¹ We shall not try to put into perspective the various aspects of these effects which can be ascribed to Roscellinus, Pierre Abelard and Duns Scotus.

² In more Ockhamian terminology: "there is no reason to admit the existence of the universal beyond the soul." "Universale est vox" Rosselinus said at an earlier date (quoted by J. Largeault, Enquête sur le nominalisme, Paris-Louvain, Nauwelaerts, 1971, p. 79).

³ One might just as well say that it records the cultural ascendance of individuality.

⁴ It is admissible to see in the nominalism put forward by Ockham and his disciples an ideology corresponding to the period in which capitalism was founded ("primitive accumulation," separation of capital and labour, liberation of capital). But such an interpretation would have to be confirmed by putting the history of capitalism on a parallel with the history of nominalism.

⁵ A whole aspect of the Renaissance (above all its second half) seems to rest on the feeling of a word-kingdom,' just as one talks about the "mineral kingdom" or the "animal kingdom."

⁶ Detached from its context, near (rejection of the entity "relation," I Sent., 30) or far, this second formula is not exempt from being equivocal: does it counsel non-exclusive unification or suppression of the superfluous?

⁷ A. Koyre, La Révolution astronomique, Paris, Hermann, 1961, p. 45.

⁸ We are deliberately omitting the difficult problem of simplicity and its objective criteria.

⁹ This list is not exhaustive. We have omitted, what is more, the numerous and various methodological "applicatians" which, frankly, do not stem from any Ockhamist principle.

¹⁰ Philosophie als Denken der Welt gemäss dem Prinzip des kleinsten Kraftmasses … quoted from 2 ed., Berlin, Guttentag, pp. 3-28, 52f. 65, 67.

¹¹ Mach, it is true, calls into play the "principle of symmetry" according to which "given two absolutely identical bodies … we expect the accelerations which are transmittable between them to be directed along the straight line which joins them, both equal and opposite "(La Mécanique, 1903, trans. E. Bertrand), Paris, Hermann, p. 211.

¹² Op. cit., p. 212.

¹³ Op cit., p. 457.

¹⁴ Benoit Mandelbrot, Sur l'épistémologie du hasard dans les sciences sociales (in Logique et connaissance scientifique, ed. Piaget), Paris, Gallimard, 1967, p. 1128.

¹⁵ A. Koyre, La révolution astronomique, pp. 329-330.

¹⁶ On Maupertuis, see Dugas, Histoire de la mécanique, Neuchâtel, Griffon, 1950, pp. 250 ff. The volume of action is defined by the product of mass, speed and space travelled (mss).

¹⁷ Between two given positions, defined by corresponding complexes of coordinate values, one can say that a system moves in such a way that the integral of Lagrange functions (expressing the action of the system) has the smallest possible value (see Landau-Lifschitz, Physique théorique, I, Mécanique, Moscow, 1960, pp. 8-12).

¹⁸ The authors quoted called the "Maupertuis principle" a reduced form of Hamilton's principle, always applied to a mechanical system but conspicuously overlooking the time factor (op. cit., pp. 196 ff.).

¹⁹ One may well ask about the statute of the ancient principle of continuity: "Natura non fecit saltus," as a famous metaphor of Leibniz runs. Formally speaking it appears to be diametrically opposed to economy: Nature does not fashion the economy of intermediary states, to which, moreover, corresponds the idea of differential equations. But physically speaking continuity may imply a relative economy of energy. In the view of Liebniz, there is not sufficient reason to admit any "leap" in nature; in other words, to admit leaps would lead to a multiplication of adequate reasons.

²⁰ Newton, Mathematical Principles of Natural Philosophy…, trans. A. Motte, ed. Cajori, University of California Press, 1947, p. 398.

²¹ Enquête sur l'entendement humain, trans. A. Leroy, Paris, Aubier, 1947, p. 101.

²² Cf. Kant, Critique de la raison pure, trans. Trémesaygues-Pacaud, Paris, PUF, 1944, p. 458: "But the fact that this harmony is also found in nature is the general supposition of philosophers of the school which recognises that one should not multiply principles when not necessary (…) One can therefore see that the very nature of things offers a substance with a rational unity (…) Although this unity is a simple idea…".

²³ F. Dagognet, recently said: "Nature is an ill-written text which needs re-writing in a rational idiom." Recherches hégéliennes, Bulletin d'information no. 7, University of Poitiers, 1973, p. 17 (summary of statement published from notes).

²⁴ V. Jankélévitch, L'Alternative, Paris, Alcan, 1938, p. 71.

²⁵ De l'angoisse à l'extase (1928) quoted from Les débuts de l'intelligence, Paris, Flammarion, 1935 p. 105 ff.

²⁶ Freud, Deuil et mélancolie, in Métapsychologie, coll. "Idées" Paris, Gallimard, 1969, p. 167.

²⁷ Projet de psychologie scientifique (1895) quoted here from Laplanche-Pontalis, Vocabulaire de la psychanalyse, Paris, PUF, 1967, pp. 339-341.

²⁸ Later Freud issues certain doubts on the definition of pleasure by the reduction of the volume of excitation (see for example Pulsion et destin des pulsions (1915) in Métapsychologie, p. 17) But the economical viewpoint is in no way removed and the economic function of psychism remains guaranteed in any event by the principle of constancy according to which psychism tends to keep the energy of investment constant, if not at a low pitch. We know that Freud did not coin the term Lustprinzip because it can be found in Fechner (1848). Avenarius (op. cit., p. 13) talks of the "reactions of displeasure… due to inappropriate expenditure of energy." ("Unlustreaktionen … bei unzweckmässigen Kraftverwendungen").

²⁹ Husserl, Recherches logiques, I, Prolégomènes à la logique pure, trans. H. Elie, Paris, PUF, 1959, pp. 219-222.

³⁰ See e.g. Logique et équilibre, Etudes d'épistémologie génétique II, Paris, PUF, 1957, especially pp. 27-117.

³¹ Piaget, ibid., pp. 41-42.

³² But we are not trying to be exhaustive. Thus we shall not mention a certain imperfection in the system of the laws of symmetry (cf. in this respect Feynman, La nature des lois physiques, trans. into Fr., Paris, R. Laffont, 1970, pp. 117 ff) nor the mathematical fact of the indissociability of minimum and maximum.

³³ Piaget, op. cit., pp. 36-37, insists on the radical difference between the state of rest, which closed systems tend towards, and psychic equilibrium: "The best balanaced states (…) correspond to the maximum of activity and openness in exchanges." This proposition, which smacks a little of Spinoza (see Ethique, pt. V prop. XL) seems at first sight to contradict the definition of equilibrium by least action. The problem disappears if one realises that the states of equilibrium, e.g. those consisting of logical systems, presuppose consid erable intellectual activity and guarantee a "maximum of associations," although the reasoning or the calculations which they admit are made econom ically, by a "minimum of changes" (op. cit., pp. 42-3). The question is one of knowing if, and to what extent, the known world should be assimi lated to a closed system (cf. E. Hutten, Les concepts de la physique, Paris, Dunod, 1969, p. 126).

³⁴ André Lwoff, L'ordre biologique, Paris, R. Laffont, 1969, p. 173.

³⁵ Freud, Au-delà du principe de plaisir, (1920) in Essais de Psychanalyse, trans. S. Jankélévitch, Paris, Payot, new ed. 1972, p. 80. (In agreement with the terminology recommended by Laplanche and Pontalis, op cit., we have substi tuted in the translation used "instincts" by "pulsions." We have also underlined the term "resolution").

³⁶ Le monde comme volonté et comme représentation, Supplement to book IV, trans. Burdeau, ed. Roos, Paris, PUF, 1966, p. 1211.

³⁷ Freud, Abrégé de psychanalyse, (1938) trans. A. Berman, Paris, PUF, 1949, p. 8.

³⁸ Piaget, Logique et équilibre, pp. 42-43.

³⁹ Although we shall attempt to do so here, it seems possible to us to find this dual polarity in the opposition—which is considerable nowadays—of philosophies of difference to philosophies of identity.