¹ See ‘Article on Utilitarianism: Short Version’, § 14–16, Deontology Together with A Table of The Springs of Action and the Article on Utilitarianism (Oxford, 1983 (CW)), pp. 320–8, at 323; ‘Hume's Virtues’, Deontology (CW), pp. 345–63, at 350, where Bentham noted that Hume did not see that ‘pleasure and pain form[ed] the only key for opening the lock’.

² See ‘Hume's Virtues’, p. 350: ‘Hume made a most important distinction between impressions and ideas. I do not know what people did before this distinction. It was a great discovery.’

³ See ‘Hume's Virtues’, p. 350: ‘Hume does not see the connection between passion, and pleasure and pain. . . . Passion is a fictitious entity.’

⁴ See ‘A Dissertation on the Passions’, § I, A Dissertation on the Passions: The Natural History of Religion, ed. T. L. Beauchamp (Oxford, 2007), p. 3: ‘Some objects produce immediately an agreeable sensation, by the original structure of our organs, and are thence denominated good; as others, from their immediate disagreeable sensation, acquire the appellation of evil. . . . Some objects again, by being naturally conformable or contrary to passion, excite an agreeable or painful sensation; and are thence called Good or Evil.’

⁵ See A Treatise of Human Nature (bk. I, pt. I, sect. 2), ed. Norton, D. F. and Norton, M. J. (The Clarendon Edition of the Works of David Hume, vol. 1) (Oxford, 2007), p. 11Google Scholar: ‘The first kind [i.e. the sensations] arises in the soul originally, from unknown causes. . . . An impression first strikes upon the senses, and makes us perceive heat or cold, thirst or hunger, pleasure or pain of some kind or other.’

⁶ Pleasure and pain cannot be only impressions of sensation, when they ‘are not only necessary attendants of beauty and deformity [supposing that they are impressions of reflection], but constitute their very essence’ (A Treatise of Human Nature (bk. I, pt. I, sect. 2), p. 195).

⁷ An Introduction to the Principles of Morals and Legislation (Oxford, 1996 (CW)) (henceforth IPML), p. 11.

⁸ This idea is championed by Philo, in Part X of Dialogues Concerning Natural Religion (Indianapolis, 1986), p. 65: ‘You must allow that if pain be less frequent than pleasure [a position which is extremely doubtful], it is infinitely more violent and durable. One hour of it is often able to outweigh a day, a week, a month of our common insipid enjoyments.’ Maupertuis, in a text quoted by Bentham, Essay de philosophie morale, ch. 2, expresses the same idea (Moreau de Maupertuis, P. L., Oeuvres, 4 vols. (Hildesheim and New York, 1974), vol. 1, pp. 171–252, at 201–4)Google Scholar. Philip Schofield has drawn my attention to a passage in Bentham, ‘Of Sexual Irregularities’, Of Sexual Irregularities, and Other Writings on Sexual Morality, ed. P. Schofield, C. Pease-Watkin and M. Quinn (Oxford, 2014 (CW)), pp. 1–45, at 16–17 (UC lxxiv.106), where he takes an interest in the same psycho-physiological characteristic.

⁹ [Bentham], The Influence of Natural Religion on the Temporal Happiness of Mankind (New York, 2003), p. 35.

¹⁰ Like Hume, Bentham spent some time discussing this idea in Influence of Natural Religion, p. 35.

¹¹ Pathological in Bentham means relating to the science of the pathē, of passions, of passivity towards oneself, which is therefore apparently a science as much of pleasurable passions as of unpleasant ones. However, the centre of gravity of the word leans towards illness and pain: see ‘A Table of the Springs of Action’, Deontology (CW), pp. 79–115, at 87, 89.

¹² ‘Of Sexual Irregularities’, pp. 16–17.

¹³ Bentham began work on the Table a decade before it was published.

¹⁴ ‘A Table of the Springs of Action: Marginals’, in Deontology (CW), pp. 5–73, at 6; see on the same page: ‘Correspondent real entities in which these fictitious entities [i.e. desires and aversions, wants, hopes and fears, interests] have their root: Pleasures and pains’. In his article ‘Bentham's Concept of Pleasure: Its Relation to Fictitious Terms’, Jeremy Bentham: Critical Assessments, ed. B. Parekh, 4 vols., (London and New York, 1993), vol. 2, pp. 214–24, at 216, Goldworth quotes UC xiv.26 in emphasizing the same point. The assertion is repeated in Bentham's Essay on Logic: see The Works of Jeremy Bentham, published under the superintendence of his executor, John Bowring, 11 vols. (Edinburgh, 1843) (henceforth Bowring), vol. 8, pp. 213–93, at 247.

¹⁵ See, for instance, ‘Table of the Springs of Action’, p. 98.

¹⁶ From this point of view, the following is paradigmatic: ‘For exposition of obligation, convenience might recommend the bringing to view its connection with expressions of will and command: necessity requires ditto as to pleasures and pains’ (‘Table of the Springs of Action: Marginals’, p. 7).

¹⁷ ‘Table of the Springs of Action’, p. 98.

¹⁸ ‘Table of the Springs of Action’, p. 98.

¹⁹ See ‘Table of the Springs of Action: Marginals’, p. 10.

²⁰ And, therefore, to focus more on punishments than on rewards.

²¹ After all, didn't Bentham, on the most crucial point of utility and its principle, decide late in life that he wanted radically to change the principle of utility into a principle of happiness? He followed that direction to an extent, but had neither time nor inclination to rewrite all his works in light of this modification.

²² Of Laws in General (London, 1970 (CW)), p. 1. The passage appears in the revised edition, Of the Limits of the Penal Branch of Jurisprudence (Oxford, 2010 (CW)), pp. 24–5.

²³ ‘Of Sexual Irregularities’ (CW), p. 16. The full sentence reads: ‘Instead of the phrase desire of amity at the hands of the Almighty Being, or desire of ingratiating oneself with, or the desire or recommending himself to the favour of the Almighty Being, some persons would naturally enough be disposed to say in one word fear.’

²⁴ See ‘Table of the Springs of Action: Marginals’, p. 42: ‘Utility put aside, all notions are upon a level. None too extravagant or mischievous to be supported, to all alike is the characteristic ipsedixitist formulary applicable: “Law of Nature”, “fitness of things”, “moral sense”, “common sense’’.’

²⁵ ‘Essay on Nomenclature and Classification’, Chrestomathia (Oxford, 1983 (CW)), pp. 139–276, at 268–9n.

²⁶ Thus IPML does not quite adopt the same perspective as Table of the Springs of Action, which itself adopts a different point of view from Influence of Natural Religion. The former adopts a still classical perspective of classification, whereas the second only seems to adopt a classificatory perspective, for the Table is in reality the ultimate scheme that makes it possible to move on to calculation. That is at least what Bentham considered it to be. Description is nothing more than the schematic disposition of psychic material to be mathematically considered. Finally, the criticism of natural religion aims at something else, namely at showing, first, that utilitarian calculations cannot apply to it, and second, that there are more drawbacks than advantages for societies in the phenomenon of natural religion.

²⁷ Goldworth, ‘Bentham's Concept of Pleasure’, p. 216.

²⁸ Taken alone, this last argument is not conclusive. Whereas it might encourage us to take pleasure as a kind of fictitious entity, it can, of course, be applied with equal facility to pain, which, just like pleasure, is incapable, on Bentham's analysis, of definition.

²⁹ Bentham introduced the concept of ‘interesting perceptions’ in IPML (CW), p. 42.

³⁰ ‘A Table of the Springs of Action: Marginals’, p. 11.

³¹ See Bayes, Thomas, ‘An Essay towards solving a Problem in the Doctrine of Chances’, Philosophical Transactions of the Royal Society of London 53 (1763), pp. 370–418CrossRefGoogle Scholar.

³² See A Treatise of Human Nature (bk. I, pt. I, sect. IV), pp. 12–13, where Hume speaks of the ‘gentle force which . . . is the cause why, among other things, languages so nearly correspond to each other’.

³³ See ‘A Table of the Springs of Action’, p. 88: ‘Constructed in different languages, a Table of this sort affords an interesting specimen of their comparative copiousness and expressiveness.’ Maupertuis expresses the same idea in Réflexions philosophiques sur l’origine des langues et la signification des mots (Paris, 1740), § II, pp. 4–5: ‘[P]lusieurs Langues ne paroissent être que des Traductions les unes des autres; les expressions des Idées y sont coupées de la même manière et, dès lors la comparaison de ces Langues entre elles ne peut rien nous apprendre. Mais on trouve des langues, . . . qui semblent avoir été formées sur des plans d’idées si différents des nôtres, qu’on ne peut presque pas traduire dans nos Langues ce qui a été une fois exprimé dans celles-là. Ce serait de la comparaison de ces langues avec les autres qu’un Esprit philosophique pourroit tirer beaucoup d’utilité.’

³⁴ ‘Pathematics’ was the word chosen in De l’Ontologie, ed. P. Schofield, J. P. Cléro and C. Laval (Paris, 1997), pp. 172, 173.

³⁵ Bergson, H., Essai sur les données immédiates de la conscience (An Essay on the Immediate Data of Consciousness), Œuvres (Paris, 1970), pp. 1–157, at 25Google Scholar. He also added, six pages later, that we must be careful not to transfer ‘the quantity of the cause into the quality of the effect. At this very moment, the intensity which was nothing but a certain shade or quality of sensation becomes a quantity or a magnitude.’

³⁶ Bergson, Essai sur les données immédiates de la conscience, p. 108.

³⁷ Bergson, Essai sur les données immédiates de la conscience, pp. 108–9.

³⁸ ‘Codification Proposal, Addressed by Jeremy Bentham to All Nations Professing Liberal Opinions’, ‘Legislator of the World’: Writings on Codification, Law and Education (Oxford, 1998 (CW)), pp. 241–384, at 252–3.

³⁹ Baumgardt, D., Bentham and the Ethics of Today, with Bentham Manuscripts Hitherto Unpublished (Princeton, 1952), pp. 566–7Google Scholar. The manuscripts for the discussion from which Baumgardt quotes, which were written about 1776, are UC xcvi.128–31.

⁴⁰ See Rationale of Judicial Evidence, Specially Applied to English Practice, 5 vols. (London, 1827), vol. 3, p. 279–80 (Bowring, vol. 6, pp. 189–585, and vol. 7, pp. 1–644, at vol. 7, p. 83n.).

⁴¹ There is no direct evidence that Bentham knew Bayes's ‘Essay toward solving a Problem in the Doctrine of Chances’, but there is some indirect evidence. In ‘Draught of a New Plan for the Organisation of the Judicial Establishment in France: Proposed as a Succedaneum to the Draught presented, for the Same Purpose, by the Committee of Constitution, to the National Assembly, December 21st, 1789’, printed in London, 1790, ch. 2, tit. 2, p. 10 (Bowring, vol. 4, pp. 285–406, at 327), Bentham almost certainly alludes to de Condorcet, Nicolas's Essai sur l’application de l’analyse à la probabilité des décisions rendues à la pluralité des voix (Paris, 1785)Google Scholar, which was itself deeply indebted to Bayes's essay and recognized its importance.

⁴² Corrected by mathemes, if I may use the phrase in a Lacanian rather than in a Benthamian way.

⁴³ See ‘An Introductory View of the Rationale of Evidence, for the Use of Non-Lawyers as well as Lawyers’, in Bowring, vol. 6, pp. 1–187, at 7: ‘The adjective branch of law, or law of procedure, and therein the law of evidence, has everywhere for its object, or at least ought to have, the giving effect throughout to the several regulations and arrangements of which the substantive branch or main body of the law is composed.’ Bentham then adds a paragraph that is like the transposition of the two definitions of pleasure: ‘As to the main or substantive branch, it has for its ultimate fruits happiness and unhappiness, in infinitely diversified and ever changing proportions; but, in the meantime, for its immediate fruits, it has those fictitious indeed, but indispensably employed creatures of imagination and language, viz. rights and obligations: rights its sweet fruits, pregnant with whatever is good, whether in the shape of security or pleasure: obligations its bitter fruits, evil in themselves, good in so far as they are the indispensable instruments of all created good, being necessary as well to the creation, as to the preservation, of all law created rights.’ Roughly the same words are used ibid., Bowring, vol. 6, p. 205n., and ‘Constitutional Code’ (bk. i, ch. 5), in Bowring, vol. 9, pp. 1–662, at 25.

⁴⁴ Principles of Judicial Procedure, in: Bowring, vol. 2, pp. 5–188, at 15: ‘A procedure code is an accessory code, which has for its end in view, and occupation, the giving execution and effect to a correspondent principal code. Hence comes a natural supposition; the substantive code should, as mathematicians say, be given, or the adjective can have no meaning; the substantive being throughout a necessary object of reference. To a certain extent and degree, this is correct and undeniable. To a certain extent it does not apply.’

⁴⁵ ‘Fragments on Universal Grammar’, in Bowring, vol. 8, pp. 339–57, at 347–8: ‘An adjective is the name of a quality or relation, accompanied with an intimation of existence of a subject in which it is, to which it belongs, of which it is a or the property. Celer puer, a boy in whom is the quality of celerity. The corresponding abstraction-denoting substantive, is the name of the quality unaccompanied by any such intimation of such substantive existence. Though the name of the abstract fictitious entity, the quality, be prior in the order of tradition, to the adjective name, it was not probably in the order of existence. Bonus existed before bonitas − (as its brevity imports) humanus before humanitas.’

⁴⁶ For a particularly clear statement see ‘Principles of Judicial Procedure’, Bowring, vol. 2, p. 15: ‘The procedure code, in so far as it is clear it ought to be, has for its purpose, and end, and occupation, two things: the exercising, for the avowed purposes mentioned in the substantive code, powers of all sorts over persons and things; and, in the next place, coming at the truth of the case in regard to matters of facts, to wit, such matters of fact as are necessary to give warrant and justification to the exercise of those same powers – say means of execution and means of proof, or, in one word, evidence. Of these two desiderata, the first mentioned is the first in the order of design, and in the order of importance. But in practice, that which is to constitute the warrant, must precede the operation for which it is to afford the warrant.’

⁴⁷ Hume makes use of a double definition of affectivity: as an impression of reflection (Treatise of Human Nature, bk. I, pt. I, sect. II, p. 11) and as an ‘original modification of existence’ (Treatise of Human Nature, bk. II, pt. III, sect. III, p. 266).

⁴⁸ See ‘A Dissertation on the Passions’ (Sec. II, § 9), p. 13n: ‘That property is a species of relation, which produces a connexion between the person and the object is evident: The imagination passes naturally and easily from the consideration of a field to that of the person to whom it belongs.. . . Property therefore is a species of causation.’

⁴⁹ See Hume, ‘Essays Moral, Political, and Literary’, The Philosophical Works, 4 vols. (Aalen, 1992), vols. 3–4. On this point, Hume's Essays seem directly to contradict bk. I of Treatise of Human Nature.

⁵⁰ Foucault, Dits et écrits, 1954–1988, 4 vols. (Paris, 1994), vol. 1, p. 1462.

⁵¹ What I call an inversion problem, for example, is the one that Bayes solved, as opposed to the one that Bernoulli solved. Bayes wondered, if one has data for only a few cases from which to make an induction, how much one could trust that induction. Bernoulli, having as many cases as he wanted, wondered what selection of cases would be enough to achieve certainty and precision in an assumption. It would be a serious mistake to believe that these are the same problem, even though it might seem so, when they are expressed merely verbally, for conditional probabilities must not be dealt with as probabilities applied to large numbers. To solve Bayes's problem, one must use means quite different from those needed to solve Bernoulli's problem. The theory of fictions could study the inversions of the real and the fictitious with the same methodical care as the mathematician's, without remaining at the level of a verbal approach. Another example of inversion problems would be the problems of maxima and minima that are not only the object of the theory of fictions, but form some of its essential patterns.

⁵² Oddly enough, modern economists seem to have heeded Bergson when he wrote, concluding a reflection on utilitarianism: ‘What do we mean by a greater pleasure except a pleasure that is preferred?’ This statement is not far removed from Bentham's position.

⁵³ Hobbes, Of Man (ch. 10), The Collected Works of Thomas Hobbes, ed. W. Molesworth and J. Bohn, 12 vols. (London, 1992; first published, 1839–45), vol. 3, p. 75. After mentioning the little power sciences have upon most men, Hobbes makes an exception for arts, of which mathematics is ‘the true mother’.