C O M M E N T A R Y
A thing's "intrinsic denominations" or inner determinations are those of its features that inhere in its descriptive make-up, encompassing all the features that indicate its qualitative properties as contrasted with its relationships to other things. (The term is taken from the Port Royal Logic (pt. I, chap. 2) of
1662 by Leibniz's correspondent Antoine Arnauld, one of the major theorists of the Cartesian school.)
From his earliest years, Leibniz was intrigued by the question of a "principle of individuation" to address the problem of what determines a substance as the individual item it is, in its distinction from all others. We are here told that the crux lies in its qualitative makeup: no two things are qualitatively entirely alike (though they can, of course, be qualitatively similar in many respects). This "principle of the identity of indiscernibles" has also been characterized as a "principle of the dissimilarity of the diverse." If distinct things could be wholly alike in their internal constitution, then there would be no assignable reason why one of those should bear the particular (and differentiating) rela- tionships it bears to others, thus violating Leibniz's fundamental "principle of sufficient reason." (See sec. 32 below.)
Leibniz is indebted for his Principle of the Identity of Indiscernibles to Ni- cholas of Cusa (1401-64), who asserted that "there cannot be several things exactly the same [aequalia], for in that case there would not be several things, but the same thing itself. Therefore all things both agree with and differ from one another" (De Venatione Sapientiae, 23). Compare De docta ignorantia, iii, I: "All things must of necessity differ from one another. Among several indi- viduals of the same species there is necessarily a diversity of degrees of perfec- tion. There is nothing in the universe which does not enjoy a certain
singularity, which is to be found in no other thing." The principle also plays a
role in Spinoza's Ethics, where he maintains that "In the natural realm two or more things cannot be of the same nature or attribute" (I, prop. 5).
KEY W O R D S :
monad/monade
difference/différence interne
internal intrinsic denomination/denomination intrinsèque
SECTION 10
10.1 also take it for granted that every created being is subject to change, and in consequence the created monad also, and even that this change is con- tinuous in each one.
10. Je prends aussi pour accordé, que tout être créé est sujet au changement,
et par consequent la Monade créée aussi, et même que ce changement est con- tinuel dans chacune.
(PNG, sec. 2.) One monad by itself and at a single moment cannot be dis- tinguished from another except by its internal qualities and actions, and these
can only be its perceptions—that is to say, the representations of the com- pound, or of that which is without, in the simple—and its appetitions—that is to say, its tendencies from one perception to another—which are the principles of change.
(NE, p. 56.) Nothing takes place suddenly, and it is one of my great and best confirmed maxims that nature never makes leaps. I called this the Law of Con- tinuity. . . . I have also pointed out that in consequence of imperceptible vari- ations no two individual things could be perfectly alike, and that they must always differ more than numerically.
(NE, p. 473.) In nature everything happens by degrees, and nothing by jumps; and this rule about change is one part of my law of continuity. But the beauty of nature, which insists upon perceptions which stand out from one another, asks for the appearance of jumps.
(GIL 168; Loemker,p. 515; Ariew & Garber, p. 516; to de Voider [1699].) No transition happens by a leap.. .. This holds, I think, not only of transitions from place to place, but also of those from form to form, or from state to state. For not only does experience confute all sudden changes, but also I do not think any a priori reason can be given against a leap from place to place, which would not militate also against a leap from state to state.
(G III, 52; Loemker, p. 351,- "Reply to Malebranche" [1687].) A principle of general order which I have noticed... is of great utility in reasoning.... It takes its origin from the infinite, it is absolutely necessary in Geometry, but it suc- ceeds also in Physics, because the sovereign wisdom, which is the source of all things, acts as a perfect geometer, following a harmony to which nothing can be added.... It may be enunciated thus: "When the difference of two cases can be diminished below every given magnitude in the data or in what is posited, it must also be possible to diminish it below every given magnitude in what is sought or in what results," or, to speak more familiarly, "When the cases (or what is given) continually approach and are finally merged in each other, the consequences or events (or what is sought) must do so too." Which depends again on a still more general principle, namely. "When the data form a series, so do the consequences" [datis ordinatis etiam quaesita sunt ordinata). C O M M E N T A R Y
Change—and the activity that produces it—is the most fundamental feature of a monad. Its characteristic mode of operation is, after all, what defines it as the thing that it is. The internal principle which regulates a monad's changes is called appetition by Leibniz. (See sec. 15.)
Life is change. If monads did not constantly change, they would be to this extent inert and so fail to be living beings. And this would run counter to Leib- niz's fundamentally organic view of nature. Only God, who is altogether extra- temporal, is an exception here. To be sure, change is sometimes so slow as to be unobservable. His theory of "minute perceptions" lying beneath the thresh- old of conscious recognition serves Leibniz at this point also.
His speaking of "the created monad" here suggests that Leibniz is quite pre- pared to characterize God, the necessary being or substance as a monad, as well. (Compare sees r8 and 47.) But God is, of course, unchanging, whereas all created monads are changeable, and indeed ever-changing. They are accordingly en-