What is meant by “a mechanistic world-picture”? Dijksterhuis’s *The Mechanization of the World Picture* revolves around this question. He asks: “When we say this, are we thinking of the meaning of ‘tool’ or ‘machine’ implied by the Greek word μηχανή (that is, of viewing the world [whether or not it includes the human spirit] as a machine)? Or does it mean that natural events can be described by means of concepts and handled through the methods of mechanics, this branch of science (in which case the word is used in a very different sense from its original one, signifying the science of motion)?”[1]
In the end, Dijksterhuis gives his answer: the so-called mechanization of the world picture does not lie in the metaphor of “machine” — after Newton, the machine metaphor that lingered in the concept of “mechanics” has already faded away almost completely[2]; rather, the key lies in the rise, out of this etymological lineage, of “mechanics” (as a mathematized science of motion), and this constitutes the fundamental difference between classical science and medieval science.[3] He emphasizes that the unique significance of the mathematization that took place in modern mechanics lies “not only because it uses mathematical tools to simplify and clarify arguments that could, if necessary, also be expressed in everyday language, but because in a stricter sense the basic concepts of mechanics are mathematical concepts; mechanics itself is a mathematics.”[4] Galileo’s famous saying expresses the classical scientific view of nature: “The book of nature is written in the language of mathematics.”
Here there are four key concepts that are interwoven with one another — “nature,” “machine,” “mechanics,” “mathematics.” One may say that in the process of “the mechanization of the world picture,” nature became machine, “mechanics” (in the sense of Archimedes) became “mechanics” (in the sense of Newton), and this mechanics became a mathematics… At the end, one might perhaps add one more line: “mathematics” became “nature” — this is the theme I am trying to elucidate in this essay.
What I mean by “the naturalization of mathematics” is roughly what we usually speak of as “the mathematization of nature.” The reason I want to play with words in this way is to highlight a certain hint — here “nature” is not only “nature” as the object of objective knowledge, but also, and more importantly, its original sense: “nature” as “own-so-being,” as what is “just so by itself,” as “essence.”
Thus, “the naturalization of mathematics,” besides meaning that “the natural world became a great book written in mathematics,” also means that “nature,” as “essence,” “ground,” “principle,” or “inner cause,” the field of so-called “immanence” opened up by the ancient Greek natural philosophers, was from then on occupied by mathematics.
Dijksterhuis also mentions the transformation of the idea of “nature” or “essence”: “The ‘essential’ thinking that seeks the true nature of things had to be replaced by ‘functional’ thinking that attempts to determine the interdependence of the behavior of things.”[5] But in fact, modern natural scientists still claim that they are investigating the nature of things. Rather than saying that classical science abandoned the inquiry into “nature,” it would be more accurate to say that it changed the understanding of “nature” — a modern scientist may well think that when he establishes a certain mathematical formula, he has, to some extent, disclosed the nature of things or the causes of phenomena.
The concept of “mechanics” derives from “machine,” “tool,” while the concept of “nature,” at its source, means something exactly opposed to this. In ancient Greece, “natural things” were defined together with their opposite, “artificial things.” Aristotle says: “Of existing things, some exist by nature, others by other causes. … All natural things evidently have in themselves a principle of motion and of rest. On the contrary, … products of art … have no such inner impulse of change.”[6]
A machine, as a technical artifact, has no immanence; its origin and purpose are both external to it. As Dijksterhuis puts it: “In fact, the machine presupposes a conscious intelligent maker who manufactures the machine and sets it in motion in order to realize a specific purpose.”[7] This is precisely why Dijksterhuis thinks that, in the “mechanization” of the world picture, the metaphor of “machine” is not important. He says: “Science itself has neither an otherworldly creator of the cosmos nor a world-external goal that the Creator wanted to achieve through creation; the machine metaphor at most helped make the particulate view of nature acceptable to Christian thinkers…”[8]
However, if we notice that “the world (the natural world)” and “machine” originally corresponded precisely to two sharply opposed realms, those of immanence and transcendence, then the paradoxical proposition of “the mechanization of the natural world” itself already implies some major transformation — that is to say, the boundary between the realm of immanence and the realm of transcendence established by the ancient Greeks has been broken. If it is indeed true that the metaphor “nature became machine” took place, then we should not be too surprised if no external maker or goal is found in this new world, because once the boundary between immanence and transcendence has dissolved, this world of course no longer needs an external principle, just as it no longer requires an internal principle either.
Dijksterhuis then says: “If the machine metaphor does in fact provide an essential characteristic of classical scientific thought, we might then expect that at least some teleological ideas would occupy an important place in it. Therefore, in studying a machine, if we ask only what causes the motion of some part of it, without considering the immediate goal to be achieved through such motion, then as far as ability is concerned, we would not regard it as a machine but only as an arbitrary mechanical system.”[9]
Indeed, since a machine is a technical artifact belonging to the realm of transcendence, if classical mechanics never inquires into external purposes, then it cannot be called a “mechanical science”; yet from another angle, if “nature” still means an immanent realm that exists “not by other causes” but “by itself,” if “natural things” mean having the capacity to subsist on their own without mutual dependence on other things, then can classical mechanics still be called a “natural science”? Dijksterhuis himself is quite clear that in classical mechanics the essentialist thinking that investigates the nature of things has been replaced by functional thinking that seeks to determine the “interdependence” of things’ behavior. Then we may likewise say: “In studying nature, if we ask only about the interdependence between the motion of some part of it and the other parts, without considering the inner cause from which this motion arises or the true nature of the thing, then as far as ability is concerned, we would not regard it as nature but only as an arbitrary mechanical system.”
In fact, once “the mechanization of nature” occurs, we are inevitably compelled to alter our understanding of both “nature” and “machine” at the same time. “Mechanics,” as a mathematics, can be either a kind of “natural science” that does not investigate immanence or a kind of “mechanical science” that does not investigate transcendence. If classical mechanics has already forgotten “machine,” then it has perhaps forgotten “nature” to an equal degree.
Of course, just as “natural science” still continues the traditional conception of “nature,” Dijksterhuis also admits that “mechanism” is not without any historical source in the concept of “machine”: “Many physicists often have a strong need to conceive as concretely as possible the physical reality behind phenomena, the imperceptible causes of the things encountered in sense experience. They have continually sought hidden mechanisms, and have taken it for granted, without hesitation, that these mechanisms are essentially of the same type as the simple machines human beings have used since ancient times to lighten their labor, so that a skilled mechanic can roughly imitate, by means of mechanical models, the real course of events occurring in the microcosm. In the past as in the present, the pursuit of this goal has often been regarded as the true characteristic of classical science and as the true meaning expressed by the adjective ‘mechanistic.’”[10] In other words, the tradition of “mechanism” is embodied in the search for “mechanism” or “structure.”
But here we need to note that “mechanism” or “structure” is a different concept from “cause”; in classical science, “mechanism” at most is only one kind of cause — if the motive cause of a machine is its maker or operator, the final cause is the function the machine is meant to realize, and the material cause is its material substance, then its structural mechanism probably corresponds to the “formal cause.”
So, what does the shift from “mechanics” to “mechanics” mean? If the core of “mechanism” is the concern with “mechanism,” or rather with the “formal cause” of the mechanical framework, then the core concept of “mechanics” — as its Chinese translation suggests — is “force” (vis/force).
As Dijksterhuis says, “force is such an ambiguous term, so burdened with anthropomorphic associations, that without definition the word cannot be used at all in scientific reasoning”[11]; and it was only through mathematization that the concept of “force” was ultimately defined precisely in Newton, which marked the establishment of classical mechanics.
The reason “machine” and “nature” could merge and dissolve within “mechanics” was precisely the “mathematization” of “force”: a new definition of mathematics replaced the traditional meanings burdened by “force,” and this completed the mechanization of nature. So what exactly was replaced by mathematics?
Perhaps the concept of “force” from the very beginning was a key to connecting the realms of immanence and transcendence, precisely because of the “many anthropomorphic associations” burdened upon it. Whether this Chinese character or its Latin equivalent (vis), it was originally linked with concepts such as “vigor,” “strength,” and “energy,” and from there gave rise to images of “exerting force,” “applying force,” “using force,” and so on. The associations evoked by this word are often related to human beings, more precisely to a person’s will or body.
Besides the natural things of the realm of immanence and the technical tools or mechanical devices of the realm of transcendence, in the classical world there seems to have been another special domain: the existence of human beings as subjects. Human beings are both a kind of “natural thing” that takes itself as its own principle, and also the ultimate source of artificial things. The human being as maker of artificial things is the external cause of a machine’s operation, while the human being as a natural thing interrupts the inquiry into external causes. And the concept of “force,” with its distinctive anthropomorphic associations, accomplished the linking of immanence and transcendence. On the one hand, associations such as “push,” “exert force,” and “apply force” drive “force” toward the realm of transcendence; on the other hand, associations such as “vitality,” “energy,” and “capacity” draw “force” back into the realm of immanence,
At the same time, the anthropomorphic associations of “force” naturally overlap with the concept of “cause.” For example, Kuhn (quoting Piaget) mentions that “the concept of [cause] in the narrow sense originally derived from the egocentric idea of an active agent, a person who pushes or pulls, exerts a force or displays a motive power. It comes very close to Aristotle’s concept of efficient cause, which for the first time played a significant role in technical physics in the seventeenth-century analysis of collisions.”[12]
Before Newton, when scientists thought about the concept of force, what often came to mind was something akin to “vitality” inherent in objects. For example, Westfall notes that in Huygens, “force represented not an action upon an object but the tendency a body has in motion. Thus it resembled Descartes’ ‘force of motion in bodies,’ and approximated what we call momentum, a concept acceptable to mechanistic philosophers.”[13] And “the ‘force’ used by Leibniz can readily be transformed into our term ‘kinetic energy.’ His natural philosophy was very different from Descartes’, but he still accepted the premise that force is not something acting upon bodies and changing their state of motion, but something bodies possess.”[14]
This way of thinking of force as an inner power of things is an echo of the line of inquiry into immanence that goes back to ancient Greek natural philosophy. Therefore, Newton’s act of restoring the status of “force” to the center of science was naturally regarded by mechanists of the time as a revival of Aristotelian natural philosophy. In Kuhn’s words: “To most seventeenth-century corpuscularians, the concept of gravity as an intrinsic attracting principle looked too much like the Aristotelian ‘tendency to motion,’ which had been unanimously rejected. The great advantage of the Cartesian system was precisely that it eliminated all such ‘occult qualities.’ Cartesian corpuscles were wholly neutral, and gravity itself was explained as a result of collisions; the concept of an intrinsic principle of attraction at a distance seemed to be a relapse into the mysterious ‘sympathies’ and ‘potencies’ that had made medieval science so absurd.”[15]
Dijksterhuis also points out: “Leibniz and Huygens’ criticisms of Newton’s theory contained many unjust elements, but their concern about the possible effect of the reintroduction into physics of the concept of force as the cause of motion was not unreasonable…. In fact, in physics the word ‘force’ too often plays a role essentially no different from the ‘qualities’ and ‘powers’ of scholastic philosophy. A physicist who laughs at explanations given in terms of ‘qualities’ is quite satisfied with expressions such as ‘a force is exerted,’ and even today merely uttering this magical word is enough to satisfy beginners in physics or chemistry in their demand for causality: why do heavy objects in one’s hand fall the moment they are released? Because the earth attracts them! Why does a solid body not break into the smallest particles? Because these particles attract one another! …”[16]
In other words, when Newton brought the concept of “force” into the center of mechanistic science, this necessarily also accompanied the rebirth of a line of thought concerning “immanence,” “inner tendency,” or “inner principle.” Yet the revival of immanence at the center of an already developed tradition of transcendence in “mechanics” seems to have led to a kind of annihilating collision — this contact released a tremendous light, creating the brilliance of classical mechanics, but from then on the realms of immanence and transcendence both disappeared from sight.
Newton’s transformation of the concept of “force” lay not only in its successful mathematization or precise definition, but also in the alteration of the relation between “force” and “cause.”
On the one hand, Newton removed the immanence of “force.” Definition 4 of the *Principia* clearly states: “An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line. — This force exists only during the action, and does not remain in the body when the action has ceased, for the body maintains the state it has acquired only by its inertia. But impressed forces have various sources, such as impact, pressure, or centripetal force.”
Although Newton still retained expressions such as “force of inertia,” the “force” in classical mechanics from then on was after all conceived according to “impressed force,” that is to say, as the cause of the change in a body’s motion, it cannot be within the body itself.
So is “force” then a kind of external cause? Probably not either; at least, it changed the mechanistic tradition’s understanding of external cause. Dijksterhuis mentions: “Newton introduced the concept of force in the sense of the cause of the change in the velocity vector of a particle, thus consciously breaking with seventeenth-century mechanism, in which a change in the motion of one body could only be brought about by another moving body”[17]
The transformation here in the status of “force” is not merely a shift from the “cause of motion” to the “cause of change in velocity.” In fact, in classical science “force” was never the “cause of motion” either. If A exerts a push on B, thereby causing a change in B’s motion, then the efficient cause is not this “force” but the thing “A” itself.
In short, in the traditional line of thought, if understood according to the immanent “vitality” or “potentiality,” “force” should be regarded as the inner cause of motion in a thing; while if understood according to the transcendent “push” or “impact,” then “force” is in fact the occurrence of “causality” itself — when the active agent as cause gives a force to the passive recipient as effect, the two become a causal relation; force is the transmission of causality, not cause itself. And Newton’s “force” both retained the meaning of “cause” from the line of immanence and was fully constructed according to the mechanistic thinking of the line of transcendence.
In fact, given the establishment of Newton’s third law, external “force” can no longer “transmit” some causal relation conceived according to efficient causation. For causality, by definition, one term is cause and the other is effect; logically and temporally, there is always some distinction of priority and sequence. When Aristotle imagined the act of pushing, he clearly expressed the difference in status between the two sides: “Taken together, teaching and learning or action and suffering (the active and the passive, the mover and the moved) are not identical in unqualified sense, though the thing in virtue of which they exist—motion—is the same. For the activity in virtue of which A is acting on B and the activity in virtue of which B is being moved by A are not the same in definition.”[18] But after Newton’s third law, force and reaction force, the agent applying the force and the body receiving it, are completely equivalent; “universal gravitation” is everywhere, so do any two objects in the world stand in mutual causation? Once that is so, the concept of causality loses all meaning.
“Force” itself becomes the cause, but what does that mean? What difference is there between saying “the reason why B changed is that it was subjected to a force” and saying “the reason why B changed is that it received love”? In other words, is “force” merely an empty word? As Galileo says in a question-and-answer passage cited in the Dialogue Concerning the Two Chief World Systems:
When Simplicio answers the question “Why do heavy bodies fall?” with “gravity,” “Salviati said: ‘You are mistaken, Signor Simplicio; you should say, everybody knows that it is called gravity.’11 He goes on to say that to describe a frequently recurring phenomenon with a particular name can indeed make us imagine that we have some degree of understanding of it, but that all our so-called explanations of natural phenomena ultimately amount to assigning names to causes that are unknown in essence: ‘gravity,’ ‘force,’ ‘impressed force,’ ‘the informing intelligence,’ ‘the assisting intelligence,’ or, in general, ‘nature’.”
As Salviati says, if classical mechanics merely makes “force” into a “cause” in order to explain phenomena, then it has explained nothing at all; it has merely changed the label. What gives classical mechanics’ explanations real substance is that, through the mathematical definition of “force,” an explanation in terms of force means some definite measurement and prediction. Dijksterhuis says: “… can we speak of the earth’s gravity, cohesion, affinity, and the like? Indeed we can, so long as we keep in mind that the cause of a phenomenon is nothing but the giving of a name, and that only when the action of the forces thus mentioned can be defined exactly by some mathematical law does this name contain real knowledge,”[19]
Thus it is not some real “force” that has become the cause; rather, the mathematical system designated by the symbol “force” has become the “cause” explaining phenomena. Replacing all the “forces” in classical mechanics with “love” would not affect its system: a “classical mechanics system” that says “A exerts a gravitational force of 10 newtons on B” and a “classical love system” that says “A exerts a force of 10 Empedoclean units of love on B” would not differ in any substantive way. In the development of classical mechanics, the concept of “force” is merely a medium, a catalyst-like medium; it performs a kind of sleight of hand or shell game, allowing the philosophical tradition of nature in the realm of immanence and the mechanical tradition in the realm of externality to permeate one another, so that the core concerns of both are dissolved into thin air. In the end, all the ambiguity, mystery, and anthropomorphic metaphors attached to the concept of “force” are hollowed out; it is mathematics that, in the name of “force,” takes over the new domain of “nature.” Mathematics is no longer merely a tool for studying the mechanism of natural things; it becomes “nature” itself. It is not just a language for describing causal relations among things, but becomes the “cause” of things—when Aristotle set out to investigate causes, what he sought was some potential within a thing or another thing acting as mover; when a scholastic philosopher set out to investigate causes, what he sought was some notion such as a “hidden quality” or an “informing intelligence”; when a modern scientist sets out to investigate causes, he will usually, under the name of “force,” look for some formula written in mathematical language.
But can mathematics, as cause, satisfy humanity’s questioning after causes? And does the inquisition into “nature” within the tradition of immanence therefore lose its meaning? Although the mathematical mode of inquiry in classical mechanics has achieved enormous success, the fact that a question has not received a satisfactory answer does not mean that the question itself is illegitimate. It is like searching in a dim forest, where one becomes lost and bewildered, whereas searching for things in an open plain is clear and straightforward; does that mean one should stay away from the forest and search only in the open? If you have spent two thousand years searching in the forest and are still completely lost with nothing to show for it, while in the open plain you spent only two hundred years and gathered cartloads of things, does that prove you should never again set foot in the forest?—But the key issue is not whether the terrain is clear or whether the harvest is abundant; the key is, what exactly are we looking for? If what we are looking for is still buried deep in the forest, then what is the point of digging up more and more stones in the open plain? In the transition from classical science to modern science, we must pay attention not only to how much more precise the new science is conceptually, how much more efficient it is methodologically, and how much richer its results are, but also to how the thing we are seeking has changed.
January 15, 2010
[1]《The Mechanicalization of the World Picture》 p. 4, I2 (all quotations not otherwise noted follow Zhang Butian’s translation)
[2] see p. 497, V4
[3] see p. 499, V7
[4] p. 499, V7
[5] p. 500, V9
[6] Aristotle: Physics, trans. Zhang Zhuming, Commercial Press, 1982, p. 43, 192b.
[7] p. 495, V2.
[8] p. 495, V2
[9] p. 496, V3
[10] p. 497, V4.
[11] pp. 366–367, IV 136
[12] [U.S.] Thomas Kuhn: The Essential Tension, trans. Fan Dainian, Ji Shuli, et al., Peking University Press, 2004, p. 21, p. 22
[13] [U.S.] Richard S. Westfall: The Construction of Modern Science—Mechanism and Mechanics, trans. Peng Wanhua, Fudan University Press, 2000, p. 141
[14] Ibid., p. 146
[15] [U.S.] Thomas Kuhn: The Copernican Revolution—Planetary Astronomy in the Development of Western Thought, trans. Wu Guosheng, Zhang Donglin, Li Li, Peking University Press, 2003, pp. 251–252, pp. 258-259
[16] IV: 318, p. 483. My own translation.
[17] IV: 298, p. 468, my own translation. By introducing the concept of force in the sense of a cause of change in the velocity-vector of a material point, Newton consciously breaks with seventeenth-century mechanicism, in which a change in the motion of a body could only be brought about by another moving body
[18] Aristotle: Physics, trans. Zhang Zhuming, Commercial Press, 1982, p. 74, 202b21
[19] IV: 318, p. 484. My own translation.
Latest Comments
- Gu Chi
2010-01-16 09:33:30
“‘Essential’ thinking must be replaced by … ‘functional’ thinking.” It should be changed to “substantive” … “functional form.” In that case it actually reads a bit more smoothly.
- Gu Chi
2010-01-16 11:48:09
This paper was written in a great rush; not even the chapter structure had been established. It is only in the shape of a reading report. If I still feel inclined later, I can go find two more works and look them over, and then perhaps write something like an article on “force as a medium.” In terms of empirical cognition, “force” is the medium of tactile experience and bodily action; that is to say, we perceive objects through “force,” and we also alter objects through “force.” In the history of science, “force” is the medium connecting physics and mathematics, the medium connecting empirical intuition and theoretical system. But in whatever context, the role force seems to play is mediatory; yet in the modern world picture it has acquired a certain ontological status, even to the point of playing the role of some ultimate reality.
- unic
2010-02-23 20:16:03 Anonymous 210.77.59.5
“‘Essential’ thinking must be replaced by … ‘functional’ thinking.” It should be changed to “substantive” … “functional form.” In that case it actually reads a bit more smoothly.
Is it “functional form” or “functional quality”?
Could you explain a bit more, the relationship between substantive–function X, and the reason for your choice of wording. - Gu Chi
2010-02-24 10:22:26
The substitute wording was imposed on me by the translator of this book, the famous Senior Brother Butian. He adjusted his translation, so of course I had to adjust mine as well.
Literally speaking, “substantive” and “functional” are indeed more apt. I also said in the article that when ancient people pursued causes, what came to mind was one entity after another, one thing as the cause of another thing. Whether visible things or transcendent things, ancient people often imagined them in the mode of entities; even ultimate “Ideas” were imagined as one “thing” after another, such as the capitalized “Good,” “Beauty,” and the like. By contrast, “functional” thinking takes a different point of departure: modern people, when asking after causes, no longer say that one thing is the cause of another thing, but instead want to give some quantitative relation; what a function means is precisely a quantitative relation or numerical expression. The ultimate Ideas of modern people are then imagined as one “formula” after another. - unic
2010-02-25 00:54:22 Anonymous 210.77.59.5
But here one must note that “mechanism” or “structure” is a different concept from “cause.” In classical science, “mechanism” at most is only one kind of cause—if the efficient cause of a machine is its maker or operator, the final cause is the function that machine is meant to realize, and the material cause is its material substance, then its structural mechanism would probably correspond to the “formal cause.”
Does form itself have a cause? Why do I feel that form is not essential enough?
Modern people no longer say that one thing is the cause of another thing, but instead want to give some quantitative relation; what a function means is precisely a quantitative relation or numerical expression. The ultimate Ideas of modern people are then imagined as one “formula” after another.
y=ax+b; at this point we can still say that the change in X is the cause of the change in Y. What is the difference between this and substantiveness? Is it because the change in X itself is also a kind of quantitative change, and the properties, even the essence, of all the objects of study are being attempted to be understood as number? - Gu Chi
2010-02-25 12:21:49
Formal cause is one of Aristotle’s four causes. Modern people, influenced by classical mechanics, understand the concept of cause in a much reduced way, and it is hard for them to understand the ancient concept of cause. In Aristotle’s case, it is precisely form that is taken as the primary essence.
For example, when we ask for the cause of a murder case, or, that is, “what” brought about this result, the “what” here can be spoken of on multiple levels. First, one may say it was caused by Zhang San; that is the efficient cause. Second, one may say it was caused by the desire to steal money; that is the final cause. Third, one may say it was caused by poisoning; that is roughly the formal cause. Finally, one may say that because human beings have the potential to be killed, they can be killed; that is the material cause. Merely giving a cause at one level is often not complete enough. But we find that the formal cause among them is decisive: if all you have is Zhang San, no one necessarily dies; if all you have is the aim of stealing money, killing someone is not necessarily required either; but once the structural relation of killing is given, then no matter whether the agent is Zhang San or Li Si, and whether the purpose is theft or revenge, so long as the operational form of poisoning is fixed, the result of murder comes about.
As for y=ax+b, you can say “the change in X is the cause of the change in Y,” but you must keep in mind that y=ax+b and x=y/a-b/a are equivalent, so why can you not say “the change in Y is the cause of the change in X”? Of course you can define which is the independent variable and which is the dependent variable; but on what grounds do you decide which is the dependent variable? Only if you already have a causal relation in advance can you decide which one is the dependent variable, but the formula by itself cannot determine that. This is what I mean when I say that in the world of Newton’s third law, once all things are connected by formulas, every pair of things is mutually causal and completely equal; temporality disappears, the entire world is motionless, and causality loses its meaning. - Gu Chi
2010-02-25 12:36:53
The four causes—material cause, efficient cause, formal cause, final cause—roughly correspond to the following sequence of questions:
A certain result has occurred:
My goodness, how could that be possible? — material cause
Who did it? — efficient cause
How did it happen? — formal cause
What on earth was it for? — final cause
What modern science studies is mostly the question of how things happen, and it cannot answer the other questions. And the most everyday and primitive concept of cause is probably the inquiry into the efficient cause, that is, the substantive mode of seeking the original instigator.
Translated from the Chinese original with AI assistance. The original text is authoritative.
Leave a Reply