* * * * *

I devoted my Master's thesis to critically appraising the paradoxes of confirmation and the solutions they were offered. At the defense Yehuda Elkana asked me what working on it had taught me? If it taught me anything, I told him, it is that that was not the way to do philosophy of science, which, unlike the armchair analytical variety I was practicing, had to somehow relate to the realities of scientific development. But what bearing the “is”s of history could have on philosophy's “oughts,” I admitted, I had no idea. I decided to devote my PhD to answering that question, but to approach it historically. The initial plan was embarrassingly pretentious. It envisaged a work comprising six main chapters devoted to closely scrutinizing the histories of science written by Auguste Comte, William Whewell, Ernst Mach, Émile Meyerson, Pierre Duhem, and (my hero at the time) Alfred North Whitehead to determine the extent to which their historiographies lived up to their philosophies. Within weeks it became clear that putting the question to Whewell's case would alone fully furnish a PhD and more. Within a few more weeks, it became equally clear that the historical question of discerning the problems Whewell's works had been grappling with had come to interest me far more than what his undertaking had to offer toward any grappling with my own. By the time the dissertation was submitted in the mid-1980s, I had forgotten about my initial question altogether. And in more ways than one, the rest was history.

In this regard, my initial turn to history consisted in a turn away from philosophy, but in another sense it did not. For by identifying the historical task of reading Whewell's works with that of discerning the questions he had meant them to answer (as opposed, say, to discerning his influences), I was wearing my Collingwoodian and Popperian biases on my sleeve. I even gave the approach a sexy name: “erotetic contextualism” (Fisch Reference Fisch1991a, §1.2).Footnote ² Indeed, the extent to which my initial questions regarding the possible bearing of history of science on its philosophy had been wholly surpassed, was nicely (if unwittingly at the time) confirmed by the way I treated the history I was writing as unreflectively applied philosophy. My philosophy wholly and dogmatically informed my history, which, in turn, was not expected to teach it anything new – an approach cruder than even Lakatos's! But over the next fifteen years or so this was to change – slowly, yet dramatically.

* * * * *

The last of the series of historical works that I devoted during the 1980s and 1990s to early nineteenth-century British science and mathematics (see especially Fisch Reference Fisch1985a; Reference Fisch1987; Reference Fisch1988; Reference Fisch1991a; Reference Fisch1991b; Reference Fisch1991c; Reference Fisch1994c) was a paper published in 1999 on the making of George Peacock's 1830 Treatise on Algebra that described the work as one of “creative indecision,” which, despite ultimately convincing no one, had played a crucially important role in the transformation of British mathematics during the 1830s and 40s (Fisch Reference Fisch1999).Footnote ³ Writing the paper left me somewhat baffled and unsure as to the broader historiographical significance of all my historical writing so far. Knowingly oblivious to the hold the paradigms or conceptual frameworks to which the heroes of my stories were committed might have had on their thinking, I analyzed the works in party-line Popperian and Collingwoodian fashion, as imaginative attempts, constrained only by the limits of their authors’ creativity, to solve the problems that I believed they had believed they were facing.

The history I wrote focused on individuals – on their deliberations, on what they deemed wrong, and on their attempts, sustained or aborted, to put right. I did so not only because I was less interested and less versed in writing the history of institutions or collectives. I did so in principle, 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 by means of which, individual practitioners plied their trade. And I still do. Such collectivities obviously determine an agent's setting and point of departure. They determine the language he speaks, the training he receives, as well as his standing and professional prospects at any given moment. But I firmly believed, and still do, that as the exclusive produce of human endeavor, it is individual human endeavor that should ultimately explain the being and becoming of such collectives, rather than the other way round.

The individuals I studied – Whewell, John Herschel, Charles Babbage, Peacock, William Rowan Hamilton, James Clerk 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 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 those with which they chose to replace them. I was not interested in justifying their moves, only in understanding their reasons for making them.Footnote ⁴

The difficulty that began to present itself in the course of writing the Peacock paper, and to which I have devoted much of my writing and teaching since, is that although the difference between actions willed and reasoned, and moves involuntarily prompted or caused, is categorical,Footnote ⁵ the distinction I was implicitly advocating between them was turning out to be far less clear-cut than I had assumed. Although I purported to assess the work and thinking of those I studied in the light of their norms and standards,Footnote ⁶ I had, as noted, little appreciation and no understanding at all of the nature of the formative hold their norms and standards had on their very capacity to reflect and reason. As a result, I failed to even grasp the difficulties involved in accounting for the very possibility of normatively criticizing and modifying a normative outlook from within – a problem to which my avidly Popperian studies of the 1990s remained, as did Popper himself (see esp. Popper Reference Popper and Freeman1976),Footnote ⁷ blissfully oblivious, despite the fact that the practitioners I was studying were doing exactly that!

By the time the Peacock paper was underway, I had begun to realize that the deliberations on the nature of science and mathematics of Whewell, Peacock, Herschel, and Hamilton were not easily accommodated by the simple Popperian format of trial-and-error. It was, as I shall explain shortly, a far more tortured and convoluted process that ran up against the very basics of their respective worldviews, and hence of their deepest convictions. What I was beginning to realize was that one's capacity for self-criticism was in principle considerably more limited than Popper's philosophy had led me to expect. It was a realization that 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.

Taking their cue from Collingwood's “logic of question and answer” (Collingwood Reference Collingwood1939, chap. 5), my historical studies sought initially to retrace the erotetic trajectory of self-questioning by which their heroes arrived, via various intermediate stations, at their final positions. This is never an easy task, but in this case it proved especially tricky since none of them left any record of their pondering. The works they published, even when narrated in the first-person, hardly ever adopted an autobiographical, or even a reflective stance. They presented and argued for their conclusions but refrained from attempting to recapture the process by which those conclusions were reached. None of them kept diaries or log books of the kind that could 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 evolved, I was forced to work backwards: starting from the works they eventually produced and working my way 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 as to the problems to which they might have been responding, and the questions they might have been asking themselves, as they had made their way in the opposite direction toward the various culmination points 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 such foreknowledge as our subjects could not have had; to recapture the essential open-endedness of their state of relative innocence as to the eventual outcome of their efforts. All of which, as Collingwood urged repeatedly, requires an 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 archeological examples and analogies,Footnote ⁸ lacking any direct evidence of my subjects’ deliberations, to ignore the conclusions I knew they would eventually reach in favor of attending empathetically to their ponderings was simply not an option. Although I agreed with Collingwood's approach wholeheartedly, the question I constantly found myself having to ask in these essays ran counter to the natural, lived, forward-looking direction of erotetic reasoning it purported to describe. 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 – which is a different matter entirely! The former is the kind of question those I was studying were constantly asking themselves; the latter was one they would never have asked themselves. Reasoning from given question to possible answer is to attempt to emulate their first-person reasoning. But to reason back, as I was, from the answers they proposed to the possible question they might have been asking themselves, is to adopt a decidedly external, third-person outsider's view of one's subjects’ reasoning, that ran in the opposite direction to the deliberative path they were following.

Trying to follow my subjects’ forward looking deliberations by keeping my eyes fixed to the rear-view mirror, as it were, certainly ran counter to the narrative sequence I sought to recreate, but this kind of reverse engineering did have one important advantage. Backtracking from product to process prompted me to consider my subjects’ finished works as emerging possibilities rather than as confidently presented final conclusions; to imagine how they might have seemed to their author just prior to their final endorsement. And in doing so, my attention was naturally drawn less to the details, than to the more general form and structure of these works. It was then that I became aware of the odd yet telling feature that they shared, on which my current writing now focuses. I am referring to the way in which 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, William Rowan Hamilton, celebrated Irish physicist and mathematician, insisted 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. To the former, the subjective, theoretical science of dynamics, he writes, “I account 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.” Rather, he described the “wondrous convergence” of the two sciences as owing to “some mysterious union” residing in “the Divine Mind.”Footnote ⁹

Three years earlier, George Peacock's seminal Treatise on Algebra published in 1830 proposed splitting modern algebra into two awkwardly related, yet quite separate algebras, pertaining, as in Hamilton, to very different spheres of mathematical activity: “Arithmetical algebra,” on the one hand, conceived of as the science of number and its relations duly devoid of such paradoxical notions as negative and imaginary quantities, and “symbolical algebra” on the other, 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, no simple subsuming of the two was assumed. Peacock explicitly envisaged symbolical algebra not as a generalization of, or abstraction from its arithmetical counterpart, nor did he view the latter as a mere application of the former to numbers. He conceived of them as the fruits of independent, yet curiously supplementary mathematical efforts, attributing to arithmetical algebra the role of “science of suggestion” for its symbolic counterpart, and insisting that the provable formulae (equivalent forms) of each be preserved as valid formulae of the other.

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 rudely, 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 (Whewell Reference Whewell1834; Reference Whewell1847, vol. I, chap. 2).

To the 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 when taken together, strongly imply a similar, and even cruder split (though never explicitly presented as such) segregating the factual and the formal components of mathematical physics to near-incongruous spheres of intellectual pursuit. The upshot was a rude conjoining of a thoroughly Baconian, or Laplacian conception of “natural philosophy” (i.e. realist, causal, explanatory) with a wholly formal Lagrangean conception of its mathematization (i.e. non-realist, instrumental, non-explanatory).

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 to have then 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 forced to grope creatively toward some kind of new. 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 in both optics and dynamics prior to turning his full attention to quaternions in the mid-1830s in acknowledged critical response to the formalist side of Peacock's two-fold algebra.

Inventively undecided; creatively split; tortured, yet confident; reactionary, yet avant-garde – curiously, my own descriptions of the works I was studying were beginning to resemble their own strained, hybrid content! It was as if I lacked the terminology to properly assess them. Indeed, the Popperian-Collingwoodian vocabulary to which I was committed failed to do them justice. Rational agents, it implied, were expected to face up to the problems they encountered and to boldly address and attempt to solve them. An inability to fully relinquish past commitment in favor of provably less problematic options, it firmly implied, is a form of weakness, a lapse of fully-fledged 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 so clearly displayed.

And yet the more I studied them and their authors, the more impressed I became with the dedication, the intensity of engagement, and the sheer novelty, depth, and brilliance they displayed. But my evaluative vocabulary held me back.

What was even more confusing was trying to do justice to their historical role – which again seemed paradoxically two-sided, and at the same time quite incomprehensible from a Popperian or Collingwoodian perspective. On the one hand, despite their authors’ status and standing, and despite being widely known and discussed, all of them swiftly vanished from the historical record without leaving a visible trace – at least in the accepted sense of the term. The hybrid depictions of science and mathematics proposed by the works of Whewell, Peacock, Hamilton, and Herschel, all failed to generate a following. One would be hard-pressed to name a single bona fide Whewellian philosopher of science,Footnote ¹⁰ a Peacockian algebraist or philosopher of mathematics,Footnote ¹¹ or anything like an Herschelian or Hamiltonian philosophical school of mathematical physics. And yet, the four maintained close contact, and to an extent developed their different hybrid positions in response to one another, while commanding each a major presence, and playing a centrally important role during the middle years of the radical reform of British science and mathematics during the first half of the century.Footnote ¹²

Here again I found myself obliged to talk in near-oxymoronic terms of the crucially important role these works played, despite their seemingly total lack of impact, of how they failed to convince anyone, yet were centrally formative in the type of reaction their works produced. I had obviously come up against a curiously complex historical moment that puzzlingly defied the philosophical and historiographical sensibilities with which I had confidently purported to approach it. It was without doubt an extraordinarily pregnant moment in the course of a major turning point in the life of British science and mathematics, but the problems it raised did not strike me even then as uniquely anomalous in any way. They owed, I felt, not to something out of the ordinary about the objects of my researches, so much as to a significant failing in the way I was approaching them – which, I was beginning to understand, had to be seriously rethought. The process took the best of a decade, and required going back to philosophical basics.

* * *

The problem is a general one, by no means confined, or even specially related to science. It is also almost unanimously considered to be insurmountable. If one concedes “critical rationalism” as I did and still do – namely, viewing knowingly criticizing A as a necessary condition for acting rationally on, or with respect to A – and if one further realizes, as I then did not, but do now, that the very articulation of a problem or shortcoming, let alone mounting an argument to prove its existence, constitutes a normative judgment, and that, therefore, in order to criticize anything, a set of relevant standards of propriety must already be in place, it follows that, since a functioning standard of propriety cannot deem itself inappropriate, the norms one utilizes in normative self-criticism are incapable of being subjected to such criticism. But if one is incapable of normatively criticizing one's own normative commitments (except for consistency, coherence, and clarity), how can one's normative commitments ever be said to have been modified or replaced rationally? Put differently, to modify or replace one's normative commitments rationally, is to do so for a reason. But the only viable normative reason an agent could have for modifying or replacing his normative framework is to have found it normatively wanting, but that, it would seem, is impossible!

If it is true that a normative framework cannot be normatively faulted by those whose framework it is, then, as far as science is concerned, we appear to be left with one of two choices. We can either follow Popperians in insisting on the potential rationality of all scientific endeavor by denying the very idea of framework dependency and framework replacement in science (e.g. Popper Reference Popper1994), or we can follow Carnap and Kuhn in insisting on framework dependency and framework replacement by excluding framework replacement from the realm of scientific reasoning. But we can't have it both ways. If practitioners are unable, in principle, to scientifically fault the frameworks constitutive of their scientific reasoning, then frameworks are either a fiction or must be deemed immune to scientific critique! Or so it seems.

Not unlike the heroes of my historical studies, I refused to make that choice and, working against the grain, sought the hybrid middle ground, which to the best of my knowledge no one had yet seriously tried, namely, to insist with Carnap, Kuhn, and Friedman on the strongest form of framework-, or paradigm-dependency in science, while retaining a firm commitment both to the possibility of rational framework transitions in science and to a firm identification of rationality and criticism late of Popper.Footnote ¹³ The ensuing work, The View from Within: Normativity and the Limits of Self-Criticism, purports to break the deadlock by giving the initial intrasubjective neo-Kantian setting an essentially intersubjective neo-Hegelian twist. It argues in a word that although, as we have seen, one can never be convinced by normative criticism leveled against one's very heartfelt commitments, exposure to the articulated challenge of trusted and sincere critics is nonetheless capable of subverting one's initial commitments. By virtue of its particular structure, exposure to sincere normative criticism, analyzed in the book in some detail, allows one to experience, if briefly, how one is normatively portrayed by others. Not unlike a disturbing playback, seeing oneself momentarily as others do, can at times destabilize a conviction's wholeheartedness to the point of ambivalence. Once ambivalated, the norms in question lose their volitional grounding and normative hold, and demand, rationally, to be reassessed. In this way, I argue, one may be rationally motivated by argument (though never directly convinced) to modify or replace one's norms. The point being that the degree of self-estrangement and self-alienation it requires, demands a potentially “ambivalating” echo-chamber of intersubjective trusted normative criticism that far transcends the possible boundaries of even the keenest intrasubjective, self-reflection.

While The View from Within explores and expounds upon this idea philosophically, my current work applies it to the historiography of scientific paradigm shifts – first in general, but for the most part to revisit the middle and crucial years of “the second scientific revolution” in British science by retelling some of the stories I had told in the past.Footnote ¹⁴ It proposes to analyze paradigm shifts as two-stage processes in which practitioners of voice and standing are first “ambivalated” by exposure to criticism leveled from without, and later (inadvertently) succeed in promulgating their newfound indecision within their communities by means of a particular form of published work.

To account for the first stage, I extend and rework Peter Galison's novel notion of the scientific “trading zone” – the “locales” of professional engagement outside one's home community, as when bidding for financial support, “trading” with neighbor disciplines for techniques or instruments, offering scientific opinion, engaging students, the media, the public, or the historians, sociologists and philosophers of one's fields. In such settings, I argue (going a major step beyond Galison) one is frequently exposed to the friendly and trusted bemused questioning of genuinely curious professionals, on whose thinking the framework constitutive of one's own thinking may have far less of a grip. Trading abroad, practitioners are, therefore, often required to articulate and defend such basics of their field that are passed over in silent agreement back home. Here, I argue, one finds the destabilizing and “ambivalating” potential of a science's external critique.

The second stage is achieved when the doubts and indecision of such individuals are found to inform their creative efforts to overcome them. Such efforts, I argue by the extended examples of my former historical work, typically take the form of uneasily split, hybrid attempts to re-represent their field's basic assumptions by retaining some of the old, while groping imaginatively toward new possibilities. When analyzed prospectively, such works can be seen to represent anxious, yet highly creative departures from heartfelt commitment capable of motivating others to seek cleaner and more radical breaks with the old. Classic examples are Tycho's planetary theory, Galileo's analysis of projectile motion, Poincare's geometrical conventionalism, all of which unstably straddled the old and the new, unwittingly preserving, and therefore propagating, the keen ambivalence that begot them, and in doing so, prompting others to take a firmer stand. However, the main portion of my new project is devoted to applying these historiographical tools to the four intertwined hybrid accounts of science and mathematics produced during the 1830s by the four British thinkers mentioned above whose indecision emerges, in the light of my recent work, as the crucial driving force behind the major transition they can be shown to have jointly straddled.

* * * * *

Thinking back on twenty-five years of oscillating between history and philosophy of science, made possible by this unusual issue of Science in Context, I now realize just how much the answer I finally arrived at to Elkana's original question recapitulates the gradual and painful process by which it was arrived at. History of science, I now realize, has served as a major transformative critical trading zone for my philosophy and vice–versa!Footnote ¹⁵ My excursions into the history of science resulted in a profound philosophical ambivalence toward my Popperian-Collingwoodian point of departure, which resulted in turn in the neo-Hegelian hybrid straddling of Popperian and neo-Kantian themes that grounds The View from Within, which is now being applied back to history and comes full circle.

Can this count as a viable answer to how and why I write history of science? Probably not. I wrote history of science the way I did at each juncture for the philosophical reasons I had at the time. These have changed, and with them both the “how” and the “why” of my historical work. What hasn't changed is the fact that in writing history I remain as philosophically motivated and as philosophically wary as I was, but where this might take me next, I cannot say.