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Chapter Five

Mathēsis and the Emergence of Early-Modern Science

© Jeff Kochan, CC BY 4.0

1. Introduction

Place a grain of wheat on the ground in front of you. Does this amount to a heap of grain? No, of course not. So, add a second grain. Is it a heap now? No. A third grain? No. A fourth grain? No. A fifth grain? No. And so it goes also after a sixth grain, a seventh grain, an eight grain, and a ninth grain. When a tenth grain is added, we still do not have a heap.

But we do have a pattern. The pattern is this: if some grains do not make a heap, then adding one more grain will not turn them into a heap. On the basis of this pattern, we can now make more specific predictions. We can predict that adding an eleventh grain will not make a heap, nor will adding a twelfth grain, a thirteenth grain, or a fourteenth grain. The pattern, then, has the character of a general prediction: when you add one grain to a non-heap, the result will be a non-heap. A single grain cannot determine the difference between a non-heap and a heap.

The second-century Greek physician, Galen of Pergamon, exploited the predictive power of this pattern when he wrote:

I know of nothing worse and more absurd than that the being and not-being of a heap is determined by a grain of corn. And to prevent this absurdity from adhering to you, you will not cease from denying, and will never admit at any time that the sum of this is a heap, even if the number of grains of wheat reaches infinity by the constant and gradual addition of more. And by reason of this denial the heap is proved to be non-existent, because of this pretty sophism. And so it follows from this sophism that the mountain also does not exist.1

The ‘you’ to whom Galen addressed his comment was the ‘dogmatic’ physician. Galen argues that the dogmatist cannot reject the implication of the pattern without appearing silly. However, the dogmatist will then be forced to reject the existence of heaps, which is also silly. The dogmatist is thus faced with a paradox for which no solution is obvious.

This is a case of turnabout being fair play, because the dogmatist had already laid out the same kind of argument against Galen and other empirical physicians. In the above passage, Galen is demonstrating that the paradox cuts both ways, causing potential problems for the dogmatist as well.

Galen tells us that the dogmatist has challenged the empiricist physician’s claim that a belief will be credible if it is supported by evidence which has been seen ‘very many times.’ To this, the dogmatist asks: How many times? Ten? The empiricist says no, ten times is not enough. The dogmatist then asks: Eleven times? No, says the empiricist, eleven times is also not enough. The pattern has now appeared, and the dogmatist leads the empiricist into the paradox. If the empiricist insists on the method of ‘seeing very many times,’ she will be forced to admit the impossibility of empirical knowledge.

For if something that was seen forty-nine times and yet in all these times was not accepted nor considered to be true, now by the addition of this one single time comes to be considered acceptable and true, it is obvious that only by being seen a single time has it become acceptable and true. The inevitable conclusion is that seeing a thing once — although at the outset this was not accepted and considered true — has on this occasion such force that when added to something which was not acceptable and not considered true as to make it acceptable, and vice versa.2

The dogmatist argues that one observation is enough to produce knowledge. The ‘force’ of this single observation derives from the physician’s ‘know[ing] from the very beginning what things have to be eliminated and disregarded as being superfluous and unnecessary, and what things have to be examined and to be judged carefully as to their usefulness and their necessity.’3 What the dogmatic physician is insisting on here is the need for an a priori standard by which to differentiate between epistemically desirable and epistemically undesirable phenomena. Moreover, the force of this standard in use will be immediate, manifesting itself on the basis of a single act of observation. At best, the empiricist’s little-by-little method fails to reflect the immediacy and constructivity of reason. Today, this kind of dogmatism is more commonly called ‘rationalism.’

The paradoxes generated by this pattern of argument pose a threat to empiricists and rationalists alike. More generally, they threaten confidence in both inductive and deductive forms of inferential reasoning. Scepticism about induction is well known, and has often been discussed in terms of the underdetermination of theory by data, a topic which we earlier addressed in Chapter Three. No matter how many times the empiricist observes the phenomena, no knowledge will arise without the mediation of some additional, unobserved element. For the rationalist, this additional element is the a priori. For the sociologist of knowledge, it is grounded in social convention. As we saw in Chapter Four, Heidegger grounds the a priori in a historical tradition, a stance which is compatible with that of SSK. By posing the socio-historical contingency of the a priori, the latter two positions reject the absolutism of the rationalist. For them, scientific knowledge is objective, but not absolutely so.4

Galen’s second-century response to the dogmatic physician is similar to these responses. He rebuffs the dogmatist’s charge that the empiricist cannot produce ‘technical’ — that is, objective — knowledge: ‘you would be acting both unjustly and wrongly in pestering us to specify, of a thing which when seen once only is not “technical” according to your argument, how many times it must be seen in order to become “technical.”’5 The injustice lies in ridiculing the empiricist ‘because we cannot state with exactitude the precise number […], but are only able to give a general notion.’6 Based on this argument, the dogmatist will insist that a definition of ‘heap,’ in order to be objective, must be precise rather than general; it must exactly specify how many grains make a heap. Yet, as Galen has already shown, the dogmatist cannot do this without appearing silly. Indeed, by specifying the precise number of grains with which a non-heap becomes a heap, the dogmatist reveals his purportedly ‘technical’ knowledge of heaps is, in fact, lamentably subjective.

Galen then expands this critique to encompass the dogmatist’s medical knowledge in general. He points out that the dogmatist’s a priori standard ‘is not uniform, universal, comprising all of you, because you have different views and each one of you holds an opinion completely contradictory to the opinion of the others.’7 The implication is that objective knowledge is marked, to some substantial degree, by social agreement. The paradox of the heap relies on this idea, since, because most people agree that heaps exist, the dogmatist will appear silly if he claims that they do not.

If you wish, speak, it will not cause me to be angry with you; if, however, you should say of something which people continually see under the same conditions throughout their lives, that it is non-existent, it will not help you at all. […] I for my part adhere to and follow that which is known to men, and accept what is obvious without inquiring into the cause of each individual thing. Therefore I say of what has been seen but once, that it is not ‘technical,’ just as a single grain of wheat is not a perfect heap; if, however, it is a thing that is seen many times in the same way, then I call it ‘technical.’8

For Galen, objective knowledge has a social aspect — it is ‘that which is known to men’ — and a historical aspect — it is based on that which is ‘seen many times in the same way.’ However, he also notes that such knowledge is ‘obvious without inquiring into the cause of each individual thing.’ When it comes to heaps, this may be true. But what about disease? At least in the case of unfamiliar diseases, it would seem that close attention to causes may help in the development of an effective treatment. This was a point made by Galen’s dogmatic opponent.

But just because the number of concomitants of diseases is so great and there is such variety in what causes evacuation and what is vomited up and what is introduced into the organism, while those things that affect it from the outside are still more numerous, the Empiricist is still less able to judge which of them are beneficial and which harmful.9

Here the dogmatist reinforces the claim that the physician requires a standard by which to reliably distinguish between causes which are, and those which are not, necessary for the understanding and effective treatment of disease. Galen accepts the need for such a standard, but dismisses the idea that it be subjected to systematic enquiry.

[I]t has been found that what has been seen many times becomes ‘technical.’ With regard to the cause, however, which makes it completely ‘technical’ and when it begins to be completely ‘technical,’ I am of opinion that it is idle to demand this. For I find that not a particle of harm befalls arts and men in their modes of life and activities for being ignorant of such things.10

Objective medical knowledge is produced through serial, disciplined observation, but the question of what norms guide those observations is of little interest to Galen. For him, it is enough to know those norms in a vague and general way, much as we do the norms used to distinguish between a heap and a non-heap. There is, he thinks, no great need to specify them in a systematic or precise way. In Heidegger’s term, Galen has no interest in thematising the norms which guide successful medical thinking. In SSK’s terms, he is happy to rely on those norms as a resource, but resists turning them into a topic. Galen’s attitude may thus strike one as distinctly unscientific. Moreover, it seems to be an attitude hostile to epistemology, in general, and, insofar as Galen attributes a social aspect to medical knowledge, to SSK, in particular.

In fact, as we will see in this chapter, later physicians became increasingly interested in understanding the methods by which reliable medical knowledge is produced. More than a millennium after Galen, Renaissance empirical physicians began to topicalise and systematically investigate the informal logic which they thought must underpin their techniques of medical discovery. As historians have long recognised, these physicians were innovators in the rationalisation of scientific method, and hence key contributors to the rise of early-modern empirical science.

The Renaissance empiricists examined in this chapter accepted the dogmatist’s view that physicians must know something in advance, from the very beginning, in order to successfully diagnose and treat disease. Moreover, they agreed with the dogmatists that this a priori knowledge was a knowledge of causes. However, they resisted the dogmatist’s claim that, on the basis of this knowledge, only one observation is needed to properly diagnose a disease. Indeed, the empiricists continued to defend their doctrine of serial observation, of medical knowledge gained little by little through a practice of ‘seeing many times in the same way.’

The epistemology of these empirical physicians thus appears to have been circular: they claimed both that they already possessed knowledge of health and disease at the very beginning of their enquiry, and that their knowledge of health and disease was the consequence of their method of serial observation. They argued, however, that this epistemic circle was not a vicious one. Like Galen over one thousand years earlier, these Renaissance physicians argued that their a priori knowledge was of only a general, imprecise sort. Their empirical method, then, was meant to transform this general and imprecise knowledge into specific and precise knowledge. Hence, their account of knowledge was not viciously circular, because it involved two different sorts of knowledge, one linked to the other by an empirical method of investigation.

As already noted, this method of investigation bears striking similarities to what Heidegger called a thematising articulation, a topic to which we gave detailed attention in Chapter Four. One key aspect of this process of articulation is the transformation of informal, often tacitly held knowledge into explicit, formalised knowledge. The efforts of Renaissance physicians to understand this process, as a central feature of their own medical practice, provides further historical support for Heidegger’s existential conception of science. Moreover, this historical case also allows us to more fully explore one particular facet of Heidegger’s existential conception, namely, the mathematicisation of natural knowledge. With this, we expand on a topic first addressed in Chapter Two under the label of ‘the mathematical projection of nature.’ The role of mathematics in the emergence of early-modern science has been a key point of debate among contemporary historians of science, a debate which, in many ways, reiterates the long-standing feud between empiricists and rationalists alluded to above. Heidegger’s concept of mathēsis, or ‘the mathematical,’ as well as its relation to what is commonly referred to as the ‘Scientific Revolution,’ adds a further perspective to this debate, one which seeks to combine the best insights from both camps. In addition, as we will see near the end of this chapter, Heidegger’s account of modern science as mathēsis also challenges the historiographic commonplace that the Scientific Revolution coincided with the expungement of Aristotelian ‘final causes’ from scientific practice in the seventeenth century. On Heidegger’s account, final causes were not abandoned, but instead radically transformed — to wit, mathematicised. This claim will lay the ground for a more detailed discussion in Chapter Six about the rise of seventeenth-century experimental philosophy. For now, let us start with a review of Heidegger’s account of mathēsis, and then move on to consider the deliberations of empirically minded physicians during the three centuries prior to the emergence of early-modern science. These topics will lead us into the heart of key historiographic debates over the existence and nature of the Scientific Revolution.

2. Modern Science as Mathēsis

As discussed in previous chapters, the thing has been typically defined as a property-bearing substance. Heidegger writes that this definition seems ‘natural,’ in the sense of ‘what is understood without further ado and is “self-evident” in the realm of everyday understanding.’11 Yet he challenges this construal of the ‘natural’ as being self-evident, and thus not amenable to further analysis, arguing instead that ‘[t]he “natural” is always historical.’12 The prevailing definition of the thing did not ‘just fall absolutely from heaven, but would have itself been based on very definite presuppositions.’13 Indeed, as was argued in Chapter Four, one key presupposition determining the prevailing definition of the thing was the Aristotelian claim that the structure of the thing may be usefully modelled on the structure of the proposition. According to Heidegger, this proposition-based account of the thing has played a central role in the development of the modern scientific understanding of the thing as an object of investigation.

One consequence of this definition is the treatment of a thing in abstraction from its concrete circumstances and other unique features. A definition of the thingness, or whatness, of the thing, as such, is a generalised definition which deliberately overlooks all the peculiarities distinctive of any one particular thing. Thus Heidegger writes:

[A] botanist, when he examines the labiate flower, will never be concerned about the single flower as a single one: it always remains an exemplar only. That is also true of the animals, for example, the countless frogs and salamanders which are killed in a laboratory. The ‘this one’ (je dieses) which distinguishes every thing, will be skipped over [übersprungen] by science.14

In this section, we will consider in detail Heidegger’s account of modern science as a form of understanding which ‘skips over’ the individual specificities of the things it investigates. Heidegger elaborates this account by characterising modern science in terms of the ancient Greek concept of mathēsis, or what he also calls ‘the mathematical’ (das Mathematische). These considerations, arising out of a 1935–1936 lecture course, present a further development of his earlier account of the mathematical projection of nature. What he had earlier treated as a central element of science, in general, now becomes a defining feature of modern science, in particular.

For Heidegger, mathēsis refers to that fundamental characteristic of modern science which distinguishes it from both ancient and medieval science. He addresses, and rejects in turn, attempts to distinguish modern science on the grounds that it begins with facts about things rather than with speculative propositions and concepts, that it uses experiments to get information about the behaviour of things, and that it relies on calculation and measurement in its investigations of things. On all three counts, Heidegger argues, there is no substantive difference between ancient and medieval science, on the one hand, and modern science, on the other. First, ancient and medieval science also observed the facts, and modern scientists also rely on speculative propositions and concepts. Second, the use of experiments, in the broad sense of controlled tests to gain information about things, was already familiar in the ancient and medieval periods. Heidegger comments that ‘[t]his kind of experience lies at the basis of all technological contact with things in the crafts and the use of tools.’15 Third, ancient science also made use of measurement and number.

Heidegger argues that it is not reliance on facts, as such, which is decisive for modern science, but ‘the way the facts are conceived.’ Likewise, it is not the experiment, as such, that matters, but ‘the manner of setting up the test and the intent with which it is undertaken and in which it is grounded.’ And so too with calculation and measurement: ‘it is a question of how and in what sense calculating and measuring were applied and carried out, and what importance they have for the determination of the objects themselves.’16 Hence, it is not that facts, experiments, calculation and measurement are deployed, but how and to what end they are deployed, which distinguishes modern science. This points us towards the historically specific existential conditions of possibility governing what ‘essentially and decisively rules the basic movement’ of modern science.17 It points us, in other words, towards the phenomenon of mathēsis. Heidegger suggests that mathēsis is something which governs modern science at a basic level. It thus includes a strongly normative component.

Heidegger defines mathēsis as ‘the teaching’ (die Lehre), in the sense of ‘the doctrine’ or ‘the apprenticeship,’ which in turn has a double sense: ‘teaching’ as entering into an apprenticeship (in die Lehre gehen) and then learning or studying; and ‘teaching’ as what is taught. Heidegger means here teaching and learning ‘in a broad and at the same time essential sense, not in the more recent, narrow, hackneyed sense of “schools” and “scholars.”’18 He furthermore distinguishes two fundamental features of modern science as mathēsis: (1) ‘work experiences,’ or ‘the direction and way of controlling and using [or manipulating] what is’; and (2) ‘metaphysics,’ or ‘the projection of the fundamental knowledge of being, upon which what is establishes itself as knowable.’19 These two fundamental features are ‘reciprocally related,’ and always occur together in the activities of scientifically engaged human beings.20

We have already encountered this twofold structure in Chapter Four, where our attention was primarily on the metaphysical projection of the thingness of things, as a constructive aspect of thinking, rather than on scientists’ work experiences in respect of those things. Nevertheless, already there we encountered the historical interplay between things, experienced as property-bearing substances, and thinking, construed as propositionally structured rule-following. In this chapter, and in Chapter Six, we will treat the experience of things more directly as work experience, that is, as experiences which arise from the direct engagement with and manipulation of material things. Our focus in this chapter and the next will, in other words, be directed more towards the existential conditions enabling physical experimentation in modern science. As we will see, the experimental manipulation of things is, indeed, reciprocally related to the metaphysical projection of the thingness of things. The experimental set-up is a material instantiation of, as well as the material basis for, the metaphysical projection. Hence, Heidegger’s account of modern science in term of mathēsis recognises a central place for the material practices of experimental science without rejecting a role for metaphysics. His account can thus be assimilated to neither of the conventional empiricist and rationalist interpretations of the Scientific Revolution. It must be immediately emphasised, however, that Heidegger did not develop this strand of his existential conception of science in any great detail. Additional material from the history of science will allow us to develop and refine Heidegger’s account of modern science in a way which he did not, and which is, I think, consistent with his intentions.

According to Heidegger, the word mathēsis stems from the Greek word mathēmata, the name for a specific kind of thing. These are things insofar as they are learnable, or amenable to study.21 However, as he also points out, we do not, strictly speaking, learn a thing. We learn instead how to relate to a thing, for example, how to observe it, how to use it, or how to produce it. Hence, when we learn a thing, we are really learning something about our relation to it. Heidegger illustrates this point with the example of a rifle. We do not learn a rifle, he writes, but its usage. The acquisition of the usage happens through the usage itself, that is, through ‘exercise’ or ‘practice’ (Übung).22 In our practice with the rifle, we learn to load it, to control its trigger, and to aim it.

However, Heidegger argues that ‘practising’ (Üben) is only one kind of learning. There is another, more fundamental, kind of learning which actually makes it possible for us to learn through practice. This more basic learning allows us to perceive what a weapon is, what a use-item is, and, most generally, what a thing is. Heidegger argues that we do not learn the ‘what’ of a weapon only once we have learned the ‘how’ of its usage. On the contrary, ‘[w]e already know [what a weapon is] beforehand, and must know it; otherwise we could not even recognise the rifle as such,’ we could not, that is, tell the difference between a rifle and a non-rifle.23

Yet, although we must first know what a rifle is if we want to learn its usage, this prior knowledge is something we need only have in a ‘general’ and ‘indefinite’ way. In other words, when it comes to learning the usage of a thing, prior knowledge of the whatness of the thing is certainly necessary, but we need only possess it in a tacit way, as a kind of general and indeterminate background knowledge. When, in contrast, it comes to learning in the sense of mathēsis, we must deliberately ‘take note’ of (zur Kenntnis nehmen) what the thing is, doing so ‘specifically and in a determinate way.’ Such deliberate ‘taking note’ is the very ground of learning as mathēsis.24 This is a kind of learning in which — by taking note of what we already know — we begin to transform our pre-existing knowledge of what a thing is from a general and indefinite state into a specific and determinate state. Such is the case, Heidegger claims, when a specific rifle model is brought into existence: ‘[w]hen it becomes essential, in a general sense, to make available a thing like the one whose usage we are practising, that is, when it becomes necessary to produce it.’ This requires ‘a becoming-acquainted [Kennenlernen] with what fundamentally belongs to a firearm and with what a weapon is.’ Compared to the knowledge gained of a rifle’s usage, this is ‘a more basic acquaintance, one which must be learned beforehand, so that such a rifle type and its corresponding tokens may come to exist at all.’25

So what is it about the rifle which both the sharpshooter and the gunsmith must know in advance, but of which only the gunsmith need take note in order to fulfill her task? More generally, of what does one need to take note in order to learn in the sense of mathēsis? The answer, Heidegger tells us, is that ‘the producer must know beforehand what Bewandtnis fundamentally accompanies the thing.’26 The German word Bewandtnis is a tricky one to translate. In this passage, Heidegger uses it without pausing to explain its meaning. However, if we turn to an earlier discussion, in §18 of Being and Time, we can get a better sense of what the term means in the context of Heidegger’s existential account of science. Crucially, Heidegger treats the noun Bewandtnis together with the closely related verb bewenden. Below is my translation of the key passage in Being and Time in which the term Bewandtnis first appears.27 As will be immediately evident, Heidegger is introducing the term in the context of his discussion of readiness-to-hand, a concept we have already encountered numerous times in previous chapters.

That the being of the ready-to-hand has the structure of a reference or assignment [Verweisung] — means: it has in itself the character of directedness [Verwiesenheit]. What-is is thereby discovered as that which is directed towards something. With what-is, at this something, there is an end [es hatsein Bewenden]. The being-character of the ready-to-hand is end-directedness [Bewandtnis]. In end-directedness, there is a letting-be [bewenden lassen] with and at something. The relation of ‘with… at…’ [»mitbei…«] will be denoted by the term ‘assignment.’28

In respect of Heidegger’s phenomenological account of scientific practice, the meaning of Bewandtnis is best understood as ‘end-directedness.’ I do not recommend this translation for general application throughout Heidegger’s work, but only as the best translation when it comes to his reflections on science as mathēsis. This is a philosophical translation with a particular, narrow aim.29

Being and Time provides the following concrete example for what Heidegger means by end-directedness, as well as the ‘with… at…’ relation of assignment: ‘with the ready-to-hand thing we call “hammer,” there is the end-directedness of being at work, hammering; with hammering, the end-directedness of being at fortifying; with fortifying, the end-directedness of being at sheltering against bad weather.’30 Transposed to our example of the rifle, we can say that with the rifle there is the end-directedness of being at work, shooting; with shooting, the end-directedness of being at impacting at a distance; and with impacting at a distance, the end-directedness of being at subjugating others. Put otherwise, the task at which the sharpshooter works with the rifle is shooting. With the rifle, at this task, there is an end: proximally, impacting at a distance; more distally, subjugating others. The being of the rifle, its readiness-to-hand, is a directedness towards this end, it is that towards which the rifle is, essentially, directed. Heidegger writes that the ‘at-which’ [Wobei] of an end-directedness is also a ‘towards-which’ [Wozu], and that with this towards-which there can be yet another end-directedness.31 Hence, shooting is the end towards which the rifle is directed. With the towards-which of the rifle, proximally directed towards shooting, there is a further, more distal, end: impacting at a distance. The end-directedness of the rifle points towards shooting, and shooting, in turn, points towards impacting at a distance, and impacting at a distance points towards subjugating others.

However, this iteration of assignment finally comes to an end in a ‘primary’ towards-which. Heidegger writes that the ‘primary “towards-which” is a “for-the-sake-of-which” [Worum-willen].’32 For example, in the case of the hammer, the iteration bottoms out in ‘protection.’ The hammer points towards hammering, which points towards fortifying, which points towards sheltering, which points, finally, towards protection. That for the sake of which one hammers, fortifies, shelters, is the subject’s protection, which Heidegger describes as a ‘possibility’ of the subject’s existence.33 Returning, once more, to our rifle example, we may take the primary towards-which of the rifle — that for the sake of which the rifle, ultimately, exists — to be sovereignty. With the rifle, one shoots, impacts, subjugates, for the sake of the subject’s sovereignty, an ontological possibility of its existence. Ultimately, at work, with the rifle, there is a directedness towards sovereignty as end. According to Heidegger, in order to work with the rifle in a way which lets it be what it is, one must already have a knowledge of its end-directedness, and, hence, the final end towards which it points. This is an antecedent knowledge which the sharpshooter and the gunsmith both possess in a general and indefinite way, and of which only the latter need deliberately take note, developing it, through mathēsis, into a more specific and determinate knowledge.

Now consider the example of a plant collector. A plant collector is more like a sharpshooter. In order to pick a plant and put it in her collection, she must already know what a plant is. If she did not know this, then she would not even be able to identify a plant, to tell the difference, for example, between a plant and a platypus. But this prior knowledge need only be of a general and indeterminate sort. On its basis, the plant collector can take a particular plant for her collection, without deliberately taking note of that plant’s general plantness, or whatness. In contrast, the botanist will deliberately take note of the general plantness of the plant. In the course of her work, she ‘skips over’ the individual specimens, taking them only as tokens of a general type. Nevertheless, it is with these individual specimens, by being concretely at work with them, that the botanist learns — develops a specific and determinate knowledge of — the type. This learning is mathēsis, and, according to Heidegger, it marks the difference between ancient and medieval science, on the one hand, and modern science, on the other.

It should be emphasised that, in the examples of both the plant collector and the botanist, the particular, concrete plant is being treated as something ready-to-hand in a work-world. In other words, we are considering it as it is experienced by the one who is at work with it. From this perspective, then, there is no basic ontological difference between the plant and the rifle. Both are things ready-to-hand within a work-world. On Heidegger’s account, then, in being at work with either the particular plant or the particular rifle, there is an end-directedness. Furthermore, in both cases this end-directedness ultimately bottoms out in that for the sake of which the ready-to-hand thing is what it is. This for-the-sake-of-which is an existential possibility of the subject.

In the case of the hammer, this existential possibility is the subject’s protection. In the case of the rifle, it is the subject’s sovereignty. What about the plant? Here the answer is less obvious. On first blush, there does not seem to be anything for the sake of which the plant is what it is. This doubt is tied to our intuition that the plant is, in the first instance, not something ready-to-hand, but something present-at-hand. Yet this intuition was challenged in Chapters One and Two. According to Heidegger, a thing within the world is experienced, most immediately, as ready-to-hand. Only on this basis can it be subsequently experienced as present-at-hand within in the world. Hence, the what-being of a scientific thing should be understood fundamentally in terms of its readiness-to-hand, which is to say, in terms of its end-directedness. From this it follows that the scientific thing — that which in scientific work is let be what it is — is for the sake of an existential possibility of the subject. Heidegger argues that we already know this possibility, and must know it, when we intelligibly experience the scientific thing, as such, not to say when we start working with it. This possibility is the ultimate end towards which the what-it-is of the scientific thing is directed. The hammerness of the hammer points, finally, towards protection, and the rifleness of the rifle, finally, towards sovereignty. To what, then, does the plantness of the plant, finally, point?

Heidegger does not answer this question. Instead, he concentrates on the more general question of to what existential possibility the thingness of the scientific thing itself finally points. We will consider the specific content of Heidegger’s answer to this question in Chapter Six. In the meantime, in order to properly appreciate the grounds for that answer, we must first gain a firmer grip on the more formal characteristics of Heidegger’s answer: namely, that the scientific thing — as something with which scientists are at work — possesses an end-directedness pointing towards a final end. We must know this end-directedness beforehand if we are to successfully identify and work with the thing. In scientific work, we deliberately take note of this end-directedness, bring it into the foreground, and thereby seek to articulate our prior general and indeterminate knowledge of it into a more specific and determinate knowledge. This is how we study mathēmata, things insofar as they can be learned. This is a process of mathēsis, whereby we learn what we already know.

Formally, then, Heidegger views the scientific thing in terms of its end-directedness, a feature which we deliberatively experience only insofar as we relate to the thing through mathēsis, that is, only insofar as we study or learn it. A further formal feature of the scientific thing is, therefore, epistemic circularity: we can only know it because we already know it. This may raise the worry that Heidegger’s account of mathēsis attributes to science a fallacious form of reasoning. On this account, so the worry goes, the conclusion of a scientific inference is already among its initial premises; hence, science gives us no reason to accept its conclusions as valid.

But we are already familiar, from Chapter Four, with Heidegger’s response to this worry in respect of logic, construed as the science of the rules of reason. The worry there was that, since science is grounded in rules of reasoning, and since logic is identical with those rules, then logic grounds logic.

In response, Heidegger rejected the premise which equates logic and rules. Logic may presuppose rules, but rules do not entail logic. Indeed, only when the rules of reason have been rendered in a specific and determinate way do they count as rules of logic. The job of logic, as the science of thinking, is to deliberatively take note of the general and indeterminate rules which implicitly govern informal reasoning, and then to study them in a way which specifies and determines them, in other words, clearly explicates them in a formal system. Hence, it is not the case that the conclusions of the science of logic are already among its premises, because the relation between premises and conclusion is interpretative rather than inferential. The science of logic is a practice in which informal thinking becomes formalised, in which general and indeterminate rules of reason are rendered specific and determinate. If there is a circularity here, then it is not vicious.

We can now see that logic is a particular case of the more general scientific practice of mathēsis. Our past discussion of this case, in turn, shows why we need not worry about the circularity of mathēsis: this circularity is interpretative rather than inferential, hermeneutical rather than logical, and so virtuous rather than vicious. It is a fundamental feature of science conceptualised as an ultimately informal existential practice, rather than as a logically determinate system of precisely defined concepts. Furthermore, science, as a form of reasoning, is guided by rules. Logic may seek to thematise and define those rules, but the natural sciences will be less concerned with explicating and determining the dynamics of their own thinking, and more interested in reliably explicating and determining the whatness of the material things they take to be the object of that thinking. According to Heidegger, these sciences ultimately attend to the end-directedness of natural things. The rules of reason governing this attention help scientists to reliably distinguish relevant from irrelevant phenomena vis-à-vis their understanding of what the thing is. In other words, these rules play a normative role in scientific research.

As a scientific practice, then, mathēsis is ruled by norms. As we also saw in Chapter Four, Heidegger traces philosophical descriptions of the norm governing the relationship between thinking and things back to Plato’s mythic and polysemous image of the cosmic demiurge. According to Heidegger, this image — as well as its cognates, the sun and the idea of the good — mark Plato’s discovery of the a priori element in our understanding of things. The image of the demiurge, in particular, reflects the impulse of some early Greek thinkers to construe thinking and things in terms of craft production. As Heidegger observes in this context, ‘[a]ll forming of shaped products is effected by using an image, in the sense of a model, as guide and standard.’34 Hence, the normative aspect of mathēsis, as a productive practice, stands as an a priori image in the experience of working with things, as a projective image guiding the pursuit of a specific and determinate knowledge of those things. Heidegger describes this image as a Grundriss, a ‘ground rendering’ or ‘basic blueprint.’ For present purposes, we should note the dual nature of the blueprint representing the normative element in scientific practice. On the one hand, a blueprint helps guide the act of production. On the other hand, it represents, schematically, the end result of production. A blueprint is thus both a set of directions, and an image of that towards which those directions point. As a model of scientific practice, it captures, consequentially, both the how and the what of that practice. To experience the scientific thing in terms of its end-directedness thus means to experience it in light of an image of both its direction and its end. This image enables, is the condition of possibility for, that experience.

That mathēsis is guided by a basic blueprint lies at the core of Heidegger’s account of modern science. Heidegger views this blueprint in terms of a ‘measure.’ He writes that ‘[t]his basic plan (Grundriss) […] provides the measure [Maßstab] for laying out of the realm, which, in the future, will encompass all things of that sort.’35 Hence, the ground plan regulates scientific practice by imposing a general measure, a measure meant to apply to all things falling within the plan. Note that, although Heidegger introduces the concept of ‘measure’ in the context of his discussion of the mathematical, we are not meant to view this measure in quantitative terms. One can, for example, take the measure of a thing without judging it according to some quantitative unit. For example, the common phrase ‘taking the measure of a man’ need not imply quantification. On the other hand, one cannot judge a thing quantitatively without also taking its measure. In Heidegger’s account, the mathematical and the quantitative are connected, but the former is a broader category than the latter: ‘[i]n no way […] is the essence of the mathematical defined by numberness.’36 Hence, while the practice of mathēsis may include numerical calculation, it cannot be reduced to such calculation. To render a general and indeterminate knowledge more specific and determinate does not necessarily mean to render it more numerically precise.

In addition to circularity and normativity, there is a third parallel between the present discussion and our earlier discussion of Heidegger’s phenomenological history of logical practice. This has to do with the source of normativity, of the measure regulating modern scientific practice. Recall from Chapter Four that Heidegger describes the temporal aspect of scientific work experience in terms of ‘original time,’ that is, time as experienced in the course of our immersion in a work-world. Original time becomes intelligible to us in terms of two types of relation: in-order-to relations; and for-the-sake-of-which relations. The manifold of in-order-to relations is an existential space within which a particular piece of equipment is let be what it is in its readiness-to-hand. This manifold, in turn, is revealed only in light of the for-the-sake-of-which relation. Only on the basis of the for-the-sake-of-which do we experience the intelligibility of things within a work-world. As we saw in Chapter Four, Heidegger also viewed the for-the-sake-of-which as a social phenomenon, rooted in, and continually nourished by, tradition. Hence, according to him, the source of normativity, of the measure regulating scientific practice, is tradition.

The multiplicity of in-order-to relations serves the same role as the iteration of assignment, or what Heidegger also calls the ‘totality of end-directness’ (Bewandtnisganzheit), in which a particular thing is let be what it is in its end-directedness.37 And just as the multiplicity is revealed only in light of the for-the-sake-of-which, so too does this totality of end-directedness bottom out in the for-the-sake-of-which. In being at work with the thing in a way which lets it be what it is, we must already possess an at least general and indefinite knowledge of the thing’s final end. Heidegger describes this ultimate end as an existential possibility of the subject. We may now more decisively identify it as a possibility afforded by the historical tradition in which the subject finds itself. According to Heidegger, the final end of modern scientific practice, that towards which it is ultimately directed, is rooted in an existential possibility of the subject’s own socio-cultural history. Furthermore, this end has the formal structure of a ground plan, a basic blueprint laying out the measure against which all things falling within its domain — all potentially scientific things — will be judged.

In one last link to the discussion in Chapter Four, the socio-historical provenance of the ground plan of modern scientific practice suggests a solution to the sociological problem of ‘priming.’ Recall Bloor’s distinction between a self-referring practice, in which things acquire their meaning, and the priming element which gets that practice going. I argued that the for-the-sake-of-which, as the a priori element which grounds the multiplicity of in-order-to relations, serves as such a priming element. It is just a small step to now apply that argument to Heidegger’s description of the for-the-sake-of-which as an a priori ground plan which both directs, and serves as the final end for, the modern scientific practice of mathēsis.

As we will see in what follows, this move has consequential implications for the historiography of early-modern science. Specifically, it offers an at least partial answer to the question of how the Scientific Revolution got going. Here, the Scientific Revolution is understood as the emergence of a new cognitive and material domain in which to make sense of the things of nature. On Heidegger’s account of mathēsis, this new domain traces its origin back to a socio-historically conditioned possibility within the everyday work-world of early-modern subjectivity. Furthermore, because Heidegger argues that this socially contingent possibility is manifest in experience, whether informally or formally, as an image — a ground rendering or basic blueprint — we may treat it as a social image. As we will see later in Chapter Six, this allows us to connect Heidegger’s existential conception of science in yet another way to SSK, specifically, to David Bloor’s linkage between knowledge and social imagery.

Let us now return to Heidegger’s argument that the decisive difference between ancient and medieval science, on the one hand, and modern science, on the other, cannot be explained by the claim that modern science uniquely emphasises facts, measurement, and experiment as the grounds for natural knowledge. For Heidegger, it is rather the difference in the way the facts are conceived, the way the measurement or experiment is done, which is decisive. The question is not whether facts, measurement, and experiment are employed — they are employed in all three periods — but to what end they are employed. According to Heidegger, it is the kind of end-directedness possessed by modern scientific things which distinguishes them from their ancient and medieval predecessors, namely, their directedness towards a basic blueprint, a single regulative ground plan, in respect of which they are let be what they are. In establishing facts about things, in measuring and experimenting on those things, mathēsis skips over their token specificities, instead taking note of the regulative ground plan according to which the scientific thing, in general, becomes intelligible as what it is.

The similarities and differences between ancient science, at least as exemplified in the earlier example of Galen, and mathēsis seem straightforward enough. Despite their specific disagreements, Galen’s empiricist and rationalist physicians agree, in general, that medical knowledge should be ‘technical’ or objective, that is, grounded in fact. They also agree on the necessity of an a priori standard according to which physicians take the measure of, and are thus able to discriminate between, epistemically relevant and irrelevant phenomena. In a broad sense, then, ancient science is concerned with both facts and measures. However, Galen’s empiricist and rationalist appear to disagree on the need for experiment. Recall the rationalist physician’s argument that reliable judgements can be made on the basis of a single observation, thereby dismissing the necessity of working with things over time. For the empiricist, in contrast, one must proceed ‘little by little,’ slowly acquiring knowledge over time through a method of disciplined serial observation of the things.

This disagreement between the ancient rationalist and empiricist over the need for a method of enquiry seems conjoined with their further disagreement over the necessary degree of determinateness of the physician’s a priori knowledge of the measure of medical knowledge. The rationalist requires such knowledge to be fully determinate, a condition which then enables immediate judgement on the basis of one observation. Galen’s empiricist, on the other hand, is content to leave such knowledge indeterminate, or obscure, arguing that ‘not a particle of harm befalls arts and men […] for being ignorant of such things.’ In contrast to mathēsis, then, Galen’s empirical method does not seek to turn a general and indeterminate knowledge of the thingness of things into a particular and determinate knowledge. To his credit, Galen may thus avoid charges of circularity. However, as already mentioned, it is hard to see the scientific merit of his position. Indeed, how should reliable discrimination be achieved in the absence of an increasingly determinate knowledge of the standard which guides such discrimination?

As we will see in the next section, this question also troubled Renaissance physicians. They answered with the argument that a determinate knowledge of the norms guiding their medical practice was both necessary and to be gained little by little through an incremental method for working with the things. As a consequence, these Renaissance physicians faced the same worry about circularity which arises in Heidegger’s account of modern scientific practice as mathēsis. And their practical response to this worry turns out to have been not so very different from Heidegger’s own. This suggests that the decisive difference between mathēsis and medieval scientific practice was, perhaps, not quite so straightforward as Heidegger had imagined. Yet, without this difference, mathēsis can no longer provide an explanation for the rise of a definitively modern science, in short, for the Scientific Revolution. So, let us now consider this Renaissance method in some detail, before then comparing it with Heidegger’s account of early-modern mathēsis.

3. Renaissance Regressus and the Logic of Discovery

According to John Randall, Renaissance scholars at the University of Padua, in Northern Italy, developed an account of scientific enquiry which they described as a ‘double process.’38 According to this account, a proper scientific method will begin with some observed effect, seek the cause of that effect, and then use that cause to explain the effect. This amounts to a recommendation that the effect be explained in terms of a cause which can itself be known only through that effect. The explanation of the effect thus seems to presuppose knowledge of that very same effect. Hence, scientists appear to explain only what they already know. As a consequence, there would seem to be no need for a method by which scientists acquire knowledge because they already possess the knowledge in question.

According to Randall, this double process had already been described in 1334 by Urban the Averroist.39 A more concretely developed account can be found later in the writings of Jacopo da Forlì (ca. 1364–1413/14), who taught medicine and natural philosophy at Padua. Forlì wrote:

[I]f when you have a fever you first grasp the concept of fever, you understand the fever in general and confusedly. You then resolve the fever into its causes, since any fever comes either from the heating of the humor or of the spirits or of the members; and again the heating of the humor is either of the blood or of the phlegm, etc.; until you arrive at the specific and distinct cause and knowledge of that fever.40

From this description, it is clear that Forlì did not consider the circularity of the espoused method to be irremediably vicious. Indeed, as he describes, the knowledge of the effect — the fever — undergoes a transformation in the course of the method. It is not, strictly speaking, the same knowledge in the end that it was at the beginning. Forlì emphasised the need for a procedure by which a general and confused knowledge of the effect is ‘resolved’ into a specific and distinct knowledge of that same effect. Randall describes this as ‘a clear case of the method of medical diagnosis.’41

During the fifteenth century, there was an increasing focus on this double process, which came to be called regressus in order to emphasise its exclusion from the charge of being a circulus vitiosus, a vicious circle. Paul of Venice (ca. 1369–1429) launched an early defence of the regressus against this charge, arguing that:

Scientific knowledge of the cause depends on a knowledge of the effect, just as scientific knowledge of the effect depends on a knowledge of the cause, since we know the cause through the effect before we know the effect through the cause. This is the principal rule in all investigation, that a scientific knowledge of natural effects demands a prior knowledge of their causes and principles. — This is not a circle, however. […] [T]he knowledge of why (propter quid) the effect is, is not the knowledge that (quia) it is an effect. Therefore the knowledge of the effect does not depend on itself, but upon something else.42

This ‘something else,’ which distinguishes the regressus from a vicious circle, was addressed by Agostino Nifo (ca. 1473–1538/45), a student and later a teacher of medicine and philosophy at Padua. He called it negotiatio, and included it as the third of the four kinds of knowledge which comprise the scientific method:

The first kind is of the effect through the senses, or observation; the second is the discovery (inventio) of the cause through the effect […]; the third is knowledge of the same cause through an examination (negotiatio) by the intellect, from which there first comes such an increased knowledge of the cause […]; the fourth is a knowledge of the same effect propter quid, through that cause known so certainly […].”43

Nifo further specified negotiatio as an intellectual act of ‘composition and division’: ‘negotiatio is directed toward the cause as a […] definition. But since a definition is discovered only through composition and division, it is through them that the cause is discovered in the form […] from which we can then proceed to the effect.’ What Forlì earlier identified as the process by which a general and confused knowledge of a thing is ‘resolved’ into a specific and distinct knowledge of that same thing is now identified by Nifo as an intellectual process of negotiatio, or definition. Through negotiatio, an originally confused and general knowledge of a cause is rendered more definite.

Nifo’s concept of negotiatio was further developed by Jacopo Zabarella (1533–1589), who also taught philosophy at Padua, but, unlike those of his predecessors mentioned above, did not have a degree in medicine.44 About the role of negotiatio in the regressus, Zabarella wrote:

When the first stage of the procedure has been completed, which is from effect to cause, before we return from the latter to the effect, there must intervene a third intermediate process (labor) by which we may be led to a distinct knowledge of that cause which so far has been known only confusedly. Some men knowing this to be necessary have called it a negotiatio of the intellect. We can call it a ‘mental examination.’ […] [S]till they have not shown how it leads us to a distinct knowledge of the cause, and what is the precise force of this negotiatio…. There are, I judge, two things that help us to know the cause distinctly. One is the knowledge that it is, which prepares us to discover what it is. […] The other help, without which this first would not suffice, is the comparison of the cause discovered with the effect through which it was discovered, not indeed with the full knowledge that this is the cause and that the effect, but just comparing this with that. Thus it comes about that we are led gradually to the knowledge of the conditions of that thing; and when one of the conditions has been discovered we are helped to the discovery of another, until we finally know this to be the cause of that effect.45

According to Zabarella, in order to gain knowledge of what a cause is, we must first know that it is. This knowledge-that enables a knowledge-what of the cause, a knowledge which is not immediately grasped, but which only becomes clear and distinct through a fragile method of mental comparison. By this method, we are ‘led’ to a distinct knowledge of the ‘conditions’ of the thing under investigation. For Zabarella, these conditions can also be understood as the ‘principles’ from which the relation between cause and effect may be securely determined. As our knowledge of these conditions or principles improves, we acquire an increasingly determinate knowledge of the whatness of the cause, and hence also of its necessary relation to the effect.

Randall suggests that Zabarella represents the climax of a long historical development in which scientific knowledge was increasingly recognised to rely on a form of experience which distinctly differs from ‘ordinary observation,’ in the sense of the ‘accidental or planless collection of particular cases.’46 Scientific experience is disciplined by method. Forlì called this method ‘resolution.’ Nifo called it negotiatio. Zabarella called it ‘mental examination.’ The necessity of this method undermines the claim that reasoning from effect to cause and then from cause back to effect must be viciously circular. Indeed, the method appears to be necessary just because the circle is not vicious. The knowledge of the cause at the beginning is not identical with the knowledge of the cause at the conclusion. The required method mediates between these two distinct ways of knowing the cause, joining them in a manner which then also transforms our original knowledge of the effect.

This method, then, is a method of discovery. Randall argues that the Paduan philosophers worked out ‘a logic of investigation and inquiry’ to accompany the existing Aristotelian theory of proof.47 Zabarella, in particular, paid an ‘ever closer attention to the way of discovery, to the careful and painstaking analysis of experience, to the method of resolution.’48 Strikingly, Zabarella justified the need for a method of discovery by pointing to the finitude of human cognitive abilities:

Since because of the weakness of our mind and powers the principles from which demonstration [i.e., proof] is to be made are unknown to us, and since we cannot set out from the unknown, we are of necessity forced to resort to a kind of secondary procedure, which is the resolutive method that leads to the discovery of principles, so that once they are found we can demonstrate the natural effects from them. […] It is certain that if in coming to any science we were already in possession of a knowledge of all its principles, resolution would there be superfluous.49

This may be read as a critical response to Galen’s dogmatic physician, whom we met at the start of this chapter. Zabarella argues that because we lack the innate ability to immediately grasp, with clarity and confidence, the principles governing natural phenomena, we must rely on a method which enables us to articulate those principles on the basis of our finite sensory experience. Furthermore, Randall attributes to Zabarella the additional claim that, because this method serves to discipline and direct our experience of phenomena, it must be distinguished from the comparatively free and unstructured sensory experience indicative of more familiar, everyday modes of perception.

Yet, Randall seems to have been too optimistic in his assertion that Zabarella successfully worked out a logic or method of scientific discovery, as opposed to having just demonstrated the need for such a method. Indeed, when Zabarella turns to a discussion of different modes of discovery, his account is remarkably thin on detail. As we saw above, after first characterising ‘mental examination’ as the method by which a confused and indeterminate knowledge of the cause gets transformed into a clear and determinate knowledge, Zabarella then describes this transformation in terms of ‘just comparing’ the cause with the effect such that ‘it comes about’ that we are ‘led gradually’ to the conditions of the cause. But what rules structure this comparing, and so guide us to the correct causal conditions? Zabarella does not say. However, it appears that, if he had entertained the existence of such rules, then he would likely have considered them to be rules of reason. Consider his discussion of induction as a method of discovery. In his view, a universal stands to a particular as cause stands to effect. The relevant notion of cause is, in this context, an Aristotelian notion of formal cause. Furthermore, knowledge of the universal is gained inductively through experience of the relevant particulars. In other words, the formal cause is known through its effects. Thus, Zabarella writes: ‘One says that “human” is something truly sensible, not because the senses recognise humans as something universal, but because particular individual humans are sensible.’50 Zabarella’s thus roots knowledge of universals in sensory experience:

[A]ll our knowledge takes its origin from sense, nor can we know anything with our minds unless we have known it first by sense. Hence all principles of this kind are made known to us by induction […]. [I]nduction does not prove a thing through something else; in a certain sense it reveals that thing through itself. For the universal is not distinguished from the particular in the thing itself, but only by reason [ratio].51

It turns out, then, that a crucial ingredient in the regressus, which serves to enable scientific knowledge, is our capacity for reason. But what role does reason play in transforming a confused knowledge that the cause is into a determinate knowledge of what it is? Zabarella writes that induction ‘does not take all the particulars into account, since after certain of them have been examined our mind straightaway notices the essential connection, and then disregarding the remaining particulars proceeds at once to bring together the universal.’52 Reason thus allows us to apply a measure of salience to the data of our sense experience, to distinguish epistemically relevant particulars from epistemically irrelevant ones. It equips us with a standard by which to discriminate the essential from the accidental, the good data from the bad data, in our search for the clear and determinate cause or causes of a particular sensible effect. Reason, in other words, provides the norms enabling proper scientific judgement. A successful method is one which, among other things, embodies these rational norms. Zabarella seems to have never addressed the discriminative power of reason explicitly in such terms. He did not, in other words, thematise this intellectual power in such formal terms as ‘measure,’ ‘rule,’ or ‘norm.’ Nevertheless, his inquiry does explicitly uncover a normative element in thinking which, as we saw in Chapter Four, will later be formally articulated by Kant as a ‘faculty of rules.’

The question now arises of where Zabarella thought this discriminative power, these rational norms, to come from. It appears that he took them to be, not innate and self-evident structures in reason, but the endowment of an external and mysterious intelligence. As Harold Skulsky has argued, ‘[t]he inductive process to which a writer like Zabarella pays tribute […] depends ultimately, not on reason, but on the generosity, or more properly the grace, of an alien will.’53 Eckhard Kessler similarly observes that, for Zabarella, because our irremediably finite epistemic power is capable of ‘containing the universal structure only in a confused and unintelligible way, it had to be illuminated by the agent intellect [intellectus agens], so that the universal in the individual was rendered distinct and intelligible.’ Zabarella furthermore held that the intellectus agens could be identified ‘with God himself as the principle of intelligibility.’54 Nicholas Jardine views this as evidence for the reliance of Zabarella’s scientific method on ‘divine revelation,’ and he equates Zabarella’s notion of intellectus agens with the Holy Spirit.55 However, Jardine appears to carry this argument too far, concluding also that Zabarella took clear and determinate knowledge of the cause to be ‘formed in the imagination through a merely passive observation of the world.’56 It would seem that the point is, instead, that finite human beings may well actively observe natural phenomena, but, in the absence of normative guidelines for structuring that observation, they will not achieve proper scientific knowledge of those phenomena.57 This has been argued by Charles Schmitt, who provides evidence that ‘Zabarella did take it upon himself to go out and look at nature; and, what is more important, he observed carefully what he saw and applied it to the crucial philosophical questions in which he was interested.’58 What Zabarella does not do, however, ‘is consciously, and with forethought, attempt to test a particular theory or hypothesis by devising a specific experiment or observational situation by which to resolve the question.’59 Schmitt thus concludes that ‘Zabarella can be called an empiricist with some justification, but he is clearly not an experimentalist,’ at least not in the early-modern sense of that term.60

We saw earlier that Randall believed Zabarella to have drawn a clear distinction between scientific experience, on the one hand, and ordinary observation, in the sense of ‘accidental or planless collection of particular cases,’ on the other. On this basis, Randall attempts to turn Zabarella into a proto-experimentalist, thereby establishing a clear continuity between the method of regressus and the Galilean experimental method which would emerge in the years shortly afterwards. We may now conclude that the distinction was more subtle than that, too subtle, in fact, to justify naming Zabarella a precursor to the Galilean experimental method. While his approach to observation was careful and goal-oriented rather than accidental and planless, he did not seek to discipline or control, much less to create, the act of observation in the manner distinctive of subsequent early-modern experimentalists. There was something missing in Zabarella’s conception of scientific method, something which prevented him from making the final step towards a modern scientific way of working with and thinking about nature. In fact, Randall recognised that absence, but he apparently minimises its significance:

There was but one element lacking in Zabarella’s formulation of method: he did not insist that the principles of natural science be mathematical. […] With this mathematical emphasis added to the logical methodology of Zabarella, there stands completed the ‘new method’ for which men had been so eagerly seeking.61

From the perspective of Heidegger’s existential conception of science, this missing mathematical element appears to be the key feature separating Renaissance regressus from early-modern mathēsis. Furthermore, Heidegger argued that the emergence of early-modern experimental science was possible only because natural science had itself become mathematical, in the sense of adopting mathēsis as its core method of discovery. On this account, it seems to follow that Zabarella could not be a precursor to early-modern experimentalism because he did not experience the things of nature mathematically, as mathēmata. But before we can properly delineate the dependency of early-modern experimental science on the mathematical projection of nature, we must first more carefully consider the similarities and differences between Renaissance regressus and early-modern mathēsis.

4. From Renaissance Regressus to Early-Modern Mathēsis

There are three broad features in respect of which regressus and mathēsis may be usefully compared. These are: circularity, finitude, and method. Not only do these features figure prominently in both regressus and mathēsis, the relation of each to the others is also similar in both cases. To begin with, regressus and mathēsis are both manifestly circular accounts of scientific reasoning. In both cases, too, the account can be defended against charges of vicious circularity. As we saw in the previous section, Zabarella argued that the ‘weakness of our mind and powers’ renders us incapable of immediately possessing, with clarity and confidence, the scientific principles determining the causes of observed natural phenomena. Indeed, according to Zabarella, if we falsely believe ourselves capable of spontaneously grasping such principles, then we might claim to possess scientific knowledge of a phenomenon simply because we have observed it. Reasoning in a tight circle, we would be attempting to justify our knowledge of the phenomenon by citing our knowledge of it. This circle of reasoning is vicious. Zabarella argues that we cannot justify such claims to clear and immediate scientific knowledge, because our cognitive powers are weak rather than powerful, because they are finite rather than infinite. His argument that the circle of scientific reasoning is virtuous rather than vicious depends on his acknowledgement that our cognitive powers are ineluctably finite in scope.

Although cognitive finitude is, as we saw in Chapter Three, a central element in Heidegger’s existential conception of science, he did not explicitly draw a connection between this and his account of modern science as mathēsis. The necessary connection between regressus and finitude made by Zabarella may now help us to explicate a similar connection between mathēsis and finitude in the case of Heidegger.

The circularity of mathēsis lies in its being a kind of learning, or discovering, in which we learn or discover something which we already know. We do not get this knowledge out of the things themselves, by simply observing or otherwise dealing with them, but, as Heidegger writes, ‘in a certain sense’ we bring it already with us. When we deal with a thing, we bring with us a ‘fore-conception’ of the thingness of the thing.62 More specifically, in dealing with a plant, we bring with us prior knowledge of the plant-like of the plant. In other words, the whatness of a thing is not something we get out of the things themselves, but is instead a projection which enables us to make sense of those things in terms of what they are. Heidegger argued that this projection, or fore-conception in our understanding, plays a central role in all acts of understanding. He thus defines understanding as an act of interpretation which depends on a perhaps only vaguely specified fore-conception, or prior understanding, of its subject matter. Understanding is thus a circular phenomenon: ‘Any interpretation which is to contribute understanding, must already have understood what is to be interpreted.’63 Because this circle in understanding is ineliminably present in all cognitive acts, in general, it must also be ineliminably present in all acts of scientific cognition, in particular. Heidegger recognised that this renders scientific demonstration circular, but rather than viewing this as a catastrophe, he took it to be an inevitable aspect of finite human existence. This circle of understanding, he writes, ‘is the expression of the existential fore-structure of Dasein itself.’64 It is, in other words, a basic structural feature of the subject’s projective understanding. This existential structure is expressed in modern scientific cognition, in mathēsis, as a metaphysical projection of the thingness of things in terms of a basic ground plan or blueprint. As we saw in Chapter Three, Heidegger radically reinterprets the meaning of metaphysics, arguing that the basis for metaphysical knowledge, as such, is ‘the humanness of reason, i.e., its finitude.’65 The hierarchy of explanation in Heidegger’s account of modern science thus breaks down like this: the circularity of scientific practice is to be explained in terms of the ineliminably projective element in mathēsis; and this ineliminably projective element is to be explained in terms of human finitude. In a nutshell, scientific demonstration is circular because scientific cognition is finite.

This is not precisely the same as the connection made by Zabarella between circularity and finitude. For him, finitude explains why the circle is virtuous rather than vicious. For Heidegger, it explains why there is any circle at all. The reason for this difference can be uncovered by addressing the third broad feature shared by both regressus and mathēsis: method. For both Zabarella and Heidegger, because we cannot immediately grasp, with clarity, the principles governing observed natural phenomena, we need to find a method which will help us to get clear on those principles. Method is thus meant, by both, to steer us towards scientific knowledge in spite of our cognitive finitude. But how it does this differs profoundly between the two. For Zabarella, method is meant to overcome the limitations of finitude. He seems to have believed that, through careful, goal-oriented acts of observation, we can prepare our minds to receive epistemic inspiration from God, the intellectus agens. Thus human cognitive finitude must, on Zabarella’s account, be understood in contradistinction to the infinite cognitive power of God, for whom the issue of circularity never arises because omniscience makes inferential or interpretative reasoning unnecessary.

As we saw in Chapter Three, Heidegger had a profoundly different account of finitude, an account he developed specifically in contrast to the one proffered by Kant. Both Heidegger and Kant viewed cognitive experience as being comprised of two distinct faculties: the first, receptivity; the second, constructivity (or projectivity). However, whereas Kant took finitude to be a constraint on receptivity, Heidegger took it to be a constraint on projectivity. For Kant, as Heidegger reads him, finitude is a state of deprivation which prevents us from gaining cognitive access to the intrinsic, independently existing properties — the essence, or whatness — of a thing. For Heidegger, on the other hand, finitude is more directly connected to projectivity. The essence of a thing is not something we receive from it, but something it possesses as a result of the socio-historically conditioned metaphysical projection within which it is let be what it is. On Heidegger’s account, not even an infinitely powerful intellect could grasp the intrinsic, independently existing essence of a thing, because no such essence exists. Hence, the finitude of our receptivity is not the issue; the issue is, instead, the finitude of our projectivity. The range of possible conceptualisations of a thing is conditioned by the historical tradition of the subject attempting to make sense of that thing. Only within the finite scope of possibilities enabled by the subject’s tradition can it experience a thing as intelligible, not to mention develop a clearly defined understanding of what it is.

This process of articulation is advanced, for both Heidegger and Zabarella, by method. Both view method as a means of sharpening up the intelligibility of observed phenomena by clearly defining the causal conditions of those phenomena. Indeed, both even understand this process against the background of the distinction, addressed in Chapter Two, between that-being and what-being, between knowing of a thing that it is and knowing of it what it is. Recall Zabarella’s argument that knowledge that a cause is enables us to discover what it is. This discovery process involves a comparison of cause and effect, through which we are gradually led to scientific knowledge of the causal principles underlying the observed effect. The method of regressus, by which our understanding of the observed phenomenon is rendered increasingly determinate, thus presupposes a distinction between the that-being and the what-being of the phenomenon. It presupposes, in other words, a version of the minimal realist doctrine introduced in Chapter Two.

To conclude this section, it remains only to emphasise that Zabarella’s reflections on method seem to have been motivated by an account of finitude similar to the one which Heidegger attributed to Kant, namely, one developed in contrast to the notion of an infinitely powerful intellectus agens. For Zabarella, method helps us to painstakingly transcend our finite human condition and achieve scientific knowledge through communion with a divine intelligence. For Heidegger, method helps us, not to transcend the finitude of our existence, but to articulate the historically engendered epistemic possibilities within that existence. In this case, the self-evidence of ordinary understanding is transcended in pursuit of a more robust, conceptually clear, and critically well-grounded knowledge of nature. Hence, for both Zabarella and Heidegger, method is tied to the metaphysics of transcendence. But, unlike Zabarella, Heidegger does not treat transcendence as a solution to finitude, construed as a problem for knowledge. He views it instead as the critical exploration of the finite range of the sometimes only vaguely understood epistemic possibilities which a scientist inherits through her participation in a shared historical tradition. It was for this reason that Heidegger reinterpreted metaphysics as being grounded in finitude, rather than as being, as Zabarella ostensibly thought, a means by which to overcome such finitude.

These respective conceptions of method, including the relation between method and finitude, imply dramatically different accounts of the norms which govern that method. In the case of Zabarella, because method transcends finitude, the norms which govern it must be similarly transcendent. In the case of Heidegger, because method discloses the latent possibilities within a historical tradition, the norms governing it must be embedded within that tradition. This points to two different understandings of the source of the a priori norms which govern scientific practice. In one case, the ultimate source of normativity is timeless. In the other case, it is historical.66 As we will see in the next section, these two perspectives motivate two different historiographic strategies for explaining the transition from late Renaissance to early-modern science. Insofar as that transition is construed as a process of mathematicisation, these two strategies also enroll divergent conceptions of the mathematical impulse giving rise to early-modern science. In the first case, the mathematicisation of science is an act which allows practitioners to slip free from the historical constraints of their epistemic tradition. In the other case, it is an act of critical interpretation, in which practitioners discover and exploit a possibility latent in their historical tradition, employing it as a new measure in the production of reliable natural knowledge.67

5. Mathematics and Metaphysics at the Cusp of the Early-Modern Period

Randall’s argument for a strong continuity between the Renaissance method of regressus and the method distinctive of early-modern natural philosophy was quickly and influentially challenged by the historian of science Alexandre Koyré. As we have seen, Randall argued that ‘[t]here was but one element lacking in Zabarella’s formulation of method: he did not insist that the principles of natural science be mathematical.’68 Koyré seizes on this statement, insisting that the missing mathematical element was not as trivial as Randall implies, but instead ‘forms […] the content of the scientific revolution of the seventeenth century.’69 For Koyré, the mathematicisation of regressus marks a radical historical discontinuity in knowledge-making practices, and, more specifically, a sudden and profound usurpation of Aristotelian natural philosophy by a resurgent Platonism. This was, in Koyré’s view, the usurpation of empirical experience by rational theory: ‘Experience is useless because before any experience we are already in possession of the knowledge we are seeking for.’70 Koyré thus demonstrates his allegiance to a Platonic doctrine of innate ideas, that is, ideas which we somehow possess independently of, and prior to, empirical experience. He also demonstrates his allegiance to the same doctrine as Galen’s rationalist critic of empiricism. This move has its merits if one believes that the circularity of the Paduan method is vicious, and that it must be broken through escape into a non-experiential realm of pure thought, an orthodoxly understood metaphysical realm lying beyond the worldly realm of physical sensation.

There is some modest reason to think that Koyré’s interpretation of the history of science may have been influenced by his reading of Heidegger, that his emphasis on the mathematicisation of method tracked Heidegger’s own description of the historical shift to mathēsis. Indeed, a 1931 French translation of Heidegger’s 1929 inaugural lecture ‘What is Metaphysics?’ included an introduction by Koyré, in which he describes Heidegger as ‘one of those great metaphysical geniuses whose influence marks an entire period.’71 The period in question was, of course, Koyré’s own. Yet, it seems that Koyré failed to properly understand both Heidegger’s stance towards metaphysics, and, more specifically, towards Platonism, as well as his view of the role played by mathematics in early-modern natural philosophy. With respect to Heidegger’s stance towards Platonism, recall that Heidegger reinterprets Plato’s fundamental and unifying idea of the good in terms of what Heidegger dubbed the ‘for-the-sake-of-which’ (Worumwillen). The for-the-sake-of-which lends a compelling intelligibility and coherence to experience by guiding us in our discrimination between cognitively valuable and cognitively irrelevant or deceptive phenomena. Like Plato’s idea of the good, captured also in the mythical image of the cosmic demiurge, the for-the-sake-of-which denotes the a priori rules of reason which bring together things and thinking in the production of natural knowledge. The phenomenological importance of Plato’s theory of ideas, then, lies in the emphasis it puts on our compulsive feeling — our affectivity— towards the basic rules of reasoning, rules which help us to distinguish between epistemically good and bad phenomena. However, whereas Plato sought to explain this feeling of compulsion in terms of receptivity towards a supernatural realm of ideas, Heidegger attempted to instead explain it in naturalistic terms, as receptivity towards the manifold intersubjective history of a prevailing cultural tradition. In both cases, the phenomenology of this feeling of compulsion — this experience of objective necessity — is recognised and described, but the respective causal explanations given for that experience are dramatically different. In the first case, the cause is supernatural; in the second case, it is natural. Indeed, for Heidegger, our affective experience of the a priori signals our deep epistemic dependency on a shared historical tradition, rather than our ability to transcend tradition in an act of pure reason. This manifold tradition provides the range of possibilities available to us for making sense of nature, for rendering it intelligible, and metaphysics, on Heidegger’s account, is a study of the conditions of historical possibility generated by and sustained within this tradition.

Despite his enthusiasm for Heidegger’s alleged metaphysical ‘genius,’ Koyré seems to have missed the fact that Heidegger’s ambition was to deconstruct, rather than to champion, Platonic rationalism. For Koyré, the early-modern mathematisation of natural philosophy was initiated by ‘some of the greatest geniuses of mankind, a Galileo, a Descartes.’72 He argues that it was an act of ‘pure unadulterated thought, and not experience or sense-perception […] that gives the basis for the “new science” of Galileo.’73 Koyré thus identifies mathematics with metaphysics, construed as Platonism, and hence describes Galileo unequivocally as a Platonist.74

During the late Renaissance and early-modern periods, however, there also existed a distinctly Aristotelian culture of mathematics. Indeed, when Randall writes that mathematics was the missing element in Zabarella’s method, he had Aristotelian mathematics in mind.

[W]ith rare exceptions the Italian mathematicians down through Galileo, when they possessed a philosophical interest at all, were not Platonists but Aristotelians in their view of mathematics, of its relations to physics, and of the proper method of natural knowledge. […] What they constructed as ‘new sciences’ it remained for Descartes to interpret in the light of the tradition of Augustinian Platonism.75

In Chapter Four, I recounted Heidegger’s interpretation of Descartes as first modelling his conception of the subject on Aristotle’s narrow construal of logos as proposition, but then decisively mathematicising that construal in order to establish the indubitable certainty of pure reason. We may now more precisely specify Descartes’s mathematicisation of the rules of reason as having been predominantly Platonist in its motivation. By understanding those rules as being valid independently of experience, Descartes hoped to secure them as the absolute basis for incontrovertible, universal knowledge. A Platonic interpretation of mathematical experience thus underwrote Descartes’s rationalistic claim to epistemic absolutism.

That Galileo was, in fact, more motivated by an Aristotelian interpretation of mathematical experience is a point which has been recently pressed by Peter Dear: ‘Galileo aimed at developing scientific knowledge […] according to the Aristotelian (Archimedean) deductive formal structure of the mixed mathematical sciences.’76 These mathematical sciences were ‘mixed,’ rather than ‘pure,’ because they were principally concerned with questions about the physical world rather than with abstract mathematical objects. The chief sixteenth-century examples of mixed mathematical science were astronomy and optics, the former calculating the positions and movements of celestial objects and the later studying the behaviour of light rays construed in geometrical terms. As Dear notes, sixteenth-century astronomical and optical practice also differed from the pure mathematical sciences of geometry and arithmetic in that they made wide use of specialised instruments, such as quadrants and astrolabes, in order to produce precise empirical observations.77 Thus, according to Dear, they represent the emergence of ‘something resembling “experimental science.”’78

Mixed mathematics was, furthermore, different from natural philosophy in that the former sought to determine the quantitative properties of things through acts of uniform measurement, while the latter sought to determine what kinds of things they were, and hence what their natural place was in a hierarchically ordered cosmos. To determine the natural kind of a thing is to determine the universal form which it instantiates. In Aristotelian terms, a thing’s natural kind is thus also its ‘formal cause,’ its ‘what-it-is.’ So, for example, the formal cause of a particular oak tree is the universal oak tree, what an oak tree is by nature, and by definition. Moreover, by subsisting in its nature, by being what it is, or the kind of thing it is, an oak tree assumes its proper place within the cosmos. There is, then, a tight association between the formal cause of a thing, on the one hand, and its natural place in a heterogeneous and hierarchically ordered cosmos, on the other. Natural philosophers, by attending to formal causes, viewed themselves as the rightful surveyors of natural phenomena within this qualitatively and hence differentially ordered cosmos.

Dear observes that the main charge laid by Aristotelian natural philosophers against mathematicians was that the latter did not provide causal explanations of natural phenomena.79 Indeed, he describes the explanations of mixed mathematicians as ‘operational,’ and he contrasts these with the explanations proffered by Aristotelian natural philosophers.80 Yet, as we can know see, this contrast should be more strictly specified as one between operational explanations, on the one hand, and explanations in terms of formal causes, on the other. Indeed operational explanations are also, in a broad sense, causal explanations, and hence they were neither unknown nor unappreciated by Aristotelian natural philosophers. Recall, for example, the fourteenth-century Paduan natural philosopher and physician Jacopo da Forlì’s description of regressus in terms of the resolution of a general and confused knowledge of fever into a specific and distinct knowledge of its causes, which will in turn lead back to a specific and distinct knowledge of the fever itself. Forlì’s goal was to explain fever as being caused by such physical operations as the heating of the humor, spirits, or members of the patient’s body. The type of cause at play here is not a formal cause but rather what Aristotle called an efficient cause, which is ‘the primary source of change or rest.’81 Because Aristotle viewed change as movement, the efficient cause is also sometimes called the ‘moving cause.’ Resolving the fever into its precise causes involved discriminating between probable and improbable efficient causes, for example, between the heating of the spirits and the heating of the humors as the most likely reason for the fever. As we saw, Agostino Nifo later more precisely articulated Forlì’s concept of resolution in his concept of negotiatio, which Zabarella then called mental examination. The regressus could thus involve negotiatio in the empirical determination of the efficient causes which produce change in natural bodies.

Dear seems to overlook this when he describes negotiatio as a ‘mysterious process,’ a ‘form of contemplation’ which presumes ‘the mind’s innate ability to grasp universals.’82 These universals were apparently the essences, or formal causes, of the phenomena under study. According to Dear, regressus was a ‘logical technique […] designed to generate true scientific knowledge, which for an Aristotelian had to be certain knowledge.’83 The Paduan regressus theorists allegedly believed that negotiatio was a strictly logical practice which allowed the contemplative mind to ‘intuitively’ grasp, as necessary, abstract and universal things, formal causes, which in turn were meant to correspond to something ‘metaphysically real.’84 In short, according to Dear, the Paduan theorists were committed to a form of rationalism.

Although this description may stick, in some degree, to Zabarella (who was not a physician), it seems mistaken as a general characterisation of the Paduan physicians. For them, regressus involved an empirical search for the physical causes of illness. The heating of the humors of the body was not understood to be an abstract, metaphysical phenomenon: it was understood to be a physical operation which could be studied and, hopefully, physically manipulated so as to restore the patient to health. In fact, the study of the efficient causes of disease appears to have been a common endeavour in late Renaissance medical practice. At the very least, it managed to cross north over the Alps. Indeed, as Dear himself notes, an operational emphasis on efficient causes also characterised the work of the sixteenth-century Swiss physician Paracelsus and his many followers.85

Moreover, as Randall makes clear, the Paduan method was not generally meant to produce rational certainty, least of all through acts of pure intellectual contemplation: ‘at no time do the Paduan medical Aristotelians attribute any such perceptive power to intellect.’86 Zabarella was not a medical Aristotelian, and so his case may have been different. But consider Nifo’s identification of regressus with ‘physical demonstrations,’ and his claim that the empirical ‘science of nature is not a science simpliciter, like [pure] mathematics. Yet it is a science propter quid [i.e., demonstrative].’87 Nifo furthermore notes that Aristotle, in the Meteors, ‘grants that he is not setting forth the true causes of natural effects, but only in so far as was possible for him, and in conjectural or hypothetical fashion.’88 Since even Aristotle himself admitted that the empirical study of nature may not yield certain knowledge, it is not surprising that the medical Aristotelians of Padua demanded no more of their own method.

Dear seems to have exaggerated the epistemic difference between Paduan medical Aristotelians, on the one hand, and sixteenth-century Aristotelian mixed mathematicians, on the other. In fact, both groups appear to have been involved in empirical studies of natural phenomena, and neither side made strong claims to the sort of epistemic certainty typically attributed to the rationalistic demonstrations of logicians and pure mathematicians. Koyré, in turn, appears to have more clearly recognised the empirical and conjectural nature of the Paduan regressus method, but he viewed this as an ailment in need of remedy through the metaphysical salve of Platonism. Hence, where Dear sees too much orthodox metaphysics in the Paduan method, Koyré sees too little. Their interpretations thus move in opposite directions: Koyré’s away from empirical experience and deeper into metaphysics; Dear’s away from metaphysics and deeper into empirical experience. In contrast to both of these interpretations, I want to suggest that the movement in question was never a movement to or from experience. The key point of contention here is the definition of metaphysics. Both Koyré and Dear understand metaphysics in the orthodox sense, as being opposed to empirical experience. On a Heideggerian reading, in contrast, metaphysics is bound together in a reciprocal relationship with experience. The mathematical projection of nature — within which things are experienced in terms of a single, basic measure — operates in continuous concert with the particular, concrete ways in which scientists work with — and, above all, seek to take the measure of — those things.

The greater the number of natural phenomena which have been successfully drawn into the realm of intelligibility circumscribed by this basic measure, the more compelling the mathematical projection becomes as the existential basis for knowing nature. In this way, by expanding the effective reach of a particular way of working with nature, scientists progressively entrench in social practice the metaphysical measure which guides and gives meaning to that work. Through this work, the projected measure increasingly becomes that for the sake of which scientific work is done. In other words, through this process, the things with which one works are progressively experienced in terms of their directedness towards this final measure. The things thus lend themselves more and more easily to an explanation in terms underpinned by that measure, the final end in light of which scientific practice lets things be what we already know them to be, if only in a general and indeterminate way.

This self-reinforcing reciprocal relation between metaphysical projection and work experience would seem to confound the more common historiographic claim that the emergence of early-modern science was the consequence of a historical swing either towards or away from either rationalism or empiricism. On a Heideggerian account, early-modern science received its impulse not from one or the other, but instead from a transformation in the existential relationship between metaphysics and experience, between abstract understanding and concrete action, between theory and experimental practice. As we will see below, this transformation was, above all, a transformation in the role played by the notion of ‘final cause’ in the early-modern pursuit of natural knowledge. The remainder of this chapter will thus consider the relationship between the concrete practices characteristic of, but not limited to, the mixed mathematical arts, on the one hand, and the metaphysical notion of ‘final cause,’ on the other. A better understanding of this relationship will put solid ground under our feet when, in Chapter Six, we go on to develop a more detailed and concrete historical analysis of the transition from late Renaissance regressus to early-modern mathēsis.

6. Nature, Art, and Final Causes in Early-Modern Natural Philosophy

It has become a historiographic commonplace that the emergence of early-modern science was accompanied by the collapse of the so-called art-nature distinction. This distinction was allegedly a barrier to the free application of the experiment in the investigation of nature. According to this widely received view, the key pillar upholding the art-nature distinction was the Aristotelian concept of final cause. Hence, the breakdown of this distinction entailed a rejection of final causes.

In this section, I will challenge this historiographic commonplace. In doing so, I will begin to apply Heidegger’s notion of mathēsis more directly to contemporary debates in the history of early-modern science, an application which will extend into Chapter Six. My main claim here will be that no consequential breakdown in the art-nature distinction was necessary for the emergence of early-modern science, because the distinction, while important, was never as strict or inflexible as has often been suggested. As a consequence, there was no corresponding need to eliminate final causes from explanations of experimentally produced natural phenomena. Indeed, despite early-modern rhetoric to the contrary, the coherence and intelligibility of experimental manipulations of nature required that a central role be given to final causes. Without allowing room for final causes in explanations of the artful manipulation of nature, we will achieve an only partial, and perhaps not entirely coherent, understanding of early-modern scientific practice. As we will see, the claim that early-modern experimental operations cannot be properly explained without reference to final causes is a specific example of Heidegger’s more general claim that early-modern mathēsis was a matter, not just of working with the things, but also of the metaphysical projection of the thingness of those things. According to Heidegger, the ultimate end towards which the end-directedness of scientific things points, their final end, is a basic blueprint. This blueprint is, in Aristotelian terms, the final cause of those things.

In the last section, I addressed Dear’s distinction between operational and causal explanations, arguing that operational explanations, by making reference to how things happen, appeal to efficient causes, and thus are also causal explanations. But they are not causal explanations of the type most valued by sixteenth-century Aristotelian natural philosophers: they are not explanations in terms of formal cause. These explanations address a thing in terms of what it is, rather than of how it happens. In other words, they explain it in terms of the kind of thing it is, in terms of the specific thingness manifested in the thing. For example, a sixteenth-century explanation of fever in terms of the heating of the humors specifies that the heating causes the fever, that this is how fever happens. Yet, notice that it also says something about what fever is: namely, that it is the kind of thing which occurs when the humors are heated. There is, then, an important connection between efficient and formal causes, because operational explanations in terms of the former implicate a role for the latter.

Once fever has been defined in terms of the processes by which it occurs, it becomes possible, at least in principle, to treat it by intervening in those processes. On the medieval definition, one could mitigate a fever by artificially cooling the patient’s humors: for example, by immersing her in a basin of cool water. Such an intervention may help to return the patient to a natural state of health. This is an important point. Recall that, for Aristotle, change is a kind of movement. Medical interventions, as the efficient causes of health, may also be called the moving causes of health, because to restore a patient’s health means to move her back into a natural state. Aristotle wrote that ‘the movement of each body to its own place is motion towards its form.’89 We saw in the last section that a thing, by being what it is, instantiates its form. In so doing, it takes its proper place in the cosmos. We can now add that a thing, by becoming what it is, moves towards its form, and, in so doing, also moves to its proper place — or what we may be more inclined to call its proper state — in the cosmos. The physician directly intervenes in the operations of the patient’s body — operates on her — in order to bring her back into proper form, good shape, a natural state of health. Health is thus that for the sake of which the physician performs the operations, and those operations are likewise performed in order to restore the patient’s health.

In their respective accounts of the Scientific Revolution, both Dear and SSK practitioner Steven Shapin observe that ‘that for-the-sake-of-which’ an operation occurs was known to Aristotelians as the ‘final cause.’90 Dear furthermore recognises a distinction between the formal cause of a thing, the kind of thing it is, on the one hand, and its final cause, on the other. The motivation for this distinction, he writes, ‘was to understand in the most fundamental way what things were and why they behaved as they did.’91 Yet, while Aristotle did distinguish in this way between formal and final causes, he also argued that the two are often identical, and, furthermore, that they coincide with the efficient, or moving, cause: ‘the “what” and “that for the sake of which” are one, while the primary source of motion is the same in species as these.’92

For example, the process of growth initiated in an acorn can be explained only in light of the end, or final cause, of that process: namely, a mature oak tree. The final cause explains why an acorn grows into an oak tree rather than into an artichoke. Similarly, according to Aristotle, it explains why ‘the healable, when moved and changed qua healable, attains health and not whiteness.’93 A movement towards form has a directedness, a regularity, which distinguishes it from chance occurrence, and this regularity of movement is what a reference to final causes is meant to explain. Final causes explain why something becomes what it is: why an acorn becomes an oak tree. They thus serve to explain generative movement qua generative, that is, qua movement which we experience as organised and directed towards form. Formal causes, in contrast, explain what something is. Their focus is on being, rather than on becoming. What an oak tree is can be explained without reference to the generative movements which brought the oak tree into being. Final and formal causes can thus be viewed as different modes of explanation with respect to the same thing. This is a difference between a directed process and its natural outcome, between a thing’s regulated actualisation and its resultant actuality. In the case of the oak tree, the operation is internal: oak trees reproduce themselves through acorns. Here, the formal and final causes are similarly located in the oak tree. They are equally situated in the very thing about which they are meant to provide an explanation.

Accordingly, Andrea Falcon has argued that, for the Aristotelian student of nature, formal and final causes were often not distinguishable in practice.94 Indeed, Aristotle reiterates this point in On the Generation of Animals: ‘first, the final cause, that for the sake of which a thing exists; secondly, the formal cause, the definition of its essence (and these two we may regard pretty much as one and the same).’95 Aristotelian natural philosophers could thus be justified in speaking not of two distinct causes but of only one single ‘formal/final’ cause.

Crucially, the same cannot be said of Aristotelian students of art. For them, formal and final causes are separated because, in art, the source of movement lies outside the moving body, the emergent work of art. As Aristotle wrote: ‘[A]rt is a principle of movement in something other than the thing moved, nature is a principle in the thing itself.’96 Hence, when the physician immerses a feverish patient in a basin of cool water, the source of the movement meant to restore the patient to health lies, at least in significant part, outside the patient, in the physician, or, more accurately, in the medical art of the physician. Furthermore, as noted above, medical art is not a random activity, but an activity directed toward a specific end, namely, health. The physician is the site of both the activity (efficient cause) and the principle (final cause) which organises and gives an overall meaning to that activity. The patient, on the other hand, is both the object of treatment (material cause) and the site of health (formal cause) to which the physician endeavours to return that body. In contrast to generation in nature, the formal cause — the ‘what’ — and the final cause — ‘that for the sake of which’ — are not united in art, because they each exist in a different location. Yet, in the medical arts, there are exceptions to this general rule, and such cases serve to weaken the distinction between nature and art. Hence, Aristotle writes that ‘a doctor doctoring himself: nature is like that.’97 Or, to take another example, one walks about ‘in order to be healthy.’98 Just as with the oak tree, in this case the respective locations of the final and formal causes are now the same, and so the two causes become indistinguishable in practical terms. In addition, the efficient cause is now located, as with the oak tree, in the body being moved: the patient is also the agent, a self-mover.

One may object that, even when there is no necessary difference between nature and art with respect to location of causes, an important distinction may still be made by pointing to the deliberative character of artful movement in contrast to natural movement. According to this argument, the doctor deliberately sets out to doctor herself, while the oak tree reproduces itself automatically, that is, without deliberation. But Aristotle challenged this distinction as well. He observes that ‘art does not deliberate.’ Hence, ‘[i]f the ship-building art were in the wood, it would produce the same results by nature.’99 Self-awareness thus seems to play no necessary role in Aristotle’s conception of art. For him, the regulative movements of art can be just as non-deliberative as those of nature. This recalls Heidegger’s own observations, discussed in Chapter Four, about the non-deliberative character of our actions when we are immersed in a work-world. The master fiddler does not deliberate over the placement of her fingers while she is fiddling. She just fiddles. Hence, if the art of fiddling were instead located in the fiddle, the fiddle would play itself, in just the same way an oak tree reproduces itself through an acorn: namely, non-deliberatively, without self-awareness, but nevertheless with a directedness which serves to organise the corresponding operations. In fact, Heidegger recognises in Aristotle a distinction between the ‘end’ (telos) towards which a thing is directed, on the one hand, and the ‘goal’ or ‘purpose’ of that thing, on the other. On this basis, Heidegger concludes that for Aristotle: ‘telos is not “goal” or “purpose,” but “end.”’ One may attribute to a thing the cause of its own activity without also attributing to it self-awareness or consciousness.100 For both Heidegger and Aristotle, the end-directedness of both natural and artful movement may be explained without recourse to the intellectualist concepts of ‘goal’ and ‘purpose.’

In addition to their shared interest in non-deliberative practice, there is another important parallel between Heidegger’s work and Aristotelian natural philosophy. Readers will have already noticed that Heidegger, like Aristotle, uses a concept of the ‘for-the-sake-of-which.’ Indeed, Aristotle’s observation that health is that for the sake of which one walks about, and that one walks about in order to maintain one’s health, recalls Heidegger’s own close association between the concepts ‘for-the-sake-of-which’ and ‘in-order-to.’ As we saw above, and more fully in Chapter Four, Heidegger links these two concepts in his discussion of equipment, or ready-to-hand things, that is, things as we experience them in use. We use a pen, for example, in order to make marks on a page, so as to communicate. The use of the pen is an in-order-to of graphic communication. Yet such communication is more than just mark-making. The marks on the page must be shaped and organised such that they convey a meaning. Only then will they count as communication. Graphic communication is thus that for the sake of which one uses the pen. Only once we have acquired the skills for such communication can we use the pen in order to convey a meaning. Hence, Heidegger writes that ‘[o]nly so far as the for-the-sake-of a can-be is understood can something like an in-order-to (a relation of assignedness) be unveiled.’101 This understanding of the for-the-sake-of-which — of the final cause — allows for a ‘projection […] in whose luminosity things of the nature of equipment are encountered.’102 In partly more Aristotelian terms, an understanding of the final cause of a thing opens up (‘projects’) a space of intelligibility in which the formal cause, or whatness, of the thing may be realised through the efficient cause, or operations, by which that thing comes to be experienced as what it is. So, the understanding, or the art, of graphic communication informs one about what kinds of marks will contribute to meaning, and hence also about how the pen is to be used in order to produce those kinds of marks. As a consequence, an understanding of the final cause, whether deliberative or non-deliberative, marks the difference between random, meaningless behaviour and results, on the one hand, and organised, meaningful practices and products, on the other. Heidegger’s concept of understanding thus plays much the same role as Aristotle’s concept of art with respect to production: both are directed towards the for-the-sake-of-which, towards the final cause or end. Such understanding brings with it rules for regulating our behaviour in a sensible way, for successfully choosing between cognitively good and cognitively bad courses of action in order to produce meaningful results. It explains, for example, why a carpenter qua carpenter produces cabinets rather than crockery.

It is worth reiterating that the rules or instructions originating in the for-the-sake-of-which need not be articulated, much less formalised, in order to perform their regulative function: they can be non-deliberative, unreflective, or tacit. They do not entail the self-awareness of the moving, or efficient, cause. On this point, Aristotle and Heidegger agree, but Aristotle goes further by applying the idea, not just to art, but also to self-generation in nature. This returns us to the issue of intentionality and naturalised epistemology, addressed at the end of Chapter Four. We saw there that Bloor’s call for a naturalised account of scientific reasoning need not entail the naturalistic reduction of intentional states to non-intentional states. For such a reduction presupposes that intentional states necessarily include propositional content. Yet Heidegger rejects this presupposition, arguing that intentional actions — actions exhibiting a directedness — can also be non-propositional in character. This underpins the present claim that intentional states may be non-deliberative. Intentional acts are not necessarily conscious phenomena, and so intentional activity may be ascribed to something without supposing that thing to possess a consciousness. When Aristotle argues that nature displays intention through the directedness of its activities, but that it does not deliberate, he would appear to espouse an account of natural intention which does not presuppose a sentient nature. In Aristotle, natural things move themselves to their proper place in an ordered cosmos, but, like the master fiddler, they do not have to think about doing so — they just do it. Aristotle appears to have imagined nature as a master artist, unreflectively performing itself.

It is this ‘performance’ which Aristotelian natural philosophers took as their object of study. By cataloguing the final/formal causes which govern the self-movement of nature, they hoped to achieve a dense and precise understanding of the ordered cosmos. If each thing moves naturally to form, to its own proper place in the cosmos, then a catalogue of these various forms would also provide a kind of conceptual map of the heterogeneous and hierarchically ordered places which constitute the qualitatively complex structure of the world. In the most abstract of terms, this conceptual map was meant to articulate in clear and explicit terms the implicit role played by final causation in regulating natural operations in the world. It may thus be viewed as a kind of cosmic operations manual, with the proviso that the original operator, just like the master artist, has no need for such a manual. Indeed, the master artist is likely to find a manual purporting to explicate her practice as, at best, an over-simplification of what she actually does. On the other hand, she may also find it difficult to articulate, in clear and determinate propositional terms, what she finds evident in her art but lacking in the manual.

These considerations should now make us wary about the oft-made claim that early-modern practitioners can be distinguished by their rejection of the Aristotelian distinction between art and nature. Historiographically, this distinction has often been viewed as an obstacle to the rise of the mechanical philosophy on which the new experimental practice is thought to have been based. Shapin writes that ‘the precondition for the intelligibility and the practical possibility of a mechanical philosophy of nature was setting aside that Aristotelian distinction.’103 Dear, who, as we have seen, emphasises the importance of mixed mathematics in the development of experimental practice, argues that ‘[t]he art-nature distinction impinged on the use of artificial contrivance in the making of natural knowledge — that is, it compromised the legitimacy of using in natural philosophy the sorts of procedures used by mathematicians.’104 Like Shapin, Dear suggests that ‘[t]he widespread adoption of various forms of “mechanical philosophy” went along with a drastic weakening of the art-nature distinction in philosophical thought,’ and he then adds that this ‘provided ontological vindication of the primacy of the mathematical sciences.’105 It is a historiographic commonplace that early-modern experimental philosophy was enabled by the rising fortunes of the mechanical philosophy. However, Shapin and Dear also maintain that the Aristotelian distinction between art and nature was a central barrier to the rise of the new experimentalism. I think that we should not accept this claim. Let me explain my disagreement by addressing Dear’s more detailed argument.

On closer inspection, it appears that the true barrier to experimental practice was, according to Dear, Aristotelian final causes: ‘[t]o the extent that Aristotle’s natural philosophy sought the final causes of things, and thereby to determine their natures, experimental science was therefore disallowed.’106 At the root of the rejection of the art-nature distinction was, therefore, the rejection of final causes. This would seem to make sense since, as we have seen, Aristotle distinguished art and nature by the location of their respective final and efficient causes. For the things of nature, the principle of their movement is internal, while for the things of art, the principle of their movement is external. However, for Aristotle this distinction was not, as Dear suggests, an ‘absolute separation.’107 Indeed, recall Aristotle’s argument that nature is like a doctor doctoring herself. Hence, in some special cases, art moves its object internally, and these special cases provided Aristotle with an analogical model for his account of natural generation. There was, for him, no absolute distinction to be drawn between art and nature, because he understood natural processes, in general, by analogy to special cases of artistic process.

Yet, Dear argues that natural and artificial causes were considered distinct because the regularity of natural processes could be ‘subverted’ by artificial causes.108 For example, ‘[a]n aqueduct […] is not a natural watercourse; it reveals the intention of its human producer, which thwarts that of nature.’109 But this example can also speak for an affinity between art and nature. From an Aristotelian perspective, the natural tendency of liquid water is to move as close as possible to the centre of the earth. The aqueduct does not thwart or subvert this tendency, but is entirely dependent on it for the successful delivery of water. The final cause which gives sense to the operations of the aqueduct is thus compatible with the final cause which gives sense to the operations of the natural watercourse: both facilitate the movement of liquid water to its proper place in the cosmos. This is not to say that artifice cannot be used to subvert the natural tendencies of things, but only that this possibility does not warrant an absolute separation of art and nature. Indeed, Aristotle wrote that ‘if things made by nature were made also by art, they would come to be in the same way as by nature. […] [G]enerally art partly completes what nature cannot bring to a finish, and partly imitates her.’110 In general, then, Aristotle viewed the respective operations of art and nature as complementary rather than as contradictory.

This point is emphasised in Dear’s description of the early-modern experiment as ‘mimetic, not semiotic.’111 The artifice of experiment imitates nature, rather than signifying it. According to Dear, mimesis is a primary characteristic of experimental manipulation.112 The experimental philosopher reproduces, or mimics, natural processes using artificial means, with the goal of generating new knowledge of nature, ‘especially knowledge of an operational kind.’113 Historically, this move involved what Dear describes as ‘[a] subtle redefinition of natural knowledge — and thus of nature itself.’114 He refers to the 1647 book, Discours du vuide, by the French physician and college teacher Pierre Guiffart, as evidence for this subtle redefinition. Dear cites Guiffart as stating:

There is a very notable difference between art and nature: art cannot produce anything without nature; it not only needs nature to furnish the material, but it also needs nature’s natural inclinations to go along with it, so that thereby it supplements nature’s rules and produces its own work.115

The subtle redefinition alleged to appear in this passage is that
‘[k]nowledge of nature, rather than being about identifying purposes [i.e., final causes], is now, insensibly, becoming about characterising “rules” […] of nature.’116 On the basis of this perceived distinction between final causes, on the one hand, and rules, on the other, Dear draws a further distinction between the ‘teleological’ explanations of Aristotelian natural philosophers and the ‘operational’ explanations of mixed mathematicians and the experimental philosophers inspired by them.117

This recalls Dear’s distinction between the operational explanations of mixed mathematicians, on the one hand, and explanations based on formal causes, as proffered by Aristotelian natural philosophers, on the other. In response to this, I argued, first, that operational explanations are also causal explanations because they refer both to efficient causes and, at least tacitly, to final causes, and, second, that final causes and formal causes are, in the realm of Aristotelian natural philosophy, effectively identical. It follows from this that Dear’s distinction between operational and teleological explanations should be regarded with some scepticism. As we have seen, explanations in terms of final causes can be viewed as explanations in terms of the rules which give meaning and direction to natural processes: they explain, for example, why an acorn grows into an oak tree rather than into an artichoke. The same point is implied in the passage from Guiffart. He argues that art relies on the support of natural inclinations so that it may act to supplement nature’s rule-governed activity. Yet natural inclinations seem just to be the natural tendencies definitive of final causes. Following its natural tendency, an acorn develops into an oak tree. Hence, as Guiffart suggests, because it relies on the natural tendencies of natural materials, art ends up supplementing, rather than violating, nature’s rules. Natural inclinations are here conceptualised as inclinations to follow the rules governing natural movement. The crucial point to be emphasised, then, is that a focus on the rules governing natural processes is simultaneously a focus not just on material causes, but also on final causes, and so it cannot be read as a rejection of the art-nature distinction. Hence Guiffart’s ability to faultlessly refer to nature’s rules while still asserting a notable difference between art and nature. For Dear, Guiffart’s affirmation of the art-nature distinction must be dismissed as ‘lip service,’ because Dear has put himself in an interpretative position where rule-based operational explanations of nature are incompatible with the Aristotelian doctrine of final cause allegedly underpinning a distinction between artificial and natural processes.118

Dear emphasises ‘manipulation’ as a key element in his explanation for the transition from late Renaissance natural philosophy to early-modern experimental philosophy, or what I have called the transition from regressus to mathēsis. The notion of artful manipulation was, he argues, a ‘Trojan horse’ by which the art-nature distinction could be circumvented, thereby allowing the applied techniques of mixed mathematicians to flood into early-modern natural philosophy.119 In response to Dear’s hypothesis, I have sought, in this section, to demonstrate two things. First, I have argued that the claim that early-modern experimental philosophy subverted the art-nature distinction should be treated with some scepticism. I have suggested that this distinction was not, per se, an obstacle for experimental practice, because artful manipulation had always been viewed as potentially compatible with natural processes. Second, I have argued that manipulation alone does not sufficiently explain the early-modern mathematisation of natural knowledge. Indeed, attention to manipulation alone explains very little. One must also attend to the governing principles which lend order and meaning to those manipulations, which explain to what end those manipulations are directed and for what end they are performed. Put otherwise, efficient causes must be married to final causes if we are to shed adequate explanatory light on the rule-governed dynamics which we observe in the worlds of both nature and art. Coherent operational explanations presuppose that for the sake of which those operations occur, because, without this presupposition, those operations would not be intelligible as anything more than random activity.

7. Conclusion

Tongue planted firmly in cheek, Shapin begins his 1996 book, The Scientific Revolution, with the following declaration: ‘There was no such thing as the Scientific Revolution, and this is a book about it.’120 Indeed, although historians of science have, in recent years, become increasingly circumspect about the notion of a Scientific Revolution, few have been willing to abandon it entirely. In particular, the idea that early-modern science was inaugurated by a sudden, radical, and complete — in short, a revolutionary — epistemic break with the past has been largely abandoned by historians, with the historiographic emphasis shifting to more nuanced considerations of both the continuities and discontinuities which exist between early-modern science and its predecessors.

The Heideggerian account of the Scientific Revolution which I have begun to outline in this chapter shares this circumspective stance. Recall that my explication of Heidegger’s account of modern science as mathēsis began with Heidegger’s insistence that facts, measurement, and experiment, broadly construed, figure as continuous threads running from modern science all the way back through medieval to ancient science. Moreover, according to Heidegger, the Scientific Revolution was sparked not by the rejection of tradition, but instead by the consolidation of an existential possibility which had, until that time, lain relatively dormant within that tradition. In this way, Heidegger’s use of the term ‘revolution’ [Umwälzung] harkens back to an older meaning of that term: not a sudden and radical break with the past, but instead a transformative, as opposed to an atavistic, return to it.

The extent to which Heidegger viewed the Scientific Revolution as powerfully tied to the past is clearly evinced by his claim that the Aristotelian concept of final cause was not, after all, abandoned by early-modern scientific practitioners. In this, as we have seen, Heidegger argues for greater historical continuity than do both Dear and Shapin. Yet, this concept was retained only to then undergo transformation in a way which profoundly altered the extant practices of fact-stating, measuring, and experimenting. Heidegger identified this transformation with the mathematisation of scientific knowledge. At its root, this mathematisation had to do, not with numerical practice, but with the development of a uniform measure, a basic blueprint, circumscribing the thingness of scientific things. It was the mathematisation of final causes, rather than their rejection, which allowed physical apparatus to flood into the knowledge-making practices of early-modern natural philosophy. It was how these apparatuses were used, and the end to which they were put, which mark a decisive transformation in the meaning of those practices. Furthermore, it was the concentration of scientific experience under a uniform measure which allowed numerical practice to likewise flood into, and give new form to, the early-modern natural philosophical experience of nature. Hence, Heidegger’s account of science as mathēsis may be read as charting a neutral course between two competing historiographic schools, each of which favours an explanation of the Scientific Revolution in terms of either the rise of experimental or mathematico-numerical practice. His account is meant to illuminate the common soil in which these two aspects of modern science are rooted, and from which they both sprang. It thus allows us an opportunity to reconnect recent historical studies of early-modern experimental philosophy with the theory-oriented studies which have typically been the brief of historians more concerned with early-modern mathematical practice. Chapter Six will give concrete, micro-historical attention to the ways in which the mathematicisation of final causes transformed the fortunes of early-modern experimental practice.

1 Galen of Pergamon (1944), On Medical Experience, 1st edn of the Arabic version, with English trans. by Richard Walzer (Oxford: Oxford University Press), p. 116.

2 Galen (1944), On Medical Experience, p. 97.

3 Galen (1944), On Medical Experience, p. 93.

4 David Bloor uses the paradox of the heap to challenge a rationalistic belief in the absolute (i.e., exceptionless) validity of deduction (David Bloor (1991 [1976]), Knowledge and Social Imagery, 2nd edn (Chicago: University of Chicago Press), pp. 182–83). The paradox seems to offer an exception, because the repeated application of deduction to apparently true premises (‘adding one grain to a non-heap results in a non-heap’ and ‘one grain is added to this non-heap’) seems to result in a false conclusion (‘this is a non-heap’). Defensive reactions to the paradox can make explicit the social labour required to maintain belief in the absolute validity of deduction. An example can be found in a paper by Colin Howson, wherein he seeks to suppress the paradox as I present it in my own work (Colin Howson (2009), ‘Sorites Is No Threat to Modus Ponens: A Reply to Kochan,’ International Studies in the Philosophy of Science 23(2), 209–12; Jeff Kochan (2008), ‘Realism, Reliabilism, and the “Strong Programme” in the Sociology of Scientific Knowledge,’ International Studies in the Philosophy of Science 22(1), 21–38). I respond to Howson in Jeff Kochan (2009a), ‘The Exception Makes the Rule: Reply to Howson,’ International Studies in the Philosophy of Science 23(2), 213–16.

5 Galen (1944), On Medical Experience, p. 118.

6 Galen (1944), On Medical Experience, p. 119.

7 Galen (1944), On Medical Experience, p. 104.

8 Galen (1944), On Medical Experience, p. 119.

9 Galen (1944), On Medical Experience, p. 93.

10 Galen (1944), On Medical Experience, p. 121.

11 Martin Heidegger (1967 [1962]), What Is a Thing?, trans. by William B. Barton, Jr., and Vera Deutsch (Chicago: Henry Regnery), p. 39.

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

13 Heidegger (1967), What Is a Thing?, p. 40.

14 Heidegger (1967), What Is a Thing?, p. 15; translation modified.

15 Heidegger (1967), What Is a Thing?, p. 67.

16 Heidegger (1967), What Is a Thing?, pp. 66–68.

17 ‘[…] was die Grundbewegung der Wissenschaft […] gleichursprünglich maßgebend durchherrscht’ (Martin Heidegger (1984b [1962]), Die Frage nach dem Ding: zu Kants Lehre von den transzendentalen Grundsätzen (Gesamtausgabe, vol. 41) (Frankfurt: Vittorio Klostermann), p. 68). Cf. Heidegger (1967), What Is a Thing?, p. 68.

18 Heidegger (1984b [1962]), Die Frage nach dem Ding, pp. 69–70. Cf. Heidegger (1967), What Is a Thing?, p. 69.

19 Heidegger (1967), What Is a Thing?, p. 66; translation modified, my brackets. Cf. Heidegger (1984b), Die Frage nach dem Ding, p. 66.

20 Heidegger (1967), What Is a Thing?, p. 66. Cf. Heidegger (1984b), Die Frage nach dem Ding, p. 66. Thus, Heidegger’s usage of mathēsis differs from that of Michel Foucault, who defines it as ‘the science of calculable order’ (Michel Foucault (1970), The Order of Things: An Archaeology of the Human Sciences (New York: Pantheon Books), p. 73).

21 Heidegger (1984b), Die Frage nach dem Ding, p. 71; cf. Heidegger (1967), What Is a Thing?, p. 71.

22 Heidegger (1984b), Die Frage nach dem Ding, p. 71; cf. Heidegger (1967), What Is a Thing?, p. 71.

23 Heidegger (1984b), Die Frage nach dem Ding, p. 73; cf. Heidegger (1967), What Is a Thing?, p. 72.

24 Heidegger (1984b), Die Frage nach dem Ding, p. 73; cf. Heidegger (1967), What Is a Thing?, pp. 72–73.

25 Heidegger (1984b), Die Frage nach dem Ding, p. 72; cf. Heidegger (1967), What Is a Thing?, p. 72.

26 ‘[…] welche Bewandtnis es überhaupt mit dem Ding hat’ (Heidegger (1984b), Die Frage nach dem Ding, p. 72); cf. Heidegger (1967), What Is a Thing?, p. 72.

27 Ernst Tugendhat comments that there is probably no word in any other language which includes the same constellation of meanings as Bewandtnis. Thus, he concludes, Heidegger’s argument in §18 of Being and Time must resist intelligible translation (Ernst Tugendhat (1967), Der Wahrheitsbegriff bei Husserl und Heidegger (Berlin: de Gruyter), p. 290 n. 6). Caveat emptor!

28 Martin Heidegger (1927), Sein und Zeit (Tübingen: Max Niemeyer Verlag), pp. 83–84; cf. Martin Heidegger (1962a [1927]), Being and Time, trans. by John Macquarrie and Edward Robinson (Oxford: Blackwell), p. 115 [83–84].

29 Other philosophical translations for Bewandtnis, as used by Heidegger, include: ‘involvement’ by John Macquarrie and Edward Robinson (in Heidegger (1962a), Being and Time), and by Hubert Dreyfus (in Hubert L. Dreyfus (1991b), Being-in-the-World: A Commentary on Heidegger’s Being and Time, Division I (Cambridge, MA: The MIT Press)); ‘relevance’ by Joan Stambaugh (in Martin Heidegger (2010b), Being and Time, trans. by Joan Stambaugh, revised edn (Albany: SUNY Press)); ‘relevance/involvement’ by Daniel Dahlstrom (in Daniel O. Dahlstrom (2013), The Heidegger Dictionary (London: Bloomsbury 2013)); ‘how it works’ by William Barton and Vera Deutsch (in Heidegger (1967), What Is a Thing?); ‘functionality’ by Alfred Hofstadter (in Martin Heidegger (1982a [1975]), Basic Problems of Phenomenology, trans. by Albert Hofstadter (Bloomington: Indiana University Press)); and ‘role’ by John Haugeland (in John Haugland (2013), Dasein Disclosed: John Haugeland’s Heidegger, ed. by Joseph Rouse (Cambridge, MA: Harvard University Press)). At the time of writing, the poplar on-line LEO German-English dictionary translated Bewandtnis as ‘matter’ or ‘reason’ ( The 2001 print edition of the well-respected PONS English-German dictionary offers ‘reason’ and ‘explanation.’

30 Heidegger (1927), Sein und Zeit, p. 84; my emphases. Cf. Heidegger (1962a), Being and Time, p. 116 [84].

31 Heidegger (1927), Sein und Zeit, p. 84. Cf. Heidegger (1962a), Being and Time, p. 116 [84].

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

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

34 Heidegger (1982a), Basic Problems of Phenomenology, p. 106.

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

36 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. 119); cf. Heidegger (1967), What Is a Thing?, p. 70. Cf. also: ‘When we hear of measure, we immediately think of number and imagine the two, measure and number, as quantitative. But the nature of measure is no more a quantum than is the nature of number’ (Martin Heidegger (1971a), ‘“… Poetically Man Dwells…,”’ in Poetry, Language, Thought, by Martin Heidegger, trans. by Albert Hofstadter (New York: Harper & Row), pp. 213–29 (p. 225)). The OED defines ‘measure,’ in one substantive sense, as a ‘standard or rule of judgement; a criterion, test; also, a standard by which something is determined or regulated.’

37 Heidegger (1927), Sein und Zeit, p. 84; cf. Heidegger (1962a), Being and Time, p. 116 [84].

38 John Herman Randall, Jr (1940), ‘The Development of the Scientific Method in the School of Padua,’ Journal of the History of Ideas 1(2), 177–206 (p. 190).

39 Randall (1940), ‘The Development of the Scientific Method,’ p. 190. Alistair Crombie suggests that the Paduan ‘double process’ was imported from Oxford around 1400 (Alistair C. Crombie (1962), Robert Grosseteste and the Origins of Experimental Science (1100–1700) (Oxford: Clarendon Press), p. 297). However, Randall’s dating indicates that its earliest known appearance in Padua was prior to 1400.

40 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 189; originally from Jacobi de Forlivio super Tegni Galeni, Padua, 1475, comm. Text I.

41 Randall (1940), ‘The Development of the Scientific Method,’ p. 189. As I have shown elsewhere, something like the Paduan double procedure — and, indeed, Heideggerian mathēsis — can also been found in Ludwik Fleck’s historical account of the medical diagnosis of syphilis (Jeff Kochan (2015c), ‘Circles of Scientific Practice: Regressus, Mathēsis, Denkstil,’ in Critical Science Studies after Ludwik Fleck, ed. by Dimitri Ginev (Sophia: St. Kliment Ohridski University Press), pp. 83–99; reprinted as Jeff Kochan (2016), ‘Circles of Scientific Practice: Regressus, Mathēsis, Denkstil,’ in Fleck and the Hermeneutics of Science (Collegium Helveticum Heft 14), ed. by Erich Otto Graf, Martin Schmid and Johannes Fehr (Zürich, 2016), pp. 85–93). See Ludwik Fleck (1979 [1935]), Genesis and Development of a Scientific Fact, trans. by Fred Bradley and Thaddeus J. Trenn, ed. by Thaddeus J. Trenn and Robert K. Merton (Chicago: University of Chicago Press).

42 Cited in Randal (1940), ‘The Development of the Scientific Method,’ p. 191; originally from Summa philosophiae naturalis magistri Pauli Venti, Venice, 1503, I, cap. ix.

43 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 192; originally from Augustino Niphi philosophi suessani exposition… de Physico auditu, Venice, 1552, I, com. Text 4.

44 Eckhard Kessler (1988), ‘The Intellective Soul,’ in The Cambridge History of Renaissance Philosophy, ed. by Charles B. Schmitt, Quentin Skinner, Eckhard Kessler and Jill Kraye (Cambridge: Cambridge University Press), pp. 485–534 (p. 836).

45 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 200–01; originally from Jacopo Zabarella, De Regressu, chpt. 5.

46 Randall (1940), ‘The Development of the Scientific Method,’ p. 199.

47 Randall (1940), ‘The Development of the Scientific Method,’ p. 201.

48 Randall (1940), ‘The Development of the Scientific Method,’ p. 204.

49 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 197–98; originally from Jacopo Zabarella, De Methodis, III, xviii.

50 Jacobi Zabarella (1985), De Methodis; De Regressus, ed. by Cesare Vasoli (Bologna: Cooperativa Libraria Universitaria Editrice), p. 99. Original text: ‘hominem enim rem sensilem effe dicimus, non quòd hominé universalem sensus cognoscat, sed qiua singuli individui homines sensiles sunt’ (Zabarella, De Methodis, bk. 4, chpt. 19). I have closely followed Rudolf Schicker’s German translation (see Jacopo Zabarella (1995), Über die Methoden (De Methodis); Über den Rückgang (De Regressu), trans. by Rudolf Schicker (Munich: Wilhelm Fink Verlag), p. 243).

51 Cited in Randall (1940), ‘The Development of the Scientific Method,’ pp. 198-99; originally from Zabarella, De Methodis, III, xix.

52 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 200; originally from Zabarella, De Regressu, chpt. 4.

53 Harold Skulsky (1968), ‘Paduan Epistemology and the Doctrine of the One Mind,’ Journal of the History of Philosophy 6(4), 341–61 (p. 341).

54 Eckhard Kessler (1988), ‘The Intellective Soul,’ in The Cambridge History of Renaissance Philosophy, ed. by Charles B. Schmitt, Quentin Skinner, Eckhard Kessler and Jill Kraye (Cambridge: Cambridge University Press), pp. 485–534 (p. 531).

55 Nicholas Jardine (1976), ‘Galileo’s Road to Truth and the Demonstrative Regress,’ Studies in History and Philosophy of Science 7(4), 277–318 (p. 301).

56 Jardine (1976), ‘Galileo’s Road to Truth,’ p. 301

57 Jardine’s mistaken assumption that, for Zabarella, no effort is required to move from confused to distinct knowledge of the cause, seems to underpin his questionable conclusion that the regressus, in general, is ‘blatantly circular’ (Jardine (1976), ‘Galileo’s Road to Truth,’ p. 308). As argued above, such effort is called for just because the regressus is not viciously circular.

58 Charles B. Schmitt (1969), ‘Experience and Experiment: A Comparison of Zabarella’s View with Galileo’s in De Motu,’ Studies in the Renaissance 16, 80–138 (p. 99).

59 Schmitt (1969), ‘Experience and Experiment,’ p. 105.

60 Schmitt (1969), ‘Experience and Experiment,’ p. 106.

61 Randall (1940), ‘The Development of the Scientific Method,’ pp. 204–05.

62 Heidegger (1962a), Being and Time, p. 191 [150].

63 Heidegger (1962a), Being and Time, p. 194 [152].

64 Heidegger (1962a), Being and Time, p. 195 [153].

65 Martin Heidegger (1997 [1929]), Kant and the Problem of Metaphysics, 5th edn, enlarged, trans. by Richard Taft (Bloomington: Indiana University Press), p. 15.

66 Recall from Chapter Four, that these two different construals of the a priori are not incommensurable. Indeed, Heidegger argues that the timeless construal rests on an experience of time in terms of a present-at-hand succession of ‘nows.’ This he then explains in terms of a more basic experience of ‘original time,’ which is enabled and sustained by a historical tradition.

67 These contrasting accounts of how the basic measure was set for modern science bring to mind contrasting accounts of poetic creation. On the one hand, poetry is divine inspiration; on the other, it is an evocation of possibilities latent in natural language. The idea of poetry as existential measure-setting became crucial for Heidegger in the 1950s. According to Charles Bambach, for the later Heidegger, ‘[p]oetry measures the limits of what is appropriate for human beings, shaping the contours of our mortal fate’ (Charles Bambach (2013), Thinking the Poetic Measure of Justice: Hölderlin-Heidegger-Celan (Albany: SUNY Press), p. 174). Indeed, Heidegger would write that poetry sets ‘[a] strange measure for […] scientific ideas.’ In so doing, poetry ‘speaks in “images” [Bildern]’ (Heidegger (1971a), ‘“… Poetically Man Dwells…,”’ pp. 223, 226). This recalls, from Chapter Four, Heidegger’s rooting of the origins of logic— the science of thinking — in Plato’s mythic image of the cosmic demiurge. In Chapter Six, I argue that Heidegger placed the origins of the early-modern experiment in a cognate image of the scientific thing.

68 Randall (1940), ‘The Development of the Scientific Method,’ p. 204.

69 Alexandre Koyré (1943a), ‘Galileo and Plato,’ Journal of the History of Ideas 4(4), 400–28 (p. 406 n. 17).

70 Alexandre Koyré (1943b), ‘Galileo and the Scientific Revolution of the Seventeenth Century,’ Philosophical Review 52(4), 333–48 (p. 347).

71 ‘[…] un de ces grands génies métaphysiques qui marquent de leur influence une période tout entière’ (Alexandre Koyré (1931), ‘L’introduction du “Qu’est-ce que la métaphysique?”’ Bifur 8, 5–8 (p. 5)).

72 Koyré (1943a), ‘Galileo and Plato,’ p. 405.

73 Koyré (1943b), ‘Galileo and the Scientific Revolution,’ p. 346.

74 Koyré (1943a), ‘Galileo and Plato,’ p. 425. In a comparison of Heidegger and Ernst Cassirer, Michael Friedman notes that Cassirer influenced Koyré’s Platonic account of the Scientific Revolution (Michael Friedman (2000), A Parting of the Ways: Carnap, Cassirer, and Heidegger (Chicago: Open Court), p. 88).

75 Randall (1940), ‘The Development of the Scientific Method,’ p. 205.

76 Peter Dear (1995), Discipline & Experience: The Mathematical Way in the Scientific Revolution (Chicago: University of Chicago Press), pp. 125–26.

77 Peter Dear (2006a), ‘The Meanings of Experience,’ in The Cambridge History of Science, vol. 3: Early Modern Science, ed. by Katharine Park and Lorraine Daston (Cambridge: Cambridge University Press), pp. 106–31 (p. 119).

78 Dear (2006a), ‘The Meanings of Experience,’ p. 119.

79 Dear (2006a), ‘The Meanings of Experience,’ p. 120; Peter Dear (1995), Discipline & Experience: The Mathematical Way in the Scientific Revolution (Chicago: University of Chicago Press), p. 36.

80 Peter Dear (2006b), The Intelligibility of Nature: How Science Makes Sense of the World (Chicago: University of Chicago Press), p. 2.

81 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. 241 [line 194b29]).

82 Dear (1995), Discipline & Experience, p. 28.

83 Dear (1995), Discipline & Experience, p. 27.

84 Peter Dear (1998), ‘Method and the Study of Nature,’ in The Cambridge Companion of Seventeenth-Century Philosophy, vol. 1, ed. by Daniel Garber and Michael Ayers (Cambridge: Cambridge University Press), pp. 147–77 (p. 152).

85 Peter Dear (2001), Revolutionizing the Sciences: European Knowledge and Its Ambitions, 1500–1700 (Basingstoke: Palgrave), p. 51.

86 Randall (1940), ‘The Development of the Scientific Method,’ p. 194.

87 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 194; originally from Augustino Niphi philosophi suessani exposition…de Physico auditu, Venice, 1552, I, comm. Text 4, Recognitio.

88 Cited in Randall (1940), ‘The Development of the Scientific Method,’ p. 194; originally from Augustino Niphi philosophi suessani exposition…de Physico auditu, Venice, 1552, I, comm. Text 4, Recognitio.

89 Aristotle (1941d), On the Heavens, trans. by J. L. Stocks, in The Basic Works of Aristotle, ed. by Richard KcKeon (New York: Random House), pp. 398–466 (p. 459 [lines 310a34–35]).

90 Steven Shapin (1996), The Scientific Revolution (Chicago: University of Chicago Press), p. 139; Dear (2001), Revolutionizing the Sciences, p. 13.

91 Dear (2001), Revolutionizing the Sciences, p. 14.

92 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. 248 [lines 198b26–27]).

93 Aristotle (1941d), On the Heavens, p. 459 (lines 310b17–18).

94 Andrea Falcon (2015), ‘Aristotle on Causality,’ in The Stanford Encyclopedia of Philosophy, ed. by Edward N. Zalta (Spring 2015 Edition), §3.

95 Aristotle (1941e), On the Generation of Animals, trans. by Arthur Platt, in The Basic Works of Aristotle, ed. by Richard KcKeon (New York: Random House), pp. 665–80 (p. 665 [lines 715a4–7]).

96 Aristotle (1941f), Metaphysics, trans. by W. D. Ross, in The Basic Works of Aristotle, ed. by Richard KcKeon (New York: Random House), pp. 689–926 (p. 874 [lines 1070a7–10]).

97 Aristotle (1941c), Physica, p. 874 (line 199b30).

98 Aristotle, Physica, lines 194b34; trans. by R. Hope and cited in Bas C. van Fraassen (1980), ‘A Re-Examination of Aristotle’s Philosophy of Science,’ Dialogue 19(1), 20–45 (p. 24).

99 Aristotle (1941c), Physica, p. 251 (lines 199b327–29).

100 Martin Heidegger (1976 [1967]), ‘On the Being and Conception of φύσις in Aristotle’s Physics B, 1,’ Man and World 9(3), 219–70 (pp. 231). See also: Martin Heidegger, Martin (1977b [1954]), ‘The Question Concerning Technology,’ in The Question Concerning Technology and Other Essays, by Martin Heidegger, trans. by William Lovitt (New York: Harper & Row), pp. 3–35 (p. 8); Martin Heidegger (2000 [1953]), Introduction to Metaphysics, trans. by Gregory Fried and Richard Polt (New Haven: Yale University Press), p. 63.

101 Heidegger (1982a), Basic Problems of Phenomenology, p. 295; translation modified.

102 Heidegger (1982a), Basic Problems of Phenomenology, p. 293.

103 Shapin (1996), The Scientific Revolution, p. 31.

104 Dear (1995), Discipline & Experience, p. 153.

105 Dear (1995), Discipline & Experience, p. 151.

106 Dear (2006a), ‘The Meanings of Experience,’ in The Cambridge History of Science, vol. 3: Early Modern Science, ed. by Katharine Park and Lorraine Daston (Cambridge: Cambridge University Press), pp. 106–31 (p. 110).

107 Dear (1995), Discipline & Experience, p. 155.

108 Dear (1995), Discipline & Experience, p. 155.

109 Dear (1995), Discipline & Experience, p. 155. Elsewhere, Dear assimilates ‘contrived situations’ to ‘interference’ with natural processes in the natural philosophical context (Peter Dear (1990), ‘Miracles, Experiments, and the Ordinary Course of Nature,’ Isis 81(4), 663–83 (p. 681)).

110 Aristotle (1941c), Physica, p. 250 (lines 199a14–17).

111 Dear (1995), Discipline & Experience, p. 159.

112 Dear (1995), Discipline & Experience, p. 159.

113 Dear (1995), Discipline & Experience, p. 159.

114 Dear (1995), Discipline & Experience, p. 157.

115 Dear (1995), Discipline & Experience, p. 157.

116 Dear (1995), Discipline & Experience, p. 157.

117 Dear (1995), Discipline & Experience, p. 158.

118 Dear (1995), Discipline & Experience, p. 161.

119 Dear (1995), Discipline & Experience, p. 161.

120 Shapin (1996), The Scientific Revolution, p. 1.