work, as made more adaptable to practical applications with late 20th century computers, could provide precisely the infrastructural assistance required to do the knowledge reconstruction that Foucault so much desired.
A member of the Dominican order, Bochenski graduated from the University of Fribourg in 1930. He served as professor of philosophy, Dean of the Faculty of Arts, and rector. He was a visiting professor in the United States in the 1950s and 1960s at U. C. L. A., the University of Kansas, and Notre Dame University, where he was awarded the honorary L. L. D degree in 1966.
While known for many writings, his most in-depth work is undoubtedly his History of Formal Logic which, beginning with the early Greeks, brings the reader forward into the first half of the 20th century. It is in this work that the historical connections among various philosophers, spanning many centuries, can be seen.
It is from the overview insights into logic furnished by Bochenski that its uniqueness as an adjunct to human scholarship can be most tightly established.
Ross Ashby was one of the most revered developers of the concept of cybernetics. He completed his career at the University of Illinois, after beginning it in his native United Kingdom.
With many writings and contributions, he is known foremost for the Law of Requisite Variety, and the interpretations which this law lends to effective human thought and system design.
A graduate of Oxford, in economics, Kenneth Boulding became a U. S. citizen in 1948. President of many scholarly organizations, including the American Association for the Advancement of Science, Boulding was one of the small group that initiated the Society for General Systems Research.
He became known as brilliant scholar, with a strong humanist bent, and a deep and sympathetic awareness of human frailty--a view consistent with C. S. Peirce's image of "fallibility".
Widely beloved as a university teacher, Boulding spent time in many locations, leaving the mark of his good-humored thought. His contributions to systems thinking are characterized by his continuous aim to expand the scope of such thought, and to see how ideas thought in various disciplines to be unique to the discipline, had their counterparts in other disciplines. In this respect, he can be thought of as an advocate of productivity in academia, and some of his ideas in that regard have been factored into the design of the Great University.
A graduate of Yale, Gibbs received one of the first Ph D.'s ever granted in the United States. He spent a year each at the universities of Paris, Berlin, and Heidelberg, and while there established the foundation for his subsequent career.
Living about a block away from Yale University for most of the rest of his life, Gibbs was appointed professor of mathematical physics at Yale. During the first nine years, his written memoirs on thermodynamics provided an outstanding contribution to science. Unlike most physical scientists and engineers, Gibbs preferred the "niceties of geometrical reasoning" to analytical methods. Inventor of a railway car brake (which he patented) and a new kind of governor for steam engines, Gibbs nonetheless saw science first and foremost as his career. His biographer, Muriel Rukeyser, made it clear that the American scientific establishment of the time was almost entirely unable to comprehend his work, whose early publication came about through the recommendations of Clerk Maxwell at Cambridge University.
It is Gibbs' definition of "system" that was chosen by Warfield to reflect his approach to the development of a science of system design. Gibbs' definition is at odds with virtually every extant definition of "system", the latter depending almost entirely on nominalist or positivist philosophical beliefs.
With a part of the Yale campus named after Gibbs, many will not want to be reminded that Yale paid him no salary for the first decade on the faculty, and paid him 2/3 of what he was offered by Johns Hopkins, to keep him on the Yale campus.
The story is told that Gibbs was the only American mathematician-physical scientist of any interest to the European community. When a group of delegates arrived at Yale at the President's office and asked to be directed to Gibbs, the response was "Who is Gibbs?"
From the biographies of Gibbs and Peirce, it is easy to see that concepts of the highest quality tend to be ignored and to languish, in deference to the usual way of doing business.
After his graduation from the University of Königsberg, Hilbert eventually joined the faculty of mathematics there. A scholar of the works of Kronecker, Cantor, Minkowski, and other notable mathematicians, Hilbert contributed to many areas of mathematics.
In terms of the present document, Bochenski points out that Hilbert conceived the idea of "metalanguage", a concept that plays a foundational role in today's computer science, and one that formalized in language the idea of Leibniz that scientists would have to develop languages of their own, if they were going to be able to communicate effectively.