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11. Natural philosophy
Leibniz is read today largely for his philosophical writings. But in his day, he was, if anything, better known for his work in mathematics and natural philosophy. Like many of his contemporaries, Leibniz was a mechanist. Indeed, he was in a sense a much stricter mechanist than the Cartesians. Because of his doctrine of pre- established harmony (see §6 above), one can always give a purely mechanistic explanation of any physical phenomenon, even in humans, unlike in the Cartesian system, where causal interaction between mind and body, direct or occasional, can disrupt the laws governing the body. However, Leibniz’s version of the mechanist programme departed significantly from other main versions of the programme of his day, particularly the Cartesian version.
Leibniz rejected the Cartesian analysis of body as extended substance (see §4 above). Instead, he argued that we must go to a deeper level of analysis, behind the extension of bodies to the substances that are the ultimate constituents of reality. Below the level of inanimate extension there are tiny organisms, souls joined to organic bodies which Leibniz, in at least one period of his thought, considered genuine corporeal substances. At a deeper level still there are the non-extended simple substances or monads that ground the reality of corporeal substances. On this view, the extended bodies of the Cartesian world are phenomena, aggregates of substances that are unified by virtue of being confusedly perceived together.
Leibniz also rejected Descartes’ central law of nature. For Descartes, God conserves the same quantity of motion in the world, the size times the speed of bodies taken together (see Descartes, R. §11). But Leibniz argued that what is conserved is not bulk times speed, but bulk times the square of speed, mv 2, a quantity associated with what he called vis viva or living force (see Motion §3). To defend this view, he used a cluster of a posteriori arguments which assumed the Galilean law of free-fall (the distance fallen is proportional to the square of the speed acquired in free-fall) together with the Principle of the Equality of Cause and Effect, in accordance with which there is always as much ability to do work in the cause as there is in the full effect. Leibniz showed that, on these assumptions, the Cartesian conservation law entails that the ability to do work can either be gained or lost in certain circumstances, whereas on the assumption of the conservation of mv 2, this does not happen. Leibniz used this strategy in the Brevis demonstratio (Brief Demonstration of a Notable Error of Descartes) (1686a), where he first published this result. In addition, he offered an a priori argument in which, arguing from certain abstract notions of motion, action and effect, together with an intuitive principle of the conservation of effect, he reached the same conclusion (Discourse §17; Dynamics preliminary specimen). This challenge to Descartes’ conservation law elicited numerous responses from the Cartesian community in what came to be called the vis viva controversy.
Leibniz saw the replacement of the conservation of the quantity of motion by the conservation of mv 2 as leading us to introduce into the world of physics something over and above the purely geometrical qualities of size, shape and motion that pertain to the extended substance of the Cartesians. This something is what he called force, the new science of which he named dynamics. While force can cause motion and is sometimes manifested in motion, Leibniz carefully distinguished the two. In emphasizing the distinction between force and motion, Leibniz was rejecting not only the Cartesian tradition, but his own early physics where, following Hobbes, he identified force with motion.
Leibniz recognized a variety of different kinds of forces in nature. At the most fundamental level, he distinguished between primitive and derivative forces, and between active and passive forces. Thus, in all, there are four basic kinds of force: primitive and derivative active force, and primitive and derivative passive force. Active force is of two sorts, living force (vis viva), which is associated with bodies actually in motion (a ball moving with a definite velocity), and dead force, which is associated with the instantaneous push from which actual motion results, as in gravitation or elasticity. Passive force, on the other hand, is the force that arises in reaction to the active force of another body. It also has two varieties, impenetrability (the force that prevents two bodies from occupying the same place at the same time) and resistance (the force that opposes new motion). The distinction between primitive and derivative force is quite different. Primitive force, active and passive, is the metaphysical ground of activity and passivity, that in a body by virtue of which it is capable of acting (doing work) or resisting. Derivative forces, for Leibniz, were particular states of activity and passivity that exist in a body at a particular time. In this way, primitive force is not a measurable quantity, but something in body that grounds the reality of the derivative forces, which are measurable quantities.
This notion of force was linked directly to Leibniz’s notion of corporeal substance: ‘Primitive active force, which Aristotle calls first entelechy and one commonly calls the form of a substance, is another natural principle which, together with matter or passive force, completes a corporeal substance’ (‘Note on Cartesian natural philosophy’  1989: 252). At least in the 1680s and 1690s, when Leibniz recognized corporeal substances, the primitive forces seem to have been the form and matter of the corporeal substances that ground the reality of the physical world. Derivative forces would then be interpreted as the momentary states of these corporeal substances. The position is somewhat different after Leibniz began to doubt the reality of corporeal substance (see §5 above). Then, he wrote, ‘I relegate derivative forces to the phenomena, but I think that it is obvious that primitive forces can be nothing but the internal strivings of simple substances, strivings by means of which they pass from perception to perception in accordance with a certain law of their nature’ (Leibniz to de Volder, 1704 or 1705). In this way, the dynamics can be regarded as another perspective on the same entities discussed in Leibniz’s more metaphysical writings.
Leibniz held that these forces (or better, the motion that they cause) obey rigorous mathematical laws. These laws include the conservation of living force, mv 2, virtually equivalent to the modern law of the conservation of kinetic energy, and the conservation of bulk times the velocity (a vector quantity), mv, identical to the modern law of the conservation of momentum. (Because Leibniz’s conservation of mv involved the directionality of the motion, it is distinct from the Cartesian conservation of quantity of motion, which Leibniz rejected.) While he disagreed with Descartes about the specific contents of the laws, he can be seen as advancing the Cartesian programme of building a physics grounded in mathematically expressible conservation laws. But even though Leibniz’s laws are expressible in mathematical terms, they – like the forces that they govern – are grounded in certain metaphysical principles that are imposed on the world by the wisdom of God: ‘Although the particular phenomena of nature can be explained mathematically or mechanically… nevertheless the general principles of corporeal nature and of mechanics itself are more metaphysical than geometrical’ (Discourse §18).
One such general metaphysical principle was noted in connection with the establishment of Leibniz’s conservation law, the Principle of the Equality of Cause and Effect. But there were others as well. Leibniz made frequent use of the Principle of Continuity, according to which nothing happens through a leap. Leibniz used this principle to refute Descartes’ laws of impact, where small changes in the initial conditions (say the comparative sizes of the bodies in question, or their motion) can result in radically different results. This principle was also used to refute atomism. If there are perfectly hard atoms, not made up of smaller separable parts, then in collision their motion would change instantaneously at the moment of impact. So, Leibniz concluded, there cannot be any such atoms in nature. Indeed, he used this argument to conclude that every body, no matter how small, is elastic. Leibniz also made appeal to the Principle of Plenitude to argue that there can be no vacuum or empty space in the world, since if God can create something consistent with his other creations, he must do so. Finally, as seen below, Leibniz used the Principle of Sufficient Reason in connection with his relativistic account of space and time.
The very fact that the world is the product of divine wisdom allowed Leibniz to appeal to final causes in his physics. This differentiates him from both Descartes and Spinoza, both of whom rejected final causes. Leibniz agreed with both that everything in nature can be explained through efficient cause alone – that is, through the laws of motion alone. But often, particularly in optics, it is much easier to solve problems by appealing to God’s wisdom, and discovering the way in which a most perfect being would have created his universe (Discourse §22; Specimen of dynamics 1695a: part I). However, the appeal to final cause only supplements the understanding of nature by efficient causes, and does not replace it. It is another manifestation of divine harmony that the explanations by efficient causes and by final causes always coincides: ‘In general we must hold that everything in the world can be explained in two ways: through the kingdom of power, that is, through efficient causes, and through the kingdom of wisdom, that is, through, final causes.…These two kingdoms everywhere interpenetrate each other…so that the greatest obtains in the kingdom of power at the same time as the best in the kingdom of wisdom’ ((Specimen of dynamics [1695a: part I] 1989: 126–7).
So far we have been discussing Leibniz’s work in relation to that of other mechanists, particularly those of the Cartesian school. But it is also important to understand Leibniz’s relations with another contemporary and often bitter rival, Isaac Newton.
In opposition to Newton, who held an absolutist conception of place and space, Leibniz argued that space is ‘only relations or order or orders of coexistence, both for the actually existing thing and for the possible thing one can put in its place’ (Remarks on Foucher  1989: 146). If Newton were right, Leibniz argued, and there was absolute space, then God could create a world in which what is currently east and west are exactly reversed, for example. But if so, by the Principle of Sufficient Reason, then God could have no reason to create one such world over another. Given that he did, he cannot have been faced with such a choice. Leibniz concludes that the two purported Newtonian worlds are really just one world, a world in which space is just constituted by the relations between things (Leibniz to Clarke, 3rd paper §5). Newton’s absolutist account of space was supposed to ground an absolutist account of motion as well. For Newton, motion was the change of place of a body with respect to absolute space. Leibniz rejected this too, arguing that motion is a completely relativistic notion, a matter of the relation between bodies over time and that alone (Specimen of dynamics part I; Leibniz to Huygens, 12/22 June 1694).
Leibniz also rejected Newton’s theory of universal gravitation. He read Newton as holding that gravity is an essential property of matter as such, and he was appalled. For Leibniz, all change in body had to happen through the intermediary of contact and collision; the idea of action at a distance that seemed to underlie Newton’s theory of universal gravitation was an intellectual disaster, a treasonable abandonment of the new mechanical philosophy and a return to the worst abuses of the schoolmen. Leibniz, whose early mechanism seemed so radical at the time, could not adjust to the new Newtonian philosophy, soon to take over the intellectual world (see Clarke, S.; Newton, I.).
While the emphasis here has been on the aspects of Leibniz’s work in physics most relevant to his philosophical programme, he was much more widely interested in the natural world. He left notes on engineering problems, on chemistry, on geology and on curious observations in natural history including the report of a talking dog, and a goat with an odd hairstyle.
Garber, Daniel. Natural philosophy. Leibniz, Gottfried Wilhelm (1646–1716), 1998, doi:10.4324/9780415249126-DA052-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/biographical/leibniz-gottfried-wilhelm-1646-1716/v-1/sections/natural-philosophy-65125.
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