PC: I do sometimes feel that science, the humanities and the arts have become rather "estranged" from one another these days, and I personally think that is unfortunate, but it seems to be a trend in our time for now.
PC: The kinds of constructive falsifiable predictions that are possible to make and test systematically in in the physical/ applied/technological sciences are of course far more difficult to make and test in the human sciences and the arts.
AS: In developing my PhD dissertation proposal, I make the point that the Humanities, primarily, and a significant (although not a major) constituency in the social sciences, seem to take it as a given that `science' (they always use scare quotes!) is somehow fundamentally `reductionist' because of its basis in measurable phenomena and the logic of computation that follows from inquiry into these.
AS: However, I sometimes wonder whether developments in mathematics over the last century or so have not encouraged the rather restricted public understanding of math as a sort of `theory of computation'? Peirce and his father both treated mathematics as the `science of necessary reasoning', of which computational matters constituted a rather restricted sub-field within the broader endeavour. Humanities academics (as quite distinct from Humanities scholars), especially, seem to have taken for granted the following line of reasoning:
THAT:
1) mathematics is an essentially computational enterprise, and
2) the `sciences' (I'm sort of caricaturing their way of arguing, here) either operate directly by measurement and calculation or by using technical devices that derive from such activity,
AND FURTHER, THAT
3) human experience involves measurable phenomena only to a small degree, the most fundamental sources of experience being essentially emotional and individual, hence escaping generalization through measurability;
IT NECESSARILY FOLLOW THAT
4) the Human Sciences MUST employ methods that engage with the personal and the emotional by developing interpretive techniques based on aesthetic, linguistic, and other Qualitative techniques.
AS: Although my summary of this reasoning may be rather cursory, even to the point of appearing to ridicule a tradition with a long provenance, I have heard this type of reasoning in arguments at academic meetings for decades. Hell, before I began studying Peirce, I used to use it myself (blush)! The fallacy, of course, is the even more radically reductionist view that math is principally (if not only) a science of computation. Listers may recall the release, some 3-4 years ago, of a book by Helen Verran, with the title *Mathematics and an African Culture*, which received a fair bit of exposure on commentary sites on the web; the value of the book, in my opinion, lies not in any of its reflections on how Africans approach the math curriculum in schools, but in how the whole enterprise could be taken on by an anthropologist who lacked both mathematical and logical training. Verran's experience of teaching math schoolteachers in West Africa was undertaken purely on the basis that because she came from a `western' society in which measurement and computation were part of the wallpaper (so to speak), she would `culturally' have been equipped to train math teachers from another kind of society.
AS: Needless to say, Verran failed to make any real dent in the situation, and what struck me in the book as being valuable to philosophers of science was the extremely narrow range of sources she consulted in making sense of the episode. She cites not a single mathematician or logician, relying, instead, on the History and Philosophy of Science programme at one or other university (I'm writing at a student LAN, and don't have the book handy to provide more detail; I guess I can't lug my entire library with me like one of the sages of Swift's Laputa!). What struck me was the reliance she placed on teaching teachers that the essence of mathematics is the interpretation of measures into calculations. Formal Logic she treats as `totalizing logic', and this term receives its due place in the book's Index.
AS: Now, I guess what I am getting at here is that the more one begins to grasp the history of both math and logic through the lens of Peirce's undoubted mastery of both (however idiosyncratic some of his inferences from history may appear to some), the more one should be led to take a wider view of both. As the `science of necessary reasoning', the discipline (as in self-control) required for mathematical inquiry seems to me to indicate that there should be no reason why one can't undertake the study of the diagrammatic forms of necessary reasoning about human experience in a non-computational way. Peirce treats the foundations of mathematics as a form of relational reasoning (which, I am led to understand, runs counter to the modern mathematical tradition; I won't debate that because I am no mathematician, but am never the less fascinated by the potential arcaneness of the topic). At 3.562 he essays an accessible account of this relational foundation (the CP source consists of material left out of an article in an educational journal of 1898), and anybody with some familiarity of anthropological field methods will immediately recognize a relation that lies at the core of ALL possible experience: the relation of sequence. Surely there can be no continuity in human affairs, the basis upon which one could say we make all those judgements and inferences we call `experience', without a sequence of generations, which Peirce very accessibly shows has proprties that are quite mathematical.
AS: I won't take this further for now, because I suspect I'm going to start blathering on without getting all my ducks in a row first. But I guess that what I wanted to suggest to Patrick and the List is that the "
trend in our time" need not be accepted as fatalistically as all that. It does, after all, represent perhaps 100-150 years' of debate in a tradition going back maybe 2500 years or more (I mean: how long ago did the distinction between naturwissenschaften and geisteswissenchaften enter the conversational lexicon of academia?). Maybe I'm overly optimistic, but surely it won't take that long for the fashion to fade away?Cheers
Arnold Shepperson
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