Creatively Undecided: Toward a History and Philosophy of Scientific Agency
304
Creatively Undecided: Toward a History and Philosophy of Scientific Agency
304Paperback
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Product Details
| ISBN-13: | 9780226514512 |
|---|---|
| Publisher: | University of Chicago Press |
| Publication date: | 11/27/2017 |
| Pages: | 304 |
| Product dimensions: | 6.00(w) x 8.90(h) x 0.70(d) |
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CHAPTER 1
Two Beginnings: An Overture in the First Person
HISTORY AND ITS POPPERIAN PROBLEMS
In 1999 I published a bulky essay on the making of George Peacock's 1830 Treatise on Algebra, which described it as a work of "creative indecision" that convinced no one, yet played a crucially important role in the transformation of British mathematics during the 1830s and 1840s. The Peacock paper was the last of a series of historical, interpretive works I had devoted during the 1980s and 1990s to early nineteenth-century British science and mathematics, and it left me somewhat baffled and unsure as to their broader historiographical significance. I was then still firmly committed to a Popperian approach to the growth of knowledge, which I applied with a relish to the stories I was telling, and which at one point I even attempted to further elaborate philosophically. Knowingly oblivious to the hold that the paradigms or conceptual frameworks to which the heroes of my stories were committed might have had on their thinking, I analyzed their works party-line Popper as imaginative attempts to solve the problems I believed they believed they were facing, constrained only by the limits of their creativity.
I focused on individuals — on their deliberations, on what they deemed wrong, and on their attempts, sustained or aborted, to put matters right — because I believed in the explanatory primacy of individual agency with respect to the knowledge claims they produced as well as to the communities, languages, institutions, and other collectivities in and with which they plied their trade. Such collectivities obviously determine an agent's setting, idiom, and point of departure, but I firmly believed that as the exclusive product of human endeavor, it is human endeavor that should ultimately explain their being and becoming, rather than the other way round. The individuals I studied — Whewell, Herschel, Babbage, Peacock, W. R. Hamilton, Maxwell, and others — all played major roles in dramatically changing the way the science and mathematics of their day was done and understood. All worked within and against the social, conceptual, normative, and institutional frameworks they were instrumental in building, modifying, or replacing. My interest lay in their rational impact — in exposing their reasons for adopting the perspectives they chose to adopt, for retaining the positions they chose to retain, for replacing those they chose to replace, and for entertaining those with which they chose to replace them. I was not interested in justifying their moves, only in understanding their own reasons for making them.
These essays thus tacitly premised an internal-external divide that differed significantly from Lakatos's notorious model. For Lakatos, the dividing line between a science's internal or rational component and its arational, external part ran between episodes in its history whose outcomes passed the test of what the historian considered to be the true method of science, and those that failed it. The rationality of scientific decision-making has nothing to do with the reasons or motivations that those who made the decisions had for making them, as long as what they actually achieved conforms retrospectively to the dictates of (the historian's pet) latter-day methodology. On a Lakatosian showing, rationality is not an evaluative category of act ing or of agency, but a category of outcomes or of moves, of the products of acting, of the produce of agency judged by hindsight. A Lakatosian historian defines the internal-cum-rational component of a science in accord with what he, the historian, deems to have been the right decision to make and the appropriate move to make at the time. My work adopted a very different approach, which located the rational in what the actors of old, who made the decisions and made the moves it studied, deemed prospectively to be the right and appropriate thing for them to do. If Lakatos judges the rationality of others by the measure of his own norms and standards of approval, I attempted to judge them by the measure of the norms and standards of approval with which I considered them to have reasoned. The inner, rational component of scientific and meta-scientific endeavor was, and remains for me, the part deliberated and pursued prospectively and self-consciously by the actors in question, as opposed to the moves they made unthinkingly. Whether or not their actions won my own approval was and remains, pace Lakatos, quite beside the point.
The difficulty that began to present itself while I was writing the Peacock paper, and to which I have since devoted much of my writing and teaching, is that although the difference between willed and reasoned, and hence rational action, on the one hand, and caused, involuntary, and hence a-rational response, on the other, is categorical, the distinction I was implicitly advocating between them turned out to be far less clear than I had assumed. Although I was assessing the work and thinking of those I studied in the light of their norms and standards, I had at the time little appreciation and no understanding of the nature of the formative hold a person's normative outlook has on his or her capacity to reflect and reason. I failed to grasp the difficulty involved in accounting for the possibility of normatively criticizing and modifying a normative outlook from within — a problem from which the likes of Lakatos exempt themselves, and to which my avidly Popperian studies of the 1990s remained blissfully oblivious, even though the practitioners I was studying were doing exactly that!
By the time the Peacock paper was under way, I had begun to realize that Whewell's, Peacock's, Herschel's, and Hamilton's deliberations on the nature of science and mathematics were not easily accommodated by the simple processes of trial and error my Popperian background led me to expect. It was a far more tortured and convoluted process, one that ran up against the very basics of their respective worldviews, and hence of their deepest commitments. This realization was initially prompted, not by philosophical argument, but by the particular difficulties I encountered in narrating the particular stories I was trying to tell. Philosophical arguments came later and with considerable force, but they might not have had the same transformative effect on my thinking had my initial Popperian leanings not been first challenged by more purely historiographical issues — a point that nicely illustrates the philosophical positions I would eventually reach that constitute the second beginning of the present project. But I am getting ahead of myself.
In addition to the influence of Popper, I was impressed by Collingwood's "logic of question and answer." My historical studies sought to retrace the erotetic trajectory of self-questioning by which their several heroes arrived, via various intermediate positions, at their final positions. This is never an easy task, but in my case it proved especially tricky, since none of them left any record of their actual pondering. The works they published, even when narrated in the first person, hardly ever adopted an autobiographical stance or even a reflective tone. They presented and argued for their conclusions rather than recapitulating the process by which they were reached. None of them kept diaries or log books of the kind that might have helped, and in their private correspondence, though typically voluminous, they rarely pondered aloud. So although my aim was to produce a forward-looking, prospective account of how their thinking developed, I was forced to work backward: Starting from the works they eventually published, working back through whatever unpublished drafts, notebooks, and letters I could lay hands on to their initial points of departure, speculating retrospectively as best I could about the problems to which they might have been responding and the questions they might have been asking themselves, as they made their way prospectively toward the culmination point of their efforts.
All historical work is to some extent marred by hindsight. Historians almost always know in advance the outcomes of the processes they are studying, and are almost always acquainted with the works eventually produced by the people whose deliberations they seek to reconstruct. Writing good history requires imaginatively ignoring any foreknowledge our subjects could not have had, attempting to recapture the essential open-endedness of their state of relative innocence with respect to the eventual outcomes of their efforts. All of which, as Collingwood urged repeatedly, requires the empathetic ability and willingness to see the world through their eyes as they pondered and deliberated how best to contend with the difficulties they believed they faced, still unsure of where exactly they were heading.
But, as in Collingwood's own archaeological examples, in the absence of any direct evidence of my subjects' deliberations, ignoring the conclusions I knew they would eventually reach in favor of attending empathetically to their ponderings was simply not an option. Although I wholeheartedly conceded Collingwood's approach, the question I constantly found myself having to ask in these essays ran counter to the natural, lived, prospective direction of erotetic reasoning it prescribed. Instead of asking at each juncture why the person I was studying chose to answer the questions he faced in the particular way he did, I was constantly forced to ask what could have been the questions he was facing that might have prompted him to so answer them — a different question entirely! The former is the kind of question those I was studying were asking themselves all the time; the latter was one they would never have asked themselves. Reasoning from given question to possible answer is to attempt to emulate their thinking. But to reason back, as I was doing, from given answer to possible question is to adopt a decidedly external, outsider's view of one's subjects' reasoning quite alien to the deliberative path they were following.
Trying to follow my subjects' forward-looking deliberations, with my eyes constantly fixed to the rear-view mirror, as it were, certainly ran counter to the narrative sequence I sought to re-create, but it did have one important advantage. Backtracking from product to process prompted me to read my subjects' finished works as considered emerging possibilities rather than as confidently presented final conclusions; to imagine how they might have seemed to their authors just before their final endorsement. And as I did so, my attention was naturally drawn less to the details than to the more general form and structure of those works. It was then that I became aware of the odd yet telling feature they all shared: These works, all written during the 1830s, insisted on describing science and mathematics by splitting them down the middle and presenting them as rather unstable, hybrid amalgamations of two quite separate and conflicting undertakings.
Thus, in 1833, we find William Rowan Hamilton, celebrated Irish physicist and mathematician, insisting on there being two, rather than one "science of dynamics": "one subjective, a priori, metaphysical, deducible from meditation on our ideas of Power, Space, Time; the other objective, a posteriori, physical, discoverable by observation" — a view he was careful to distinguish from empiricist, Kantian, and what would later be dubbed instrumentalist accounts of the relation between the two. Of the former — the subjective, theoretical science of dynamics — he writes, "I account [it] indeed higher in dignity; but do not consider it as including the other, or as adequate ground to us for the expectation of any one appearance." Hamilton viewed the "wondrous convergence" of the two sciences as owing to "some mysterious union" residing in "the Divine Mind." Three years earlier, George Peacock's seminal Treatise on Algebra of 1830 had proposed splitting modern algebra into two awkwardly related, yet quite separate algebras, pertaining, as in Hamilton, to very different spheres of mathematical activity: on the one hand, "arithmetical algebra", conceived of as the science of number and its relations, duly devoid of such paradoxical notions as negative and imaginary quantities; on the other, "symbolical algebra," perceived as a wholly formal calculus of unconstrained symbols and operations, in which negatives and imaginaries and much more could find a natural place. Here also, as in Hamilton's case, no simple subsuming of the two was assumed. Peacock explicitly envisaged symbolical algebra not as a generalization of its arithmetical counterpart, nor did he view the latter as a mere application of the former to numbers. Peacock conceived of the two, as we shall see in some detail in due course, as the fruits of independent, yet curiously supplementary mathematical efforts.
In his extensive studies of the sciences conducted throughout the decade, William Whewell, Cambridge polymath and the leading historian and philosopher of science of his day, insisted, similarly to Hamilton though less crudely, and with considerably more philosophical finesse, that each of the "inductive sciences" comprised two integrated, mutually cultivated, yet antithetical components, arrived at by means of a two-pronged methodology geared to the attainment of two quite different notions of truth. The term antithetical is his. "The Fundamental Antithesis of Philosophy" is the title of the essay he first published in 1844 and later incorporated into the 1847 second edition of the Philosophy, in which the not-quite-Kantian epistemology grounding that work is set forth systematically.
And to these explicit and acknowledged splittings presented in the works of Whewell, Hamilton, and Peacock, one should add John Herschel's meticulously compartmentalized writings on natural philosophy and mathematics, which, taken together, strongly imply a similar and even ruder split (though never explicitly presented as such) that segregated the factual and the formal components of mathematical physics to near-incongruous spheres of intellectual pursuit.
What was one to make of the fact that during the crucially formative years of their second coming of age, British science and mathematics were deemed insusceptible to unitary description by some of their keenest practitioners — a tendency that seems to have flourished briefly and noticeably in England during the 1830s and early 1840s, and then to have vanished almost as abruptly as it appeared? This is the larger question that gradually emerged from my historical work. All the dualisms in question were to some important extent strained and inherently unstable. Roughly speaking, one side of each of them pertained to or at least built upon a set of commitments from which its author originally set forth, while the other represented new and radically diverging possibilities.
All of this strongly suggested to me that, as innovative as they were, all these works bore the distinct mark of the kind of irresolvable inner struggle capable of yielding no more than a shaky compromise. They struck me more and more as plagued by profound, yet inventive indecision — as ingenious attempts to hold on to the old while being forced to grope creatively toward new options. But there was nothing fleeting or hesitant about them. The accounts of algebra and inductive science proposed respectively by Peacock and Whewell, like that implied by Herschel, represented serious, confident and detailed undertakings that took their authors years, if not decades, to develop, articulate, and refine. Hamilton never made public the explicit, twofold vision of dynamics he described privately to Whewell, yet it, too, was long in the making and strongly implied by his influential work both in optics and dynamics before turning his full attention to quaternions in the mid-1830s (in acknowledged response to Peacock's algebra).
Inventively undecided; creatively split; tortured, yet confident; reactionary, yet avant-garde — curiously, my own account of the works I was studying was beginning to resemble their own strained, hybrid structure! It was as if I lacked the vocabulary to properly assess them. Indeed, the Popperian-Collingwoodian vocabulary to which I was committed failed to do justice to these works. Rational agents, it implied, were expected to face up to the problems they encountered, to boldly address and solve them. An inability to fully relinquish past commitment in favor of less problematic options, it firmly implied, is a form of weakness, a lapse of rationality. The ideal coupling of keen and impartial refutation with bold and creative conjecture leaves no room and has little patience for the apparent dithering these works displayed.
(Continues…)
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Table of Contents
IntroductionPart One: I (Orientations) 1. Two Beginnings: An Overture in the First Person
Part Two: We (Philosophers) 2. The Philosophical Framework 3. The Problem for Science 4. Toward a Narratology of Scientific Framework Transitions
Interlude The Story So Far and That to Come
Part Three: They (a History) 5. Peacock, Babbage, and the “Heresy of the Dots” 6. Creatively Undecided: The Making of Peacock’s Two Algebras 7. Peacock’s Impact
Acknowledgments Notes References Index