1. Brief Vita
Belonging to a family of scholars, Leibniz was born in Leipzig (1646) and died in Hanover (1716). He learned Greek and Latin when he was just a child, then he mastered medieval philosophy and read modern mechanistic thinkers. Following his teacher Thomasius, the young Leibniz already hoped to reconcile Aristotle and Descartes. He devoted his doctoral dissertation to the principle of individuation, in a nominalistic way (1663). At the University of Jena, Weigel gave him his first acquaintance with mathematics. He also studied law but after his thesis, De casibus perplexis in jure, he gave up a scholarly career. In 1666 he published a Dissertatio de Arte combinatoria, made friends with various alchemists and above all with the Baron of Boineburg who became his mentor. At this time, he concentrated on politics until he turned his attention to physics.
The discovery by Huygens, Wallis and Wren of the impact laws of bodies prompted him to write two essays on natural philosophy which he sent to the Royal Society and the Académie des sciences, respectively. As a Lutherian himself, his purpose was to suggest a system of philosophy compatible with religious faith. From 1672 to 1676 he stayed in Paris, meeting, among other scientists and famous men, Huygens who completed his mathematical training. The reading of Blaise Pascal’s papers provided the impetus to set up the symbolism of the infinitesimal calculus. Before returning to Hanover, where he would pass most of the rest of his life, he took a short trip in London. On the way home, he passed through Holland and, famously, met Spinoza, who showed him the first copies of his master-piece, Ethica. In return, Leibniz taught him the falsity of Descartes’s conservation principle of quantity of motion (mass ´ velocity). During the subsequent years, Leibniz proved, using Huygens’s laws of impact, that kinetic energy (the product of mass and the square of velocity) is conserved. From this awareness of the so called vis viva, Leibniz drew some metaphysical claims, notably bringing back in 1679 the ancient notion of substance, so often scorned by modern thinkers.
While he worked as librarian and counselor of the Duke Jean-Frederic, he was supposed to research the history of Brunswick’s house. But because he slept little, he had enough leisure to maintain a huge correspondence with all prominent members of the République des Lettres, dealing with not only with scientific topics but also a wide variety of topics such as the origins of language, the union of Christian churches, and Chinese civilization. In 1682 he founded an important review, Acta eruditorium. As a mine engineer in the Harz mounts, he produced a hypothesis about the origins of the Earth within a Plutonian outlook. During his profitable voyage through Italy (1689-1690), the publication of Newton’s Principia Mathematica prompted him to bring forward his own Dynamica, in whichhe dealt in a new way with the old notion of substance, treating it as the source of action as well as subject of predicates. The problem of relationships between substances led him to his celebrated hypothesis of pre-established harmonies, in order to overcome the seeming incompatibility of human liberty and divine foreknowledge.
Because of John Locke’s death, he did not wish to publish his criticisms of the empiricist theory of knowledge. By the end of his life, he had to fight an unpleasant quarrel with Newton’s supporters concerning rival claims as to who discovered the calculus. Noteworthy also was the controversy with another Newtonian, Samuel Clarke: against Newton and Clarke, Leibniz argued that time and space are not absolute, but relative entities. When he died, quite isolated, he bequeathed to the Berlin Academy of Science his work as well as archives, which remain a focus for academic research.
2. References to Leibniz in Whitehead’s works
By his own confession, Whitehead learned most of what he knew about Leibniz from Russell’s A Critical Exposition of the Philosophy of Leibniz (1900) and Couturat’s La logique de Leibniz (1903). Russell summarized Leibniz’s thought in three main principles: (1) the form of any proposition is a subject-predicate form; (2) substances which are compatible together produce a possible world; and (3) valid propositions in every possible world are necessary and analytic, so if one demonstrates that a predicate is contained in the subject, then the proposition is true. Applied to space and time, this entails that space consists in an order between substances, while time constitutes an order of relationships of predicates. Russell’s critique of the notion that relations are always the internal relations of the subject and predicate of a proposition is grounded in his attack on Bradley’s neo-Hegelianism.
2.1. Theory of Space and Time
The first point of utmost importance is Leibniz’s relational theory of space, which somehow anticipates Einstein’s theory of relativity, while Russell in his Principles of Mathematics (1903) attempted to defend an absolute conception. Soon in MCMW, Leibnizian relativism gave Whitehead a tool to overcome the concepts of classical Newtonian dynamics. Thus Whitehead is allowed to exclude points of space from “objective reals.” Instead of material points moving into space, there are successive situations of points during all the time, and space is extracted from various orders of situations; this resembles Leibniz’ remark to Clarke, that space is nothing else but the mere possible order of things coexisting together. Russell, following Cantor, tended to assert that space was a set of points. After UA, ADG and APG, it was obvious that one could not take points as simple, but rather as quite complex “entities”: such is the lesson of projective and metric geometries vis-à-vis Euclidean geometry (remember the famous quadrilateral construction due to von Staudt). Surely Whitehead revived Leibniz’s theory of points as modalities, according to the latter’s Characteristica Geometrica, because of mere boundary of lines.
Between 1914, in the French-speaking lecture “La théorie relationniste de l’espace” and PNK, Whitehead’s relativism found its first expression in the theory of extensive abstraction, by which points and instants of time are issued within a logical frame of convergent series. Quoting Leibniz in a paper published under the title “Space, Time and Relativity,” Whitehead writes: “A point is merely the name for some peculiarity of the relations between the matter which is, in common language, said to be in space” (AE 158).
The desire to capture the notion of mental entities which give rise to corporeal, spatial objects, and further, which are combined to form the best possible world by God’s calculus of combining compatible essences led Leibniz to move from using the language of “simple substance” (1686) to “metaphysical point” (1695) and finally to “monad” (1714). The hypothesis of pre-established harmony ruling the apparent shifts exhibits that there is no such a thing as an actual interaction among them, but each of them are acting according to their own program set up by the divine plan before the creation of the universe. This program is compared by Leibniz not only to a mathematical series, but also to an inner force. As a result, he could suggest a new science called dynamica, which differs significantly from Newtonian mechanics (i.e. what we call now dynamics), since a force does not express a change of velocity—as it does in Newton’s first law of motion, where F = ma, with a = dv/dt). Rather, a Leibnizian force entails a conception where inertial motion requires its employment in order to be itself maintained.
At the beginning of PNK (§ 3.5), Whitehead’s emphasis upon the “relatedness of things” is unambiguous (PNK, 12). This keynote gives his philosophy many resemblances to Leibniz’, though obviously without any vectorial conception for supporting it. So too, both thinkers criticize reductive materialism—that represented by Cartesianism, in the case of Leibniz, and that stemming from Newton, in the case of Whitehead. Not surprisingly then, one finds remarks from CN to AI, and particularly in SMW, that praise Leibniz’s views. At the same time, in CN Whitehead voices some hesitations about the Leibnizian system, and about thinkers who (following Aristotle) insist upon the subject-predicate propositional form:
Some schools of philosophy, under the influence of the Aristotelian logic and the Aristotelian philosophy, endeavour to get on without admitting any relations at all except that of substance and attribute. Namely all apparent relations are to be resolvable into the concurrent existence of substances with contrasted attributes. It is fairly obvious that the Leibnizian monadology is the necessary outcome of any such philosophy. If you dislike pluralism, there will be only one monad (CN 150).
To understand this passage, it is helpful to recall Russell’s prejudice against monist reductionism of relations: without admitting external relations (e.g. repulsive forces in physics), an apparent pluralism may conceal a monist tendency, and so a monadology may in fact postulate only one monad. One might be tempted to compare such a view to an ontological “big crunch.”
Soon, in PNK, Whitehead’s relativism issued in ideas about events. Likewise, in R, Whitehead asserts that an event cannot exist apart from other events (R, 26). He perceives in Hume’s skepticism another source for the view of nature as discrete and discontinuous. Finally disconnections are produced so far as one begins with subjects qualified by predicates: “The disjunction of subjects is the presupposition from which you start, and you can only account for conjunctive relations by some fallacious sleight of hand, such as Leibniz’s metaphor of his monads engaged in mirroring” (R 13-14).
Hence, reading SMW, it is not unexpected that we meet yet the same two-sided aspect as in the above concerning Leibniz. The latter could have been a choice partner in the struggle against scientific materialism. Yet Whitehead is slow to recognize Leibniz as a forerunner of the organic philosophy (SMW 140). But Whitehead did not emphasize before how the main features of organisms resemble a monad, as in an organism a part represents the whole (“pars totalis”). Certainly Whitehead prefers Locke over Leibniz as successors to Descartes.
2.2. Internal or External Relationships?
In SMW Whitehead asserts that relationships between events are internal relations while external relations tie together eternal objects and events. The main feature of the materialistic conception of nature consists in connecting bits of matter with external relationships. Now if this were the case, there could be no process about a set of external relationships, for the reason that any set of such relationships could be worth anything else, deprived of any internal criterion of distinction. While Whitehead bases such arguments on modern wave mechanics, one can find similar lines of reasoning leveled by Leibniz against Descartes and other contemporary physicists who regarded matter as mere mass located in space and time and thus subscribed to what Whitehead would later call the “doctrine of simple location.”
But as we can see in the following extract, Whitehead argued that Leibniz did not have an adequate understanding of internal relationships because he himself subscribed to this “notion of simple location”:
It is obvious that the basing of philosophy upon the presupposition of organism must be traced back to Leibniz. His monads are for him the ultimately real entities. But he retained the Cartesian substances with their qualifying passions, as also equally expressing for him the final characterisation of real things. Accordingly for him there was no concrete reality of internal relations. He had therefore on his hands two distinct points of view. One was that the final real entity is an organising activity, fusing ingredients into a unity, so that this unity is the reality. The other point of view is that the final real entities are substances supporting qualities. The first point of view depends upon the acceptance of internal relations binding together all reality. The latter is inconsistent with the reality of such relations. To combine these two points of view, his monads were therefore windowless; and their passions merely mirrored the universe by the divine arrangement of a pre-established harmony. This system thus presupposed an aggregate of independent entities. He did not discriminate the event, as the unit of experience, from the enduring organism as its stabilisation into importance, and from the cognitive organism as expressing an increase completeness of individualisation. Nor did he admit the many-termed relations, relating sense-data to various events in diverse ways. These many-termed relations are in fact the perspectives which Leibniz does admit, but only on the condition that they are purely qualities of the organising monads. The difficulty really arises from the unquestioned acceptance of the notion of simple location as fundamental for space and time, and from the acceptance of the notion of independent individual substances as fundamental for a real entity (SMW 155-56).
Before AI, this is the longest analysis which Whitehead devoted to the Leibnizian philosophy, which is perceived as a hopeless attempt to reconcile its pluralist tendencies with the self-sufficiency of ultimate entities. Accordingly, the metaphor of mirroring offers an oversimplified solution. A truly interconnected universe assumes a complete reform of the nature of these primary entities. Leibniz associates internal relations with “an organising activity”; that is, one entity is internally related to another if and only if each incorporates the essence of the other. Thus, although there is something like a process of concrescence behind the reference to a “fusing ingredients into a unity,” Leibniz unfortunately maintained that relationships are simply entia rationis (to complete Whitehead’s criticism) ultimately grounded upon God’s understanding.
It seems paradoxical that Leibnizian internal relations seem, from different perspectives, to be both too strong and too weak. They are too strong, as Russell pointed out (1959, Chapter V), if the death of a woman in India could affect her husband staying in Europe even though he knew nothing about her death: in this case, Leibniz’ monadology is the equivalent to monism. (In this case, we should also worry about the possible scope of partial truths.) From a different perspective, Leibnizian internal relationships are too weak, for even if they have a fundamentum in re, they are nevertheless nothing more than mere abstractions, as Leibniz himself held: “Relations and orders have something to do with entities of reason, albeit they have their foundation in things: because we can say that their reality, as that of eternal truths and possibilities, comes from the supreme reason.” Finally it is to be noted that Leibniz has explicitly admitted many-termed relations. A relation is often defined as an accident inhering in multiple subjects (e.g. Ishiguro 1990, 136). Yet this is exactly the reason why a relation cannot be real. Otherwise, there will be an accident with “one leg” in a subject and the other in another subject, while Leibniz supposes a “non-migration thesis.” That is, an accident is not allowed to stay (to “inhere”) in different subjects, because substances are complete notions, which contain all their own predicates (they are “windowless”). So an accident is individual.
Let us turn to the assertion that Leibnizian space and time involves the doctrine of simple location. Here again, perhaps Leibniz’s views could be supported by those of Whitehead. Certainly, the phenomena which issue from monads are simply located in space and time. Now, at a deeper level, substances or monads have a situation (each of them expressing the other), which is not a location but an order. This is why the Leibnizian universe is sometimes associated with quantum mechanics, as physicists are compelled to consider a principle of non-location in response to the negative outcomes of the experiments following Einstein-Podolski-Rosen’s paradox (see Vuillemin 1984, 201-202).
2.3. Monad and Organism
In PR, almost all the allusions to Leibniz are to the famous Monadology (1714), which represents the culmination of Leibniz’ metaphysical thought. According to Monadology §60, a monad is essentially a representation of the universe, but not always distinctly—otherwise any monad would be God. However, every monad confusingly represents the whole universe, and distinctly a small set of details. This is precisely what Whitehead surely believes to be inadequately explained. Yet he does not distance himself from Leibniz but rather underlines that this is a key idea for “all monadic cosmologies,” even if the monad is superseded in PR by the subject-superject. Leibniz’s conceptions approximate those of the Whiteheadian cosmology. Whitehead’s response is grounded, as we know, on the Category of Transmutation from which the subject transmutes the datum of its conceptual feelings in order to obtain a nexus of actual entities:
This category is the way in which the philosophy of organism, which is an atomic theory of actuality, meets a perplexity which is inherent in all monadic cosmologies. Leibniz in his Monadology meets the same difficulty by a theory of ‘confused’ perception. But he fails to make clear how ‘confusion’ originates (PR 27; cf. 251).
So too, Leibniz’ famous theory of pre-establish harmonies parallels Whitehead’s Category of Subjective Unity (PR 224). In the actual world, discordance and chaos cannot prevail over unity. Thus pre-established harmony is relevant to denote coherency of the self-realization ruled by a subjective aim at each step of the process, for the plurality of feelings. But besides this first category which entails pre-established harmony, one needs another, the one of Subjective Harmony, which takes place to govern the mutual adjustment of the conceptual feelings for a congruent becoming (PR 254-55).
One of the main tasks of Whitehead’s philosophy of organism is to make explicit the meaning of an actual entity’s being present in another (e.g. PR 114). Such an idea might be connected with the Leibnizian conception of inherence of predicates in a subject—if Whitehead had not fought against a conception behind which he suspected the workings of the traditional logic of attribution. Nonetheless, it is necessary to differentiate the logical relation between universals and subjects (i.e. predication) on the one hand, and the metaphysical relation of inherence between accidents and concrete substances, on the other. In a notable passage (PR 48), however, Whitehead neglects this distinction and again blames windowless monads and the doctrine of pre-established harmony as the cause of Leibniz’ attempt to describe an actual entity through universals and without consideration of the prehensions which interrelate these entangled entities.
Of course, one must remember that Whitehead was not a professional historian and that, moreover, Leibniz was not at all well understood by philosophers and historians during Whitehead’s lifetime.
3. Final Appreciation
Are there enough features in Whitehead that indicate attempts to rehabilitate Leibniz, or at least to view him in a more positive light, as a thinker who shared important philosophical concerns, i.e. the atomic theory of actuality?
3.1. Points of Convergence
The main point of convergence between Leibniz and Whitehead is their shared desire to articulate a complete view on the universe, one that combines religious feelings and natural science. The two thinkers were scientists during some periods, and certainly drew much of their inspiration from mathematics—even if their thinking was probably not wholly based on mathematical models. Philosophy is conceived, with a touch of nominalism, as a “critic of abstractions” (e.g. SMW 59). But while Leibniz endeavors to renew with a “ornatus kόσμος” (adorned world) after the mechanistic secularization due to the Galilean physics, Whitehead attempts to plead for a revival of their alliance, accounting for the theory of relativity, disjoined from all elements of contingency. We may ascertain in each of these constructs the same penchant to refer to principles, or perhaps more than a “free and savage creation of concepts,” to quote G. Deleuze.
There are of course some other remarkable cross-references that are worth noting, even when one has to translate from one vocabulary to another. For instance, one thinks of the resurgence of appetition, in the context of God’s primordial nature—in other words (Leibnizian but equally Lockean), the “uneasiness” which allows us to realize what is likely to be produced. Again, atomism is the ultimate truth of metaphysics, while continuity similarly recovers from potentiality (PR 93, 130): atomism is a formal entity on the side of Leibniz, something like an “organising activity,” according to this very fair saying in SMW. Actual motion is even discrete for Leibniz, for whom there is a perpetual “transcreatio.” A complete monad is not separated from all form of body, in a way analogous to the bipolarity of actual entities (although Whitehead in fact denies this thesis about Leibniz). Again, regarding final causality, a new perspective also is opened.
3.2. Points of Discordance
On the other hand, Whitehead seems further less deterministic than Leibniz. God acts with persuasion and does not effect the best possible world; nor can Whitehead’s God be held responsible for the existence of evil; thus Leibniz’ theodicy becomes a merely clever conceptual scheme (e.g. PR 109). Furthermore, future events of actual entities are not so predictable that an omniscient soul could see all that they will become. But similarly, eternal objects and Leibnizian possibles are entirely independent of God’s will. Nevertheless, through their complete notions, which contain all relevant predicates, individual creatures are thoroughly conceived before their actual existence: thus, Leibniz’s universe resembles a drama which exists in written form even before being performed. By contrast, Whitehead’s concrescence tolerates creativity, his God cannot create ex nihilo and is himself limited by the principle of relativity. Another point is that Whitehead’s actual entities act directly upon each other through mutual prehensions, and not (as with Leibniz) through the mediation of God. In return, they come into being and perish, while Leibniz’ monads are immortal. Thus Whitehead asserts that while monads do change, actual entities are limited to becoming and pass into immortal objectivity after a short period of satisfaction (PR 89).
In a rarely-quoted passage of the New Essays discussing Aristotle’s definition of motion, Leibniz alludes to the possibility of an “actuation” intervening between power (δύναμις) and act (ε̉ntelέceia). It would be quite attractive to suggest that Whitehead precisely attempted to imagine what could contain such an actuation. The result would surprise Leibniz, if he were to realize that this analysis required both the opening of monads and God’s immanence in order to lead from possibility to actuality.
 See Essais de Théodicée, 1710.
 Fifth Writing § 104 (Robinet, 171).
 De ipsa natura, § 13 , Die Philosophischen Schriften [hereafter cited as GP] IV, 512-14.
 Here Whitehead refers to Russell’s book on Leibniz “for the suggestion of this line of thought.”
 New Essays on the Human Understanding II, xxv, 1 (GP V, 210).
 Cf. PNK (§ 63.2) where Whitehead evokes the same idea in a polemic against Russell’s ideas about multiplicity of spatial representations arising from sensory apprehension (PNK, 193).
 Cf. PR 190: as the constitutive elements of the universe are nothing else than universals, there is an alternative between Bradley and Leibniz. It is to be noted that in AI, III, xv, 13, “prehension” is given by referring to a “Leibnizian model,” this meaning a new concern to focus around proximity rather than discrepancy (AI, 271). Yet the claim that the Leibnizian concept as “perception” is too closely allied to consciousness ignores its distinction from “apperception,” and is, consequently, highly questionable (cf. Monadologie, § 14).
 Apparently Whitehead did not share Leibniz’ goal of a characteristica universalis, even if this was Couturat’s interpretation of UA (Couturat 1900, 362).
 Leibniz could have himself written Whitehead’s “there is an actual world because there is an order in nature” (RM, 91).
 SeeDeleuze 1986, 110.
 See PR 87 and Monadology §15. More exactly, appetition derives from conceptual evaluation of immediate physical feelings.
 Leibniz 1978 GP II, 279.
 Leibniz 1978 GP II, 252.
 Parmentier offers interesting remarks comparing Whiteheadian creativity with Leibniz’ concept of force (1986, 287-88).
 Leibniz 1978 II, xxi, 1 (GP V, 155).
Works Cited and Further Readings
Couturat, Louis. 1900. “L’algèbre universelle de M.Whitehead,” Revue de métaphysique et de morale, VIII.
Deleuze, Gilles. 1986.Le Pli (Minuit, Paris).
Ishiguro, Hidé. 1990.Leibniz’s Philosophy of Logic and Language, 2nd edition (Cambridge, Cambridge University Press).
Edward Jacob Khamara, Space, Time and Theology in the Leibniz-Newton Controversy, Frankfurt / Paris / Lancaster, ontos verlag, Process Thought VI, 2006.
Leclerc, Ivor. 1963. “Whitehead and the Problem of Extension,” in Alfred North Whitehead: Essays on His Philosophy, edited by George L. Kline (Englewood Cliffs NJ, Prentice-Hall).
Leibniz, Gottfried Wilhelm. 1978. Die Philosophischen Schriften, edited by C. I. Gerhardt (Hildesheim, Georg Olms).
Mays, Wolfe. 1959. The Philosophy of Whitehead (New York, Collier Books), especially 113-14.
Mays, Wolfe. 1961. “The relevance of ‘On Mathematical Concepts of the Material World’ to Whitehead’s Philosophy,” in The Relevance of Whitehead, edited by Ivor Leclerc et al. (London, Allen & Unwin).
Parmentier, Alix. 1968. La philosophie de Whitehead et le problème de Dieu (Beauchesne, Paris).
Robinet, André. 1957. Correspondance Leibniz-Clarke présentée d’après les manuscrits originaux des bibliothèques de Hanovre et de Londres (Paris, Presses Universitaires de France).
Russell, Bertrand. 1959. My Philosophical Development (London, Allen & Unwin).
Stengers, Isabelle. 2002. Penser avec Whitehead (Paris, Seuil).
Vuillemin, Jules. 1984. “Physique quantique et philosophie,” in Le monde quantique (Seuil, Paris).
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How to Cite this Article
Alcantara, Jean-Pascal, “G.W. Leibniz (1646–1716)”, last modified 2008, The Whitehead Encyclopedia, Brian G. Henning and Joseph Petek (eds.), originally edited by Michel Weber and Will Desmond, URL = <http://encyclopedia.whiteheadresearch.org/entries/bios/historico-speculative-context/leibniz/>.