Any scientific worker with a reasonable amount of professional respect for him- or herself, and for his or her designated fields of scientific research - and, it might perhaps almost go without saying, for the wider conversation that constitutes the socio-cultural field of discourse and action we know as `science' - will, as current textual and interactional norms (or doxa) dictate, normally begin any investigatory journey into a new field of scientific or philosophical inquiry with some form of apology regarding the current sorry state of affairs of his or her own knowledge of the field in question. In this particular case I intend to present no exception to the operation of this system of socio-cultural norms, since the field of theoretical mathematics, with its associated discourse realms is one which I have never come to inhabit, even peripherally. This in spite of having enjoyed mathematics while I was at school, and having had many very pleasant and stimulating conversations with professional mathematicians over the years.
In this continuing spirit of scholarly openness and accountability, a second thing I would like to point out before I begin, is that most, if not all, of the thoughts and ideas developed in this article are by no means mine to begin with. As I suppose to be the case with most, if not all, forms of scientific and academic writing, most, if not all, of the ideas, perspectives and arguments that I present and discuss here, though fairly new for me, and thus often only quite sketchily thought through and developed, have - though I may not necessarily be aware of precisely where and when this happened - already been examined at length, and doubtless considerably more complexity and sophistication, by numerous, more mathematically competent authors than myself.
While in this quasi-confessional modus operandum, yet one more admission - or perhaps dedication is a better word - should be made. This is that a good deal of the day-to-day inspiration for the conceptualization and writing of this piece has been gleaned from my on-going membership in one of the more dynamic and positively critical philosophical communities alive on the Internet, namely the Peirce-l e-mail discussion list[1]. which since its inception in 1993, has been ably managed, maintained and developed by its creator Joseph Ransdell of the Department of Philosophy at Texas Tech University. At the time of writing, the Peirce Telecommunity[2], in which the Peirce-l discussion list plays an central role by fostering a lively, high-level day-to-day exchange of ideas, articles, and philosophical writing by, and relating to, the American philosopher, scientist, semiotician and logician, Charles Sanders Peirce, comprises around four hundred aficionados, students, and professional scholars of Peirce's thought from all over the world. The catholic interests of Peirce Telecommunity members range from the humanities, to the arts, social sciences, law, medicine, natural science, technology studies, computer science and engineering, to name but a few, making participation in this particular virtual community a constant learning experience of the broadest possible kind.
I am further indebted to the many insights and novel interpretations contained in a recent book by one of the members of the Peirce Telecommunity, Kelly Parker, entitled The Continuty of Peirce's Thought (Parker 1998). This, together with an earlier seminal work on the historical development of Peirce's philosophy by Murray G. Murphey (1993)[3], have been invaluable reference companions and guides, furthering considerably my own understandings of Peirce's notion of continuity while working on this present article. I have, where appropriate, freely adapted some central parts of Parker's exposition, especially regarding how Peirce let mathematical conceptions ground the development of his phenomenological categories for my own uses, since I believe Parker has given us a thorough and useful presentation of the fundamental interplay between Peirce's understandings of the mathematics of infinite series and other key concepts in his philosophical thought. Otherwise, as primary sources, I have drawn on Peirce's application for funding of 1902 to the Carnegie Institution, often referred to as MS L75[4]; plus a small published volume of Peirce's writings edited by Maurice Cohen in 1923 under the title Chance Love and Logic; Philosophical Essays, as well as a collection of William James' Oxford lectures from 1908 and 1909 entitled A Pluralistic Universe[5].
When all this has been said, and as I go on to recontextualise my way through the numerous ideas, notions and arguments that have threaded and woven into one another as this text has unfolded, I make no claim that any of these borrowings, reinterpretations and possible flashes of inspiration have any form of universal legitimacy or validity. They have, after all, been dug out of the layered and ofttimes muddied sediments of a dense historical flow, permeating through a vast range of scientific and philosophical discourses and texts, all trying in various ways to understand the relationship between mathematical, and other forms of representation of the physical and experiential continuity of the physical and social realities which we inhabit, and our own construals of this continuity. This does not, on the other hand, mean to say that they a priori should all be taken as having no intrinsic value. As Umberto Eco has pointed out[6], throughout the course of the history of science and philosophy, even some completely fallacious and even quite lunatic ideas, providing they have been worked out at some length, distributed, thought about and discussed by a range of other readers and writers with different experiences and backgrounds, have serendipitously evoked some positive effects, and in best-case scenarios, even contributed in quite profound ways to furthering the search for meaning and truth in science. Whether or not this will turn out to be the case with any of the ideas discussed here remains, of course, to be seen...
So, after all the preceding apologia, I would with this article, and expressly from the point of view of a non-mathematician[7], like to examine in some detail the notion of true continuity, as first conceived of by Charles Sanders Peirce in the late 1860's, and developed further in his mature work on cosmology and metaphysics from the beginning of the twentieth century until his death in 1914. I shall also attempt to position this philosophical principle for comprehending the relations between finite mind and infinite reality - the Real, as Peirce referred to it, with a view to its more general applicablity and scope as a metaphorical device to help us frame and understand the negotiation of meaning and with it, systems of textual and interactional norms in distributed virtual environments.
[1] For more information about how to join the Peirce-l discussion list, see the following web page:
http://members.door.net/arisbe/menu/people/peirce-l/peirce-l.htm
[2] The home page of the Peirce Telecommunity is to be found at http://members.door.net/arisbe/
[3] Published for the first time in 1961, and subsequently in a slightly revised edition in 1993 - see reference list.
[4] This naming refers to the system of categorization of the manuscript in question in the annotated catalogue of Peirce's writings archived at the Houghton Library, Harvard University, developed by R.S. Robin. See list of references. Page number and date may be included if necessary as in (MS 1, 1, 1902). Online versions of MS L75, edited by Joseph Ransdell may be found at http://members.door.net/arisbe/menu/library/bycsp/l75/intro/l75intro.htm
[5] Both these collections have recently been reissued in handy paperback format (1998 and 1996, respectively) in the Bison Books series from University of Nebraska Press - see the list of references below.
[6] See for instance Eco 1998, p. vii and also Eco 1997
[7] My own area of research bridges applied linguistics, semiotics and communication science, with a special interest in how systems of norms for oral and written scientific communication and exchange, develop and change over time as actors involved in such forms of communication increasingly migrate to distributed virtual environments.