Sophie Roux
email: sophie.roux@ens.fr

Roger Ariew

Jacques Du Roure

Antoine Le Grand

Pierre- Sylvain Régis

is. Pierre-Sylvain Régis

Everything You Always Wanted to Know About the Summa quadripartita that Descartes Never Wrote 1

justified the title of this book in the following way: "A philosophical system cannot be studied adequately apart from the intellectual context in which it is situated. Philosophers do not usually utter propositions in a vacuum, but accept, modify or reject doctrines whose meaning and significance are given in a particular culture. Thus Cartesian philosophy should be regarded […] as a reaction against, as well as an indebtedness to, the scholastic philosophy that still dominated the intellectual climate" (DAS, p. 1). Moreover, it is not sufficient for the historian to compare Descartes' doctrines with the Aristotelian doctrines; rather, she should "grasp the reasons behind the various opinions" and "beyond that […] understand the intellectual milieu in which these reasons played a role" (ibid.) In DFC, Ariew expresses again the same methodological commitment: "we should not approach Descartes as a solitary, virtually autistic thinker, but as a philosopher who constructs a dialogue with his contemporaries, so as to engage them and various elements of his society in his philosophical enterprise" (DFC, p. ix).

To approach Descartes' contemporaries not only in so far as they could have been intellectual sources of his thought, but as his peers and colleagues with whom it was not only 1 I wish to thank Sorana Corneanu for her careful editing, Zeta Books and MIT

project, Descartes had the time to formulate it in slightly different ways. 5 But he always insisted that, in order to be taught, his philosophy should be shortened and presented "in order (par ordre)" -as if he was now judging that his previous writings had no order, or at least, recognizing that his order was not everyone's order. 6 And, even if he considered once the possibility of calling his textbook summa philosophiae, there is no evidence that he ever wanted to extend it further than metaphysics and physics: on the contrary, he presents it as a Latinized version of Le monde. 7 But, Ariew argues, the book that resulted from this project-Principia philosophiae-was inadequate for teaching philosophy: because it did not include logic and ethics, it was incomplete when compared to regular scholastic textbooks. Hence, the task of the "First Cartesians" would have been to write the Cartesian textbook that Descartes had not written and to write it in a form acceptable to their scholastic contemporaries, that is, to write a summa quadripartita (DFC, pp. ix-xi and passim). Desmond Clarke once captured the tendency of Cartesians to behave as sectarians who follow an intellectual Master rather than the truth by speaking of "Scholastic Cartesianism." 8 According to Ariew, Cartesians are not scholastic because of their obedience to Descartes; on the contrary they introduced some variations and innovations with respect to Descartes' doctrine (DFC, pp. 206-209 and passim). But they are scholastics because they wrote books that belong to the genre of summa quadripartita.

Summa quadripartita as a genre indeed shapes the construction of DFC. DAS was a collection of papers that were all written with similar methodological commitments, but that were thematically independent one from the other. On the contrary, DFC is quite systematically constructed as a succession of different summae quadripartitae. A first 5 See Descartes' letters to Mersenne, 11 November 1640, AT III, p. 233; To Mersenne, [December 1640], AT III p. 259; To Mersenne, 31 December 1640, AT III, p. 276; To Huygens, 21 January 1642, AT III, p. 782. (AT = Oeuvres De Descartes, 11 vols., ed. by Charles Adam and Paul Tannery, Paris: Librairie Philosophique J. Vrin, 1983.) 6 "[…] écrire par ordre tout un Cours de ma Philosophie" (AT III, p. 233); "[…] faire un Abregé, où je mettray tout le cours par ordre" (AT III, p. 259); "[…] écrire ma Philosophie en tel ordre qu'elle puisse estre aisément enseignée" (AT III, p. 276). 7 "Mon Monde se fera bientost voir au monde, & je croy que ce seroit des à present, sinon que je veux auparavant luy faire aprendre à parler latin; & je je le feray nommer summa Philosophiae, affin qu'il s'introduyse plus aysement en la conversation des gens de l'escole" (AT III, p. 782). 8 Desmond M. Clarke, Occult Powers and Hypotheses. Cartesian Natural Philosophy under Louis XIV, Oxford: Oxford University Press, 1989, pp. 222-244. This criticism of the Cartesians was a topos by the end of the seventeenth century. See the notes that Baillet's Vie de Monsieur Descartes inspired to Huygens and his letters to Meier, 26 March 1691 and June 1691, in OEuvres complètes de Christian Huygens, ed. by Société Hollandaise des Sciences, 22 vols., La Haye: Martinus Nijhoff, 1888-1950, X, pp. 54, 104, 404-405. See also Leibniz to Huygens, 20 February 1691, in id., p. 52; to Pelisson, 18 March 1692, in Leibniz, Sämtliche Schriften und Briefe, Preussische, ed. by Preussischen (Deutsche) Akademie der Wissenschaften zu Berlin, Darmstadt/Leipzig/Berlin: Akademie-Verlag, 1923-, I-7, p. 292; Leibniz to Claude Nicaise, Journal des scavants, 13 April 1693, pp. 163-164. introductory chapter contrasts Thomism and Scotism, asks the question of what was taught by the different Orders in France, and presents Descartes' changing attitudes to the Jesuits, the Oratorians and the Doctrinaires. Each of the three following chapters is devoted to the different types of text that included similarly titled doctrines: the early seventeenth-century French Aristotelian textbooks in the second chapter, Descartes' own tree of philosophy in the third chapter, and, finally, Cartesian systems in the fourth chapter. 9 Since each of these three chapters is divided according to the four canonical parts of summae quadripartitae-logic, metaphysics, physics and ethics, albeit obviously following a different order, depending on whether one is a scholastic or a Cartesian (DFC, p. xiv, p. xix, n. 19)-, DFC can be read following either the succession of types of text or the succession of philosophical domains.

Regardless of the manner in which one chooses to read it, it is quite precious to be able to count on a tool that helps us draw systematic comparisons between Descartes, the scholastics and the Cartesians. One of the many stimulating aspects of DFC has nothing to do with systematicity, though: this is the fact that, at almost every page, we get a glimpse at small figures previously unmentioned-so that, instead of contemplating from afar only a few unapproachable peaks that would tower above a flat desert, we stroll about in a region full of higher and lower hills, deeper and larger valleys. To say it in less poetical terms, DFC includes a lot of information about the circulation of Descartes' texts and about the construction of Descartes' doctrine as a canonical doctrine, but also about less known philosophers, about the doctrines that they held, about the editions of the books that they published. One of the interesting points that Ariew makes concerning logic is that, by the end of the century, Cartesians and Scholastics converged to write quadripartite logics based on conception, judgment, consequence and method (DFC, p. 165). Being not myself a metaphysician by nature, I learned a lot about univocity and equivocity (DFC, pp. 51, 57, 100-102, 117-120, 177-179) and about the different early modern theories of distinctions (DFC, pp. 101-102, 113-122, 165-166, 177-178). Many fascinating points would be worth pursuing. Before coming to broader issues, I would like to pick up and discuss two minor claims, the one concerning physics, the other concerning ethics.

In the section devoted to Descartes' physics, Ariew rightly argues that this physics has little to do with the discourses about the mathematization of the world-picture that were fashionable in Edwin Arthur Burtt's and Alexandre Koyré's times (DFC, "Descartes' tree" is a strange expression here: Ariew argues that it was not Descartes' exclusive property; contrary to Descartes' own presentation (AT IX-2, p. 14), for the sake of symmetry with the preceding chapter and with the following, he includes logic in this tree, but excludes from it medicine and mechanics (DFC, pp. 106-107). and that there is a city called Roma in Italy-admit of degrees of certainty and that the probability that such beliefs are true is higher if a longer code was broken or if we can rely on a greater number of testimonies that Roma is an Italian city. But, says Ariew, moral certainty does not admit of degrees: it would have been, for Descartes as for the Scholastics, an absolute entity, since certainty and probability were separated as demonstrative science and probable opinion. It is true that the distinction between certainty and probability was such a strong distinction that Descartes and the Cartesians never felt free to admit that they were advancing only probable hypotheses.11 However, as has been established by Sven K. Knebel in the context of post-Tridentine theology, Jesuits from the early seventeenth century proposed a distinction between three types of possible, which was quickly applied to other notions, such as causality, freedom, indifference, evidence and certainty. 12 The thirteenth century had established a distinction between, on the one hand, the possibile physice, physical power, and, on the other, the possibile metaphysice, logice or mathematice, defined by the conceivability or at least the non-contradiction of the terms of the proposition at stake. A second distinction was added in the early seventeenth century, the distinction between possibile physice and possibile morale, where the former is the power which a being has in general to do or not to do something, while the latter is that power in so far as it can be associated with extrinsic circumstances that favor its actualization or, on the contrary, hinder it, in other words, that power in so far as it is sometimes actualized. Where this becomes interesting for us is that idea that, in so far as the moral possibility is sometimes actualized but sometimes not, it is capable of some quantification; the Jesuit texts use an eloquent analogy with a dice game in order to illustrate the difference between what is physically possible (all the possible outcomes) and what is morally possible (the outcome that finally obtains when the dice is rolled). As such, this distinction would demonstrate the reestablishment of a statistical conception of modalities, which would constitute the conceptual womb in which the theory of probabilities developed. 13 To say it in a word, Knebel established that the distinction between moral certainty and physical certainty was formed in a context where the analogy with dice games implied a certain measure of quantification. In this sense, Ariew's claim that, historically, moral certainty admits of no degree and is not to be equated with high probability should be qualified.

Ariew shows quite convincingly the role that Claude Clerselier's edition of Descartes' letters played in the elaboration of a Cartesian ethics (DFC, pp. 153-156). But I would like to discuss the claim that "the Cartesians created a Neo-Stoic ethics" (DFC, pp. 206-207, 209). Descartes himself entertained subtle relations to Stoic ethics, which indeed underwent a striking revival in the seventeenth century (DFC, pp. 150-151). 14 It was noted long ago that the second maxim of the Discourse on Method has a Stoic allure and that Descartes recommended Élisabeth to read Seneca's De vita beata. [START_REF][END_REF] But we also know that, at the same time, Descartes criticizes the Stoics because "they do not adequately explain how to recognize a virtue, and often what they call by this fine name is nothing but a case of callousness, or vanity, or desesperation, or parricide." [START_REF]Discours de la méthode[END_REF] If Descartes on this issue is always debatable, it is Le Grand that I would like to discuss more closely here. Before his conversion to Cartesianism, Le Grand wrote two ethics books in French, Le Sage des Stoïques and 7 L'Épicure spirituel. 17 The first and most popular of these books defended the theses that wise men can live without passions, that passions are not natural to human beings, and that they do not help them to develop their virtues. After his conversion to Cartesianism, however, Le Grand changed his mind on passions and he explicitly distanced himself from his former book: I may have qualifications to make and questions to ask, but they are obviously dependent on the many things that Ariew taught me to see and understand. Now, in the following, I would like to put DFC, or at least its last chapter on Cartesians, in a somewhat broader perspective. It cannot be denied that there were some Cartesians who wrote books organized as summae quadripartitae and that some of these books were intended for teaching.

One should be grateful to Ariew for having explored in such detail these books, as well as other books written by Cartesians. However, it seems to me that Ariew's scholastic perspective leads him to entangle teaching Cartesianism and writing summae, writing summae and writing systems. In the following discussion, I would like to disentangle these different elements and ask the two following questions: First, while Descartes insisted that some order should be introduced in his philosophy if it was to be taught in the schools, what has such an order to do with the presentation of philosophy as a system or as a summa quadripartita?

Second, what did teaching philosophy mean for Descartes and his followers? 17 Le Sage des Stoïques, ou l'homme sans passions, selon les sentiments de Sénèque, The Hague: Samuel Broune and Jean L'Escluse, 1662; L'Épicure spirituel, ou, L'empire de la volupté sur les vertus, Paris: Pierre de La Forge, 1669. There were many reprints of these books, some of them with slightly different titles. 18 Antoine Le Grand, The Institution, in An Entire Body of Philosophy, trans. R. Blome, London: Roycroft, 1694, Part X, chap. 13, § 1, pp. 367-368.

It is precisely in the second half of the seventeenth century, while Ariew's Cartesians were busy writing their summae, that our notion of a system was elaborated. The term "system" is attested in French since 1552; however, until the mid-seventeenth century, it referred, as its Latin equivalent "systema," to the cosmological order of the planets, or, more rarely, in music, to a sequence of intervals. 19 However, during the second half of the seventeenth century, its use spread and it began to designate any kind of order and disposition. As Bouhours noted en 1675:

Il y a quelques années, que ce mot n'estoit connu en notre langue que des philosophes et des mathématiciens; c'était un mot d'art en quelque sorte, le système du monde, le système de Copernic.

Depuis que M. de la Chambre a fait le système de l'âme, on s'est accoutumé à ce mot, & comme il signifie proprement constitution & situation, on s'en est servi dans le figuré, pour exprimer bien des choses. 20 Furetière, after mentioning the use of "sistème" in astronomy, notes that it is also used in physics and in medicine:

On appelle aussi en Physique le sisteme des sens, du mouvement, de la nourriture, &c., la manière dont on suppose & on conçoit que ces organes sont disposes. Entre les Medecins il y en a qui suivent le sisteme des saveurs; l'autre qui suivent le sisteme des quatre qualités, d'autre le sisteme des acides et des alcalis. Ce Medecin fait un nouveau sisteme des fièvres. 21 Régis himself, in the dictionary that he inserted at the end of the first volume of his Physique, has an entry "physics," where he gives a general definition of a system: "ce qui fait qu'une chose agit d'une certaine manière en vertu de sa composition et des dispositions qui font sa nature," then he mentions not only the systems of the world, but also, like Furetière, the systems of the senses, of motion, of food. Interestingly enough, though, Régis ends up his 19 Ulrich Ricken, "Quelques aspects de l'évolution du champ notionnel Ordre-Système au XVII e siècle," in M. Fattori and M. Bianchi (eds.), Ordo. Atti del II. Colloquio Internazionale del Lessico Intelletuale Europeo (Roma, 7-9 gennaio 1977), Roma: Edizioni dell'Ateneo e Bizzarri, 1979, pp. 471-487. 20 Dominique Bouhours, Remarques nouvelles sur la Langue française, Paris: Sébastien Mabre-Cramoisy, 1675, p. 57-58. Cureau de la Chambre, Système de l'Ame, Paris: Jacques d'Allin, 1664, Préface, justified indeed the title of this book in the following way: "Je n'ai pû trouver de terme qui expliquast bien mon dessein, que le mot de Systeme. Car de luy donner pour titre Discours de la Nature de l'Ame, il est esté trop vague. […] De luy donner aussi celuy des Actions de l'Ame, il eust esté trop resseré. […] De sorte que apres avoir remarqué que les Astronomes en faisant le Systeme du Monde, qui n'est autre chose que l'ordre & la disposition qu'ils donnent à tous les corps dont le Monde est composé, n'examinent point la nature de ces corps-là, et ne cherchent que leur situation, leur figure, leur grandeur & leurs mouvemens, j'ai creû que je pouvois emprunter d'eux ce terme-là, puisque j'avois les mêmes visées pour le regard de l'Ame." 21 Furetière, Dictionnaire universel, Paris: A. and R. Leers, 1690, article "sistème." 9 entry with a comparison between a hypothesis and a system, which implies that the word "system" does not only refer to the structure and composition of things, but, also, to propositions that are ordered in such a way that they compose a coherent whole: "L'Hypothèse est un Système plus particulier, et le Système une Hypothèse plus générale, ou, pour mieux dire, le Système n'est qu'un composé de plusieurs Hypothèses." 22 It is however in the Avertissement that opens his Physique that Régis gives the most precise definition of this new meaning of "système": "Nous entendons par SYSTÈME non une seule hypothèse, mais un amas de plusieurs hypothèses, dépendantes les unes des autres et tellement liées avec les premières vérités qu'elles en soient comme des suites et des dépendances nécessaires." 23 Here, Régis could have taken inspiration from Descartes: there are several passages where Descartes, as a duelist who would challenge his enemy, exclaimed that if this or that proposition is false, then, the whole of his philosophy is false. Though Descartes may have borrowed the image of a tree from Abra de Raconis and transferred it from physics to the whole of philosophy, I am not sure that Abra de Raconis ever stressed the coherence of his propositions in this way.

To sum up, the word "système," which was used mainly with reference to the disposition of the planets, began to designate the disposition of anything, including, in the case of a Cartesian like Régis, the order and disposition of propositions in a book. Ariew is not concerned with such new meanings. And that's because he does not believe that his heroes formulated systems in the sense of consistent sets of propositions depending on a few basic tenets. With a fully British sense of understatement, Ariew notes that "in his 1654

Philosophy, Du Roure tries to follow an order sketched by Descartes, though he does not integrate all the materials completely" (DFC, p. 161), that "despite his enthusiasm […] Du Roure's Morale, like his Logique, gives the impression of something that has not fully come together" (DFC, p. 195), or, still, that Régis' Système général "is a very odd work […] [which] does not seem very systematic" (DFC, p. xii). I could not find any similar quotations concerning Le Grand, but he surely does not fare better. Still, the fact that Du Roure, Régis and Le Grand failed to be systematic does not imply that they had not the intention of being systematic, to wit, of proposing a coherent set of hypotheses depending on a few basic tenets. In the case of Régis at least, this was quite important, since he thought-it is immaterial here to know if he was justified to think so-that the difference between the 10 arbitrary hypotheses advanced by Claude Perrault in his Essays de physique and his own true hypotheses in physics was precisely that his hypotheses were organized in a system. The Avertissement I already quoted goes on in the following way: Thus, Régis' Système général can be seen as a summa quadripartita, but it can also be read as a system of hypotheses that are presented as true because they depend on first truths and form a coherent whole. Consequently, it seems to me that we could conjecture that the first Cartesians contributed to forge our notion of a system, not so much because they wrote summae quadripartitae, as because they tried both to establish the supremacy of their works over works like Perrault's Essays and to answer the criticisms about framing hypotheses that was addressed to them. In any case, it is interesting to note that what Descartes described as presenting his philosophy "in order" gave way to at least two interpretations that were different but not incompatible: on the one hand, it meant complying with the order of domains and disciplines that was canonical in summae quadripartitatae; on the other hand, it meant insisting on the coherence of all the propositions together.

In the second place, I would like to insist that studying scholastic textbooks and Cartesian systems should not make us forget that Descartes and his followers raised wideranging questions about the teaching of philosophy-namely, where, how, by whom and to whom was philosophy to be taught? First, let us come back to Descartes himself. As I have already noted, Ariew's project finds its origins in the letters where, by the end of 1640, Descartes formulated the project of presenting his philosophy in such a way that it could be taught in the Schools, which implied to shorten it, to order it differently, and to put it in Latin. These are important letters for understanding the genesis of Descartes' Principia philosophiae. However, these are not the only things that Descartes wrote about how his philosophy could be taught; he seems to have been especially careful to delineate the kind of students whom he was addressing himself to.

On the one hand, he asserted that his writings might be studied virtually by everybody. Thus, in a letter to Vatier, Descartes explained that in Discours de la méthode, he did not dare to explain in detail why our beliefs concerning material beings can be subject to doubt, because "these thoughts did not seem to me suitable for inclusion in a book which I wished to be intelligible in part even to women." 25 On the other hand, he insisted that his readers should not be excessively learned. For example, at the very beginning of La recherche de la vérité, he explained that an honnête homme "is not required to have read absolutely every book or diligently mastered everything that is taught in the Schools. It would, indeed, be a kind of defect in his education if he had spent too much time in book-learning (en l'exercice des lettres)." 26 In other words, Descartes was at the same time encouraging those who may have hesitated to approach his writings because they were uneducated and insisting that, in the case of those who were well educated, all their learning was not enough. The condition sine qua non was in both cases to be ready to spend time, care and attention enough in perusing Descartes' books. In the Lettre-Préface to Principes de la philosophie, he rehearsed the idea: I should like to assure those who are over-diffident about their powers that there is nothing in my writings which they are not capable of completely understanding provided that they the trouble to examine them. I would, however, also like to warn the others that even the most excellent minds will need a great deal of time and attention in order to look at all the things which I set myself to include. 27 My point is not to play Descartes the honnête homme against Descartes the scholastic.

Being not a Martin Schoock rediviva, neither is it not to claim that Descartes wanted us to stop reading books. (According to Schook's Admiranda Methodus, Descartes required from his disciples to forget all the books and the whole tradition of learning in order to submit themselves to Descartes as to their master. 28 But, in fact, if Descartes condemned those who spend too much time studying books, he did not, for that, condemn reading books in general.) But I think that Descartes' description of his ideal readers may have contributed to making it possible that philosophy reached other readers than the captive audience of boisterous students, and that French Cartesians realized this possibility. 25 Descartes to Vatier, 22 February 1638, AT I, p. 560, transl. CSM III, p. 86. (CSM = The Philosophical Writings Of Descartes, 3 vols., trans. by John Cottingham, Robert Stoothoff, and Dugald Murdoch (Volume 3 including Anthony Kenny), Cambridge: Cambridge University Press, 1988.) 26 La recherche de la vérité, AT X, p. 495, transl. CSM II, p. 400, to be compared with the criticism of those who spent all their time in schools (Regulae ad directonem ingenii, AT X, p. 371). 27 Lettre-Préface, Principes de la philosophie, AT IX-B, p. 13. 28 Théo Verbeek (ed.), La Querelle d'Utrecht, Paris: Les impressions nouvelles, 1988, pp. 189, 197 and passim. Malebranche would have put it, worldly experimentalists like Jacques Rohault, and, further, polished conversationalists like Bernard Le Bovier de Fontenelle. 29 Many testimonies indicate that, from the sixties on, the teaching of Cartesian philosophy in France was not confined to the regular teaching institutions such as the collèges de plein exercice and the universities.

Rather, Cartesian philosophy was taught in conférences or private academies and discussed in salons. The description that the Cartesian Clerselier gives of the audience of Rohault's Mercredis-"people of all stations and conditions, prelates, abbots, courtesans, doctors, physicians, philosophers, geometers, regents, schoolboys, provincials, foreigners, artisans, in a word, people of all ages, sex and profession" 30 -concords with one of the many reproaches that the Doctrinaire Jean Vincent made to Toulouse's Cartesians, among which the most famous one was Pierre-Sylvain Régis: "they divulge to all kind of human beings, kids, adults, men, women, the doctrine that in the Schools used to be diffused to only a few men." 31 The only difference between Clerselier and Vincent is that the former gives credit to this kind of mixed and motley audience, while the latter would have liked to discredit it completely.

Thus, in late seventeenth-century France, honnêtes gens, among whom some women, who were learned but not specialized, able to read short philosophy books but not ready to spend time on heavy summae, good Christians but not furious theologians, were the ones to be convinced. 32 It seems to me that, by focusing on the genre of summae quadripartitae and, thus, implicitly, on the official teaching of philosophy that took place in collèges de plein exercice and universities, Ariew sometimes misses what he himself called in DAS the "intellectual milieu" in which controversies continuously emerged between Cartesians, Scholastics and even other species of philosophers in France by the end of the seventeenth century, an "intellectual milieu" which, some fifty years afterwards, was already different from the intellectual milieu in which Descartes himself worked. To put it more precisely, if 29 For a study of the various social figures of the philosopher, see Dinah Ribard, "Philosophe ou écrivain? Problèmes de délimitation entre histoire littéraire et histoire de la philosophie en France, 1650-1850," Annales HSS, 2 (2000), pp. 355-388. 30 Claude Clerselier, Préface, OEuvres posthumes de Rohault, ed. by Claude Clerselier, Paris: Guillaume Desprez, 1682, n.p. Other sources attest to the fact that a certain number of persons of quality, young students (for example Pierre-Sylvain Régis) and women (for example Madame de Bonneveaux or Madame de Guerderville) attended these lectures. 31 Jean Vincent, Discussio peripatetica in qua philosophiae cartesianae principia … dilicude examinantur, Toulouse: Colome and Posuel, 1677, IV, sect. 526, p. 521. Bernard Le Bovier de Fontenelle, Éloge de M. Régis, in OEuvres complètes. Tome VI. Paris: Fayard, 1994, pp. 143-144, explains that Régis' success was such that the magistrates of the city awarded him a pension. 32 This is one of the things that I tried to show in Sophie Roux, "A French Partition of the Empire of Natural Philosophy (1670-1690)", in Daniel Garber and Sophie Roux (eds.), The Mechanisation of Natural Philosophy, New York, Dordrecht, Boston, London: Kluwer, 2012, pp. 55-98. Ariew's point is to describe the variety of Cartesian doctrines at the end of the seventeenth century, especially in as much as they paradoxically appeared in the scholastic form of a summa, I cannot but repeat that I admire without any reserve the fine-grained description that he succeeded in giving of such a doctrinal variety in such a short volume. But, when Ariew implies that the success of Cartesianism in France at this period is to be explained by the Cartesian textbooks that Du Roure, Régis and Le Grand wrote, I cannot agree. 33 If this is the explanandum, one should go beyond the genre of the summa and admit that other social forces were at stake. This is all the more true since the books taken by Ariew as typical for this genre, the books by Du Roure, Le Grand and Régis, although all organized as summae, did not have the same audience from a quantitative point of view, did not play the same role in the reception of Descartes' philosophy in France, and did not contribute in the same way to shape French Cartesianism. I launched a systematic search in Catalogue collectif de France: I retrieved less than 20 copies of Le Grand's Institutio philosophiae secundum Renati Descartes nova methoda adornata et explicata, 34 20 copies also of all the books written by Du Roure, about 60 copies of Régis' Système général, 75 copies of Fontenelle's Entretiens sur la pluralité des mondes and, finally, 120 copies of Rohault's Traité de physique. Du Roure seems to have printed his books in his own house, which was no more a good sign at that time than it would be now, and I have almost never seen him mentioned in the exchanges of the late seventeenth century. The only known Cartesian to have exchanged with Du Roure may have been Johann

Clauberg. Du Roure met Clauberg in Paris in 1648. In a compilation of Cartesian papers published in Amsterdam in 1683 under the title Cartesiaanse redden-konst: met het onderscheid tusschen de Cartesiaanse en schoolse philoosophie, Dutch translations of Clauberg, Dilly and Du Roure are to be found. 35 It is moreover to be noted that at the end of his Initiatio philosophi, Clauberg quotes a letter that Du Roure sent him after reading the Defensio; in this letter, Du Roure suggested to dub those who follow Descartes "rational philosophers (Philosophes Raisonnables)" because the foundation of Descartes' philosophy 33 DFC, p. 205: "Thus the Cartesians were able to replace the Aristotelians in the Schools. How exactly did they accomplish that? Well, they tried to supplant the Aristotelians by producing Cartesian textbooks that would teach the whole collegiate curriculum […] in a Cartesian mode. They attempted a revolution across all aspects of the curriculum, not just in the sciences and metaphysics." 34 The Historia naturae, variis experimentis et ratiociniis elucidata, secundum principia stabilita in Institutione philosophiae, which, before being published as the third part of An Entire Body of Philosophy, was much more popular than the Institutio. 35 DFC,p. 191,n. 138 Le Valois. 37 But what these authors write when they mention him seems to indicate that they had not really read him, except perhaps for Bayle, and that it was simply difficult to know exactly who he was. His audience was not French, but English: he lived in England from the age of 27 to his death; except for the three books that he published in French before his conversion to Cartesianism, he published in Latin or English; he dedicated the different editions of his Institutio to the Academici Cantabrigiensis universitatis; finally it is to be noted that he engaged controversies only with English philosophers, to wit Samuel Parker and John Sergeant. As for Régis, he was indeed quite important, even if not as important as Rohault. But although he had a long career of public teacher and personal preceptor, contrary to Le Grand who wrote the Institutio "in usum juventutis Academicae," he does not seem to have published his Système général for students, and in any case he was never studied in collèges or universities.

In a word, studying Du Roure, Le Grand and Régis is interesting in itself and challenging as such. But, beyond that, understanding their "intellectual milieu" would imply to differentiate the French context of the forties, in which Descartes himself made his works known, from the French context of the fifties and early sixties, in which Du Roure published some of his books in his own house; further, to distinguish those two contexts from the French context of the eighties and nineties, in which Régis published a Cartesian textbook while the Académie des sciences was flourishing; and, finally, to set apart those three contexts from the English context, where, thanks to Recusant families, a Catholic missionary like Le Grand could survive in an overtly anti-Catholic England.

Ariew concludes his introduction with the following words: "Much work remains to be done; as Descartes would have said: I leave this task to my 'nephews-and to my nieces 36 Johann Clauberg, Initiatio philosophiae cartesianae sive Dubitatio cartesiana, ad metaphysicam certitudinem viam aperiens, Leiden: A. Wyngaerden, 1655, pp. 436-437. I thank Domenico Collacciani for this reference. 37 Pierre Bayle to Jacob Bayle, April or May 1679, at http://bayle-correspondance.univ-st-etienne.fr/?Lettre-168-Pierre-Bayle-a-Jacob; in the article "Rorarius," Dictionnaire historique et critique, Rotterdam, 1715, p. 442, Le Grand's Dissertatio de carentia sensus & cognitionis in brutis is mentioned among other Cartesians publications concerning animal machines; Système abrégé de philosophie, in OEuvres diverses de M. Pierre Bayle, La Haye: La Compagnie des Libraires, 1737, IV, p. 426, alludes to Le Grand's physics. Antoine Arnauld, Lettres au Père Malebranche, in OEuvres completes de Messire Antoine Arnauld, Paris: S. d'Arnay, 1775-1783, XXXIX, p. 150: "Vous pouvez voir ce qu'en dit dans sa philosophie cartésienne le Père Antoine le Grand, que j'apprends etre un religieux de Saint François". Louis Le Valois, Sentimens de M. Descartes touchant l'essence et les proprietez des corps corps, opposez à la doctrine de l'Eglise, et conforme aux erreurs de Calvin, sur le sujet de l 'Eucharistie, Paris: Étienne Michallet, 1680, I, chap. 4, p. 84.

  190). 10 However, I would like to qualify one of the three claims defended in the section "Hypotheses and Moral Certainty" of the third chapter. Here are these claims: "(1) Descartes frequently used the concept [of moral certainty] before his formal definition of it in the Principles […]. (2) Descartes borrowed the concept from the Schoolmen […]. And (3) against most commentators, despite what could be inferred from Descartes' examples of code-breaking and of knowing where Rome is, moral certainty should not be equated with high probability" (DFC, pp. 143-144). I completely agree with the two first claims, but I would like to qualify the third one. If I understood it well, Ariew's main argument in favor of this claim is not conceptual, but historical. Conceptually, one could believe that the examples brought out by Descartes in Principia philosophiae IV 205-believing that a code was broken

I

  confess my self formerly to have pleaded their Cause [that is, the cause of the Stoics] in my Discourse entitled, L'Homme sans Passions, and not only to have maintained SENECA's Opinion, but also according to my slender Ability, endeavour'd to advance and exalt it. But forasmuch as I now follow the sentiments of DES CARTES, and my business is not to explain the Opinions of others, but only to lay open Truth, no understanding man will reproach me of Lightness or Inconstancy, for going about to unfold the usefulness of the Passions, and leaving the Stoicks, consider Man, not as translated amongst the Glorified Saints in Heaven, but as placed amongst his Mortal Brethren here on Earth." 18 My point is obvious: if Le Grand thought that his former Stoic beliefs and his more recent Cartesian beliefs on passions were not compatible, can we really call his doctrine "neo-Stoic"?

  Ce qui [i.e., that all the hypotheses are like necessary consequences of first truths] ne sçauroit convenir aux hypotheses purement arbitraires, telles que sont celles de la plus-part des Philosophes modernes. Il n'y a rien de plus commun que les hypotheses arbitraires […]. Il n'en est pas de meme des systèmes que des hypotheses arbitraires […]. Nous nous servirons donc comme les autres, du droit de faire des hypotheses […]. Mais pour n'en établir que d'exactes, nous ferons ensorte qu'elles dependent absolument des premières verités." 24

  . would have been to accept "only what we conceive and what Reason can teach us." 36 Le Grand was more important than Du Roure. Perhaps because his Institutio philosophiae had been the object of a quite brief notice in Journal des scavants on 20 February 1679, he was known by Pierre Bayle, Antoine Arnauld and the Jesuit Louis

On the two meanings of 'first' in the title Descartes and The First Cartesians, see Martine Pécharman's paper in this issue.

It would be difficult for me not to agree: Ariew refers to the introduction I wrote for a special issue of Early Science and Medicine (Forms of Mathematization (14th-17th Centuries),Volume 15, Issue 4-5, 2010), in which I argued that, even if we did not believe anymore in the big picture of the Scientific Revolution there were still many work do be done about what "mathematization" implied for different authors in the Medieval, Renaissance and Early Modern Period.

This was a leading fad in the first book written in English about the natural philosophy of the French Cartesians, Desmond Clarke's Occult Powers and Hypotheses. See in particular pp.183-200, 229-232, 243- 244.

 12 Sven K.Knebel, Wille, Würfel und Wahrscheinlichkeit Wille, Würfel und Wahrscheinlichkeit. Das System der moralischen Notwendigkeit in der Jesuitenscholastik 1500-1700, Hambourg: F. Meiner, 2000. See also id., "The Renaissance of Statistical Modalities in Early Modern Scholasticism," in R. L. Friedman and L. O. Nielsen (eds.), The Medieval Heritage in Early ModernMetaphysics and Modal Theory, 1400-1700, Dordrecht: Kluwer, 2003, pp. 231-251.

Sven K.Knebel, Wille, Würfel und Wahrscheinlichkeit, pp.

148-156. If I may refer to my own work, L'Essai de logique de Mariotte. Archéologie des idées d'un savant ordinaire, Paris: Classiques Garnier, 2011, pp. 95-98, analyses how Mariotte adapted the distinction between three kinds of possibles to physics. 14 See also Jacqueline Lagrée, Juste Lipse et la restauration du stoïcisme: Étude et traduction des traités stoïciens De la constance, Manuel de philosophie stoïcienne, Physique des stoïciens, Paris: Vrin, 1994; Id., Le

Régis, article "système," Dictionnaire inséré à la fin de la Physique, in Système de Philosophie, Paris:Anisson, Posuel, Rigaud, 1690, vol. I, n.p.

Avertissement, La Physique, in id., vol. I,

Ibid. The relation between hypothesis and system is discussed inClarke, Occult Powers and Hypotheses,


Nicolas Canry
email: nicolas.canry@univ-paris1.fr

Pro…t-led or Wage-led Regimes: the E¤ect of Saving Behaviours

Keywords: Cycles, Income share, Post-Keynesian theory, Saving, Unemployment. JEL Classi…cation: E12, E21, E24, E25

In this article, we modify the saving function of the Bhaduri-Marglin model and obtain a hump-shaped curve of output in function of wage-share: the nature -exhilarationist or stagnationist-of the economic regime depends on the level of income distribution. Economic policy can thus consist of shifting income distribution by redistributive policy in order to stimulate output. These conclusions remain valid in open economy, even if the exhilarationist regime is then more likely to arise. At last, we adopt a dynamic perspective by adding a wage equation to the model, which is thus characterised either by cycles or an underemployment equilibrium.

Introduction

Many Post-Keynesian authors [START_REF] Rowthorn | Demand, Real Wages and Economic Growth[END_REF][START_REF] Dutt | Stagnation, Income Distribution and Monopoly Power[END_REF][START_REF] Economica Bhaduri | Unemployment and the Real Wage: the Economic Bases for Contesting Political Ideologies[END_REF][START_REF] Lavoie | The Kaleckian Model of Growth and Distribution and its Neo-Ricardian and Marxian Critics[END_REF] have tried to show that the relation between growth and income distribution (between wages and pro…ts) was not clear cut. Income distribution determines growth through its e¤ects on both investment and consumption behaviours. Let us suppose an increase of pro…t share in total value added: this is likely to increase investment by …rms but, in the same time, it will have a negative impact on consumption by households. If the …rst e¤ect is more important than the second one, the regime is exhilarationist. On the contrary, if the negative e¤ect on consumption (we could also say: the positive e¤ect on saving) outweighs the positive e¤ect on investment, the regime is stagnationist. The main conclusion is that the nature of the regime crucially depends on the respective sensitivity of both investment and saving to income distribution evolutions. Unfortunately, these sensitivities (which are re ‡ected by constant parameters in this kind of model) are supposed exogenous in the comparative static frame that these authors have adopted. These models thus study the conditions that an economy must ful…l to be either exhilarationist or stagnationist but dynamic issues explaining how an economy switch from one regime to another are rarely tackled.

One way to introduce such dynamic issues consists of introducing non linearity in investment behaviour by …rms. Many contributions which adopted the framework of disequilibrium theory focused on this way in the early 1980s [START_REF] Artus | Investissement, contraintes de débouchés d'emploi et contraintes …nancières : estimation d'un modèle à plusieurs régimes[END_REF][START_REF] Muet | Investment, Pro…tability and Classical Unemployment[END_REF]. These models generally assume that investment equation depends on two components: one for demand e¤ect, one for pro…tability e¤ect. Actual investment is determined by the "binding"component (i.e. the weakest component). Accordingly, an economy can switch from one regime to another because of a change in the component which restricts investment. However, this framework remains static and the links relating income distribution to economic growth are not the core of the issue anymore.

In this article, we adopt a di¤erent perspective: instead of modifying investment function, we focus on saving function. In that perspective, we refer to the Bhaduri-Marglin model that we very slightly modify by changing its saving function. The pretty intuitive hypothesis that we then introduce is that propensity to save by agents increases with their income. Thanks to this new simple hypothesis, we show that the nature of the regime does not depend only on exogenous parameters anymore ; it also depends on the level of income distribution. Our main conclusion is thus that the e¤ect of wage-share variations (or, symmetrically, of pro…t share variations) depends on the initial level of wage share. Note that the hump-shaped curve we …nally get had already been suggested by [START_REF] Taylor | Income Distribution, In ‡ation and Growth[END_REF] 1 .

The …rst section of this article is devoted to a brief presentation of the Bhaduri-Marglin model (1990). In section 2, we modify the saving function of the Bhaduri-Marglin model and show how it allows to generate an inverted U-shaped curve between wage-share and output. In the third section, we brie ‡y analyse the implications of the model for economic policy. In the fourth section, we enrich our model by opening the economy. In the …fth section, we adopt a dynamic perspective by introducing a wage equation in the model: we then show that the dynamic can either be characterised by cycles (the economy switching periodically from wage to pro…t-led regime and vice versa) or converge toward a Keynesian equilibrium (characterised by both low wage share and high unemployment rate). At last, we conclude.

The Bhaduri and Marglin model (1990)

The Bhaduri-Marglin model analyses the e¤ects of income distribution on growth through the impact of pro…t-share evolutions upon investment and savings. The authors show that the level of activity can be supported either by wages increase (wage-led regime) or pro…ts increase (pro…t-led regime).

In their model, consumption is given by:

C = (1 s w )W + (1 s p )P (1)
where W is the payroll, P are the total pro…ts (Y = P + W ), s w and s p are saving propensities of workers and capitalists respectively, with s p > s w . It follows that:

S K = z [(s w s p )! + s p ] (2)
with K, the level of physical capital in the economy, S the saving, ! = W Y (wage share), z = Y Y (where Y is the output level when the capital stock is fully used; z is the rate of capacity utilisation), and = Y K (constant). The investment function has two explicative variables: the pro…t rate r = P K and the rate of capacity utilisation z, which captures a demand e¤ect:

I K = i 0 + i r P K + i z Y Y = i 0 + z(i r (1 !) + i z ) i r ; i z > 0 (3)
where ! = W Y . As I K = S K , we get a relation between z and !:

z = i 0 (i r (s p s w )) ! + ((s p i r ) i z ) (4)
The "Keynesian stability" condition, according to which saving must be more sensitive to variations of z than investment, implies that the denominator of equation (4) must be positive. The equilibrium of the model z is thus positive if i 0 is positive, which is assumed afterwards.

An economy is wage-led if @z @! > 0 and pro…t-led otherwise. The nature of the economic regime rests only on the sensitivity of both saving and investment to variations of the wage-share !, i.e. the economy is wage-led if:

i r < s p s w (5)
From a graphical standpoint, the nature of the regime depends on the sensitivity of the slope of both saving and investment curves to variations of wage-share. Therefore the market equilibrium condition implies either an increasing or a decreasing relation between wage share and output. The e¤ect of pro…t on output is then unclear.

Nevertheless, two important limits of the Bhaduri-Marglin model must be underlined:

-It seems that the pro…t-led regime is unlikely to occur for realistic values of parameters of this model [START_REF] Blecker | Distribution, Demand and Growth in Neo-Kaleckian Macromodels[END_REF]. In the extreme (but usually assumed by many Post-Keynesian authors) case where s w = 0 and s p = 1, the condition for which the economy is pro…t-led becomes (from equation ( 5)) i r > 1, which is incompatible with the condition of Keynesian stability. Thus, with this extreme but very usual hypothesis on saving behaviours, the regime is necessarily wage-led.

To get a pro…t-led regime in the Bhaduri-Marglin model, both strong sensitivity of capital accumulation to pro…t rate and weak propensity to save pro…ts (rather counterintuitive hypothesis) must be assumed.

-In his review of the Bhaduri-Marglin model, [START_REF] Taylor | Income Distribution, In ‡ation and Growth[END_REF] suggests that the nature of the economic regime can directly depend on the "initial" level of wageshare: the greater it is, the more likely is the economy to be pro…t-led (in other words, when wage-share is high, its decrease should boost the level of activity). This rather intuitive interpretation can be illustrated by an inverted U-shaped curve. However, this representation does not correspond at all to the analytical model of Bhaduri-Marglin, since the sign of z ! from (4) does not depend on !. In the Bhaduri-Marglin model, only an "exogenous" shift of parameters in saving (s p or s w ) or investment (i r ) functions will allow to switch from one regime to another. Evolutions in income distribution a¤ect the level of activity in the economy but not the nature of the regime (wage or pro…t-led).

Formalising the "Taylor curve"

In this section, we enrich the Bhaduri-Marglin model in order to give a mathematical formalisation of this "Taylor curve", which has, to our knowledge, never been carried out. Indeed, formalising the "Taylor curve" implies to introduce nonlinearities, either in the investment function or in the saving function of the model.

In this article, it is the saving function which is modi…ed. In most of Post-Keynesian models indeed, it is assumed that agents (workers or capitalists) save a constant part of their income; this (constant) saving rate depends only on the kind of the income, wage or pro…t. This means that, for each kind of income, the marginal propensity to save is constant. On the contrary, we suppose here that:

-on the one hand, the propensity to save income is not related anymore to the nature of income: for every agent, it depends only (and more generally) on level of income of each agent (whatever this income, wage or pro…t).

4

-on the other hand, the marginal propensity to save income is positive. If we note s i the average propensity of agent i to save its income Y i , we then have:

s i = S i Y i = f (Y i ) (6)
Moreover, we suppose that f has the shape of a logistic function, i.e. we suppose that : i) In this frame, we distinguish workers from capitalists only by assuming that the pro…t of each capitalist exceeds Y , whereas the wage of each worker does not 2 . This hypothesis suggests that capital incomes are more concentrated than labours incomes.

f (0) = 0 ii) f 0 = ds i dY i 0 8Y i 0 iii) 9Y > 0 f 00 (Y ) = 0 iv) 8Y i < Y f 00 (Y i ) > 0 and 8Y i > Y f 00 (Y i ) < 0 v) lim Y i !Y f (Y i ) = s and lim Y i !1 f (Y i ) = 1. The saving rate of agent i is thus depicted in …gure 2.

Saving behaviour by workers

We assume that each (employed) worker j supplies one (indivisible) unity of labour, which allows to produce a unities of …nal good (once capital is installed). The average labour productivity a is supposed constant and identical for all workers. If employed, this worker earns a wage w (identical for any employed worker). If unemployed, the worker earns no income (for simplicity, we suppose that, in that case, w = 0). Propensity to save wage by worker i is given by :

S w;j w = s w;j (w) (7)
As workers cannot increase their labour supply, every increase of output involves hiring of new workers by …rms, so that only wage variations allow to increase the income of employed workers. Moreover, if wage w exceeds the labour productivity a, …rms will have no interest to produce: this is the reason why w can vary from 0 to a 3 . At last, to ful…ll conditions i) to v) presented above, we suppose that:

s w;j = s w a = s! = s w (8)
with > 1 and 1. Without loss of generality, we suppose afterwards that = 1.

Figure 3 displays average propensity to save wage by workers depending on wage share level !, for di¤erent values of . In these simulations, we suppose that s = 0:4 (note that in the Bhaduri-Marglin model, propensity to save wage is constant and does not therefore depend on wage share at all: this case is presented on the …gure for s w = 0:2). Note that the more important is , the weaker is the propensity to save wage, whatever the wage share level !.

Saving behaviour by capitalists

We assume that each "capitalist" k supplies a …xed quantity m of capital, each unity of capital allowing to produce unities of output (in the case of full utilisation of capital, which is not necessarily the case in our model). As all capitalists are identical, they earn the same pro…t rm, where r = P K is the pro…t rate at macroeconomic level. Average propensity to save pro…t by capitalist k is given by:

S p;k rm = s p;k (rm) (9)
On the one hand, as we assume that each capitalist earn an income superior to Y (see …gure 2), we must suppose that:

r Y m (10)
On the other hand, we suppose that propensity to save pro…t s p;k is an increasing function of pro…t rm. In this section, we suppose that m is constant, so that the evolution of capitalists'income depends only on r, which can be written:

r = P Y Y Y Y K = z (11)
The return on capital is then bounded by the productivity of capital , so that we can suppose that:

s p;k = e s r ; 0 1 (12)
From ( 11) and ( 12), we thus get:

s p;k = e s ( z) = s p (13)
To be in accordance with …gure 2, it is necessary to suppose e s = 1. The main di¤erence with the saving rate by workers is that capitalists'income increases with the rate of capacity utilisation z: as capital can be underemployed in our model, an increase of output will increase both rate of capacity utilisation and individual income of capitalists. Nevertheless, this result makes our model more complicated to solve.

Equilibrium

With our new hypotheses on saving behaviours by agents, equilibrium condition of the model (equation ( 4) of the Bhaduri-Marglin model) is given by:

z(i r e s(1 !) z s! ) ! + ((e s(1 !) z i r ) i z ) i 0 = 0 (14)
In a …rst step, we will suppose that = 0, which means that saving rate by capitalists is constant (and equal to 1), as in Bhaduri-Marglin model, so that only saving behaviour by workers is modi…ed (by comparison to the Bhaduri-Marglin model): this …rst step allows to get a model which is very easy to solve. In a second step, we will suppose that > 0: with such a condition, the model becomes much more complicated to solve, which compels us to use simulations to present results of the model in that case. At last, as i z has a quite weak impact on our main conclusion, we will suppose that this parameter is equal to 0.

3.4. First case: endogenous propensity to save wage ( > 1), constant propensity to save pro…t ( = 0, s p = e s) From equation ( 14), it results that economy is wage-led if:

! < s p i r s(1 + ) 1= (15)
Figure 4 displays the level of activity (captured by the rate of capacity utilisation z) according to wage share level ! for di¤erent values of . For the simulations, values of parameters are: s = 0:4, e s = 1, i r = 0:7 and i 0 = 0:12. From …gure 4, we notice that the greater is , the greater is the rate of capacity utilisation z, whatever !: this can be easily explained by remembering that propensity to save wages decreases with (for any !). Moreover, the greater is ;the more sensitive is z to wage share evolutions. But the main conclusion from …gure 4 is that whatever , there is a threshold value ! of wage share, separating a wage-led from a pro…t-led area. In the Bhaduri-Marglin model, this threshold value does not exist, whatever the values of the parameters in the model. On …gure 5, we present the result of the simulation when = 0 (other parameters remaining unchanged, by comparison with …gure 4), which corresponds to the Bhaduri-Marglin model when s p = 1, s w = 0:2, i r = 0:7 and i 0 = 0:12 (in this case the regime is wage-led whatever the level of the wage share). Thus a very simple change on saving behaviours by households is su¢ cient to generate a frame in which the nature of the regime depends on wage share variable. To the left of ! (see equation ( 15)), every rise of wage share increases output since positive e¤ect on consumption outweighs the (possible) negative e¤ect on investment (note that investment itself may even be supported by an accelerator e¤ect in this case). On the contrary, to the right of ! , output level is restricted by insu¢ cient investment and pro…t-squeeze (every wage share decrease will support investment more than it depresses consumption in this area).

At last, note that:

-on the one hand, the greater , the greater ! , the threshold value of wage share separating the two regimes.

-on the other hand, the greater , the greater the sensitiveness of z (the rate of capacity utilisation) to variations of income distribution.

Table 1 sums up the main conclusions of these simulations:

Table 1. Value of the threshold ! for di¤erent values of .

3.5. Second case: endogenous propensity to save wages ( > 1) and pro…ts ( > 0)

We now assume that propensity to save pro…t is also endogenous. The purpose of this section is only to show that the main conclusion of the previous section is not a¤ected by this additional hypothesis. Thus we take the same values for parameter as previously. We take = 3 and make simulations for three di¤erent values of : = 0 (as in the previous section), = 0:2 and = 0:4. From …gure 6, we notice that the greater is , the greater is the rate of capacity utilisation z whatever !, because the propensity to save pro…t decreases with (for any !). Moreover, the greater is , the more sensitive is z to wage share evolutions, especially in the pro…t-led regime. Thus the introduction of endogenous propensity to save pro…ts makes the model much more complicated but it does not a¤ect its main conclusions at all, namely the nature of the regime -wage or pro…t-led-directly depends on the level of income distribution. This is why, it will be assumed, in next sections and for more simplicity, that = 0.

Implications for economic policy

One central conclusion of the model presented in previous section is that there is (at least from a theoretical standpoint) a value of wage-share ! for which output is at its optimal level. In this frame, economic policy can consist of leading a redistributive policy which moves the wage-share closer to ! . This could be carried out through a …scal policy, which would transfer income from one kind of agent (worker or capitalist) to another (note however that the purpose of this policy is not equity but e¢ ciency). Such a policy requires a good diagnosis of the economic situation, since a given level of output can result from two di¤erent values of wage-share (one in the wage-led area and one in the pro…t-led area). Indeed, the …scal transfer directly depends on the economic regime in which the economy actually is. Fiscal policy consists of boosting demand through the support of either consumption by households or investment by …rms. For example, if the economy is in the wage-led regime, economic policy will transfer capital incomes toward "labour incomes" (or households) 4 .

Opening of the economy

Net exports

Our model can be enriched by opening the economy. The equilibrium on goods markets is thus given by:

S K = I K + X M K (16)
and the equation of net exports formation must be formulated. [START_REF] Bowles | Wages, Aggregate Demand and Employment in an Open Economy: an Empirical Investigation[END_REF] assume that net exports are positively related to the national pro…t rate r:

X M K = x 0 + x r r x r 0 (17)
Many explanations can support this hypothesis: a wage share increase may bring about in ‡ation and a loss of competitiveness; higher pro…t rate will increase investment and R&D expenditure, which will improve technical progress and eventually competitiveness; higher pro…tability makes easier for …rms to reduce their markup on foreign markets, etc.

In the Bhaduri-Marglin model, the new condition for the economy to be wageled is then:

i r + x r < s p s w (18)
So Bowles and Boyer conclude that the economy is more likely to be pro…t-led in the frame of an open economy. In our model, the economy is wage-led if:

! < s p i r x r s(1 + ) 1= (19)
So, the value of the threshold ! separating wage and pro…t-led regimes is now weaker (than in the case of a closed economy).

Foreign direct investments

Another way to open the economy is to suppose that investment may be carried out either within the country or overseas, according to the gap between national and worldwide pro…t rates. In this perspective, investment function is given by:

I K = i 0 + i r (r r) ( 20
)
where r is the worldwide pro…t rate 5 . Equation ( 20) can be rewritten as follows:

I K = (i 0 i r r) + i r r (21)
Actually, only the constant term of investment function is negatively a¤ected by the introduction of foreign investments. As the threshold ! does not depend on this constant term, the main conclusions of our model remain unchanged, which is of course not satisfying. As suggested by [START_REF] Blecker | Distribution, Demand and Growth in Neo-Kaleckian Macromodels[END_REF], the way through which globalisation is more likely to a¤ect national investment is a change in the sensitivity of investment to pro…t rate, i.e. an increase of i r in equation ( 20). Table 2 gives the evolutions of the threshold ! (separating wage and pro…t-led regimes) as i r increases.

Table 2. Value of the threshold ! for di¤erent values of i r .

Eventually, the impact of globalisation can be simulated as a shock to the economy which modi…es both the constant term (which decreases) and parameter i r (which increases) in investment function. This shock thus brings about both a decline in output and a shifting of ! to the left, which means that "after" openness, the economy is pro…t-led for weaker values of the wage-share (this result is in accordance with Bowles and Boyer conclusion). This shifting might also make the economy switch from one regime (wage-led regime) to another (pro…t-led regime) as it is depicted in …gure 7. Indeed, a drop of wage share may now boost national investment (by improving national pro…tability relatively to worldwide pro…tability) and increase output (in spite of consumption reduction). At last, redistributive policy is likely to be more di¢ cult in such a context, especially because of capital incomes ‡ight. Fig. 7. The relation between wage share and rate of capacity utilisation before and after international openness.

A dynamic model

We now introduce dynamic aspects in our model. For that, we propose a very simple wage equation that we combine with our inverted U-shaped curve (corresponding to equilibrium on the goods market). So, the dynamic dimension of the model comes from the endogeneity of the wage share. In our model, we suppose that labour productivity a remains constant over time, so that wage share remains constant if real wage remains itself constant 6 . We simply suppose that when employment level (captured in our model by the rate of capacity utilisation) is high, workers manage to get higher (real) wages w, because their bargaining power is stronger when the economy is closer to full-employment. Thus, we suppose that, beyond a certain value z of the rate of capacity utilisation z, real wage is positively related to z:

w = w for any z < z w = w + z otherwise (22)
Note immediately that these equations can be rewritten as:

! = ! for any z < z ! = ! + z otherwise ( 23
)
with ! = w a and = a . On Figure 8, we accordingly combine our inverted U-shaped curve with our wage-setting curve. On the one hand, output is set on the goods market by aggregate demand, which itself depends on the wage share (through its impact on both investment and consumption). As long as wage share is below ! (but beyond A), there is a virtuous dynamics: wage increases support consumption (and maybe also investment) and eventually output, which in turn brings about wage increases. On the contrary, beyond ! , pro…ts are squeezed so that every wage increase depresses investment more than it boosts consumption. Only a decrease of the wage share could recover investment and output in this area. This wage drop is actually allowed by the recession consecutive to investment decline. So, this dynamics generates cycles (pretty similar to those depicted by the model of [START_REF] Goodwin | A Growth Cycle[END_REF] around one …rst equilibrium. Nevertheless, we see on …gure 8 that this dynamics may also bifurcate to another equilibrium, where wage share and output are both very low. This is the case if the wage share reduction is too important during the recession period (of the cycle). As soon as investment is restored when consumptions drops, cycles are maintained although the model is demand constrained. However, a strong wage austerity may also depress consumption so much that it prevents investment to recover in spite of the increase of pro…t share. Consumption and investment thus fall together. Cycles disappear because neither consumption nor investment can sustain demand and output, which induces a cumulative slump: slowdown exacerbates wage-share fall, whereas the economy is in the wage-led area. Finally, this "cumulative recession" stabilises to a new equilibrium, characterised by high unemployment and weakness of global demand. This is the reason why we call it a "Keynesian equilibrium". Fig. 8. Combining the inverted U-shaped curve with a wage-setting curve.

An interpretation of the French economic dynamic since 1970

Thanks to this model, we propose an interpretation of growing unemployment which characterised the French economy in the 1980s and 1990s. In the 1960s, unemployment remained below 3 %. This situation strengthened the bargaining power of trade unions in a context of labour productivity growth slowdown. This partly explained the takeo¤ of wage-share in the 1970s which squeezed pro…ts and reduced investment (Bruno and Sachs, 1985). At the beginning of the 1980s, the competitive disin ‡ation was run with the purpose to decrease unemployment by promoting exportations through in ‡ation …ght [START_REF] Blanchard | Competitiveness through Disin ‡ation: an Assessment of the French Macroeconomic Strategy[END_REF] and investment through pro…t recovery (and wage austerity). Unfortunately, the rise of pro…t-share in the 1980s came along with a very short decrease of unemployment. Our model proposes an explanation of the lasting and joint increase of unemployment and pro…t-share (which reached historical high levels in the 1990s without sensitive e¤ect on investment) from 1982 to nowadays: the French economy might well be stuck for …fteen year in a "Keynesian equilibrium" because wage-share dropped too much, which has a strong negative e¤ect of demand.

Conclusion

In this article, we enrich the Bhaduri-Marglin model ( 1990) by supposing that saving behaviours (more precisely, average propensity to save income) by agents vary as their income changes. Such a pretty simple hypothesis allows to generate a analytical framework where the nature of the economic regime -wage or pro…t-led, as underlined by Bhaduri and Marglin-depends directly on income distribution, i.e. the level of the wage share (or pro…t share symmetrically): this means that there exists a threshold value of wage (or pro…t) share ! which separates the two distinct regimes. To the left of ! , economy is wage-led, to its right, economy is pro…t-led. Such a result is obtained by just assuming that, for "extreme" income distributions, national saving rate increases a lot. This result has also important implications for economic policy. First, to a same level of unemployment can correspond very contrasted economic policies, depending on whether the economy is wage or pro…t-led. Secondly, economic policy must try to move income distribution closer to ! . We then show that the pro…t-share area is likely to be larger as international openness arises. In the same time, economic policy will be more di¢ cult to lead (greater capital mobility, increasing …scal competition, etc.). At last, we introduce in such a framework a wage formation equation to make this model dynamic. We then show that the model can generate economic cycles, the economy oscillating between wage and pro…t-led regimes: if economy is in its wage-led area, a virtuous cycle can happen: wage increases support consumption and eventually output which in turn brings about wage increase. Unfortunately, wage share will …nally go beyond ! , which will depress investment and cause a recession. This recession dampens wages, which in turn restores output, and so on. However we show that a too large wage decrease can reduce consumption so much that investment will not take o¤ despite pro…t restoration. In that case, investment and consumption decline together as in a typical Keynesian unemployment case. This theoretical result allows to understand the trajectory of the French economy from 1970 to nowadays. Tables Table 1. Value of the threshold ! for di¤erent values of .

Table 2. Value of the threshold ! for di¤erent values of i r .

Fig. 1 .

 1 Fig. 1. Graphical characterisation of wage and pro…t-led regimes.

Fig. 2 .

 2 Fig. 2. The average propensity to save income by agent i in the model.

Fig. 3 .

 3 Fig. 3. The propensity to save wage for di¤erent values of .

Fig. 4 .

 4 Fig. 4. The relation between wage share and rate of capacity utilisation for di¤erent values of .

Fig. 5 .

 5 Fig. 5. The relation between wage share and rate of capacity utilisation in the Bhaduri-Marglin model (case of a wage-led regime).

Fig. 6 .

 6 Fig. 6. The relation between wage share and rate of capacity utilisation for di¤erent values of .

Fig. 9 .

 9 Fig. 9. The relation between wage share and unemployment rate in France from 1970 to 2005.

FiguresFig. 1 .

 1 Figures

Fig. 2 .

 2 Fig. 2. The average propensity to save income by agent i in the model.

Fig. 3 .

 3 Fig. 3. The propensity to save wage for di¤erent values of .

Fig. 4 .

 4 Fig. 4. The relation between wage share and rate of capacity utilisation for di¤erent values of .

Fig. 5 .

 5 Fig. 5. The relation between wage share and rate of capacity utilisation in the Bhaduri-Marglin model (case of a wage-led regime).

Fig. 6 .

 6 Fig. 6. The relation between wage share and rate of capacity utilisation for di¤erent values of .

Fig. 7 .

 7 Fig. 7. The relation between wage share and rate of capacity utilisation before and after international openness.

Fig. 8 .

 8 Fig.8. Combining the inverted U-shaped curve with a wage-setting curve.

Fig. 9 .

 9 Fig. 9. The relation between wage share and unemployment rate in France from 1970 to 2005 (sources: INSEE, National Accounts).

We also suppose, which is a strong hypothesis, that capitalists are not workers, and vice versa.

This result implies that, in our model, a < Y .

It will be quite the contrary (for example, economic policy could thus boost investment either through subsidies or through tax incentive measures) if the economy is pro…t-led. Moreover, note that redistributive …scal policy allows to increase households (workers) incomes without increasing labour costs.

5 Remember that we suppose, for simplicity, that i z = 0

.6 If labour productivity grows at a constant pace, wage share is constant as long as the real wage grows at the same pace as productivity.

Footnotes 1 Note also that, for simplicity and following [START_REF] Taylor | Income Distribution, In ‡ation and Growth[END_REF][START_REF] Taylor | Reconstrcuting Macroeconomics: Structuralist Proposals and Critiques of the Mainstream[END_REF], we use indifferently the terms "exhilarationist regime" and "pro…t-led regime" in this article i.e. an economic regime in which a rise of pro…t-share increases output (precisely the rate of capacity utilisation), even though these terms correspond to di¤erent concepts in Post-Keynesian literature. Likewise, we use indi¤erently the terms "stagnationist regime" and "wage-led regime" i.e. an economic regime in which a rise of wage-share increases output.