Specimen Dynamicum (1695)
Various Concepts in Specimen Dynamicum
Leibniz argues in this paper that the concept of force is crucial for the philosophy of nature; here it is clear that he has in mind Descartes's notion of corporeal substance as "extended substance", and he wants to develop the philosophy of nature by employing the concept of force. But what is force in Leibniz? Forget about all you understand by "force" in the contemporary usage. We've got to read carefully what Leibniz says. (All quotations are from G. W. Leibniz, Philosophical Texts, ed. by R.S. Woolhouse and R. Francks, Oxford, 1998)
I have suggested elsewhere that corporeal things contain something other than extension, indeed something prior to extension, namely the force of nature implanted in all things by the Creator. This force does not consist of a mere faculty, of the kind with which the Schools seem to content themselves, but instead is endowed with a conatus or effort (nisus), such that it will attain its full effect unless it is impeded by some contrary striving. (sect. 2)
I recognize that all corporeal action arises from motion, and that motion itself comes only from other motion, either already in the body or impressed from outside. But when we analyse it, motion, like time, does not really exist: for a whole never exists if its does not have coexistent parts. Thus there is nothing real in motion but the momentary state which a force endowed with an effort for change must produce. Therefore, whatever there is in corporeal nature besides the object of geometry, or extension, reduces to this. (sect. 3)
Active force (vis) (which some not unreasonably call power (virtus)) is of two kinds. There is primitive active force, which is inherent in all corporeal substance as such, since it is contrary to the nature of things that there should be any body which is wholly at rest; and there is derivative active force, which is as it were the limitation of primitive force brought about by the collision of bodies with each other, and which is operative in various ways. Primitive force---which is none other than the first entelechy---corresponds to the soul or substantial form; but for that very reason it relates only to general causes, which are not enough to explain phenomena. (sect. 6)
Passive force is similarly of two kinds, primitive and derivative. The primitive force of being acted upon or of resistance constitutes what, if properly understood, the Scholastics call primary matter. It is what explains why bodies cannot interpenetrate, but present an obstacle to one another, and also why they possess a certain laziness, as it were, or repugnance to motion, and will not allow themselves to be put into motion without lessening to some extent the force of any body which is acting on them. The derivative force of being acted upon therefore shows itself in various ways in secondary matter. (sect. 7; notice the concept of inertia appears in another name.)
By derivative force, then the force by which bodies actually act and are acted upon by each other, I mean nothing other than that which is associated with motion (local motion, that is), and which in turn tends to produce further local motion. ... Motion is the continuous change of place, and so requires time. But as a movable thing which is in motion moves through time, so at any given moment it has a velocity, ... Velocity taken together with direction is called conatus, while impetus is the product of the mass (moles) of a body and its velocity. (sect. 9; notice the concepts of velocity and momentum appear.)
Just as the value of a motion taken as extended over time is derives from an infinite number of impetuses, so in turn the impetus itself, even though it is momentary, is derived from an infinite series of increments imparted to the moving body. (sect. 11)
Force, therefore, is also of two kinds. One is elementary, and I call it dead force, since there is no motion in it as yet, but only an urge (solicitatio) to motion, like that in the ball in the tube, or in a stone in a sling before the string is released. The other is in fact ordinary force, which is accompanied by actual motion. This I call living force. Centrifugal force, then is an example of dead force, as is the force of gravity or centripetal force, and the force by which a stretched elastic body tries to spring back into shape. But in the case of an impact which arises from a heavy body which has been falling for some time, or from a bow which has been springing back into shape for some time, or from some similar cause, the force is living force, and it arises from an infinite number of continued impulses of dead force. (sect. 12)
The first thing we must recognize is that force is something fully real, even in created substances, whereas space, time, and motion have something of the nature of beings of reason: they are not true or real in themselvews, but only in so far as they involve the divine attributes of immensity, eternity, and activity, or the force of created substances. It follows immediately from this that there is no vacuum in space or in time, and also that motion considered apart from force (that is, considered as involving only the geometric notions of size and shape, and changes in them) is really nothing more than changes of place. Therefore motion, in so far as we experience it ... is nothing but a relationship ---as Descartes also recognized, when he defined it as the removal of something from the neighbourhood of one body to that of another. (sect. 37; a clear statement of Leibniz's relationalism.)
For the contemporary reader, it may be quite hard to make sense of Leibniz's notion of force. It must be noted that the basic idea is that there should be "moving force", something which can cause and sustain motion. In this respect, Leibniz's notion of force is quite different from the Newtonian notion. According to the Newtonian mechanics, force appears when a motion and its velocity is changed, and hence a force is associated with acceleration; otherwise, i.e. in any inertial motion, force is absent. Leibniz, on the contrary, asserts that a force is necessary even for a uniform, non-accelerated motion.
Also, one may ask: why do we need two kinds of force, active and passive? For an attempt at making sense of this, see Matsuou (1996).
Reference
松王政浩（1996）ライプニッツにおける「集合的」可能世界論の展開、博士学位論文、京都大学大学院文学研究科。
Last modified, May 27, 2005. (c) Soshichi Uchii