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Chapter Six

Mathematics, Experiment, and the Ends of Scientific Practice

© Jeff Kochan, CC BY 4.0 http://dx.doi.org/10.11647/OBP.0129.06

1. Introduction

In Chapter Five, we familiarised ourselves with Heidegger’s concept of mathēsis. This concept lies at the heart of his attempt to understand the emergence of early-modern science in terms of mathematisation. In particular, mathēsis — as a kind of learning or studying wherein we learn what we, in a general and indeterminate way, already know — is meant to capture the mathematisation of the pre-modern Aristotelian notion of final cause. As we saw, Heidegger grounds his analysis in our experience of the thing as ready-to-hand within a work-world, that is, as something with which we are at work. According to Heidegger, such a thing has an end-directedness. When we work with (rather than against) it, we let it be what it is in its directedness towards some end; we let it, so far as is possible, fulfill that end.

I suggested that this end is the final cause of the thing, that for the sake of which we let the thing, in the course of working with it, be what it is. Heidegger argues that, in the case of early-modern scientific work, the end of the thing is a ground plan, a basic blueprint. As the final cause of the thing, this basic blueprint provides the measure against which our work with the thing makes sense. It guides our judgement about what is, and what is not, relevant as we work with the thing, and thus also our basic understanding of the thingness of the thing.

According to Heidegger, the measure given by the ground plan applies to the scientific thing as such. All potential scientific things will be circumscribed within the experiential realm laid out according to this measure. This circumscription forms the basis of mathematisation. The totality of end-directednesses within this realm — and thus also the ends of the corresponding scientific practices — becomes consolidated under one uniform measure — a single, final end. Hence, the scientific thing is what it is insofar as it conforms to this measure. This conformity is not, however, a strict determination. Recall that those things which the ground plan renders knowable are initially known in an only general and indeterminate way. Through mathēsis, this knowledge may then be developed into something more specific and determinate, and this determination may take a number of different shapes. All of these shapes will, however, still share the same general form. For example, individual plants and animals may refer to two different categories — the plant-like and the animal-like — but those two categories, in turn, refer to a single, more general category — the thing-like. Similarly, we may refer to things either in quantitative or operational terms, but we must first be able to refer to them as things. Hence, even though all scientific things conform to the same general measure, they are nevertheless amenable to specification and determination in a variety of different ways.

As a consequence, mathēsis, as the mathematical projection of the thingness of things, as a basic projective structure in the subjectivity of the subject, served to facilitate the influx of both numerical and instrumental practices into early-modern natural philosophy. By allowing for the consolidation of all potentially scientific things under one general measure, mathēsis expanded the range of application for concrete mathematical techniques. If a thing could be drawn within the scope of scientific experience, then one could also quantify it. Mathēsis likewise enabled and expanded the range of application for concrete instrumental techniques. Hence, scientific things came to be increasingly viewed as a legitimate subject matter for artful manipulation. Quantification and manipulation are thus two different possibilities for specifying the uniform thingness of the scientific thing. Thus, as was claimed at the close of Chapter Five, Heidegger’s introduction of mathēsis, as a central and collective existential impulse behind the rise of early-modern science, charts a middle course between the historiographic Scylla and Charybdis of mathematics and experiment.

This is not so much a rejection as it is a resolution of the historical difference between what Thomas Kuhn identified as mathematical and experimental traditions in the physical sciences.1 Each tradition represents a different way of specifying and determining the same general and indeterminate knowledge of things. Kuhn’s traditions may thus be better described as sub-traditions within a broader tradition in which scientific thinking is guided by a uniform measure against which scientific things are experienced as intelligible. The shared root of these two traditions in mathematical projection furthermore helps to explain why these two traditions could eventually come together, especially, as Kuhn observes, in the case of nineteenth-century physics.2 Like the hills on either side of a valley, a bridge can be built to join them. However, Heidegger’s account reminds us that, despite the distance between them, each hill nevertheless forms one side of the same valley.

Peter Dear also challenges Kuhn’s distinction between mathematical and experimental practices, arguing for an ‘intimate relationship’ between the two, manifested most spectacularly in the late-seventeenth-century mathematico-experimental work of Isaac Newton.3 Yet, as we saw in Chapter Five, Dear locates the heart of experimental practice not, as Kuhn did, in the tradition represented by Robert Boyle’s mid-seventeenth-century experimental philosophy and the Royal Society of London (of which Boyle and then Newton served as President), but instead in the physical apparatuses and artful manipulations of the Aristotelian tradition of mixed mathematics. Indeed, Dear argues that ‘Boylean experimental philosophy was not the high road to modern experimentation; it was a detour.’4 Since Kuhn’s experimental tradition was precisely the Boylean one, it would seem that Dear has not really, after all, discovered an intimate relationship between the two sides of Kuhn’s distinction.

Steven Shapin, in contrast, preserves Kuhn’s distinction, and emphasises the importance of Boyle’s experimental philosophy as a forebear of the Newtonian programme.5 In fact, Shapin even strengthens Kuhn’s distinction by carefully outlining Boyle’s resolve in insulating experimental philosophy from techniques of mathematical demonstration. According to Shapin, Newton would later both adopt Boylean experimental practice and marry it to those same mathematical techniques.6 Yet, as we will see later in this chapter, although Boyle eschewed mathematical forms of persuasion, his experimental philosophy was not incompatible with mathēsis. Indeed, I will argue that Boylean experimental philosophy was, in the Heideggerian sense, strongly mathematical. Although Boyle rejected the concrete techniques of specification typical of mathematical practice, his understanding of the thingness of scientific things was nevertheless guided by a uniform measure. This uniform measure influenced, in turn, the way Boyle worked with, or manipulated, those things.

Shapin notes that Boyle’s suspicion of mathematics included the rejection of an ‘ontology’ contending that ‘physical qualities were uniform.’7 Instead, Boyle allowed that ‘substances like air and water varied in their physical properties from one locale to another and from one time to another.’8 In other words, Boyle rejected an ontology which insisted that the properties of token instances of the same type always be specified in the same way. But Boyle’s tolerance of context-dependency in the specification of physical properties is compatible with my claim that he was a mathematical philosopher in the Heideggerian sense. Boyle could have both understood the thingness of things according to a single uniform measure, and allowed that this thingness be specified and determined in different context-sensitive ways. What appears to have been important to him was the existence of a common ontological measure against which these localised differences could then be meaningfully judged.

In fact, Boyle’s belief that the ‘extension of experimental culture’ could be achieved through the imposition of ‘universal metrological standards’ may be viewed as a concrete manifestation of his tacit, or unconscious, commitment to a uniform metaphysical standard according to which experimental experience, in general, was to be organised.9 I use the term ‘unconscious’ in acknowledgement of Kuhn’s observation that, because seventeenth-century experimental philosophers like Boyle typically decried metaphysics and celebrated experiment, the interaction which did occur between the two was ‘usually unconscious.’10 Consequently, as an explicit concept by which to make sense of Boyle’s experimental practice, mathēsis figures into the present account as an analyst’s category rather than an actor’s category.

My method is thus not historicist in the currently prevailing sense, defined by Shapin as a ‘practice devoted to interpreting historical action in historical actors’ terms.’11 Nor is it presentist, in the sense of using present-day terms to understand the past. Mathēsis is not an established present-day term. It is a term originating in ancient Greek discourse, as well as the etymological source of the present-day words ‘mathematical’ and ‘mathematics.’ Heidegger returns to the ancient term in order to re-introduce a meaning which no longer forms an explicit part of present-day usage. Indeed, this ancient meaning also appears not to have figured in Boyle’s use of the term ‘Mathematicks.’ According to Shapin, especially in the context of the experimental philosophy, Boyle understood mathematics largely as a set of techniques for producing deductive certainty and numerical precision. By addressing the etymology of the word, Heidegger sought to recover a meaning which had become sedimented in subsequent culture, thus continuing to influence participants without figuring into their active vocabulary. Hence, mathēsis might be viewed as a tacit actor’s category, with its influence on Boylean experimental culture being inferred through its explicit effects on the linguistic and non-linguistic practices of that culture.

In what follows, I will argue that Boyle was, in the Heideggerian sense of mathēsis, a mathematical philosopher. My focus will be on Boyle’s dispute with the natural philosopher and mathematician Francis Line. A key point in this controversy was the legitimacy of Aristotelian final causes in experimental discourse. Boyle decried final causes as metaphysical, and condemned Line’s use of them. He commented, ‘I am not very forward to allow acting for ends to bodies inanimate, and consequently devoid of knowledge.’12 This implies an understanding of final causes which links them to sentience and knowledge. Yet, as we saw in Chapter Five, neither Aristotle’s nor Heidegger’s concept of final cause necessarily ascribes sentience or knowledge to the thing whose movements it was meant to help explain. Hence, I will argue, the term ‘final cause’ included a sedimented meaning, one which Boyle neglected in his dispute with Line. Furthermore, the dynamics of Boyle’s argument against Line reveal his own tacit, or unconscious, reliance on final causes in this sedimented and neglected sense.

This notion of final causes ties directly into mathēsis. Indeed, the final cause is the mathematical measure which allows us to make sense of the operations of both nature and art. Heidegger’s account of seventeenth-century science especially focuses on the mathematisation of Aristotelian final causes, that is, their consolidation under a single uniform measure. This account gives particular attention to the roles of Galileo and Newton. I will first review Heidegger’s brief discussion of these two figures, before teasing out the implications of his comments for our understanding of the early-modern experiment. Then I will move on to Boyle’s dispute with Line, showing that the historical line Heidegger traces from Galileo to Newton runs directly through Boyle. In the penultimate section, I will bring Heidegger’s concept of the mathematical into dialogue with David Bloor’s concept of social imagery, and briefly explore some general implications of this combination for the historiographic method of the sociology of scientific knowledge (SSK).

Before we leap into the main current of the chapter, it bears emphasising that what follows is not an exercise in intellectual history. Recall, once more, that Heidegger defined mathēsis in terms of a twofold reciprocal relation between a mathematical projection of nature, on the one hand, and work experiences, on the other. Hence, in explicating and expanding on Heidegger’s argument, I will give significant attention to the materiality of early-modern scientific and technological experience, in general, and Boyle’s experimental manipulations of nature, in particular. My goal is to capture, if only roughly, the way in which material practice and metaphysical project came to mutually reinforce one another, each giving strength to the other, until a powerful new way of understanding and intervening in natural processes emerged, a novel intellectual and material culture, a new way of being in the world.

2. The Galilean First Thing and the Aims of Experiment

In her 2004 book, The Body of the Artisan: Art and Experience in the Scientific Revolution, Pamela Smith argues that ‘the methods, goals, and episteme of art’ are ‘central to an understanding of the Scientific Revolution.’13 In particular, she emphasises the crucial contribution of an ‘artisanal epistemology’ to the emergence of early-modern science. This epistemology was widely manifest in the artistic activity of the sixteenth and seventeenth centuries, and it provides evidence for a ‘form of cognition’ unique to the craft operations of the period.14 In step with Dear’s emphasis on the seventeenth-century preoccupation with operational explanations, discussed in Chapter Five, Smith argues that these artisans were more concerned with understanding the processes of nature than with creating representations of nature. To this end, they developed a deep and sophisticated expertise about the way matter behaves under a diverse range of conditions, with a particular interest in cases involving the generation and transformation of matter.15 This expert knowledge was not abstract and theoretical, but embodied and practical: ‘in the sixteenth and seventeenth centuries the pursuit of natural knowledge became active and began to involve the body; that is, one had to observe, record, and engage bodily with nature.’16 Echoing the earlier ‘craftsman thesis’ of Edgar Zilsel, Smith argues that communication by these expert artisans with physicians, scholars, princes, and city governors created a social dynamic from which ‘new attitudes toward nature and a new discourse about it emerged.’17 Furthermore, like Zilsel, who claimed that these social developments provided only ‘necessary conditions,’ not sufficient conditions, for the rise of early-modern science, Smith also cautions that her account of artisanal practice offers an only ‘partial answer’ to the question of what brought about the Scientific Revolution.18 Although she places more stress on the contribution of artisans, Smith nevertheless emphasises that this period was marked by a ‘mutual influence’ between artisans and humanists, between practitioners and theorists, an influence which was ‘reciprocal and dialectical,’ an influence which ‘runs both ways.’19 Her book, then, is not a reductionist account of science in terms of the skilled manipulation of matter by elite artisans, but instead a powerful reminder of the necessary and profound role played by those artisans in a larger social transformation. In so arguing, she reinforces a point against intellectualist accounts of the Scientific Revolution represented by, among others, Alexandre Koyré’s reductionist emphasis on theoretical imagination as both necessary and sufficient for the emergence of early-modern science. Indeed, Koyré explicitly rejected Zilsel’s claim for an artisanal influence on Galileo’s work.20 John Randall was likewise dismissive of Zilsel’s craftsman thesis, which he viewed, incorrectly, as necessarily rooted in a Platonic metaphysics.21

It is important to recognise that Heidegger’s account of the Scientific Revolution in terms of mathēsis predates the mid-twentieth-century swing towards theory-dominant explanations of early-modern science. As noted in Chapter Two, Heidegger was a reductionist champion of neither theory nor practice, but was instead concerned with gaining a better understanding of the complex relationship between the two. Recall his exclamation that ‘it is by no means patent where the ontological boundary between “theoretical” and “non-theoretical” behaviour really runs!’22 However, when it comes to historical analysis, Heidegger, like Smith, puts his emphasis on one side of this dynamic: in his case, giving more attention to intellectual rather than to pragmatic factors. Yet, just as Smith urges us, despite the one-sidedness of her account, to keep the reciprocal nature of the dynamic in mind, so too should we approach Heidegger’s own historical comments in the same fashion. Heidegger gives scarcely any attention to the material practices of early-modern science, but his account does not preclude such attention. In fact, as we have already seen in the last chapter, he explicitly styles mathēsis as a reciprocal relation between ways of working with things, on the one hand, and the metaphysical projection of the thingness of things, on the other.

In this section, I will first gloss Heidegger’s brief historical comments on the emergence of early-modern science, and then suggest how these comments may relate to the more practice-based accounts proffered by historians like Smith. This will further strengthen the point, made in Chapter Five, that an analysis of manipulation alone cannot properly explain the profound historical changes we are hoping to understand. In order to make sense of early-modern accounts of nature, we must give attention to both efficient and final causes, to both operations and ends. In order to understand what early-modern natural philosophers were up to, we should focus not just on the fact that they manipulated nature using experimental equipment, but also on the way they selectively ordered those manipulations with the intention of producing reliable natural knowledge. I have proposed that Heidegger’s account of the Scientific Revolution be interpreted as a story of change in the prevailing conception of final causation in respect of natural processes. I consider this interpretation compatible with Zilsel’s and Smith’s respective macro- and micro-historical attention to the transformation in relations between humanists and artisans, practitioners and theorists, during the same period. This is a proposed interpretation, rather than a straightforward gloss, of Heidegger’s account, because this is not how he explicitly described matters. I believe, however, that what follows is consistent with his overall approach in the 1920s and 1930s, though I will also note some consequential points of critical departure from a few of his more specific claims.

Recall from Chapter Five that, for the Aristotelian natural philosopher of the late Renaissance, the natural movement of a thing was understood as movement to proper place, or, to form. This natural movement was regulated by the thing’s final cause. From this it follows that a fundamental change in natural philosophical conceptions of motion should also involve a fundamental change in corresponding conceptions of final cause. As the understanding of natural motion fundamentally changes, so too does the understanding of the rules or guidelines which give order and meaning to that motion. Although Heidegger did not have much to say about changes in early-modern conceptions of final causation, he does give brief but crucial attention to the corresponding changes in early-modern conceptions of natural motion. A review of Heidegger’s observations on this point will help us to render more explicit the implied corresponding changes in prevailing conceptions of final causation during that same period.

Heidegger’s discussion focuses on Newton’s First Law of Motion, his principle of inertia, which reads: ‘Every body [corpus omne] continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by a force impressed upon it.’23 Heidegger points out that the phrase corpus omne, or ‘every body,’ indicates Newton’s rejection of the fundamental Aristotelian distinction between terrestrial and celestial bodies.24 Indeed, under this law, the thingness of things is no longer subject to any kind of qualitative division: Newton’s First Law treats all things as being basically the same, as being circumscribed by the same basic blueprint. Furthermore, according to Heidegger, Newton’s law is a formal articulation of an understanding of thingness which had already been expressed in Galileo’s earlier account of free fall. For Heidegger, Galileo’s key innovation was to explain the difference in the time it takes for distinct bodies to fall to earth ‘not from the different inner natures of the bodies or from their own corresponding relation to their particular place,’ but from the external forces acting on them, for example, the resistance of the air.25 With this, Galileo rejects the Aristotelian attempt to contrastively explain a difference in natural motion between two bodies by reference to a difference in their inner orientations towards distinct places within a qualitatively differentiated cosmos. This latter kind of explanation is no longer valid because all things are now conceived of as belonging to qualitatively identical places in the cosmos. Heidegger writes that with Galileo the cosmos is now understood to be ‘the realm of the uniform space-time context of motion.’26 In qualitative terms, the heterogeneity of places within the cosmos has now become a homogeneity of positions within a uniform spatial realm.

There is a clear affinity between Heidegger’s account of Galilean motion and his earlier discussion of place in the context of the change-over from practical immersion in a work-world to a theoretical understanding of things as objects. In Being and Time, Heidegger writes that:

In the ‘physical’ assertion ‘The hammer is heavy’ we overlook not only the tool-character of the entity we encounter, but also something that belongs to any ready-to-hand equipment: its place. Its place becomes a matter of indifference. This does not mean that what is present-at-hand loses its ‘location’ altogether. But its place becomes a spatio-temporal position, a ‘world-point,’ which is in no way distinguished from any other.27

Here, Heidegger is describing the nascent experience according to which early-modern mathematical physicists began to make sense of nature. In his later discussion of Galileo’s free-fall experiments, he emphasises the sharp contrast between this way of experiencing nature as intelligible and the way distinctive of orthodox Aristotelians of the same period.

Both Galileo and his opponents saw the same ‘fact.’ But they interpreted the same fact differently and made the same happening visible to themselves in different ways. […] Both thought something along with the same appearance but they thought something different, not only about the single case, but fundamentally, regarding the essence of a body and the nature of its motion.28

In contrast to his more orthodox contemporaries, Galileo’s work experiences were shaped by a projection of nature in which the qualitative differences between things, so central to the prevailing Aristotelian image of the cosmos, had now become a matter of indifference. He presupposed uniformity vis-à-vis the thingness of things. At a basic phenomenological level, he experienced all things as the same. Methodologically, by drawing attention to the phenomenology of this basic Galilean experience, Heidegger seeks to uncover the ontological core of Galilean natural philosophy. Indeed, as Heidegger argued, ‘[o]nly as phenomenology, is ontology possible.’29

For Heidegger, an ontological commitment to the qualitative uniformity of things is clearly evident in Galileo’s final book, the 1638 Discourses and Mathematical Demonstrations Relating to Two New Sciences, from which he paraphrases Galileo as stating ‘Mobile mente concipio omni secluso impedimento’: ‘I think in my mind of something moveable that is left entirely to itself.’30 This generic moveable body will become the corpus omne of Newton’s First Law. Free from external influence, it exists in an autonomous state of uniform and perpetual motion (or rest). The social field of intelligibility in which the existence of such a thing can make sense is what Heidegger dubbed the mathematical projection of nature. He now identifies this shared projection with the mente concipio of Galileo: ‘There is a prior grasping together in this mente concipere of what should be uniformly determinative of each body as such, i.e., for being bodily. All bodies are alike. No motion is special. Every place is like every other, each moment like any other.’31 This is, for Heidegger, the missing mathematical element which marks the emergence of early-modern science: ‘[t]he mathematical is the “mente concipere” of Galileo.’32 Thus the key feature of early-modern mathēsis, what crucially distinguishes it from Renaissance regressus, discussed in Chapter Five, is the uniformity or univocality in its projection of the thingness of the things. As Heidegger argues, ‘[a]ll determinations of bodies have one basic blueprint (Grundriss).’33 In other words, as we saw in Chapter Five, all bodies — and, more broadly, the thingness of all things — are experienced and understood according to one basic and uniform measure. Against this measure, ‘the structure of every thing and its relation to every other thing is sketched in advance.’34 Where the community of orthodox Aristotelian natural philosophers experienced a qualitatively differentiated, hierarchically ordered cosmos, Galilean philosophers now see a uniformly ordered world in which every place, and every thing, is qualitatively like every other.

On the basis of his conception of the mathematical projection in terms of a basic blueprint, Heidegger concludes that ‘[n]ow nature is no longer an inner capacity of a body, determining its form of motion and place.’35 He seems here to have in mind a definition of nature in terms of final cause, that is, in terms of a principle regulating a thing’s natural movement and place in the cosmos. If, as Heidegger argues, this final cause can no longer be viewed as something internal to the thing, then it must be viewed as external to that thing. However, this does not seem to be Heidegger’s conclusion. Instead, he argues that ‘[n]ature is now the realm of the uniform space-time context.’36 But this seems like a non sequitur. It is difficult to see how this space-time ‘realm’ is supposed to determine the form of motion and the place of a thing. It would seem, rather, to be the arena in which such a determination may occur. Hence, a definition of nature in terms of this realm does not replace the inner capacity of a thing to move towards its proper place in the cosmos. Instead, one may say that the thing retains an inner capacity to follow specific rules of motion, rules which guide it to its natural place. But this place is not unique to the thing’s kind, or category; it is rather a generic place, qualitatively identical to every other place, in the uniform space-time realm. It would thus be more consistent with Heidegger’s overall account to describe the mathematical, not as replacing the inner capacities of things, but rather as rendering those capacities uniform in a way which mirrors the uniformity of the post-Aristotelian cosmos. In a uniform world, a differential, or pluralistic, account of final causes becomes unnecessary. Because this world admits of no differences, there is no need to reckon difference in the fundamental rules governing the natural movements of things. Indeed, now only one basic set of rules is needed in order to understand these movements at their most primitive level. In this way, the mathematical projection opens up an experiential space in which the concept of a universal physical law first becomes intelligible, and then realises its formal articulation in Newton’s First Law: every body continues in its state of rest, or uniform motion in a straight line, unless it is compelled to change that state by a force impressed upon it. In the Newtonian universe, it is an implicit assumption that every physical thing possesses a capacity to consistently follow this basic and universal law. This law now serves as the final cause of a thing’s most primitive form of motion: it is what regulates that motion; it is that for the sake of which the thing moves, elementally, through a uniform space-time realm.37 In achieving pure conformity to this universal law — and so escaping the contingent effects of external, localised causal forces — the thing assumes its proper place, or state, in the post-Aristotelian cosmos, that is, a place where it is left entirely to itself, to be at rest, or to move uniformly in a straight line, without interference from without.

Yet, Heidegger argues that Newton’s First Law ‘speaks of a thing that does not exist. It demands a fundamental representation of things which contradicts the ordinary.’38 The problem is that, although every thing may be capable of following this law, there is no basis in ordinary experience to accept this because we do not ordinarily encounter things as being unaffected by external forces. Put in Galileo’s terms, we do not ordinarily experience a thing ‘left entirely to itself.’ What is more, Heidegger argues that ‘[t]here is also no experiment which could ever bring such a body to direct perception.’39 Hence, the new mathematical projection of nature puts at its centre an elemental understanding of the thing which is closed off not just from ordinary experience, but from experimental experience as well. We can encounter it neither in ordinary life nor in the laboratory.

Heidegger argues that this mathematical understanding of the thing, which places it beyond the scope of experimental observation, also makes possible the experiment as ‘a necessary and prime component of [scientific] knowledge.’40 Because the mathematically projected thing is a necessary condition for the possibility of experimental knowledge, it cannot also be something discoverable by experimental means. Heidegger writes that ‘[i]t is precisely the projecting-open of nature in the mathematical sense that is the presupposition for the necessity and possibility of “experiment.”’41 The idea seems to be that the art of experiment, as a set of operations for investigating nature, is necessarily guided by a mathematical — more precisely, an axiomatic — understanding of things as primitively autonomous, as left purely to themselves in a qualitatively uniform world. One may picture the cosmic demiurge, forging the ‘First Thing’ into existence, and then sending it out, alone, into the empty expanse of space, where it sails unobstructed under the rule-governed constancy of its own internal inertia.

But the experimental practitioner will never discover this First Thing, because she works in a world populated by an untold number of things, each impinging on the autonomy of the others. What the axiomatic image of the First Thing gives the experimentalist is an understanding of things which permits her to meaningfully distinguish their fundamental thingness, their whatness or essence, from the effects wrought on them by the external contingencies of their local environment. Hence, a thing falls to the earth, not because it is composed essentially of earth, but because the earth exerts an external influence on it, accelerating it downward. The earth thus interferes with the autonomy of the thing, accelerating it out of its indigenous state of uniform rectilinear motion (or rest). In doing so, it allows the thing to become an object of experimental observation. More specifically, the experimentalist can now empirically investigate the acceleration of the thing as caused by the earth. Furthermore, because the thing’s relationship to the earth is not unique, one can predict that the earth will affect other things in the same way. Hence, a heavier or lighter body should also accelerate towards the earth at the same rate: the effect should be universal, as determined by the mathematically projected basic blueprint of nature.

As Heidegger observes in respect of Galileo’s free-fall experiment, this prediction was not confirmed, because two simultaneously released bodies, of differential weight, hit the earth’s surface at different times. Yet Galileo was able to reason that this was not evidence of a difference in the respective relations of the two bodies to the earth, but rather of the differential effect of a further external influence, air resistance, on the bodies. Again, the axiomatic image of the First Thing allows this further effect to be explained away as irrelevant to the phenomenon under test. In a vacuum, or near vacuum, this effect should not be present, as was famously confirmed by David Scott when he let a hammer and a feather fall freely from an equal height during the 1971 Apollo 15 moonwalk. The point is that the thing, as mathematically projected, allows the experimentalist to identify certain causal influences as irrelevant to the effect under study, in the interests of isolating just those causes responsible for that effect. Because the project establishes the a priori uniformity of all bodies, including their uniform receptivity to fixed rules of motion, an observed difference in the behaviour of two bodies must indicate, not an essential difference in the bodies themselves, but rather a difference in the external causal nexuses which act on those bodies. To artificially achieve the same observed effect in the behaviour of the two bodies is to have successfully eliminated the difference in their respective causal nexuses — as Scott dramatically demonstrated on the moon’s surface. In this way, the experimental practitioner isolates the cause of a particular behaviour, or effect, and then demonstrates the regularity of this causal relation.

This artificially facilitated isolation of causes, and the accompanying determination of the relevant causal relation, is a process of discrimination which presupposes a stable standard of judgement. According to Heidegger, this standard is provided by the mathematical projection of the thingness of things, which stipulates that no observable effect on the thing is essential to the nature of that thing, and so all such effects can, in principle, be eliminated without compromising the indigenous nature of the thing. The thingness of the thing is thus defined in terms of the purity of its conformity, in the absence of external influence, to what Newton formalised as the First Law of Motion. The experimentalist cannot empirically demonstrate the existence of this pure state, but she can employ it as a norm by which to justify the elimination of noise from an experimental system, that is, the externally generated effects interfering with the specific causal relations which the experiment is meant to isolate and test. In principle, all observable effects might be eliminated from an experimental system, thus leaving the thing entirely to itself, in a purified state of mathematically projected thingness. But this marks the limit of possibility for experimental practice, because it makes scientific knowledge of things impossible. In practice, the experimentalist is rather more concerned with isolating and stabilising specific causes, so as to reliably demonstrate, or explain, specific effects.

This artificially facilitated act is a demonstration of the kind which Paduan medical Aristotelians called propter quid, that is, a demonstration of why an effect is. Recall, from Chapter Five, Agostino Nifo’s four stages of scientific method. First, one observes an effect. Second, one discovers the cause of that effect. Third, one gains precise knowledge of the cause through negotiatio, or definition. Fourth, on the basis of this precise knowledge, one now knows the effect propter quid, that is, in a well-reasoned, or well-grounded, manner. Nifo argued that this well-grounded knowledge of an effect carries the certainty of demonstrative knowledge, but only in an empirical, not a mathematical, sense. Negotiatio is not a purely rational, or intellectual, operation, but also includes a material element. The isolation and definition of a relevant cause requires the physical manipulation of the causal system under investigation. As argued in Chapter Five, these manipulations require a principle to guide them, to give them order and meaning, otherwise they would amount only to random behaviour. In the case of early-modern science, this principle was the missing mathematical element enabling the transition from medieval regressus to early-modern mathēsis. In Aristotelian terms, this element supplies the final cause guiding experimental manipulations, the organising principle, or source of intelligibility, for the new experimental philosophy. Crucially, this element includes an a priori conception of the thingness of the thing, a conception which is not discovered inductively through observation of the thing under investigation — as Jacopo Zabarella had argued in the case of regressus — but which is instead already known before the investigation has even begun. It serves as a basic axiom upon which that investigation becomes possible. According to Heidegger, this is a uniform conception of the thing as law-abiding and autonomous, a thing which, when left to itself, conforms absolutely to an inherent and universal principle of inertia, a principle which would become formally articulated in Newton’s First Law. This uniform conception — the Galilean First Thing — provides a basic blueprint for the metaphysical projection of the thingness of things in general, a projection which Heidegger uses to explain the emergence of early-modern science.

More narrowly, this mathematical conception renders intelligible the technical stabilisation of the thing in an artificial set-up where most of the causal forces acting on it are systematically eliminated, or rendered irrelevant, in the interests of isolating specific, observable, and contingent causal effects, effects the artificially induced repetition of which evince a regularity in the thing’s relation to its artificially controlled environment. In this way, the art of experiment may be viewed, not as a violation of natural processes, but instead as an attempt to complement or complete them. Viewed from within the mathematical project, the new experimental philosophy does not seek to impose a final cause on the thing from without, so as to override its natural tendencies, but instead to organise and employ artificial operations in accordance with an image of the thing as it is when left to its own indigenous, rule-governed nature.42 The aims of experimental practice are thus twofold. First, and more familiarly, the experiment aims to disclose specific regularities in an artificially controlled experimental system, a system comprised of two or more interacting things: for example, the uniform acceleration of a body vis-à-vis the earth. Second, and more provocatively, the experiment employs artificial means to move, or manipulate, the thing in a way which brings it closer to being what it is, to achieving its proper place in the uniform space-time realm as an internally disciplined and wholly autonomous thing. It seeks, in other words, to treat things in accordance with the one basic blueprint of the mathematical projection. The second aim provides the phenomenological background against which the first aim can be intelligibly pursued. The regularity of a relation between two things presupposes the constancy and rule-conformity of each thing on its own, and this presupposition is provided by the mathematical projection of the Galilean First Thing. As a consequence of this projection, the practitioner understands the goal of her artificial manipulations to be in conformity with nature’s own indigenous dispositions. Experimental art thus not only imitates nature, but also, to repeat a passage from Aristotle first cited in Chapter Five, ‘art partly completes what nature cannot bring to a finish.’43 As we will see in the next section, within this mathematically structured experience, experimental manipulations acquire an aura of transparency, they are experienced as granting neutral access to an independently existing and stable natural order. They are experienced, in other words, as disclosing objective matters of natural fact.

3. Releasing Experimental Things

Historian of science Robert Kohler has argued that the scientific laboratory is governed by a ‘logic of placelessness’: ‘Laboratory workers eliminate the elements of place from their experiments.’44 This claim is stronger than Heidegger’s claim that the mathematical projection of nature ‘overlooks’ place, rendering it a matter of ‘indifference.’45 Yet the difference between elimination and indifference has been lost on some critics of Heidegger’s existential account of science. Karin Knorr-Cetina, for example, writes that Heidegger’s account of science ‘is founded on nothing more than the decontextualization from which it was derived.’46 William Blattner likewise argues that, for Heidegger, natural science ‘releases’ things from situatedness, ‘decontextualizes them.’ Dimitri Ginev follows in step, presenting Heidegger as asserting the ‘disappearance of any situatedness (or place) in what becomes mathematically projected.’ However, although Heidegger does argue that the thing is ‘released’ in the mathematical projection, this means neither that it becomes decontextualised, nor that its place is eliminated. It means, instead, that the thing comes to be experienced differently. Its situatedness in an everyday environment becomes unimportant for the subject’s understanding of what it is. Its context has not been eliminated, but instead replaced by the artificially constructed and controlled environment of the laboratory. Laboratory practitioners still experience the thing as situated, but its situation has changed dramatically. The thing is now encountered in a different context, an artificial context designed to move the thing closer to its natural place, as determined by the mathematical projection, the place to which it is now understood to properly belong.47

The claim that the experiment helps move the thing to its proper place in a mathematically projected world challenges the more common view that the experiment serves to control the thing. On the present account, the experiment does not control the thing, but rather the causal nexus in which the thing is situated, and it does this in the interest of letting the thing be what it is. This is the meaning of Heidegger’s statement that the thing is ‘released’ [entschränkt] by natural science from the confines of its everyday situation.48 In German, the noun Schrank can mean ‘bound,’ in the mathematical sense of the upper or lower bounds of a finite number set. But it also carries the more general meaning of a limit, fence, or barrier. Hence, the phrase etwas in Schranken halten means to restrain something, to hold it back, to rein it in. When a thing becomes entschränkt, it is ‘dis-bounded,’ released from the bounds, bonds, or barriers which had restrained it — it is set free. Recall, from the last section, the mythical image of the cosmic demiurge, forging the First Thing in her workshop, sending it off to sail, alone and unhindered, across the empty expanse of space, ruled only by the constancy of its own internal inertia. Now imagine that thing suddenly plunging into the blooming and buzzing causal nexus of the world as we ordinarily experience it. It is from this latter situation that the experimentalist seeks to release the thing, stripping away the causal interference which prevents it from being what it is, and thus turning it back towards the purity of its own mythical beginnings.49

The question now is: how did late Renaissance practitioners come to understand the thing in this way? What caused this profound shift in the phenomenology of their scientific experience of things? The short answer is: the emergence of the mathematical as an increasingly powerful influence on scientific cognition. Yet Heidegger argues that ‘this mathematical must […] be grasped from causes that lie even deeper.’50 With this, he points us towards the conditions of possibility for the early-modern mathematical experience of things.

Heidegger’s own attempt to shed light on these conditions is not especially helpful, but he does hint at the direction in which a further explanation may be pursued. Sticking close to his own philosophical preferences, Heidegger looks for the ‘deep’ causes of the mathematical in the work of Descartes. In particular, he focuses on what was probably Descartes’s first philosophical work, Rules for the Direction of the Mind, an unfinished manuscript which he may have written in 1628, and which was already mentioned in Chapter Four. In this work, declares Heidegger, ‘the modern concept of science is coined.’51 The Rules provide substantial evidence for the formal articulation of the mathematical, particularly in respect of its tendency to ‘explicate itself as the standard of all thought and to establish the rules which thereby arise.’52 Accordingly, as we saw in Chapter Four, Descartes develops a concept of thinking in terms of the res cogitans, the thinking thing, which he defined in the first-person singular. The thinking thing thus becomes an individual ‘I’; thinking is always an ‘I think.’ As a consequence, through Descartes’s efforts, the mathematical becomes grounded in the ‘I,’ which itself becomes the basis for all thought, all the rules which govern reason. Recall, furthermore, Descartes’s claim that all knowledge statements, in addition to positing the ‘I’ principle as their necessary ground, also always posit an equally fundamental principle of non-contradiction. This second principle secures the purity of the ‘I,’ and so also the purity of reason. The individual ‘I’ is the condition of possibility for thinking, as such, and the principle of non-contradiction is the condition of possibility for the purity of that thinking.

There is a striking similarity between this early-modern understanding of the thinking thing, on the one hand, and the early-modern understanding of the physical thing, on the other. The res cogitans shares an important homology with the res extensa, the extended, or corporeal, thing. Just like the Galilean First Thing, introduced above, the Cartesian ‘I’ is individual and autonomous, governed only by the constancy, the purity, of its own inner principle. This similarity should not come as a surprise. As we saw in Chapter Four, Heidegger insisted on the unity of things and thinking. Because the concept of each is dialectically bound to the other, the historical development of one will reflect that of the other. According to Heidegger, this dialectical relation was located by Aristotle in the ‘is’ of the proposition, but subsequently obscured when Descartes buried it in the ‘I’ of the subject. Kant then re-discovered it in the individual subject’s feeling of ‘respect’ [Achtung] for the law, its phenomenological understanding of itself as a law-abiding being, as a being capable of being affected by the law. Heidegger then construes Kant’s notion of respect as self-respect, and argues that, for Kant, the individual subject is bound by rules which it gives to itself. In opposition to this, Heidegger argues that rule-following is not individualistic, but presupposes one’s participation in a tradition, an awareness of one’s historical being-with-others. Recapping the argument of Chapter Four, the principle of unity which binds together things and thinking in the coherent production of scientific knowledge is, for Heidegger, rooted in tradition, a historical and social phenomenon, which has been subject to a string of philosophical articulations over the generations, tracing back through Descartes’s ‘I’ to Aristotle’s ‘is,’ and then to its beginnings in Plato’s mythical image of the demiurge. Heidegger identifies this principle of unity with the for-the-sake-of-which, his version of the Aristotelian final cause. Hence, he outlines a philosophical history of the notion of final cause from Plato’s demiurge, through Aristotle, Descartes and Kant, to his own concept of the subject, Dasein. For Heidegger, ‘Dasein’s very Being [i]s the sole authentic “for-the-sake-of-which.”’53 In other words, the source of the principles which give order and meaning to our experience of things is our own social and historical existence.

This is a radical reinterpretation, but not a complete rejection, of the ancient Greek craft analogy. The mythical world of the demiurge is now reformulated as the social world. The art which unifies things and thinking, which organises and thus renders intelligible our experience of things, the art which helps things by letting them become what they are, is a finite and social human art. More specifically, the rules which guide that art are finite, social rules. Hence, Heidegger argues that the intelligibility of Newton’s First Law, as universally applicable to all corporeal things, is possible only on the basis of a particular historical projection, namely, a mathematical projection of the uniform thingness of things. This projection must, furthermore, be understood as a finite and historical feature of human social existence. Heidegger locates its distal cause in the ancient image of the cosmic demiurge, but his account of this mythical image in historical and social terms provides an opportunity to also locate its causes in more proximal socio-historical human actions, including the actions of the late Renaissance artisanal class.

The influence of this artisanal class on Galileo’s natural philosophy was a key feature of Zilsel’s craftsman thesis, which placed at its centre the macro-sociological transition from feudal to capitalist patterns of social organisation in that period. But more micro-sociological explanations are also possible. Smith, for example, points to recent research suggesting that late Renaissance craft methods were the result of a carefully thought-out technology, one which depended crucially on the maintenance of a strict consistency in the physical materials to which those methods were applied.54 Such practical concerns with uniformity in craftwork would seem to manifest themselves also in the experimental practitioners’ desire to maintain the stability and uniformity of experimental things in order to reliably reckon the regularities in their causal relations with one another. As argued above, this uniformity finds its ultimate expression in Galileo’s principle of inertia, where a thing left to itself is just like every other thing, moving or resting with a constancy determined by a single, universal rule. The differences between things are thus to be judged by differences in the external causes which play on them in their bumpy passage through the heavy traffic of the cosmos. Likewise, the differences between artisanal products, when each is wrought from the same uniform material, are to be judged by differences in the operations to which they have been subjected in the intensive manufactory of the terrestrial workshop.

Based on the present interpretation of Heidegger, I suggest that the proximal sensibility of the artisanal workshop may have provided early-modern experimental practitioners with a powerful analogy by which to conceptualise the thing in terms of material uniformity and reliable responsiveness to standardised methods of manipulation. The point is that artisans provided natural philosophers with more than just an example of embodied knowledge-making, that is, knowledge won through the manipulation of natural materials; they also demonstrated an attitude towards embodied knowledge-making which prized the uniformity of both methods and materials. They put much effort into developing a sophisticated material diagnostics according to which the response of a particular material to standardised techniques of manipulation and manufacture could be reliably predicted. For example, Smith notes Paracelsus’s sixteenth-century observation that ‘carpenters of his day knew how to choose, cut, and prepare wood panels, so that even after centuries very little warping and twisting takes place.’55 Likewise, the use by Renaissance sculptors of ‘consistent alloys […] indicates that they knew their materials and went to some trouble to procure what they needed.’56 Late Renaissance artisans were thus compelled by principles of control and prediction in their work with materials. These materials were controlled for consistency, so that their behavioural responses to standardised forms of manipulation could be anticipated with confidence. Establishing the uniformity of material dispositions was thus a key value of artisanal practice.

Ursula Klein and Emma Spary argue that early-modern laboratories emerged as sites where this intense interest in the stabilised connection between manual techniques and material responsiveness flourished: ‘[l]aboratories […] represented a strand of early-modern expertise developing around the manufacture of materials, as well as chemical techniques such a distilling, smelting, or dissolving.’57 Indeed, the metallurgical practice of smelting is especially suggestive in this regard. As Christoph Bartels has argued, the ‘beginnings of both early-modern science and technology are closely linked to mining and metal production.’58 The efficient manufacture of base metals was both a physically and an intellectually demanding undertaking, one which required ‘hands-on knowledge and skill as well as text-based and mathematical knowledge.’59 Base metals like copper, mercury, tin, and lead do not ordinarily occur in their elemental forms, but must be extracted from natural ores through a complex process known as smelting. This process frees the base metal from the ore, using intense heat in a controlled environment to induce a chemical transformation in which unwanted substances are driven off in the form of gases and slag. It bears emphasising that the smelting process does not simply melt the base metals out of the ores in which they are present. Instead, smelting is a transformative process in which base metals are ‘released’ from the chemical bonds which bind them together with sulfur, oxygen, or silicon in their ordinarily occurring ore state. According to Bartels, the depletion of metal-rich ores in Europe’s leading mining districts in the second half of the sixteenth century, which increased the difficulty of metal production, led to a sudden rationalisation of smelting techniques, marked by innovations in ‘precision measurement, data collection, the use of mathematics, attempts at standardization, the writing of technical instructions, [and] the writing of technical books to be published.’60

There is thus a striking operational homology between smelting, on the one hand, and experimental practice as described by Heidegger, on the other. Just as Heidegger argued that the experimentalist seeks to release the thing from the ordinary causal constraints which prevent it from being what it is, so too does the metallurgist seek to release the metal from the ordinary causal constraints which prevent it from being what it is. Moreover, there was a rapid increase in the rationalisation and publication of smelting techniques during the period just prior to the emergence of the modern experiment in the early seventeenth century. In the case of both smelting and experiment, the object of pursuit is a product of art, and, in both cases, the artful production of this object seeks to return it to its pure, indigenous state. In neither case, however, can one speak of an opposition between art and nature. Instead, the operational dynamic is one in which art comes to the aid of nature by progressively stripping away the external causal constraints which prevent the thing from being what it is, thereby allowing it to more fully realise its proper place in the cosmic order. Because these artful manipulations are experienced, within the mathematical projection, as facilitating natural processes, they carry with them an aura of transparency; they are understood to provide practitioners with neutral access to an independently existing natural order, that is, to objective matters of fact.

Heidegger’s account of the early-modern experiment thus lends conceptual support to recent historiographic attempts to explain the emergence of early-modern science, in part, by reference to the skilled artisanal manipulation of materials. In particular, Heidegger’s account throws light on that for the sake of which these manipulations were often performed: a cultural image of the First Thing. These historical studies, in turn, lend support to Heidegger’s philosophical account, most strikingly the studies of late Renaissance and early-modern metallurgy. If, as historians like Bartels, Klein, Smith, and Spary argue, the emergence of early-modern science was consequentially linked to mining and metal production, then it is possible that the mythical image of the First Thing found concrete, existential support in the artisanal experience of manufacturing pure metals. The pursuit of pure metals through increasingly sophisticated and rationalised metallurgical practices offers a powerful analogy for the natural philosophical pursuit of the Galilean First Thing through the practices of experiment. In this way, early-modern work experiences, on the one hand, and the mathematical projection of nature, on the other, may be viewed as reciprocally related, as serving to mutually reinforce one another.

Heidegger writes that ‘[t]he more exactly the ground plan of nature is projected, the more exact becomes the possibility of experiment.’61 In other words, the more precise the projected ground plan becomes, the more legitimate and unequivocally compelling experiment becomes as a method by which to render nature intelligible. The mathematical projection is the condition of possibility for the experiment, and so the more secure it becomes, the more powerfully it comes to shape our experience of nature, the more apt we will be to regard the experiment as a preferred means of investigation. Yet, it is also the case that, the more effectively the experiment verifies a mathematical conception of nature, the more secure the mathematical projection becomes as the existential basis for that conception. An effective experiment not only verifies a theory, it also reinforces the authority of the projection in which both experiment and theory become possible as a means by which to make sense of nature. According to Heidegger, the modern physical experiment does this by producing an ever more exact account of the thing, through ever more precise acts of numerical measurement.62 These rigorous acts of measurement serve to increase the precision of our understanding, and hence to reduce vagueness, or equivocation, in our descriptions of nature. In rigorously disciplining things by experimental means, we facilitate increased rigour in our thinking and theories about those things. Numerical measurement thus offers an effective and efficient means by which to underwrite an unambiguous, determinate, and logically consistent account of natural order. Numerical measurement furthermore becomes compelling as an investigative technique to the extent that the thingness of things is itself projected as inherently unambiguous, as pure and naturally amenable to precise determination.

This emphasis on exactitude allows for a further specification of the argument, made in the previous section, that the aims of experimental practice are twofold. First, the experiment discloses specific regularities in the relation of one thing to another. For Heidegger, this disclosure, as we can now see, is one which tends towards precision in its specification of the thing’s behavioural regularities. Second, the experiment moves the thing closer to what it is, to being an internally disciplined and autonomous thing. This movement, as we can also now see, involves the material simplification and control of the thing’s causal environment, thus disambiguating the thing’s behavioural responses, allowing them to be unequivocally individualised, such that their regularities may then be exactly specified. As noted earlier, the second aim provides the phenomenological background against which the first aim may be intelligibly pursued. The material reduction of causal ambiguity in an experimental system allows the experimental practitioner to specify natural processes as precisely defined regularities, or even as exact laws. Heidegger argues that only through the specification of such regularities, ‘only within the purview of rule and law[, do] facts become clear as the facts that they are.’63 This is so because the physical matter to which a statement of natural fact refers has itself been isolated from the multifarious and competing causes of its ordinary environment, thereby allowing the regularities of its specific environmental relations to be clearly individuated and precisely measured. In the course of this process, the matter in question thus becomes a matter of fact, a discrete thing to which an unambiguous propositional statement of fact may then be applied. In the next section, we will apply Heidegger’s account of the early-modern experiment in a concrete, micro-historical case study of one dramatic dispute between two seventeenth-century natural philosophers: Robert Boyle and Francis Line.

4. Boyle versus Line: A Study in Experimental Fact-Making

In their 1985 book, Leviathan and the Air-Pump, a classic of the SSK literature, Steven Shapin and Simon Schaffer argue that seventeenth-century experimental practice depended crucially on the emergence of a clearly defined community of experimental philosophers. Admission into this community required one to accept the view that artificially produced matters of fact could provide a legitimate basis for reliable knowledge of nature.64 This social restriction helped to define the boundaries of the experimental community, determining those who were, and those who were not, to be counted among its members. According to Shapin and Schaffer, the establishment of the epistemic rule that reliable natural knowledge must rest on experimental matters of fact depended, in important part, on the prior definition of an experimental community through social rules of inclusion and exclusion. Hence, as they see it, the epistemic problem of how best to acquire knowledge of nature was contingent on the social problem of how best to define the community of natural philosophers: ‘the effective solution to the problem of knowledge was predicated on a solution to the problem of social order.’65

This insight from SSK can help us to expand on Heidegger’s claim, cited at the end of the last section, that scientific facts become clear as the facts they are only within the purview of rule and law, that is, only within a domain of practice in which causal regularities are disambiguated and thus more precisely specified. Shapin and Schaffer’s argument that solutions to problems of knowledge are based on solutions to problems of social order suggests that effective epistemic techniques for the causal disambiguation of matters of fact are (necessarily but not sufficiently) contingent on the deployment of effective social techniques for the specification of membership in the relevant epistemic community. By demanding commitment to the epistemic primacy of experimentally produced matters of fact, early-modern experimental philosophers effectively eliminated, as irrelevant, explanations based on causes which could not be experimentally produced. On first blush, this may suggest that only efficient, or operational causes, were meant to play a role in the new experimentalists’ explanations of natural phenomena. However, as we have already seen, explanations in terms of operational causes, if they are to explain causal regularities, must make at least tacit use of final causes. Hence, the social dynamics of exclusion which specified the early-modern experimental community could not have rejected final causes, as such, without threatening the intelligibility of the experimental enterprise. It should follow, then, that these dynamics functioned instead to disambiguate between the legitimate and illegitimate uses of final causes in explanations of experimentally produced phenomena. The burden of this section will be to demonstrate that the social logic of early-modern experimental subjectivity served to disambiguate final causes by relying, if only tacitly, on the mythical image of the First Thing. This image functioned as the uniform measure by which to differentiate between proper and improper causal explanations of experimental phenomena. This differentiation was, at base, a social one: the image of the First Thing also enabled a discrimination between authentic and inauthentic members of the experimental community. In other words, it also guided judgements about the proper social organisation of seventeenth-century experimental philosophy.

I wish to support these claims by examining a case of controversy in seventeenth-century experimental philosophy over the correct causal explanation of the ‘Torricellian effect,’ named for mathematician and physicist Evangelista Torricelli, who first produced it in 1644. Shapin and Schaffer observe that, in the decade following its production, this experimental effect ‘was associated with […] questions of immense cosmological importance.’66 Given the diverse and dramatically contradictory causes which were proposed to explain the Torricellian effect, Shapin and Schaffer name it as ‘a key example of scandal in natural philosophy.’67

To perform a reasonable approximation of the Torricellian experiment, do the following. Take a thin glass tube, about one metre long, and hold it vertically with the lower opening of the tube blocked with one of your fingers. Then have the tube filled right to the top with mercury (wear gloves!), being careful to eliminate any air bubbles. Seal the upper opening of the tube with a finger of your other hand, making sure that there is no air trapped between your finger and the mercury. Now immerse the lower end of the tube into a beaker half-filled with mercury, and remove your finger from this lower opening while keeping the upper opening of the tube firmly covered. What happens? One might expect the mercury to drop out of the tube, pulled down by the earth’s gravity, since your finger is no longer holding it up by blocking the bottom opening of the tube. In fact, the height of the mercury in the tube does drop as some of the mercury runs out of the tube and into the beaker. However, the mercury level in the tube does not drop all the way down to the level of mercury in the beaker. Indeed, most of the mercury remains in the tube, suspended at a height of about seventy-five centimetres above the level of mercury in the beaker (assuming the experiment is being performed near sea level). Even in the absence of your finger sealing the bottom of the tube, something still seems to be holding the mercury up, thus interfering with the effects of gravity. This suspension of the column of mercury in the tube, significantly above the mercury level in the beaker below, is the main experimental effect produced in the Torricellian experiment. In what follows, I will refer to this suspended column of mercury as the ‘Torricellian effect.’ Seventeenth-century natural philosophers disputed with one another over the cause of the Torricellian effect, that is, over the legitimate answer to the question of what holds the column of mercury suspended at a height of about seventy-five centimetres.

There are two secondary features of the Torricellian experiment also worth noting. First, because the mercury level in the metre-long tube has dropped, a space of about twenty-five centimetres has now opened up in the upper portion of the tube, between the surface of the suspended column of mercury and the finger sealing the upper end of the tube. This space is known as the ‘Torricellian space.’ Second, the appearance of this space in the tube is accompanied by a feeling, in the flesh of the finger sealing the upper end of the tube, that it is now being forced down into the tube. This experience is a secondary effect of the Torricellian experiment, and this effect is normally called ‘suction.’ As we will see, however, the term ‘suction’ is problematic, as it presupposes that the flesh of the finger is being pulled rather than pushed into the tube. In other words, it presupposes that the relevant physical cause of this effect is located inside the tube rather than outside of it. In early-modern debates over the meaning of the Torricellian experiment, much depended on the position one took in respect of this fine distinction.

I will focus on one specific seventeenth-century dispute over the natural philosophical meaning of the Torricellian experiment, one which occurred between Robert Boyle, on the one side, and Francis Line, who published under the Latin name Franciscus Linus, on the other. This dispute was occasioned by the publication in 1660 of Boyle’s book New Experiments Physico-Mechanical, Touching on the Spring of the Air, and its Effects; Made, for the Most Part, in an New Pneumatical Engine. Two aspects of the title of Boyle’s book deserve emphasis. First, the title indicates that Boyle has undertaken an investigation of the cause of certain effects, the cause in question here stipulated as the ‘spring of the air.’ Second, this investigation was conducted, for the most part, using a new experimental instrument which Boyle called a ‘pneumatic engine,’ but which is usually referred to by historians of science, including Shapin and Schaffer, as an ‘air-pump.’ Stated simply, the air-pump was a sealed glass vessel from which air was evacuated by means of an attached pump.

Boyle performed several experiments within this glass vessel, investigating the results produced on an observed phenomenon when air was removed, consequentially if not entirely, from the causal nexus within which that phenomenon was embedded. For example, in Experiment Seventeen of his book, Boyle lowered the Torricellian experiment through an opening in the top of the glass vessel of his air-pump, such that the open beaker of mercury was completely inside the vessel but the vertical Torricellian tube still protruded up through the vessel opening.68 (The tube used in this case had a closed upper end, so it was unnecessary to seal it with a finger.) Boyle then sealed the vessel opening though which the tube protruded, so as to render the vessel as air-tight as possible. With everything in place, he then used the pump to evacuate as much air as possible from the glass vessel.

By removing air from the space surrounding the lower portion of the Torricellian apparatus, particularly from around the open beaker of mercury, Boyle introduced dramatic changes to the Torricellian effect. Specifically, in the absence, or near absence, of air in the glass vessel, the suspended column of mercury in the tube dropped to almost the same height as the mercury in the beaker (which itself rose slightly). In other words, the Torricellian effect had been almost entirely eliminated. On the basis of this result, Boyle argued that it must have been the presence of ambient air, pushing down on the surface of the mercury in the beaker, which counteracted the effects of gravity, thus causing the mercury in the tube to be suspended at a height of about seventy-five centimetres. Boyle’s experiment purportedly served to reduce ambiguity and increase rigour in the natural philosophical understanding of the Torricellian effect by more definitely specifying the cause of that effect, narrowing it down to the pressure of the ambient air on the surface of the mercury in the beaker.

However, Boyle was not content to simply argue that ambient air was the principal cause of the Torricellian effect. He also claimed to know what about the air produced this effect. He identified this ‘what’ as the ‘spring’ of the air. In Experiment One of New Experiments, Boyle wrote that he finds it ‘not superfluous nor unreasonable’ to ‘insinuate’ the air’s spring as a ‘likely’ cause for the experimental effects produced in the glass vessel of his air-pump.69 However, Boyle’s initial diffidence regarding the epistemic status of the air’s spring quickly disappeared. As Shapin and Schaffer observe, by the early 1660s, Boyle viewed the spring of the air as an established matter of fact rather than as a hypothesis. However, Boyle did not spell out the reasons for his growing confidence. As Shapin and Schaffer write, ‘[v]iewed naively, or as a stranger might view it, it is unclear why the spring of the air, as the professed cause of the observed results, should be treated as a matter of fact rather than as a speculative hypothesis.’70 In response to this puzzle, they make the sociological argument that ‘Boyle’s criteria and rules for making his preferred distinctions between matters of fact and [hypothetical] causes have the status of conventions.’71 These conventions, in turn, drew their legitimacy from the ‘total pattern of activities’ constitutive of the experimental culture which Boyle and his colleagues were struggling to establish.72 Shapin and Schaffer support their sociological explanation for Boyle’s discrimination between facts and speculative causes with a detailed examination of the way Boyle responded to his critics, including the Jesuit mathematician and natural philosopher Francis Line.

Before turning to Boyle’s dispute with Line, it will be useful to first briefly consider what Boyle meant when he attributed a spring to the air. At the most general level, Boyle had in mind a corpuscular conception of the air as being made up of individual microscopic particles. He thus understood the spring of the air as a disposition of individual air particles which was activated when those particles came into contact with one another, or with any other body. Hence, he writes that

our air either consists of, or at least abounds with, parts of such a nature, that in case they be bent or compressed by the weight of the incumbent part of the atmosphere, or by any other body, they do endeavour, as much as in them lieth, to free themselves from that pressure, by bearing against the contiguous bodies that keep them bent; and, as soon as those bodies are removed, or reduced to give them way, by presently unbending and stretching out themselves.73

Put briefly, air particles endeavour to free themselves when placed under pressure by an adjacent particle. Each particle possesses a ‘power or principle of self-dilation,’ which becomes actualised as an ‘endeavour outward’ when the particle is under compression.74 Boyle conceived of the earth’s atmosphere as composed of innumerable particles heaped up on top of one another, such that air particles near the earth’s surface where maximally compressed under the great weight of the atmosphere above them. In respect of the Torricellian experiment, Boyle argued that the pressure of the atmospheric air on the surface of the mercury in the beaker was the sole cause of the Torricellian effect. By placing the Torricellian apparatus in the glass vessel of his air-pump, and then exhausting most of the air from the vessel, Boyle removed the cause of this effect. As air particles were removed from the vessel, the remaining particles were able to progressively exercise their power of self-dilation, unbending themselves until they exerted scarcely any more pressure on the mercury in the beaker. In other words, Boyle used his air-pump to ‘release’ the air corpuscles remaining within its chamber from the external influence of neighbouring corpuscles. This, in turn, released the surface of mercury in the beaker from the weight of the atmosphere. As a consequence, the column of mercury in the tube descended under the force of gravity, draining out into the beaker. A key consequence of Boyle’s explanation is that it rendered the Torricellian space, between the suspended column of mercury and the top of the tube, causally inert. In Boyle’s view, the Torricellian effect could be sufficiently explained by reference to the removal of air pressure from the surface of the mercury in the beaker.

Boyle was careful to distinguish this particular explanation of the air’s spring from the general fact that the air has a spring. He emphasised this distinction by noting the contrasting explanation of René Descartes, who conceived of the air particles as lifted by heat and the ‘restless agitation of that celestial matter’ surrounding the earth to the point where they begin to whirl about, ‘each corpuscle endeavour[ing] to beat off all the others from coming within the little sphere requisite to its motion about its own centre.’75 Yet, despite the differences between these two explanations, they both assume that the air is composed of particles possessing an ‘endeavour outward,’ a disposition to push away neighbouring bodies in order to achieve for themselves a state free from external causal interference. Boyle’s and Descartes’s divergent explanations for the air’s spring thus stand as different specifications, or articulations, of the same general idea. Put in Aristotelian terms, this disposition plays the role of efficient cause in the movements or operations of these particles. Moreover, as Boyle’s own words suggest, the meaning of the particles’ outward movement, that for the sake of which they so move, appears to be a state of freedom from external influence, in other words, a state of autonomy. This autonomy may be understood as the final cause of the particles’ outward movement, as the principle according to which one is able to make sense of those minute mechanical operations, to experience them as intelligible.

Let us now turn to the explanation Francis Line gave for the Torricellian effect. Line presented his arguments in a 1661 book titled Tractatus de Corporum Inseparabilitate, or ‘A Treatise on the Inseparable Nature of Bodies.’76 Unlike Boyle, Line did not treat the Torricellian space as irrelevant for a causal explanation of the Torricellian effect. Indeed, he suggested that this space contains a fine thread of matter — like Boyle’s springs, too fine to be seen by the eye — which connects the upper surface of the suspended column of mercury to the flesh of the finger sealing the top end of the tube. This thread, or funiculus in Latin, helped to prevent the mercury column from falling below seventy-five centimetres, and thus contributed causally to the Torricellian effect. Hence, unlike Boyle’s corpuscular springs, which possess a power of self-dilation, Line’s thread possesses a power of self-contraction. This was manifest as an endeavour inward, in contrast to the endeavour outward of Boyle’s springs; where Boyle’s springs push things away, Line’s thread pulls them together. Line argued, in particular, that it pulls the mercury and the finger, at either end of the Torricellian space, towards one another. I will refer to this as Line’s ‘thread hypothesis.’ Like Boyle’s spring hypothesis, the thread hypothesis sought to explain the Torricellian effect in efficient, or operational, causal terms.77

Furthermore, Line’s thread hypothesis also sought to explain a secondary feature of the Torricellian experiment, namely, the experience of the flesh of one’s finger being forced down into the Torricellian space. He argued that the thread attached to the finger’s flesh, by its power of self-contraction, was what pulled the flesh into the tube. This explanation was also meant to explain why one’s finger was not only forced into the tube, but also why it stuck to the tube end. Indeed, much as effort is required to pull one’s palm from the hose end of an operating vacuum cleaner, so too is effort required to pull one’s finger from the top end of the Torricellian tube, that is, in Line’s terminology, to break the thread attaching one’s finger to the top of the mercury column. Line argued that Boyle’s spring hypothesis failed to sufficiently explain this secondary effect of the Torricellian apparatus.

Line also thought that his thread hypothesis had another advantage over Boyle’s spring hypothesis. As a Jesuit scholar, he was obligated to uphold the Scholastic doctrine that nature abhors a vacuum. Line thus also argued that the thread forms in the Torricellian space in order to fill the void left by the falling mercury, thereby preventing a vacuum. Thus, in addition to explaining the adhesion of one’s finger to the tube, as well as contributing to an explanation of the Torricellian effect itself, Line argued that his thread hypothesis also confirmed a widely held belief about nature: ‘And hence is confirmed that common axiom used in the schools for so many ages past, that nature doth abhor a vacuum.’78 In Line’s view, then, the prevention of a vacuum — that is, the absolute separation of bodies — was that for the sake of which the thread forms in the tube and pulls inward. The prevention of a vacuum, of the separation of the constituents of matter, was the final cause, or reason, explaining why the thread is disposed to form and contract itself. In contrast to Line, Boyle declined to give an explanation for why his corpuscular springs are disposed to dilate themselves. Although he sought to explain the Torricellian effect in terms of an efficient, or operational cause — the spring’s endeavour outward — Boyle did not likewise offer an explanation in terms of a final cause, that is to say, he did not provide a reason for why the springs always move themselves outward as opposed to in some other direction.

In 1662, Boyle published a response to Line in which he used his earlier silence about final causation as a strength in promoting his spring hypothesis over Line’s alternative proposal. Furthermore, he exploited Line’s reference to final causation in order to attack the intelligibility of the latter’s proposed efficient cause, the thread hypothesis. Boyle writes:

It seems also very difficult to conceive, how this extenuated substance should acquire so strong a spring inward, as the examiner all along his books ascribes to it. Nor will it serve his turn to require of us in exchange an explication of the air’s spring outward, since he acknowledges, as well as we, that it has such a spring.79

Here, Boyle argues that, because Line has accepted the legitimacy of Boyle’s spring hypothesis, Boyle is under no obligation to provide a further explanation of spring in terms of final causation. This implies the view that an explanation in terms of operational causes can be accepted as legitimate independently of considerations of final cause. Yet, although Boyle allows himself the benefit of this supposition, he is not willing to extend this same benefit to Line. He uses Line’s appeal to the horror vacui as a final cause to undermine the legitimacy of Line’s appeal to a self-contracting thread as an efficient cause. Yet, as his own work makes clear, there is no necessary connection between a particular efficient cause and a specific final cause. Hence, Boyle might have instead recognised the possible legitimacy of Line’s thread hypothesis in isolation from the horror vacui, and he might even have reinterpreted that hypothesis in a way more in step with his own principles.

In fact, this appears to have been Line’s strategy towards Boyle. As Boyle notes, Line claimed that ‘[i]t cannot be conceived [concipi non posse]’ on a corpuscular model how Boyle’s spring could take up more space when it dilates itself.80 Line seems to have had in mind the Aristotelian idea that ‘things can increase in size not only by the entrance of something but also by qualitative change; e.g. if water were to be transformed into air.’81 Hence, a sponge will increase in size by absorbing water, but a volume of water will increase in size by qualitatively changing from a liquid to a gas. In the second case, nothing has been added to the substance; instead the substance itself undergoes a change. On the corpuscular model, in contrast, there is no qualitative change in the basic material of water when it changes from a liquid into a gas. The corpuscles of water remain the same, but more space is opened between them. Likewise, there is no qualitative change to a corpuscular spring when it self-dilates. The more successfully it can beat back its neighbours, the more space it will take up, even as its physical size remains unchanged. It thus seems clear that Line and Boyle drew on radically different conceptions of matter in their respective interpretations of the phenomenon of spring. And both claimed to find the other’s conception unintelligible. Yet Line was willing to accept the air’s spring as a matter of fact so long as it was explained in accordance with his own non-corpuscular principles. In contrast, Boyle was reluctant to do the same for Line’s thread hypothesis. Indeed, he sought to reject that hypothesis by arguing, in part, that the principles Line used to explain it — above all, the horror vacui — were unintelligible. Given that Boyle was happy, in other contexts, to distinguish between operational hypotheses and their explanation, his attempt here to erase that distinction seems less than fully compelling.

In addition to unintelligibility, Boyle offered three other reasons to reject Line’s thread hypothesis: ‘this hypothesis of our author’s […] seems to be partly precarious, partly unintelligible, partly insufficient, and besides needless.’82 He immediately notes, however, that ‘it will not be so convenient’ to prove each of these claims in isolation from the others.83 Hence, for example, Boyle combines his argument from precariousness with charges of unintelligibility when he argues that Line’s thread hypothesis relies on a belief in the horror vacui, which has not been ‘cogently prove[d].’84 This lack of proof, concludes Boyle, ‘may help to shew his doctrine to be precarious.’85 But, if the merits of Line’s thread hypothesis can be judged independently of his belief in the horror vacui, then this argument from precariousness lacks adequate force.

Perhaps the most promising reason Boyle gave to reject Line’s thread hypothesis was that it is needless, or unnecessary. One of Line’s strongest empirical arguments for his thread hypothesis was that it explains both why one feels one’s finger being forced into the Torricellian tube, as well as why the end of the tube sticks to one’s finger. In addressing the former case, Boyle writes that

the finger that stops the tube being exposed on the upper parts and the sides to the external air, has the whole weight and pressure of the atmosphere upon it. […] [C]onsequently that part of the finger that is within the tube will have much less pressure against it from the dilated air without. By which means the pulp of the finger will be thrust in (which our author is pleased to call sucked in).86

In addressing the latter case, Boyle argues that the ‘pressure of the ambient air’ will ‘thrust in the pulp of the finger at the upper orifice of the tube, and make it stick closely enough to the lip of it.’87 Boyle immediately recognised that Line would not be convinced by this latter explanation, writing that ‘I know the examiner affirms, that no thrusting or pressure from without can ever effect such an adhesion of the finger to the tube. But this should be as well proved as said.’88 Surely, however, the onus lay with Boyle to prove that his hypothesis sufficiently explains this adhesion, rather than with his critic to prove that it does not. In any case, Line was not alone in finding Boyle’s explanation unconvincing. The powerful Dutch natural philosopher, Christiaan Huygens, commented at the time that he could ‘not see that either Linus’ hypothesis or Mr. Boyle’s is satisfactory, that is, why the siphon sticks to the finger, so that one must use some little force to draw it off.’89 It seems clear that, at the time of the dispute, Boyle’s claim to have given a sufficient explanation of ‘suction’ was not uncontroversial. Hence, it could not have provided adequate grounds for arguing that Line’s thread hypothesis was not needed for an explanation of this phenomenon.

It should be emphasised that Line, in order to provide space for his own explanation of the Torricellian effect, did not need to likewise argue that Boyle’s explanation was unnecessary, but only that it was insufficient. This would have been enough for him to justify the introduction of his thread hypothesis as necessary, but not sufficient, for a comprehensive explanation of the effect. Line’s position was consistent with the view that both his thread hypothesis and Boyle’s spring hypothesis were necessary for an explanation of the Torricellian effect, but that neither was, on its own, sufficient for such an explanation. On this basis, Line could have agreed with Boyle’s claim that his thread hypothesis was ‘partly insufficient’ without revising his original argument.90

It seems that Boyle did not fully understand Line’s position with respect to this point. Although he recognised in several passages that Line was criticising his spring hypothesis for being insufficient, in other passages he reacted as if Line were rejecting it as wholly unnecessary. In the first instance, Boyle’s observation that Line ‘denies it not, that the air has some weight and spring, but affirms, that it is very insufficient to perform such great matters’ was one which he repeated several times throughout his response to Line.91 Yet he also described Line as arguing that ‘the things we ascribe to the weight and spring of the air are really performed by neither,’ and also of trying to ‘invalidate the hypothesis of weight and spring of the air.’92 In other words, despite explicitly recognising evidence to the contrary, Boyle ultimately treated Line as employing a zero-sum strategy, whereby only one of their respective hypotheses could be explanatorily relevant. However, it was, in fact, Boyle who employed this strategy, not Line. Boyle argued that his spring hypothesis provided not just a necessary, but also a sufficient, explanation for the Torricellian effect. Hence, he viewed Line’s proposed explanation as not only insufficient, but also unnecessary, or ‘needless.’ But this appears to misrepresent the dispute. Whereas Boyle treated the choice between the spring and thread hypotheses in exclusive either/or terms, Line seems to have taken a more inclusive approach in which both hypotheses could contribute to a comprehensive operational explanation of the Torricellian effect.

In sum, the four reasons Boyle gave for his rejection of Line’s thread hypothesis — that it is ‘partly precarious, partly unintelligible, partly insufficient, and besides needless’ — do not seem to adequately justify that rejection. Two further reasons may help us to more fully understand Boyle’s response to Line. The first reason has to do with Boyle’s desire to neutralise the explanatory significance of the Torricellian space. This space had been a flashpoint for metaphysical disputes over the existence of a vacuum. The Aristotelian doctrine of the horror vacui played a central role in this dispute. As Shapin and Schaffer show, Boyle was not trying to resolve this dispute, but instead to sideline it: ‘[w]hat he was endeavouring to create was a natural philosophical discourse in which such questions [about the existence of a “metaphysical” vacuum] were inadmissible.’93 By neutralising these disputes, Boyle and his colleagues hoped to provide a solution to the problem of social order made pressing by the intense civil conflict of their period. Their solution involved creating a new mode of discourse in which metaphysics was supposed to have no legitimate place. This discourse embraced the language of ‘experimental “physiology”’ in opposition to the language of ‘metaphysics.’ This distinction set up a powerful boundary within discourse about the natural world, and ‘[d]issension involving violations of this boundary […] was deemed fatal.’94 Boyle rejected Line’s thread hypothesis because it violated this boundary by invoking the metaphysical doctrine of the horror vacui, and thereby threatened the social order which Boyle and his colleagues were struggling to establish. According to Shapin and Schaffer, this boundary was a social convention rooted in collective efforts to reestablish social and political order. Hence, Boyle’s epistemological reasons for rejecting Line’s thread hypothesis cannot be neatly separated from considerations of the social context in which the debate took place. By invoking the horror vacui — the inseparability of matter — Line not only threated Boyle’s professed empiricism, but also the conception of social order he shared with other members of the emerging community of experimentalists.

Yet, as I argued above, once Line’s thread hypothesis is separated from his commitment to the doctrine of the horror vacui, this doctrine can no longer provide a compelling reason for rejecting the hypothesis. In this light, Line’s thread hypothesis seems no more metaphysical than Boyle’s spring hypothesis. Indeed, Boyle even interprets it as an inverse of his own hypothesis: whereas he posits a spring outward, Line posits a spring inward. It is the directionality of the two hypotheses which most clearly and consequentially distinguishes them. This brings us to the second of the two further reasons for Boyle’s rejection of Line’s thread hypothesis. As an efficient, or moving, cause, Line’s thread moves itself in the wrong direction. It acts to move things together, rather than to push them apart. I have argued, in general, that the directedness of an efficient cause, as that which regulates or guides a thing’s operations and thus gives them a clear and stable meaning, is what Aristotle had meant by the notion of final cause. In this sense, any interpretation of a thing which ascribes to it a regular pattern of behaviour will rely on this notion. Without it, the regularity of the thing’s operations would appear to be a coincidence, a matter of chance, rather than the result of a power or principle belonging to that thing. Hence, when Boyle ascribed a power of self-dilation, an endeavour outward, to his corpuscular springs, he was implicitly recognising that a final cause regulates the operations of those corpuscles.95

Boyle’s tacit ascription of a final cause to the operations of his corpuscular springs was buried beneath his declaration that the spring of the air was a matter of fact. As observed above, Boyle insisted on a strict distinction between matters of fact, on the one hand, and speculative hypotheses, on the other. Indeed, first recognising the Torricellian effect to be a matter of fact, Boyle then speculated that its cause was the outward spring of the air. However, Boyle quickly dropped his speculative tone and declared this outward spring to also be a well-established matter of fact rather than a hypothesis. As Shapin and Schaffer note, Boyle did not explicate a reason for this change in his attitude, and they suggest that a sociological explanation can be given, one which makes sense of Boyle’s apparently arbitrary distinctions as having been guided by social conventions. On this basis, we can treat Boyle’s discrimination between metaphysical and empirical language as a social discrimination motivated by a specific conception of social order. This was a discrimination in which a power of outward spring could be accepted as an empirical matter of fact, while a power of inward spring was rejected as an unintelligible metaphysical hypothesis.

The credibility of Boyle’s claim to have eschewed metaphysics was contingent on his success in rendering invisible the interpretative space between the Torricellian effect and his causal explanation of that effect in terms of outward spring. Hence, the most pressing threat posed to Boyle by Line’s thread hypothesis was that it posited a power of inward spring which plausibly explained many of the same aspects of the Torricellian experiment. In this way, Line’s intervention threatened to re-expose the contingency of the interpretative space existing between the Torricellian effect and Boyle’s causal spring hypothesis, a space which Boyle had worked hard to render invisible. Building on Shapin and Schaffer’s analysis, one may conclude that Line’s thread hypothesis threatened the conception of social order which tacitly grounded Boyle’s explanation of the Torricellian effect. However, contrary to what Shapin and Schaffer argue, this threat cannot be explained in terms of Line’s appeal to metaphysics, in the form of final causes, because Boyle also shared this commitment to final causation. It would seem, instead, that Boyle viewed the threat more as directed at his particular, tacit conception of the final cause of an individual corpuscle’s movement: a state of autonomy, of freedom from the things which surround it. Yet, as we have seen, Line did not challenge Boyle’s conception of outward spring, as such. Line accepted the necessity of Boyle’s proposed cause, but challenged its sufficiency as an explanation of the Torricellian experiment. Hence, what was ultimately at stake for Boyle was not the validity of his spring hypothesis, but its exclusivity. Insofar as his hypothesis provided a solution to the problem of social order, Boyle meant for it to serve as an exclusive solution, one that was both necessary and sufficient.

These two features of Boyle’s explanation of the Torricellian effect — outward spring and exclusivity — can be fit together with two complementary features of Heidegger’s explanation of the emergence of early-modern science in terms of the mathematical. These latter two features are what I have called the First Thing, and what Heidegger called the basic blueprint. The mythical image of the First Thing helps to further explicate Boyle’s model of a spring-like corpuscle which endeavours to beat away all neighbouring bodies, thereby opening up around itself a free space in which it can realise its natural, autonomous state. This autonomous state is the final cause regulating the behaviour of Boyle’s corpuscular springs. It is that place towards which things, by exercising their power of outward spring, endeavour to move themselves. Boyle’s air-pump supported this endeavour, helping the corpuscles to realise their natural state. This end state or place is represented by the First Thing. Moreover, this end state is the only one towards which things may be legitimately directed. In other words, Boyle’s corpuscular springs can be ultimately regulated by only one final cause. Hence, the image of the First Thing also functions as the one basic blueprint governing the indigenous operations of all air corpuscles. Just as Boyle’s inward spring was meant to play an exclusive role in his explanation of the Torricellian experiment, so too was the image of the First Thing meant to serve as the one basic blueprint governing explanations of material phenomena in the new Galilean universe. The Galilean First Thing was the basic blueprint guiding Boyle’s explanation of the spring of the air. It was the tacitly held mathematical image underpinning the social logic of inclusion and exclusion which enabled Boyle and his colleagues to discriminate between legitimate and illegitimate accounts of experimental phenomena, and hence also between authentic and inauthentic members of the emerging seventeenth-century community of experimental philosophers. The success of Boyle’s refutation of Line’s thread hypothesis was consequentially determined by this tacit image. In the next section, I will argue that this tacitly held, mathematical image of the First Thing was, at root, a social image.

5. Social Imagery and Early-Modern Science

The idea that knowledge is governed by an image — a social image — has had an important, if somewhat underdeveloped, place in SSK. Indeed, David Bloor considered it so central that he gave his influential 1976 introduction to SSK the title Knowledge and Social Imagery. In this section, I will discuss the relationship between Heidegger’s mythical image of the Galilean First Thing and Bloor’s notion of social imagery. This discussion will allow us to further explore, on the one hand, the sociological aspects of Heidegger’s account of the emergence of early-modern science, and, on the other hand, the theoretical insights which SSK may draw from that account.

Bloor argues that ‘we think about knowledge by manipulating images of society.’96 A clear distinction must be drawn here between an image of society and society itself. Bloor argues that society is too complex and overwhelming for us to understand it directly. As a consequence, we must rely on simplified social models: ‘Immersed as we are in society we cannot grasp it as a whole in our reflective consciousness except by using a simplified picture, an image, or what may be called an “ideology.”’97 This image subsequently guides the way we come to think about knowledge in general. Crucially, our manipulation of social images need not be a conscious act. In other words, the connection between a theory of knowledge and a social image will often be a tacit one. This means that social imagery will often serve as an analyst’s category without also being an actor’s category. According to Bloor, an analyst should not limit her explanations to the consciously deployed categories and concepts of those actors whose behaviour she is seeking to explain. She should also seek to uncover the social categories and concepts which structure an individual actor’s thoughts and actions at a tacit, or unconscious, level. One of the key targets of this method of excavation is the social imagery which may shape and guide actors’ thoughts and actions without their being aware of it.

The claim that social imagery guides actors’ practices suggests that it plays a role similar to that of Aristotelian final causes. In other words, Bloor’s concept of social imagery appears to include a teleological element. This introduces a potential tension into the comparison between Bloor’s social imagery and the Heideggerian notion of the Galilean First Thing. Bloor strongly repudiates teleological forms of explanation as being inimical to SSK: ‘There is no doubt that if the teleological model is true then the strong programme is false.’98 Yet, this apparent tension may be resolved once we recognise that the offending aspects of what Bloor calls the ‘teleological model’ are absent from the notion of the First Thing. These aspects are, first, that the teleological model entails the existence of ‘purposive’ behaviour, and, second, that this behaviour is ‘naturally oriented towards truth.’99 The worry, in the first case, is that science is being treated as a process of ‘mind or “consciousness,”’ rather than as a configuration of socially sustained material practices.100 In the second case, the worry is that this allegedly mental process is directed towards a non-contingent (i.e., asocial and ahistorical), or absolute, truth. As we have seen, SSK entails neither of these claims. As we have also seen, the image of the First Thing likewise entails neither of these claims. As the basic blueprint of early-modern scientific practice, the First Thing can guide behaviour at a wholly tacit and non-deliberative level. Furthermore, the grounds for the First Thing are not absolute or necessary, but ultimately bottom out in the subject’s shared, historically contingent tradition. Hence, Bloor’s reservations with respect to teleology do not apply in the case of the Galilean First Thing.101

Having resolved this initial worry about a potential conflict between Bloor’s social imagery and the Heideggerian image of the First Thing, let us now turn to the example Bloor offers to illustrate his explanatory method. Drawing from Karl Mannheim’s 1925 essay, ‘Conservative Thought,’ Bloor attempts to uncover the social imagery influencing the works of philosopher of science Karl Popper and historian and philosopher of science Thomas Kuhn.102 In a nutshell, Bloor argues that Popper’s account of scientific knowledge reflects an Enlightenment ideology, while Kuhn’s account of scientific knowledge reflects a Romantic ideology. These two ideologies represent two different images according to which Popper and Kuhn organised, and thus made sense of, the empirical data regarding modern scientific knowledge production. As Bloor puts it, in the case of each thinker, ‘the same facts are fitted together to form a different picture.’103 In thinking about scientific knowledge, in developing an epistemology of scientific practice, Popper and Kuhn each manipulated a distinct image of society, and that social image powerfully influenced the different ways in which they each came to perceive the structure and dynamics of scientific knowledge.

Bloor gives considerable attention to the differences between Popper’s and Kuhn’s epistemologies, mapping them respectively onto the more general cultural categories of Enlightenment and Romanticism. Here, however, I want to focus on one strong similarity between these two otherwise divergent accounts of scientific knowledge, as well as a difference which then appears within this common perspective. According to Bloor, Popper and Kuhn shared a perception of science as the work of ‘collectivities’ or ‘social wholes.’104 In other words, both thinkers tended to view scientific practice in terms of bounded and coherent spheres of social activity. However, each then goes on to analyse social wholes in dramatically different ways. As Bloor writes, Popper treated social wholes as ‘unproblematically equivalent to sets of individual units.’105 Kuhn, in contrast, rejected such individualism. In his work, ‘[s]ocial wholes are not treated as mere collections of individuals but are seen as having properties of a special kind, e.g. certain spirits, traditions, styles and national characteristics.’106 Hence, while for Popper ‘individuality is not bound up in society,’ for Kuhn ‘[i]ndividuals can only be understood in context.’107 At root, this is a disagreement over how to specify the subjectivity of the subject, over what it is to be a human being.

Popper and Kuhn each approached scientific knowledge in terms of social wholes, but Popper treated those wholes as reducible to their individual components, while Kuhn treated them as irreducible to those individual components. At stake in this difference is the location of the principle or principles according to which a social whole is organised, according to which it is viewed as a structured unit rather than an unruly shambles. For Popper, organising principles are uniformly located in the individual parts making up the whole.108 For Kuhn, they cannot be located in the individual parts but must instead be a property of the whole itself. According to Bloor, these divergent ontologies guide the respective epistemologies of their authors, with Popper favouring a view of scientific knowledge as the property of individuals and Kuhn a view of scientific knowledge as the property of groups. For present purposes, however, what is more important than this purported disagreement is the shared belief of these two thinkers in the existence of identifiable and coherent social wholes. In this sense, when Popper and Kuhn thought about scientific knowledge, their thoughts were being guided by the same kind of social image, an image of the social group as an organised whole. As a consequence, they both also tended to view scientific knowledge in terms of organised wholes, whether of concepts, practices, or a combination of both.

The implication of this is that the Enlightenment and Romantic ideologies which Bloor used to develop his comparative study are, at least in one important sense, not so different from one another. Indeed, they appear to share a common root in an image of the social group as an organised and bounded whole. This conclusion is supported by Mannheim’s argument in the essay mentioned above, the essay on which Bloor modelled much of his discussion.

Mannheim addresses the same macro-sociological phenomenon as did Zilsel — the historical transition from feudalism to capitalism — but he picks it up at a later stage. Whereas Zilsel focussed on social changes during the fifteenth and sixteenth centuries, which he argues led to the Scientific Revolution in the early seventeenth century, Mannheim focusses instead on the emergence of conservative thought in the nineteenth century, presenting it as a response to the growing cultural hegemony of Enlightenment rationalism from the late eighteenth century onward. Like Zilsel, Mannheim analyses the usurpation of feudalism by capitalism as a process of rationalisation.109 The process was ‘revolutionary and radical just because it want[ed] to rationalize the whole social order right from the beginning in a systematic manner.’110 Nineteenth-century conservative thought grew out of a widespread and deliberate resistance to this process. In the face of rationalisation, conservative thinkers made a deliberate effort to maintain and develop the remnants of a pre-capitalist experience which had once been taken for granted but was now threatened with extinction.111 This effort led to the rise of the counter-revolutionary movement of Romanticism, which ‘seized on the submerged ways of life and thought, snatched them from oblivion, consciously worked them out and developed them further, and finally set them up against the rationalist way of thought.’112 Thus, what Mannheim dubs ‘romantic conservatism’ included two steps. First, it sought to rescue and revitalise the remnants of a disappearing pre-capitalist way of life. Second, it sought to actively articulate those remnants and develop them into an explicit and comprehensive project of intellectual resistance to Enlightenment rationalism. This second step was above all motivated by a rejection of the perceived rigidity and linearity of Enlightenment thinking, which Romantic thinkers endeavoured to replace with a more dynamic and dialectical form of thought.113 Crucially, Mannheim argues that this second move reiterated, rather than abandoned, the faith of Enlightenment rationalism in the power of reason to understand the world: ‘romantic thought (unintentionally perhaps) merely continues, though more radically, and with new methods, the same process which the Enlightenment had already hoped to complete — the thorough rationalization of the world.’114 Mannheim uses the following analogy to illustrate the fundamental similarity, as well as the subsequent differences, between Enlightenment and Romantic thought:

The conservative picture of things as a whole is like the inclusive sort of picture of a house which one might get by looking at it from all possible sides, a concrete picture of the house in all its detail from every angle. But the progressive is not interested in all this detail; he makes straight for the ground plan [Grundriss] of the house and his picture is suitable for rational analysis rather than for intuitive representation.115

The fundamental similarity between the two positions is their shared view that the world in its entirety can be captured in a ‘picture of things as a whole,’ a comprehensive image of everything that is. On the basis of this shared view, each position then employs a different method to rigorously work out the content of this world picture. The Enlightenment rationalist uses abstraction and systematisation to uncover the fixed ‘ground plan’ of the world. The Romantic thinker emphasises concrete description and the dynamic balance of competing forces in order to disclose the organic unity of the world. By each pursuing a distinct ideal of intellectual rigour, an ideal determined by standards internal to their own methods and experience, both rationalistic progressives and romantic conservatives aim to identify and define a comprehensive picture of the world construed as a whole.

Yet not every kind of conservativism depends on a conception of the world as a whole. In addition to Romantic conservativism, Mannheim identifies another form of nineteenth-century conservativism, which he dubs ‘feudalistic conservatism.’ This form followed only the first of the two steps characterising Romantic conservativism: that is, it consciously sought only to preserve and explicate elements of a pre-capitalist tradition which, by that time, existed only on the periphery of society.116 Feudalistic conservativism focusses its attention on the specific details of concrete practice, making little effort to integrate those details into an overall, coherent picture of the world. It resists the ‘subsumption of the individual and particular under one general principle’ and so ‘does not really trouble itself with the structure of the world in which it lives.’117 Unlike Romanticism, feudal conservativism did not identify itself as a counter-revolutionary response to Enlightenment rationalism. Hence, feudalistic conservatives felt little compulsion to adopt, so as to then renegotiate, the Enlightenment conception of the world as an object which could be accessed, as a whole, through the power of reason. In addition, their suspicion of theoretical abstraction, and their attention to concrete practice, were ‘exceedingly sober.’118 They displayed no traces of the romantic tendency to conceptualise the world as a dynamic unity of competing, often non-rationalisable, life forces.

One upshot of Mannheim’s argument is that, in addition to the Enlightenment and Romantic imagery Bloor discusses in his comparison of Popper and Kuhn, one can also add feudalistic conservativism. Unlike the former two positions, feudalistic conservativism was not motivated by a need to identify and elaborate a picture of the world as a whole. In this, it proves closer to a pre-Enlightenment intellectual tradition, one which concerned itself with the description and explanation of the concrete details of experience without attempting to integrate those details into one comprehensive and consistent whole. Hence, although Mannheim was mainly concerned with the nineteenth century, when Enlightenment rationalism had become well-developed and culturally dominant, his comments on feudalistic conservativism point to an earlier period, in the seventeenth century, when proto-Enlightenment rationalism posed a still relatively weak threat to the dominant feudalistic tradition.

These insights may now be applied to the dispute between Boyle and Line in the early 1660s. I want to suggest that this dispute can be understood as a conflict between an ascendant rationalism and a still-dominant feudalistic traditionalism. More to the point, I am suggesting that Boyle represents the early impulses of a rationalism which pursued a systematic model of the world as a whole, while Line represents the late tendencies of a tradition which was intensely engaged with concrete detail but had little interest in systematic analyses of a universalising scope. I want to make two arguments: first, that Bloor’s concept of social imagery may be applied, in an illuminating but imperfect way, to this episode in the history of science; and second, that Heidegger’s account of modern science explains why the application of Bloor’s concept must be imperfect.

The application of the concept of social imagery to the dispute between Boyle and Line is imperfect because it is not symmetrical. If, as Bloor argues, a social image functions as a simplified model of the world construed as whole, and if Line was a traditionalist who had no use for such a model, then the concept of a social image will not be useful in examining his case. In contrast, if Boyle represents, at least in this instance, an emerging culture of rationalism, then the concept should apply in his case. Indeed, this asymmetry picks out one of the key issues at stake in the dispute. This was the issue of what role a simplified picture of things as a whole should play in the production of reliable experimental knowledge. Since, as Bloor argues, social imagery often guides an actor’s thinking at a tacit level, the question of whether the world can be systematically treated as whole need not have been something Boyle and Line deliberately addressed in their dispute. The point is rather that we, as analysts instead of actors, may usefully illuminate the dispute in terms of this question.

In fact, the relevant analysis was already done in the last section. What I wish to pick out here with Bloor’s concept of social imagery was there picked out with Heidegger’s concept of the one basic blueprint. In short, Heidegger’s basic blueprint is an instance of Bloor’s social imagery. Both concepts are meant to highlight the exclusivity of a style of thinking, the fact that the image or blueprint serves as a comprehensive picture of things as a whole. I argued in the last section that Boyle’s thinking was guided by such an image, an a priori image in which the thingness of the thing was specified beforehand according to the Galilean First Thing. If this image was furthermore a social image, in Bloor’s sense, then it should follow that Boyle, when thinking about knowledge, was manipulating images of society. Indeed, this was one of the main points of Shapin and Schaffer’s study. They argued that Boyle’s epistemological concerns were, at root, concerns about social order, especially, the problem of disorder caused by political controversy. To this, I added the suggestion that the image of the First Thing served Boyle as a model by which to construct a clearly defined community of experimental philosophers — a social whole — in which the dangers of controversy could be effectively managed.

As we have seen, Boyle, in his dispute with Line, defended the sufficiency of his own spring hypothesis against the challenge posed by Line’s thread hypothesis. This defence appears to have been motivated by Boyle’s assumption that the phenomena of the Torricellian experiment could be subsumed under one general explanatory hypothesis. This epistemological assumption reflected Boyle’s commitment to a simplified model of society in which members took for granted a consistent base of clearly defined principles and matters of fact. Line, in contrast, appears to have taken a more eclectic view, allowing instead that both his and Boyle’s hypotheses were necessary for an explanation of the Torricellian phenomena. Underpinning Line’s assumption was, it appears, not a commitment to a competing model of the social whole, but rather a complacent disregard for the necessity of any such model. It seems plausible that Line’s epistemology, such as it was, reflected the prevailing feudal tradition — with its indifference towards simplified models of society — which was only just then beginning to face the challenge of an ascendant, rationalistic conception of the world. Hence, the dispute was not a conflict between two competing images of the social whole, but between Boyle’s perceived need for such an image, on the one hand, and Line’s apparent indifference to that need, on the other.

However, it was not the case that every follower of the feudal tradition was indifferent to the threat posed by the new rationalism. In fact, at stake in this period were conceptions not just of society and nature, but also of religion. This should not be surprising, as it is a commonplace among contemporary historians of science that conceptions of society, nature, and religion were, in Boyle’s period, not easily separated. As the historian Quentin Skinner has observed, Boyle insisted that his experimental activity supported his religious faith because it provided evidence for the ‘design’ of the world. By demonstrating that nature as a whole was created on the basis of a rational plan, Boyle hoped to provide empirical grounds for the existence of a divine creator. ‘L’horloge, donc l’horloger,’ notes Skinner, and then immediately adds: ‘During the seventeenth century, however, this familiar trope of the Enlightenment was still widely believed to carry alarming religious consequences.’119

One such expression of alarm came from the Anglican cleric and humanist Méric Casaubon. In a letter ‘Concerning Natural experimental Philosophie, and some books lately about it,’ published in 1669, Casaubon criticised members of the Royal Society for claiming that religious controversies could be settled on the basis of ‘plain reason.’120 The nub of this worry was Casaubon’s resistance to the idea that God’s creation could be understood in accordance with a basic blueprint, accessible to anyone possessing natural reason. As Michael Spiller remarks, Casaubon viewed this ambition as deluded and dangerous, because ‘reality is too vastly complex, and human beings too corrupt, irremediably frustrated by recurring and permanent vices and frailties.’121 Any attempt to know the world as a whole was bound to fail, as nature outstrips finite human understanding, making controversy inevitable.

In this dispute over the nature of knowledge, the conflict was not about what picture of the world to adopt, as it would be in the later feud between Enlightenment rationalists and Romantics, but instead about whether or not a world picture should be adopted at all as an instrument in the acquisition of knowledge. As Spiller notes, Boyle was, at best, an uneasy accomplice in the development of early-modern rationalism.122 Yet, in his dispute with Line, Boyle appears to have been strongly motivated by a simple and consistent conception of nature structured in terms of the Galilean First Thing. Line, for his part, appears to have been guided by no one picture at all, but instead by an eclectic willingness to blend together a variety of doctrines. Put in Heidegger’s terms, only Boyle comported himself in a mathematical manner. In his dispute with Line, Boyle’s thinking and conduct exemplified the emerging mathematical projection which marked the historical and existential transition from a medieval to an early-modern understanding of nature.

Heidegger argues that ‘[t]he world picture does not change from an earlier medieval one into a modern one, but rather the fact that the world becomes picture at all is what distinguishes the essence of the modern age.’123 For Heidegger, the modern age, the age of modern science, is, at base, the age of the world picture. He thus presents a theory of scientific knowledge which applies only to the modern age. According to this theory, modern science is possible only on the basis of a projected picture of the world as a whole. This projection is the a priori condition of possibility for such knowledge. The subsequent pursuit of modern scientific knowledge is conceived as the filling out, the rigorous articulation and refinement, of a picture of the world which has already been projected, albeit only generally and confusedly, in advance.124

Heidegger’s argument that thinking in terms of a world picture is a specifically modern development provides an opportunity to refine Bloor’s sociological claim that we think about knowledge by manipulating images of society. Bloor writes that this is ‘a theory about how people think. The hypotheses are not alleged to be necessary truths. […] Furthermore the range of application of the picture here presented has yet to be determined.’125 On the basis of Heidegger’s discussion of the world picture, as well as the above analysis of the dispute between Boyle and Line, we may now tentatively limit the range of application of Bloor’s theory to the modern era. SSK’s method of analysing scientific controversies in terms of conflicting, often tacitly held, pictures of society seems most applicable to modern controversies. These conflicting pictures are images of society construed as a whole, images which, in turn, motivate conceptions of knowledge construed as a whole. As human relations come, in the modern era, to be viewed in terms of social wholes, human knowing likewise comes to be viewed in terms of epistemic wholes. Hence, the modern problem of organising knowledge into a structured whole can be understood as the modern problem of organising society into a structured whole. Whether actors view knowledge as a system of concepts — organised around basic principles of logic and definition — or as a system of practices — organised around basic principles of prediction and control, or credibility and power — in both cases, the SSK practitioner will seek to uncover the underlying social image held by the actors, along with the basic principles around which that image is organised. However, in cases where groups of actors genuinely treat knowledge in a non-systematic and eclectic way, the implication of Heidegger’s argument is that there will be no underlying image of a social whole which the SSK practitioner may uncover and then use to explain the actors’ epistemic activities. The sociologist may, in these latter cases, discover shared social interests, and use these to explain behaviour, but, if Heidegger’s argument is correct, these interests will not be the components of a single, integrated social image, a shared ideology or blueprint determined by a single coherent set of basic principles.

6. Conclusion

Some readers may feel that there is an elephant in the room which I have ignored throughout this chapter. This alleged elephant is the mechanical philosophy of the early-modern period. However, while far from being irrelevant, the mechanical philosophy is, in fact, largely peripheral to the main concerns of this chapter. There is, then, no elephant in the room. So why not talk about it?

Mechanism is usually contrasted with organicism, with the attendant account of the Scientific Revolution then emphasising a transition in the prevailing image of the world from an organic to a mechanical one. What should be immediately clear, however, is that this difference in philosophical orientation — organistic versus mechanistic — is underpinned by a shared impulse to grasp the world as a single, structured whole. It is this shared impulse, rather than the difference between these two philosophies, which has been a central concern of this chapter. On this basis, we may reasonably doubt, for example, Carolyn Merchant’s claim that ‘[t]he rejection and removal of organic and animistic features and the substitution of mechanically describable components would become the most significant and far-reaching effect of the Scientific Revolution.’126 On the contrary, according to the argument presented here, the most far-reaching and significant effect of the Scientific Revolution was the institutionalisation of a concept of the world as a thing which is ordered — organised — according to a uniform measure, a basic blueprint. Both models of the world as a machine and as an organism reflect this institutionalisation, because both machines and organisms are, so we tend to think, discrete organised units, structured individuals or wholes.127

Merchant describes the Scientific Revolution as ‘the transition from the organism to the machine as the dominant metaphor binding together the cosmos, society, and the self into a single cultural reality — a world view.’128 She furthermore argues that the ancient notion of ‘[t]he female earth was central to the organic cosmology that was undermined by the Scientific Revolution.’129 This may give the impression that the organic cosmology was itself an ancient institution, supplanted by a mechanistic cosmology in the early-modern period. However, Merchant also argues that the doctrine of the world’s ‘organic unity’ emerged in the late Renaissance, citing as evidence works published only in the second half of the sixteenth century, or later.130 Hence, it would appear that an organic world picture may not have been a pre-revolutionary institution after all, but rather a revolutionary challenger subsequently replaced by its equally revolutionary rival, the mechanical world picture. The ancient notion of a female earth may well have been replaced along with its cosmological counterpart, but it does not follow from this that this ancient notion represents a cosmology, an image of the world conceived as a whole.

On these admittedly fragile grounds, I tentatively suggest that the conflict between organic and mechanical philosophies was not a cause, but rather a consequence, of the rise of early-modern science. This was a struggle between two emergent conceptions of the world as a whole. It thus presupposed that the world can be so conceived, that is, as a whole. The institutionalisation of this presupposition was, I suggest, one of the most significant and far-reaching effects of early-modern scientific culture. It entailed not just that things be conceived in terms of a uniform measure, but that the world itself also be so conceived, as a thing disciplined by a single measure, a uniform image, a basic blueprint.

We may thus question Elizabeth Potter’s attempt to assimilate the dispute between Boyle and Line to the broader ideological dispute between mechanical and organic cosmologies. Potter attempts to slot Line’s thread hypothesis into an organic philosophy, calling it a ‘non-mechanistic assumption’ which presupposes the idea of ‘[a] World Spirit or Nature having consciousness and feelings.’131 The implication is that Line conceived of the world as possessing consciousness and feeling, that is, as being a living, sentient organism.

Potter’s argument follows Boyle’s own by forcing a necessary connection between Line’s thread hypothesis and his affirmation of the metaphysical doctrine of horror vacui. Yet, as I have argued, this connection may also be viewed as contingent. Indeed, Boyle insisted on the contingency of the relation between his own spring hypothesis and any further metaphysical doctrine. So why deny the same treatment to Line? Furthermore, it is worth repeating that Line was obliged, as a Jesuit, to affirm the horror vacui. What is more, one may doubt whether this doctrine, when affirmed by a Jesuit, was meant to slot into an organic cosmology which construed the world as a living, conscious being. This construal is much stronger than the more modest claim that nature acts to prevent a vacuum. In order to attribute this act to nature, one need not ascribe to it consciousness and feeling. Like human activity, the activity of nature may be non-deliberative — as when an acorn grows into an oak tree. When Boyle attributed an outward endeavour to corpuscles of air, he presumably had this non-deliberative notion of activity in mind. Line’s thread hypothesis need not be treated any differently.

It is worth noting that Line was a skilled mechanician, with ‘a reputation for ingenuity in the construction of timepieces,’ especially sundials.132 Indeed, in his Brief Lives, compiled in the late seventeenth century, John Aubrey described Line as having constructed ‘the finest Dialls in the World,’ and also as possessing ‘great skill in the Optiques.’133 On the basis of this reputation, Line was invited by Charles II to design and build a sophisticated sundial, ultimately comprised of 250 individual units, which was installed at Whitehall in 1669.134 Hence, although Line was evidently no mechanical philosopher, he was certainly not unfamiliar with mechanical ways of thinking and working. Moreover, Line’s thread hypothesis might even be viewed in mechanical terms, since strings, lines, and threads seem, on a basic level, no less mechanical than springs. For example, Walter Charleton, elected to the Royal Society in 1663, gave substantial attention to threads in his mechanical studies of attraction and adhesion. With attraction, he asked: ‘Why therefore should we not conceive, that in every Curious and Insensible Attraction of one bodie to another, Nature makes use of certain slender Hooks, Lines, Chains, or the like intercedent Instruments, continued from the Attrahent to the Attracted […]?’ With adhesion, he observed that when amber ‘is no sooner Warmed by rubbing, but there rise out of it certain small Lines or Threads, which adhere to a mans finger that toucheth it, and such as may, by gentle abduction of the finger, be prolonged to considerable distance.’135 It is not surprising, then, that Boyle sometimes treated Line’s thread hypothesis as being inadequately mechanical rather than as not being mechanical at all. For example, he argued that Line had not adequately explained how his thread attaches itself to the surfaces inside the Torricellian space: ‘For I farther demand, how the Funiculus [i.e. thread] comes by such hooks or grapple-irons, or parts of the like shape, to take fast hold of all contiguous bodies, and even the smoothest, such as glass, and the calm surface of quicksilver.’136 Hence, Boyle does not appear to have judged Line’s thread hypothesis as necessarily non-mechanical. In fact, there is compelling reason to think that Line was quite comfortable with mechanical ways of thinking, and very little reason to think that he was committed to an organic cosmology.

More generally, I have argued that the central dispute between Boyle and Line cannot be reduced to a contest between distinct world pictures or ideologies. Instead, this dispute focussed on two different ways of conceptualising the directedness of natural processes, particularly in the context of the Torricellian experiment: either inward or outward. However, even this difference was not at the core of the dispute. At its centre, the dispute had instead to do with exclusivity versus inclusivity vis-à-vis the question of directedness. Boyle favoured an exclusive explanatory role for his spring hypothesis. Line, in contrast, sought only to win a legitimate place for his hypothesis alongside Boyle’s own. He appears to have followed a piecemeal and pluralistic approach, incompatible with exclusivity, whereas Boyle was guided by an exclusive conception, a basic blueprint and uniform measure, of the thingness of things — what I have called the Galilean First Thing. As a consequence, Boyle was, on my argument, a mathematical philosopher, while Line (a professor of mathematics in Liège) was not.

This argument entails a significant modification, but not a rejection, of Kuhn’s distinction between early-modern mathematical and experimental traditions. While still describing distinct arenas of epistemic practice, these traditions should be viewed as the sub-traditions of an emerging, broader early-modern tradition wherein things came increasingly to be experienced according to a single, uniform measure. This homogenisation of thing-experience was marked by a consolidation of the final causes of things under this one basic measure. As a consequence, the proper place of the scientific thing — the end towards which it naturally moves in becoming what it is — was rendered qualitatively uniform. Early-modern experimental philosophers did not, in practice, reject final causes in their attempts to understand the things of nature. Instead, what made their manner of working new was its dependency on a basic blueprint, a uniform projection of the thingness of things. According to Heidegger, the existential growth of this dependency was a defining feature of the mathematisation of early-modern science. This was a process whereby experimental apparatus could now be reliably used to release the scientific thing from the external constraints which prevented it from realising its own indigenous end. In other words, the experiment was designed to let the thing be what it is. Experimental art supported and supplemented nature by helping the thing approach its proper place within a mathematically projected cosmos.


1 Thomas Kuhn (1977), ‘Mathematical versus Experimental Traditions in the Development of Physical Science,’ in The Essential Tension: Selected Studies in Scientific Tradition and Change, by Thomas Kuhn (Chicago: University of Chicago Press), pp. 31–65.

2 Kuhn (1977), ‘Mathematical versus Experimental Traditions,’ p. 63.

3 Peter Dear (1995), Discipline & Experience: The Mathematical Way in the Scientific Revolution (Chicago: University of Chicago Press), p. 246.

4 Dear (1995), Discipline & Experience, p. 2.

5 Steven Shapin (1988), ‘Robert Boyle and Mathematics: Reality, Representation, and Experimental Practice,’ Science in Context 2(1), 23–58; Steven Shapin (1994), A Social History of Truth: Civility and Science in Seventeenth-Century England (Chicago: University of Chicago Press), pp. 310–54.

6 Steven Shapin (1996), The Scientific Revolution (Chicago: University of Chicago Press), p. 116. Note that, while Kuhn made the tentative psychologistic suggestion that the experimental/mathematical distinction may be ‘rooted in the nature of the human mind,’ Shapin’s account is more sociological, attributing to Boyle the conviction that ‘mathematical means of persuasion were embedded within an improper, even immoral, social order’ (Kuhn (1977), ‘Mathematical versus Experimental Traditions,’ p. 64; Shapin (1988), ‘Robert Boyle and Mathematics,’ p. 33).

7 Shapin (1988), ‘Robert Boyle and Mathematics,’ p. 47.

8 Shapin (1988), ‘Robert Boyle and Mathematics,’ p. 48.

9 Shapin (1988), ‘Robert Boyle and Mathematics,’ pp. 30, 29.

10 Kuhn (1977), ‘Mathematical versus Experimental Traditions,’ p. 44.

11 Shapin (1994), A Social History of Truth, p. xvi n. 1. Shapin offers no programmatic defence of historicism, adding: ‘nor do I believe that historicism is without its problems and proper limitation’ (Shapin (1994), A Social History of Truth, p. 328). See also Steven Shapin (1992), ‘Discipline and Bounding: The History and Sociology of Science as Seen through the Externalism-Internalism Debate,’ History of Science 30(4), 333–69 (pp. 353–59).

12 Robert Boyle (1662 [1966]), A Defence of the Doctrine Touching the Spring and Weight of the Air, Proposed by Mr. R. Boyle, in his New Physico-Mechanical Experiments; Against the Objections of Franciscus Linus. Wherewith the Objector’s Funicular Hypothesis is also Examined, in The Works of Robert Boyle, vol. 1, by Robert Boyle, ed. by Thomas Birch (Hildesheim: Georg Olms), pp. 118–85 (p. 143).

13 Pamela H. Smith (2004), The Body of the Artisan: Art and Experience in the Scientific Revolution (Chicago: University of Chicago Press), p. 19.

14 Smith (2004), The Body of the Artisan, p. 21.

15 Smith (2004), The Body of the Artisan, pp. 7, 14.

16 Smith (2004), The Body of the Artisan, p. 18.

17 Edgar Zilsel (1942), ‘The Sociological Roots of Science,’ American Journal of Sociology 47(4), 544–62; Smith (2004), The Body of the Artisan, p. 151.

18 Zilsel (1942), ‘The Sociological Roots of Science,’ p. 547; Smith (2004), The Body of the Artisan, p. 19.

19 Smith (2004), The Body of the Artisan, p. 22.

20 Alexandre Koyré (1943a), ‘Galileo and Plato,’ Journal of the History of Ideas 4(4), 400–28 (p. 401 n. 6).

21 John Herman Randall, Jr (1961), The School of Padua and the Emergence of Modern Science (Padova: Editrice Antenore), p. 130.

22 Martin Heidegger (1962a [1927]), Being and Time, trans. by John Macquarrie and Edward Robinson (Oxford: Blackwell), p. 409 [358]. (Following scholarly convention, page numbers in square brackets refer to the original 1927 German edition of Being and Time.)

23 Martin Heidegger (1967 [1962]), What Is a Thing?, trans. by William B. Barton, Jr., and Vera Deutsch (Chicago: Henry Regnery), p. 78.

24 Heidegger (1967), What Is a Thing?, p. 86.

25 Heidegger (1967), What Is a Thing?, p. 90.

26 Heidegger (1967), What Is a Thing?, p. 92.

27 Heidegger (1962a), Being and Time, p. 413 [361–62].

28 Heidegger (1967), What Is a Thing?, p. 90.

29 Heidegger (1962a), Being and Time, p. 60 [35].

30 Heidegger (1967), What Is a Thing?, p. 91.

31 Heidegger (1967), What Is a Thing?, p. 91.

32 Heidegger (1967), What Is a Thing?, p. 116.

33 Heidegger (1967), What Is a Thing?, p. 91.

34 Heidegger (1967), What Is a Thing?, p. 92.

35 Heidegger (1967), What Is a Thing?, p. 92.

36 Heidegger (1967), What Is a Thing?, p. 92.

37 Trish Glazebrook calls this the early-modern ‘homogenization’ of natural place. She correctly observes that now ‘[n]o distinction is made between things on the basis of motion toward an end.’ However, from this she then incorrectly concludes that ‘things are apprehended not in terms of [internal] essence or telos [i.e., end],’ ‘but on the basis of external force’ (Trish Glazebrook (2000b), ‘From φύσις to Nature, τέχνη to Technology: Heidegger on Aristotle, Galileo, and Newton,’ The Southern Journal of Philosophy 38, 95–118 (pp. 109, 110; my brackets); see also, Trish Glazebrook (2001b), ‘The Role of the Beiträge in Heidegger’s Critique of Science,’ Philosophy Today 45(1): 24–32 (p. 25)). But, if this were true, then the First Law would be unintelligible. Explanations in terms of external force entail a conception of internal essence, even when that essence is homogenous across entities.

38 Heidegger (1967), What Is a Thing?, p. 89.

39 Heidegger (1967), What Is a Thing?, p. 89.

40 Martin Heidegger (1999 [1989]), Contributions to Philosophy (From Enowning), trans. by Pravis Emad and Kenneth Maly (Bloomington: Indiana University Press), p. 113; my brackets.

41 Heidegger (1999 [1989]), Contributions to Philosophy, p. 113.

42 On this point, my interpretation differs from that of Glazebrook, who has Heidegger arguing that ‘[t]he experiment […] is violent in that it sets beings up to behave in ways they would not when left to themselves’ (Trish Glazebrook (2000a), Heidegger’s Philosophy of Science (New York: Fordham University Press), p. 104; see also Trish Glazebrook (1998), ‘Heidegger on the Experiment,’ Philosophy Today 42(3), 250–61). She supposes that, for Heidegger, the final end towards which a thing is naturally directed is necessarily violated by the modern experiment. This may have been the view of orthodox Aristotelian natural philosophers, but it was not, on my reading, Heidegger’s view.

43 Aristotle (1941c), Physica, trans. by R. P. Hardie and R. K. Gaye, in The Basic Works of Aristotle, ed. by Richard KcKeon (New York: Random House), pp. 213–394 (p. 250 [lines 199a14–17]).

44 Robert E. Kohler (2002), Landscapes and Labscapes: Exploring the Lab-Field Border in Biology (Chicago: University of Chicago Press), pp. 9, 6.

45 Heidegger (1962a), Being and Time, p. 413 [361].

46 Karin D. Knorr-Cetina (1981), The Manufacture of Knowledge: An Essay on the Constructivist and Contextual Nature of Science (Oxford: Pergamon Press), p. 143; William Blattner (1995), ‘Decontextualization, Standardization, and Deweyan Science,’ Man and World 28, 321–39 (p. 321); Dimitri Ginev (2011), The Tenets of Cognitive Existentialism (Athens OH: Ohio University Press), p. 4.

47 The claim that Heidegger embraced a logic of placelessness in respect of scientific things is further challenged by his 1931 statement that an explanation of the whatness of things in terms of their ‘going towards their place […] until today is not in the least refuted, in fact not even grasped’ (Martin Heidegger (1995b [1985]). Aristotle’s Metaphysics Θ 1–3: On the Essence and Actuality of Force, trans. Walter Brogan & Peter Warnek (Bloomington: Indiana University Press), p. 67). Indeed, Heidegger sought to understand the radical transformation of this kind of explanation in the early-modern period, rather than to affirm its rejection.

48 Heidegger (1962a), Being and Time, p. 413 [362].

49 Heidegger’s account of the experiment appears to share some characteristics with Nancy Cartwright’s more recent account. She writes that the experiment provides ‘the circumstances where the feature under study operates, as Galileo taught, without hindrance or impediment, so that its nature is revealed in its behaviour’ (Nancy Cartwright (1999), The Dappled World: A Study of the Boundaries of Science (Cambridge: Cambridge University Press), p. 84). Furthermore, she argues that we must already know, in some general sense, what this nature is in order to design an experiment which will successfully reveal it: ‘[w]ithout the concept of natures, or something very like it, we have no way of knowing what it is we are testing’ (p. 90). For Cartwright, these are ‘Aristotelian-style natures’ (p. 81). Hence, she concludes: ‘The empiricists of the scientific revolution wanted to oust Aristotle entirely from the new learning. I have argued that they did no such thing’ (p. 103). A detailed comparison of the respective accounts of Heidegger and Cartwright might be worthwhile, but this is not the place for it. Suffice here only to note that, on Heidegger’s account, Cartwright’s natures will ultimately refer back to a possibility in the subject’s shared historical existence, and will thus be amenable to sociological investigation.

50 Heidegger (1967), What Is a Thing?, p. 95.

51 Heidegger (1967), What Is a Thing?, p. 101.

52 Heidegger (1967), What Is a Thing?, p. 100.

53 Heidegger (1962a), Being and Time, p. 116 [84].

54 Smith (2004), The Body of the Artisan, p. 7.

55 Smith (2004), The Body of the Artisan, p. 86.

56 Smith (2004), The Body of the Artisan, p. 86.

57 Ursula Klein and Emma C. Spary (2010), ‘Introduction: Why Materials?,’ in Materials and Expertise in Early Modern Europe: Between Market and Laboratory, ed. by Ursula Klein and Emma C. Spary (Chicago: University of Chicago Press), pp. 1–23 (p. 6).

58 Christoph Bartels (2010), ‘The Production of Silver, Copper, and Lead in the Harz Mountains from Late Medieval Times to the Onset of Industrialization,’ in Materials and Expertise in Early Modern Europe: Between Market and Laboratory, ed. by Ursula Klein and Emma C. Spary (Chicago: University of Chicago Press), pp. 71–100 (p. 100).

59 Bartels (2010), ‘The Production of Silver, Copper, and Lead,’ p. 97.

60 Bartels (2010), ‘The Production of Silver, Copper, and Lead,’ p. 97.

61 Martin Heidegger (1977a [1952]), ‘The Age of the World Picture,’ in The Question Concerning Technology, by Martin Heidegger, trans. by William Lovitt (New York: Harper & Row), pp. 115–54 (p. 122).

62 Heidegger (1977a), ‘The Age of the World Picture,’ p. 122.

63 Heidegger (1977a), ‘The Age of the World Picture,’ p. 120.

64 Steven Shapin and Simon Schaffer (1985), Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton: Princeton University Press), p. 24.

65 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 282.

66 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 41.

67 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 41.

68 Robert Boyle (1660 [1966]), New Experiments Physico-Mechanical, Touching on the Spring of the Air, and its Effects; Made, for the Most Part, in an New Pneumatical Engine, in The Works of Robert Boyle, vol. 1, ed. by Thomas Birch (Hildesheim: Georg Olms), pp. 1–117 (pp. 33–39).

69 Boyle (1660), New Experiments Physico-Mechanical, p. 11.

70 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 51.

71 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 52.

72 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 52.

73 Boyle (1660), New Experiments Physico-Mechanical, p. 11.

74 Boyle (1660), New Experiments Physico-Mechanical, p. 11.

75 Boyle (1660), New Experiments Physico-Mechanical, p. 12.

76 Linus, Franciscus (1661), Tractatus de Corporum Inseparabilitate in quo Experimenta de Vacuo, tam Torriculliana, quam Magdeburgica, et Boyliana examinantur, veraque eorum causa detecta, ostenditur, vacuum naturaliter dari non posse: unde et Aristotelica de Rarefactione sententia tam contra Assertores Vacuitatum, quam Corpusculorum demonstratur (London).

77 Conor Reilly notes that Line’s thread hypothesis was not original: ‘[s]uch a concept had already been suggested under a number of different forms, by several scholars’ (Conor Reilly (1969), Francis Line S. J.: An Exiled English Scientist 1595–1675 (Rome: Institutum Historicum), p. 65).

78 Cited in Boyle (1660), New Experiments Physico-Mechanical, p. 135.

79 Robert Boyle (1662 [1966]), A Defence of the Doctrine Touching the Spring and Weight of the Air, Proposed by Mr. R. Boyle, in his New Physico-Mechanical Experiments; Against the Objections of Franciscus Linus. Wherewith the Objector’s Funicular Hypothesis is also Examined, in The Works of Robert Boyle, vol. 1, ed. by Thomas Birch (Hildesheim: Georg Olms), pp. 118–85 (p. 143).

80 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 126.

81 Aristotle (1941c), Physica, p. 282 (lines 214a36–214b2).

82 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 134.

83 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 134.

84 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 135.

85 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 137.

86 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 126.

87 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 129.

88 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 129.

89 Cited in Reilly (1969), Francis Line S. J., p. 85.

90 Elizabeth Potter also makes this observation (Elizabeth Potter (2001), Gender and Boyle’s Law of Gases (Bloomington: Indiana University Press), pp. 36, 133).

91 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 156; see also pp. 124, 162, 178.

92 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, pp. 134, 178.

93 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 45.

94 Shapin and Schaffer (1985), Leviathan and the Air-Pump, p. 80.

95 The outward endeavour of Boyle’s microscopically insensible corpuscles was metaphysical. However, he also studied sensible phenomena manifesting a similar power of motion. In a 1685 treatise, Boyle remarks on thick pieces of glass which, when cooled after removal from a furnace, burst apart, their pieces ‘fly[ing] to a not inconsiderable distance from one another’ (Robert Boyle (1685 [1966]), An Essay of the Great Effects of Even Languid and Unheeded Motion, in The Works of Robert Boyle, vol. 5, ed. by Thomas Birch (Hildesheim: Georg Olms), pp. 1–37 (p. 24)). Likewise, when a bow string is cut, ‘the bow will fly suddenly outwards, and the parts of the string will swiftly and violently shrink from one another’ (p. 26). And gemstones, when extracted from the hard cement of an aggregate rock, ‘quickly expanded themselves, as if it were by an internal and violently compressed spring, and would presently burst asunder’ (p. 27). From this, Boyle concludes that ‘bodies, which as to sense, are in a natural state of rest, may be in a violent one, as of tension, and may have […] a strong endeavour to fly off or recede from one another’ (p. 26). Boyle may have viewed these phenomena as empirical vindication for his metaphysical claim that corpuscular springs manifest an internal power of outward endeavour when released from compression.

96 David Bloor (1991 [1976]), Knowledge and Social Imagery, 2nd edn (Chicago: University of Chicago Press), p. 52.

97 Bloor (1991), Knowledge and Social Imagery, p. 53.

98 Bloor (1991), Knowledge and Social Imagery, p. 12.

99 David Bloor (1973), ‘Wittgenstein and Mannheim on the Sociology of Mathematics,’ Studies in History and Philosophy of Science 4(2), 173–91 (pp. 178, 185).

100 Bloor (1973), ‘Wittgenstein and Mannheim,’ p. 174 n. 4; citing Popper.

101 In respect of the second point, note that Bloor has more recently reiterated his identification of ‘telos’ with a non-contingent ‘inner necessity’ guiding scientific practice (David Bloor (2011), The Enigma of the Aerofoil: Rival Theories in Aerodynamics, 1909–1930 (Chicago: Chicago University Press), p. 436). As for the first point, the issue is similar to the one addressed in Chapter Four, where I argued that Bloor’s identification of intentionality with mental content does not touch a Heideggerian account of intentionality, which construes this in non-mental terms. That Heidegger did not espouse a teleological model, in Bloor’s sense, is further attested in Michael Friedman’s observation that ‘[Ernst] Cassirer’s philosophy of symbolic forms […] diverges from Heidegger’s existential analytic of Dasein precisely in emphasizing a teleological development toward the genuinely “objective” and “universally valid” realm of scientific truth’ (Michael Friedman (2000), A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court), p. 138). Friedman also notes the influence of Cassirer’s anti-naturalistic teleological historiography on such historians of science as Edwin Arthur Burtt, Eduard Jan Dijksterhuis, and Alexandre Koyré (Friedman (2000), A Parting of the Ways, p. 88; see Edwin Arthur Burtt (1925), The Metaphysical Foundations of Modern Physical Science: A Historical and Critical Essay (London: Kegan Paul, Trench, Trubner & Co.); Eduard Jan Dijksterhuis (1961 [1950]), The Mechanization of the World Picture, trans. by C. Dikshoorn (London: Oxford University Press); Koyré (1943a), ‘Galileo and Plato’; and Alexandre Koyré (1943b), ‘Galileo and the Scientific Revolution of the Seventeenth Century,’ Philosophical Review 52(4), 333–48). This historiographic tradition appears to be a central object of Bloor’s criticism. Barry Barnes criticises a similar teleological method in György Lukács’s History and Class Consciousness (Barry Barnes (1977), Interests and the Growth of Knowledge (London: Routledge & Kegan Paul), p. 48; see György Lukács (1971 [1923]), History and Class Consciousness: Studies in Marxist Dialectics, trans. by Rodney Livingstone (London: Merlin Press)). For a more recent comparison of Heidegger and Cassirer, see Peter E. Gordon (2010), Continental Divide: Heidegger, Cassirer, Davos (Cambridge, MA: Harvard University Press).

102 Karl Mannheim (1953 [1925]), ‘Conservative Thought,’ in Essays on Sociology and Social Psychology, by Karl Mannheim, ed. by Paul Kecskemeti (London: Routledge), pp. 74–164.

103 Bloor (1991), Knowledge and Social Imagery, p. 60.

104 Bloor (1991), Knowledge and Social Imagery, pp. 62, 63.

105 Bloor (1991), Knowledge and Social Imagery, p. 62.

106 Bloor (1991), Knowledge and Social Imagery, p. 63.

107 Bloor (1991), Knowledge and Social Imagery, pp. 62, 63.

108 I have elsewhere questioned Bloor’s reading of Popper, arguing that Popper is much closer to being a communitarian epistemologist than is allowed for by Bloor (Jeff Kochan (2009b), ‘Popper’s Communitarianism,’ in Rethinking Popper, ed. by Zuzana Parusniková and Robert S. Cohen (Boston Studies in the Philosophy of Science 272) (Berlin: Springer), pp. 287–303).

109 Mannheim (1953), ‘Conservative Thought,’ p. 85.

110 Mannheim (1953), ‘Conservative Thought,’ p. 149.

111 Mannheim (1953), ‘Conservative Thought,’ p. 115.

112 Mannheim (1953), ‘Conservative Thought,’ p. 89.

113 Mannheim (1953), ‘Conservative Thought,’ pp. 150–51.

114 Mannheim (1953), ‘Conservative Thought,’ p. 153.

115 Mannheim (1953), ‘Conservative Thought,’ p. 111. The bracketed text has been inserted from the German original (Karl Mannheim (1984 [1925]), Konservatismus. Ein Beitrag zur Soziologie des Wissens, ed. by David Kettler, Volker Meja and Nico Stehr (Frankfurt: Suhrkamp), p. 121). Note that Grundriss is the original term for both Mannheim’s concept of ‘ground plan’ and Heidegger’s concept of ‘one basic blueprint,’ under which, I have argued, the First Thing may be placed.

116 Mannheim (1953), ‘Conservative Thought,’ p. 88.

117 Mannheim (1953), ‘Conservative Thought,’ pp. 155, 103.

118 Mannheim (1953), ‘Conservative Thought,’ p. 159.

119 Quentin Skinner (2002), ‘Hobbes and the Politics of the Early Royal Society,’ in Visions of Politics, vol. 3: Hobbes and Civil Science, by Quentin Skinner (Cambridge: Cambridge University Press), pp. 324–45 (p. 336).

120 Reprinted in Michael R. G. Spiller (1980), ‘Concerning Natural Experimental Philosophie’: Meric Casaubon and the Royal Society (The Hague: Martinus Nijhoff), pp. 149–189. According to Richard Serjeantson, Casaubon ‘had a strong fascination with the natural world: as a young man he attempted some of the experiments in Francis Bacon’s Sylva sylvarum’ (Richard W. Serjeantson (2004), ‘Casaubon, Méric,’ in Oxford Dictionary of National Biography, vol. 10, ed. by H. C. G. Matthews and Brian Harrison (Oxford: Oxford University Press), pp. 464–66 (p. 466)).

121 Spiller (1980), ‘Concerning Natural Experimental Philosophie,’ p. 130.

122 Spiller (1980), ‘Concerning Natural Experimental Philosophie,’ p. 136.

123 Heidegger (1977a), ‘The Age of the World Picture,’ p. 130.

124 Hans-Jörg Rheinberger suggests that Heidegger’s term Weltbild (‘world picture’) ‘might be more appropriately translated as “[…] Planetary Configuration”’ (Hans-Jörg Rheinberger (1997), Towards a History of Epistemic Things: Synthesizing Proteins in the Test Tube (Stanford: University of Stanford Press), p. 25 n. 6). This has the benefit of emphasising the material aspect of the phenomenon, but it also seems to deflect attention from the projective role played by the subject in creating that phenomenon, not to mention the intersubjective (social) labour required to materially extend it to, and sustain it on, a planetary scale. See also Hans-Jörg Rheinberger (2010a), An Epistemology of the Concrete: Twentieth-Century Histories of Life (Durham: Duke University Press), p. 234.

125 Bloor (1991), Knowledge and Social Imagery, p. 154.

126 Carolyn Merchant (1980), The Death of Nature: Women, Ecology and the Scientific Revolution (San Francisco: Harper & Row), p. 125.

127 In 1940, Heidegger claimed that ‘the idea of “organism” and of the “organic” is a purely modern, mechanistic-technological concept’ (Martin Heidegger (1976 [1967]), ‘On the Being and Conception of φύσις in Aristotle’s Physics B, 1,’ Man and World 9(3), 219–70 (p. 234)). This claim is stronger, and more contentious, than is required for the present argument.

128 Merchant (1980), The Death of Nature, p. xxii.

129 Merchant (1980), The Death of Nature, p. xx.

130 Merchant (1980), The Death of Nature, pp. 103–126. Works cited include: Giovanni Battista della Porta’s Magiae naturalis (published 1558); Bernardino Telesio’s De rerum natura iuxta propia principia (published 1565); Giordano Bruno’s Spaccio de la bestia trionfante (published 1584); Tommaso Campanella’s De sensu rerum et magia (published 1620). Note that all of these works appeared after Nicolaus Copernicus’s De revolutionibus orbium coelestium (published 1543), with which the beginning of the Scientific Revolution is often credited.

131 Potter (2001), Gender and Boyle’s Law of Gases, p. 160.

132 Peter Davidson (2009), ‘Francis Line S. J., Explicatio horologii (1673),’ in Jesuit Books in the Low Countries (1540–1773): A Selection from the Maurits Sabbe Library, ed. by Paul Begheyn, SJ., Bernard Deprez, Rob Faesen, SJ, and Leo Kenis (Leuven: Uitgeverij Peeters), pp. 187–90 (p. 187).

133 John Aubrey (2014), Brief Lives, with an Apparatus for the Lives of Our English Mathematical Writers, vol. 1, ed. by Kate Bennett (Oxford: Oxford University Press), p. 151.

134 Davidson (2009), ‘Francis Line S. J., Explicatio horologii (1673),’ p. 189. Line published a detailed description, with illustrations, of the Whitehall sundial in 1673, in both Latin and English. Davidson’s entry includes reproductions of the Latin title page and one of Line’s illustrations.

135 Walter Charleton (1654 [1966]), Physiologia Epicuro-Gassendo-Charltoniana: Or a Fabrick of Science Natural, Upon the Hypothesis of Atoms (New York: Johnson Reproductions), pp. 344, 345.

136 Boyle (1662), A Defence of the Doctrine Touching the Spring and Weight of the Air, p. 142.