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1 In the preface to Metaphysical Foundations of Natural Science, Kant wonders under what conditions nature, or a particular aspect of reality, can be objects of science. He answers his own question by putting aside chemistry, at best considered “a systematic art rather than a science.” “A rational doctrine of nature thus deserves the name of a natural science, only in case the fundamental natural laws therein are cognized a priori, and are not mere laws of experience.” [1] In a word, there is no natural science except where there exists “the possibility of a mathematical doctrine of nature itself.” [2] After having refused chemistry the status of being a science, Kant continues: “The empirical doctrine of the soul must remain even further from the rank of a properly so-called natural science,” and he gives two reasons for this: “In the first place, because mathematics is not applicable to the phenomena of inner sense and their laws,” and then because the doctrine of the soul or psychology “can never become anything more than an historical doctrine of nature and, as such, a natural doctrine of inner sense” or a “natural description of the soul, but never a science of the soul.” [3] For Kant, the cause is, therefore, understood. There can be no scientific psychology as a rational theory of human behavior and, therefore, there is no science of action.

2 This does not, of course, rule out the possibility of bringing to light observable regularities in human behavior. However, what will always be lacking is the rational link that would connect these “empirical laws.” In this, Kant is not too far from Malebranche, who in Dialogues on Metaphysics and Religion notes that we know ourselves through “feeling,” rather than through “ideas.” At the beginning of the third Dialogue, Theodore remarks to Aristes: “You will never contemplate ideas without discovering some truth; but whatever attention you give your own modifications, you will never be enlightened by them.” A little further on, Theodore specifies, in terms that remain very close to those of Kant, that we have at our disposal an external natural science because we are able to mathematically grasp it, and that we clearly see mathematical truths “in the idea or archetype of extension.” Theodore goes on: “The same is not true of my being. I have no idea of it, I do not see its archetype.” [4] In other words, I can have particular and fragmented views on this or that observable aspect of human behavior, but I cannot encompass human cognizance in a unifying and rational view. Between the beginning and the end of the eighteenth century, between the end of the classical age and the richness of the Enlightenment, it seems that the constitution of a science of humanity came to seem an illusion of reason.

3 This was an age of rationalism, as this reflection of Aristes’s in the Metaphysical Dialogues attests: “[T]here are not two or several Wisdoms, two or several universal Reasons. The truth is immutable, necessary, eternal…. The eternal Word speaks the same language to all nations, to the Chinese and the Tartars as well as to the French and the Spanish…. Two times two is four among all peoples.” [5] Fundamentally, the thinkers of the Enlightenment would have had no objection to this affirmation of the unity of reason. Nevertheless, neither Malebranche (whom Brunschvicg called the founder of positivism) nor Kant believes the constitution of a science of humanity to be possible.

4 And yet, between the middle of the seventeenth century and the end of the eighteenth century, what would later be called “social mathematics” began to take shape. As both Malebranche and Kant had seen, this event was linked to mathematics’ penetration into two new spheres: the sphere of chance and the sphere of intelligent interaction between minds. The history of these achievements is well known. I will mention only two incidents: the correspondence between Pascal and Fermat in July 1654, on unfinished games of chance; and the first resolution of a head-to-head situation in 1712, by Pierre de Montmort. In both cases, detailed texts are available. In both cases, the resolution to the problem consists in transposing a concrete event and a mathematical scheme. It remains to be seen what is retained and what is lost in this passage from history to mathematics. Is the action set up as a representation of reason, the same as the action executed by an individual? Is its authenticity preserved in this transformation, or does something else appear?

5 On the response that we might make to this question depends the response that we make to the question: Is there universality in action?

I. The Mathematization of Action

6 I am asking two questions:

  1. How did the mathematization of action occur?
  2. In undertaking this mathematization, is the specificity of the action preserved or is it transformed into something else?

7 For a long time, only games satisfied the requirements of Phaedra (265e) to “cut reality according to its natural joints,” because they contain only controllable artifices and nothing natural. Mathematics grasps the structure of the action, not its execution. It does not take the concrete action as its object, but the representation of the action or, more precisely, its type. Nevertheless, the mathematization of chance, that of the interaction between minds, and that of the aggregation of individual preferences are three achievements of reason.

1. First Stage: The Mathematization of Chance

8 Leaving aside ancient and medieval reflections on divisions, one of whose founding texts is Aristotle’s Nicomachean Ethics, it was not until the seventeenth century that chance was made to defer to arithmetic. Pascal, in his Adresse à l’Académie parisienne [Address to the Parisian Academy] (1654), characterizes the emerging science in the following terms: “Thus, joining the demonstrations of mathematics to the uncertainty of chance and reconciling the elements that seem conflicting, it receives from its double origin its denomination and rightfully deserves to claim the stupendous (stupendum) name of Geometry of chance.” [6] The word “stupendous” indicates that the great mathematician could not believe what he had discovered, namely, that chance does not escape the nets of reason, provided one knows how to ensnare it. Pascal’s correspondence with Fermat on unfinished games of chance clarifies the way in which a mathematical mastery of the choices made in conditions of uncertainty may be obtained.

2. Second Stage: The Mathematization of the Interaction of Intelligent Beings

9 The second stage of the mathematization of action began in the early eighteenth century, when Pierre de Montmort established that intelligent interaction between two agents whose interests were strictly opposed to one another could also be an occasion for arithmetic. The praise bestowed by Fontenelle on his Academy of Sciences retains the echo of this discovery: “Therefore these kinds of subjects were not discussed; it was a vast uncultivated Country, where barely five or six human footprints were to be seen.” Montmort entered boldly into this territory with the courage of Christopher Columbus, and enjoyed similar success. In 1708 he published his Essai d’analyse sur les jeux de hasard [Essay on the Analysis of Games of Chance], where he revealed this New World to the Geometers. In place of the Curves, with which they were familiar, the conic Sections, the Cycloids, the Spirals, the Logarithmics, games known as Pharaon, Bassette, Lansquenet, Ombre, and TricTrac took center stage and were subjected to Arithmetic and tamed by Algebra. [7] In 1712, in the second edition of his Essai, Montmort demonstrated on a particular problem of payoffs, what is today called the theory of equilibrium in the head-to-head contest.

3. The Aggregation of Votes

10 Since the middle of the eighteenth century, with the appearance of juries in legal matters, people have been wondering how to aggregate individual choices and how to evaluate the risks of error in elections where there is a plurality of votes. This important part of what was later named “social mathematics” came about through the works of Condorcet, Borda, Poisson, Cournot, Bertrand, and other jurist-mathematicians. However, it was not until 1951 that Kenneth Arrow, in Social Choice and Individual Values, laid the foundations of the theory of the aggregation of votes.

4. Game Theory

11 The domestication of chance, the mathematization of the head-to-head contest, and the aggregation of preferences brings us to the 1920s, when the works of Émile Borel and, more particularly, those of John von Neumann led to a general mathematical notion of human interaction, the seminal work on which is Theory of Games and Economic Behavior by John von Neumann and Oskar Morgenstern, which appeared in 1944.

12 It was believed at the time that mathematics would encompass the whole field of action or, at least, would clarify its basic structures. However, this was not to be. There still exists a fairly clearly defined divide between the theory of the head-to-head contest and the ways in which Nash—(unknowingly) taking up Cournot’s ideas—extended it, on the one hand, and more complex situations or general games, on the other. The latter bear the marks of mathematics, without their field yet being unified.

13 In conclusion, mathematics helps people to discern the structures of human choices. However, between its abstract schemes and concrete decisions, there is a gap, for the models do not indicate how one must “climb down into a well and dive for things there, despite not being especially good at it,” to take up Plato’s formula from Laches (193c).

14 Mathematics presents another danger, that of leading to the belief that the characteristics of the action that are the easiest to measure are also the most important. Three centuries after Pascal, Hayek, [8] having noted by chance that in the natural sciences the pertinent features of phenomena are measurable, observes that the same is not true in disciplines that deal with complex phenomena.

15 In summary, mathematics introduces an element of universality to the representation of action, but cannot alone bridge the gap that divides the project from its execution. This provokes the question: Is there universality in action?

II. The Execution of the Action

16 Great analysts of action—Plato, Saint Augustine, and Maurice Blondel, for example—agree on one point: between a project and its realization there is a gap, perhaps even an abyss. Maurice Blondel writes in L’Action (1893): “Execution, beyond the intention that it realizes, is an original power and a new end.” [9] In La Pensée [Thought], he quotes Descartes’ letter to Mersenne of January 28, 1641, in which Descartes explains: “I claim that we have ideas not only concerning all that is in our Intellect, but even concerning what is in our Will. For we could want nothing without knowing that we wanted it, and we could only know it through an idea; however, I do not say that this idea is different from the action itself.” [10] Blondel is persuaded that Descartes is wrong: the equation between the action and the idea of the action is false. Indeed, the execution of the action brings out unexpected realities: “[I]n giving oneself over to action, does anyone ever clearly know where he will fall and, if he clearly knew it, would he act? At least it can already be clearly seen that he wants to act and why; it can even be seen that in acting light is shed upon the darkness into which he is advancing and that there is a clarity attached to every step that he takes”. [11]

17 The decision reveals the gap between projecting and acting: “Because wanting and doing are not the same.” Although it is a great deal for us to know what we really want, nosse; although it is an even greater deal to want this want itself, velle, it is an infinitely greater deal to execute it, perficere. There was already an interval between the conception and the determination; between the decision and the execution there is an abyss to cross. [12] This is the critical passage and the decisive point of action.”. [13]

18 Indeed, the execution also reveals our internal divisions. Augustine observes: “The mind commands the body and it obeys immediately; the mind commands itself and there is resistance.” [14] Blondel comments: “It is in this way that action, like a sharp sword, opens a passage to the gaze unto the shadowy depths where are prepared the great currents of inner life. By way of this narrow opening onto the conscience, it reveals to us, on the underside of this complicated world that we are, infinite perspectives”. [15]

19 Up to this point I have taken only the individual into account. I will now consider the asymmetrical relation of authority: to acquaint oneself with high-risk actions, for example, one practices the movements under the guidance of an instructor. “Obey” in Greek is peithomai, “to allow oneself to be persuaded.” It is not easy. Apprenticeship implies affective engagement, and Plato speaks of “incredulity’s strength of resistance” (Laws, VIII, 839d). We are often unaware of the reasons why a person, in any given situation, inspires trust or distrust in us. This is not the result of a conscious act: we legitimate our feelings after the fact. Does this mean that trust is irrational? Not at all: it resembles the aesthetic judgment, as described by Kant in the Critique of Judgment. Into trust or distrust enter elements of judgment that we cannot conceptualize, even though they clearly thrust themselves on us.

20 Given the practical importance of the acts by which we accord or refuse our trust, attempts have been made to discern the source of and explain the reasons for these. This is what we do when we try to foresee whether an individual is capable of fulfilling a task. When it is a question of stereotypical repetitious actions, interviews and exams are sufficient. When it is a question of anticipating how a person might react in a crisis situation—that is to say, when the normal hierarchical chains of command break down—it is more complicated.

21 In the end, it may be—this is the case when it is a question of carrying out the strategic governing of a State—that the problems to be resolved cannot be dealt with by an individual and that the authority that confronts crises must be collective. How can this be constituted? With what type of knowledge should it be endowed? This is the question Plato poses in Laws.

The Individual and Collective Action

22 Action is not collective in essence. The Athenian in Laws even says that there are moments when the individual—this is the case with Xenophon before he is elected strategist—is absolutely alone, with no recourse but reason [16] (VIII, 835c). The individual remains the key to action, but the process that gives action its plenitude is its collective organization. This is particularly true in war: “There neither is nor will never be a higher, or better, or more scientific principle than this for the attainment of salvation and victory in war” (XII, 942c). In these conditions, it is necessary to “not teach the soul or accustom her to know or understand how to do anything apart from others. Of all soldiers the life should be always and in all things as far as possible in common and together” (XII, 942c). Taken to its limit, the ideal would be to arrive at a point where “things which are by nature private, such as eyes and ears and hands, have become common, and in some way see and hear and act in common.”

23 The deep-seated reason for this is the lesson given to us by masons. They know that the small stones are just as necessary to the stability of the walls as the big ones (X, 902e). An isolated individual cannot have both mastery of the details and a vision of the whole. This provokes the question, “But with what is that intellect (noûs) concerned which, mingling (kratheis) with the senses, is the salvation of ships in storms as well as fair weather?” (XII, 961e). The Athenian replies: “In a ship, when the pilot and the sailors unite their senses with the piloting mind, do they not save both themselves and their craft?” (XII, 961e).

24 In other words, there is no contradiction between the role of the individual and that of the group, for collectivities—especially groups in action (Sartre would say “in fusion”)—are the condensation into an organic unit of a group of relationships that become corporeal, instead of remaining virtual or weak. For Plato, this is not an inevitable process but a choice. The individual condition of atomization may very well persist, causing the loss of people and cities. Making an action “collective” is not, therefore, a given. Plato would surely have liked Conrad and, in particular, The Nigger of the Narcissus, where the role of the leader, Captain Allistoun, and that of the crew are so deeply analyzed. In Conrad’s work, as in Laws, the enterprise becomes collective only insofar as all those who take part in the heat of the action are individuated.

The Nocturnal Council

25 Plato notes that to resolve this paradox, it is necessary to understand how the supreme institution of his ideal city, his “Nocturnal Council,” is formed, and how it functions. Indeed, from this study the answer should emerge to the essential question of politics: how can the downfall of cities be avoided? To counter this risk, “the city must be entrusted to it [the Council]” (XII, 969b). The council realizes what knowledge as well as action tends toward: that every citizen should be free and that, while realizing his own essence—that is to say, his “soul”—he should be in harmony with the other members of the city. The council goes beyond the generality of laws to grasp particular problems; in every situation, it tries to take a cosmological point of view that encompasses both human affairs and the order of the universe.

26 This is the reason why the council includes, as well as the wise men who are illustrious within the city, travelers who have seen foreign lands and sought there anything that might be useful to the city being founded. Each older member chooses a younger man (between thirty and forty years old), for whom he is answerable, meaning that the mingling of the generations is assured. In addition, the minister of education is a member of the council. As the technical and scientific skills of each councilor are limited to only one field, the council operates efficiently only if the transfer of knowledge and experience is fully undertaken between its members, —Socrates observes in the Banquet (175c) that this is not necessarily the case. The instrument of this perfect communication is not science; it is pistis, otherwise called trust. In other words, the truth—including scientific truth—circulates between beings only when conveyed by a transparency that springs up between them (Simone Weil).

Perfect Knowledge

27 The Athenian defines thus the knowledge toward which this supreme council must strive: “the mind (noûs) mingling with the noblest of the senses, and becoming one with them” (XII, 961d). Perfect knowledge unites intellect and the senses by blending them together. There is no separation between the sensory universe and a supposed “world of ideas.” There is only one universe, whose face apprehended by the senses and whose face approached by the mind are inseparable, for God has combined them. It is from this ultimate perspective that the foundation of cities is organized and the foundation, by each of us, of one’s own being. When at the end of Laws Megillos puts this alternative to Clinias: “[E]ither we must detain the Stranger, and by supplications and in all manner of ways make him share in the foundation of the city, or we must give up the undertaking,” Clinias, agreeing with him, solicits the help of his friend to convince the Athenian. And the final words of Laws are: “I will” (969d).

The Augustinian Praedesinatio

28 Saint Augustine calls the art of discerning our own talents and the talents of those we are connected to praedestinatio. This lucidity is difficult because, as Montaigne and Malebranche both observe, we do not have a vision of our being that renders us transparent to ourselves. Action is the laboratory where we try out what we are, often not knowing our strengths and our weaknesses. In the end, if there is an element of universality to be found in action, it is veracity—that is to say, a clearer sense of our officium, of the function for which we are made. Is this possible? Can we discern and realize our vocation, our Beruf?

29 It is clear that answering this question demands that we pass from the study of action to the study of our insertion into the universe. Only a cosmological perspective can give any meaning to this line of questioning.

III. Cosmological Considerations on Action

Action in an Evolving Universe

30 Taking a natural philosophy perspective on action would ideally mean discerning the place and the function of each particular action in the evolution of the universe. This is what philosophers call a “Godlike vision.” As this is not within reach of a finite mind, must all hope of applying reason to the process of transforming reality be renounced?

31 If everything in the universe interacted without our being able to isolate the different parts, it would be vain to hope to found a science of action. This is not the case. The natural sciences provide the causal explanation of certain types of action. An apt example is the making of human insulin using yeasts that have been given the appropriate biological characteristics.

32 More generally, chemistry and biology make it clear that nature does not spontaneously produce everything that it could accomplish according to its laws. Humanity takes part in this incompleteness by introducing among the natural realities artifacts that, in many cases, are inserted without difficulty within natural processes. From this state of things emerges the following conclusion: even if, in theory, everything is interconnected in the real, in practice it is possible to isolate a limited number of interactive groups on which reason has a causal effect.

33 In summary, three conditions are necessary to enable a universal element to emerge in an action: that its form lends itself to mathematical analysis; that the agent attains the veracity that Saint Augustine calls praedestinatio; and that the chain of causes and effects is controllable.

34 These are heavy demands. Even if mathematics is an almost inexhaustible reservoir of forms (Whitehead), we are far from being able to formally conceptualize all types of action. Furthermore—we know this from experience, and the moralists provide us with multiple examples—it is difficult to discover what one is made for. Ultimately, science sheds only a partial light on the causal order of things. This is why situating action in a cosmological perspective appears to be more a demanding and perhaps even unrealizable “program” than a natural attitude.

The “Godlike Vision” of Action

35 If we could really take a “Godlike” view of reality—that is to say, the way in which an infinite Mind that would encompass the course of things without denying that course creative (and destructive) unpredictability, perhaps we might have a complete and accurate perspective on our actions. However, this is not the case.

36 It seems to me that the modern philosophers who are the closest to this “Godlike vision” are Malebranche, Spinoza, and Whitehead.

37 In Dialogues on Religion, Malebranche asserts that we approach the Godlike vision (scientific vision of things) in what concerns the external world; on the other hand, God has not accorded us an ordered and systematic vision (an “archetype”) of our being. Spinoza attributes more extensive powers to reason. He thinks that if we can manage to see ourselves as natural beings, caught in the network of necessity, we will realize that, in the words of Saint Paul (Acts 17:28), “It is in God that we have our life, movement, and being.” In other words, we discover that we are free. Whitehead is closer to Malebranche than to Spinoza concerning the knowledge an individual has of himself. On the other hand, like Spinoza, he thinks that we do not only have the capacity to scientifically know the physical-chemical world, but also the living world and the human order. In other words, the task of the philosopher is to attempt “an essay in cosmology.” This is a complicated undertaking because the universe is evolving. Nevertheless, the “program” of a cosmological approach to action is legitimate. It becomes concrete in essays in the great English empiricist tradition, which is also a daring metaphysical and practical school.

38 What would be a successful cosmological approach to action? To know this, it is necessary to refer to the fourth part of Process and Reality, which is entitled “God and the World.” It is a question of discerning, in evolution—this is the role of categories that, in Whitehead’s philosophy, are processes of elucidation—the shifting (in each “eternal” instant) place that we hold in the universe.

39 The first task of reason is to shed light on causal interactions between realities; when this enterprise has been successfully undertaken, it seems that not everything is caught in the network of necessity—an element of free creativity emerges. This creativity is not the monopoly of a God creator; it is the fundamental character of the world. Chemistry in the nineteenth century and biology in the twentieth century made it clear that nature does not produce all that she might, according to her laws. This incompleteness reveals that the network of causal interactions is not saturated, and that there is room for the production of new beings. Similarly, all action is based on natural, determined processes. It contains an element of free creativity. Sometimes this element is very much reduced or almost nonexistent. The action is then a simple reproduction. However, this element can also be important. Action is then innovative.

40 What is in our hands is the proportion of these two components of action: blind repetition and creative innovation. There is no contradiction between the necessity of interactions and the liberty of the agent. Quite the contrary. The more the agent penetrates the network of causal interactions, the more it increases its chances of acting freely and in a new way. Freedom, in the cosmological sense of the word, does not consist in fleeing the world but in facing it and flowing into it, in such a way as to understand the play of its causal interactions deeply enough to discern in them the space for a free action. It is not a question of an agent’s appropriating actions as though actions were works and the agent an artist. The particularity of the action, unlike a work of art, is that it escapes the person who accomplishes it. The only justified sentiment of the agent being, perhaps, the awareness of freely participating—in a limited and fleeting manner—in the progress of the World.

IV. Conclusion

41 What Whitehead does not say—and what everyone decides for himself—is what the meaning of this cosmological process is. Is it the simple progress of nature, blind and “creative,” as the natural processes of Darwinism are? Or is it the test, revealed by the action, of the distance between the order of nature and the order of freedom, as in Kant’s thought? Or, again, is it the discovery, in the cosmic drama, of relations between beings who illustrate the notion of the “communion of saints” (this “commonwealth of fellow creatures,” as Whitehead calls it)? The final words of Process and Reality underline the paradox of action by evoking “the indelible importance of our immediate actions, which disappear and yet live forever.”


  • [1]
    Immanuel Kant, Metaphysical Foundations of Natural Science, trans. Michael Friedman (Cambridge: Cambridge University Press, 2004), 4. [Premiers principes de la science de la nature, trans. Jean Gibelin (Paris: Vrin, 1952), 9]
  • [2]
    Kant, Metaphysical Foundations, 9 [15].
  • [3]
    Kant, Metaphysical Foundations, 7 [13].
  • [4]
    Nicolas Malebranche, Dialogues on Metaphysics and Religion, trans. David Scott (Cambridge: Cambridge University Press, 1997), 31–2. [Entretiens sur la métaphysique et sur la religion (Paris: Vrin, 1922), vol. 1, 60]
  • [5]
    Malebranche, Dialogues, 31 [58].
  • [6]
    “sic matheseos demonstrationes cum aleae incertitudine jungendo, et quae contraria videntur conciliando, ab utraque nominationem suam accipiens, stupendum hunc titulum jure sibi arrogat : aleae Geometria.” Blaise Pascal, Œuvres complètes (Paris: Gallimard, Bibliothèque de la Pléiade, 1954), “Celeberrimae Matheseos Academiae Parisiensis,” 74.
  • [7]
    “Éloge de M. de Montmort,” in Œuvres de M. de Fontenelle, tome 6, Contenant des Éloges des Académiciens morts depuis 1718 à 1739,1742, 62.
  • [8]
    Speech given by Friedrich August von Hayek on December 11, 1974, during the Nobel Memorial Prize in Economic Science presentation. Published in American Economic Review, December 1989.
  • [9]
    Blondel, L’Action (1893), 138.
  • [10]
    René Descartes, Œuvres de Descartes, ed. Adam and Tannery (Paris: Vrin), vol. III, 295.
  • [11]
    Blondel, L’Action, 141.
  • [12]
    Blondel here takes up the analysis of Saint Augustine in Confessions, VIII, 21.
  • [13]
    Blondel, L’Action, 162.
  • [14]
    Saint Augustine. Confessions, VIII, 21. “Imperat animus corpori, et paretur statim; imperat animus sibi, et resistitur.”
  • [15]
    Blondel, L’Action, 167.
  • [16]
    “[T]here appears to be a need of some bold man who specially honours plainness of speech, and will say outright what he thinks best for the city and citizens,—ordaining what is good and convenient for the whole state amid the corruptions of human souls, opposing the mightiest lusts, and having no man his helper but himself standing alone and following reason only.” (logô hépoménos monô monos) (VIII, 865c).


Three conditions are necessary for a universal element to emerge in an action: that its form can be mathematically analyzed; that the agents of the action attain a good level of self-knowledge; and that the chain of cause and effect is controllable. These are heavy demands. Even if mathematics constitutes an almost inexhaustible reservoir of forms (Whitehead), we are a long way from being able to identify the mathematical form of every type of action. In addition—we know this from experience and the moralists confirm it—it is difficult to discover what one is made for. Ultimately, science sheds only a very partial light on the causal order of things. To overcome these obstacles, action must be situated in a cosmological perspective. This choice seems to be a “program” that is difficult to realize.

Bertrand Saint-Sernin
Member of the Institute, Emeritus Professor at the University of Paris IV–Sorbonne.
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