1 John Locke, An Essay concerning Human Understanding, Peter Nidditch, ed. (Oxford: Oxford University Press 1975), IV.iii.6,540-1.

2 In the recent literature Margaret Wilson has advanced a version of the metaphysical interpretation of superaddition, while the epistemological interpretation has been defended by Michael Ayers. See Margaret Wilson, ‘Superadded Properties: The Limits of Mechanism in Locke/ American Philosophical Quarterly 16 (1979) 143-50; Michael Ayers, ‘Mechanism, Superaddition, and the Proof of God's Existence in Locke's Essay,’ Philosophical Review 90 (1981) 210-51; Margaret Wilson, ‘Discussion: Superadded Properties: A Reply to M.R. Ayers,’ The Philosophical Review 91 (1982) 247-52.

3 Pierre Bayle, Dictionnaire Historique et critique. 5th edition. 4 vols. (Amsterdam, Leiden, La Haye, Utrecht, 1740). Where available I have used the translation in Historical and Critical Dictionary Selections, Richard Popkin, trans. (Indianapolis: Hackett Publishing, 1991). Hereafter P; thus, Dictionnaire, art. Jupiter, rem. G, 904; P114-15. References to all other works by Bayle are from Oeuvres diverses deM. Pierre Bayle, 4 vols., 1727-1731. Reprint Hildesheim 1966,5 vols., 1964-1968. Hereafter OD. Translations from articles not included in Popkin and from works other than the Dictionnaire are my own.

4 Bayle, Dictionnaire, art. Jupiter, rem. G, 904; P 115 (slightly emended).

5 Bayle, Dictionnaire, art. Dicearque, rem. M, 288; P 72.

6 John Locke, The Works of John Locke, 9 vols. (London, 1824), 3:465-6

7 Bayle, Dictionnaire, art. Dicearque, rem. M, 288; P 73.

8 It is perhaps worth observing that Bayle conceived of the Dictionary as a work of high grade popularization; one of his express aims in composing the work was to make available abstruse metaphysical and theological disputes to a well-educated, though philosophically unsophisticated audience. For this reason it is often helpful to attend to the more rigorous formulations of arguments to be found in his lecture notes and early technical writings as a way of illuminating the often simplified presentations of those same arguments in the Dictionary.

9 ‘Intelligunt per potentiam obedientialem, vim quandam recipiendi a Deo extra ordinem operante talem influxum, per quern deinde producantur effectus supernaturales a creaturis, ut si verbi gratia Deus instrueret lapidem virtute creandi aliquid, et ratiocinandi’ (Bayle, OD IV, 470).

10 ‘…quod non inde sequantur duo contradictoria, Deo verb tribuenda sit potentia faciendi quaecumque non implicant contradictionem…’ (Bayle, OD IV, 470).

11 ‘…quando res aliqua dicitur fieri naturaliter, hoc non significat fieri … juxta virtutem quandam, quae sit in rebus absolute consideratis, prae omni alia facilitate’ (Bayle, OD IV, 472).

12 ‘…illam rem fieri, secundum certas leges, quas Deus summa sua libertate, inter multas alias non minus commodas, nee minus aptitudini creaturarum congruas, elegit: unde sequitur, quod si Deus spretis illis legibus, alias sequatur nonnumquam, aeque agit secundum aptitudinem creaturae, ac in aliis casibus consuetis’ (Bayle, OD IV, 472).

13 Tous les Philosophes Chretiens conviennent, qu'il n'y a point de miracles par raport aux loix eternelles, mais seulement par raport aux loix arbitraries, qu'il a plu a Dieu d'etablir dans la Nature…. [S]i une loi emane de la necessite des choses, [et] si en consequence de cela elle est immuable, n'y attendez point d'exception en aucun cas, c'est une affaire impossible. Or entre les loix, ou les veritez eternelles et immuables, il n'y en a point de plus certaine que celle-ci, que rien n'arrive contre 1'essence des choses’ (Bayle, OD III, 545a).

14 Bayle, Dictionnaire, art. Dicearque, rem. C, 286; P 67. Bayle's early Latin work, the Dissertatio, is a sustained defense of the Cartesian account of matter as res extensia against the objections of the pseudonymous Louis de La Ville (Bayle, ODIV, 109-32).

15 ‘…nemo distincte concipit, corpora aliorum effectuum esse capacia, quam impulsonis, el eorum quae impulsionem sequuntur…’ (Bayle, OD IV, 471).

16 Bayle, Dictionnaire, art. Simonides, rem. F, 210; P 277. Similarly, Bayle observes that in order for a god or demiurge to forge a world out of an uncreated, chaotic matter, it ‘would be necessary for him to produce motion in it; and for that would it not be necessary for him to touch it and push it? ['Ne faudra-t-il pas qu'il y produise le mouvement; el pour cela ne faudra-t-il pas qu'il la louche, el qu'il la pousseT (Bayle, Dictionnaire, art. Epicure, rem. S, 373)]

17 It might be objected that even if we accept Bayle's argument, there remains an indispensable role for God in that only He can establish the laws of nature. But, according to Bayle, a materialistic atheist could simply deny that the arbitrary laws of nature find their origin in divine institution, maintaining instead that they are brute facts that admit of no further explanation. Thus, Bayle argues that for the ancient atomists, who hold that matter is eternal and uncreated, no rational explanation of the physical laws of nature that govern the interactions of atoms is possible; their obtaining can only be ascribed to the inexplicable ‘nature of things': Do not ask why in certain situations the effect of the reaction [produced by the collision of atoms] is this rather than that, because the properties of a thing admit of explanation only when it was freely created by a cause that had its reasons and its motives for producing it ['Ne demandez pas pourquoi en certaines rencontres Vejjet de la reaction est plutot ceci que cela; car on ne peut donner raison des proprietez, d'une chose, que lors qu'elle a etefaite librement par une cause qui a eu ses raisons, et ses motifs en la produisant’ (Bayle, Dictionnaire, art. Democrite, rem. R, 275).]. Elsewhere Bayle makes a similar point: ‘when an uncreated thing is such and such, it cannot be asked why it is that way. That is its nature. One must necessarily stop there’ (Bayle, Dictionnaire, art. Pauliciens, rem. H, 631; P 187). Thus Bayle seems prepared to countenance the possibility of brute facts that admit of no further rational explanation.

18 Margaret Wilson, ‘Discussion,’ 251

19 Bayle, Dictionnaire, art. Dicearque, rem. M, 288; P 73.

20 Immanuel Kant, Critique of Pure Reason, Norman Kemp Smith, trans. (New York: St. Martin's Press 1965), A351

21 In the article ‘Dicearque’ Bayle actually cites against Locke a version of the argument by the Abbe de Daingeau, which Bayle had summarized in the August, 1684 edition of the Nouvelles de la Republique des Lettres (OD IV, 110-11). However, I believe that Bayle's own formulation of the argument is philosophically superior, and it is for this reason that I have chosen to treat it here.

22 Bayle, Dictionnaire, art. Leucippe, rem. E, 101; P 130

23 Ibid.

24 See my ‘Bayle's Defense of Mind-Body Dualism,’ Aufklamng 16 (2004) 191-211. For an alternative account of Bayle's argument, see Jean-Pierre Schachter, ‘Pierre Bayle, Matter, and the Unity of Consciousness,’ Canadian Journal of Philosophy 32 (2002) 241-65.

25 ‘…si setnel supponas substantiam corpoream et spiritualem perfecti similes in carentia extensionis, nulla potest concipi ratio quapropter substantia spiritualis sit potiiis essentialiter intelligens quam substantia materialis’ (OD IV, 111).

26 ‘…evidens est si res volens sit extensa, actum volendi coextendi ipsi sive reperiri in qualibet illius parte, quaemadmodum motus coextenditur mobili, sive reperitur in qualibet parte mobilis; ergo sicut in lapide projecto nihil est quod…vere dicere posset, Ego habeo totum motum lapidi impressum: ita nihil esset in anima extensa, si vellet aliquid, quod vere dicere posset, Ego habeo integrum actum volendi’ (Bayle, OD IV, 142).

27 Gianluca Mori argues that Bayle's various criticisms of Lockean mind-body superaddition in the Dictionary are suspect in that they serve to conceal a discreet but recurring exploration of the possibility of a materialist theory of mind. See Bayle philosophe (Paris: Honore Champion 1999), 36-8; 70-4. Mori's principal evidence with regard to Bayle's refutation of Locke is an important passage from the Objections to Poiret (1679), in which Bayle openly considers the very possibility of thinking matter that his later discussions are intended to rule out. In response to Poiref s arguments on behalf of Cartesian mind-body dualism Bayle asks ‘whether God can bring it about by his omnipotent and infinite power that a body might become conscious of its own existence or of any other thing? [Quaero, num Deus virtute sua infinita et omnipotenti efficere valeat ut corpus existentiae suae, alteriusve cuiusdam rei, fiat sibi conscium?’ (ODIV, 150b)] In favor of this possibility Bayle goes on to offer the same consideration that he ascribes to Locke and the Scholastics: ‘since everything that does not involve a contradiction is possible, I ask what contradiction there would be in bodies being rendered actually thinking’ (ibid.). To be sure this passage clearly indicates that early in his philosophical career Bayle was searching for an argument that would decisively rule out the possibility of thinking matter. However, it is important to note that unlike a number of other arguments formulated in the Objections, Bayle never raises this possibility in subsequent works. If my analysis of the Achilles is correct, this is because Bayle became convinced that that argument establishes precisely the contradiction in the thinking matter hypothesis that Bayle himself had previously sought from Poiret. Further, although Bayle seems to have been aware of the Achilles from early on, the particularly forceful presentation of the argument by the Abbe de Dangeau in his Quatre dialogues (1684) seems to have been instrumental in impressing upon Bayle the full potential of the argument. Indeed, in his review of Dangeau's book in the August 1684 edition of the Nouvelles de la Republique des Lettres, Bayle goes so far as to claim that Daigneau's version of the argument ‘is a demonstration as secure as that of Geometry’ (OD I,110b). For a fuller discussion of Bayle's rejection of materialism, see my ‘Bayle's Defense of Mind-Body Dualism.'

28 That the distinctness of mind and body can, in Bayle's view, be established on the analysis of matter as res extensa can also be seen in Bayle's diagnosis of the Aristotelians’ inability to secure the immateriality of the soul: ‘Aristotle's hypotheses on the mortality and materiality of animal souls, and the real distinction between body and extension, enervate all the natural arguments for the spirituality of our soul […les Hypotheses d'Aristote sur la mortality, et la materiality de l'ame des betes, et sur la distinction reelle entre le corps et l'etendue, enervent toutes les raisons naturelles de la spiritualite de notre ame (Bayle, Dictionnaire, art. Charron, rem. O, 147; emphasis added).’ In a footnote to this passage Bayle specifies that the ‘real distinction between body and extension’ defended by the Scholastics amounts to the claim that ‘quantity is distinct from matter, as accident is distinct from substance.'

29 Bayle, Dictionnaire, art. Jupiter, rem. G, 904; P 114

30 Bayle had no working knowledge of English, a fact he lamented on several occasions. What direct acquaintance he had with Locke's philosophical works was acquired from French and Latin translations. An extract of the Essay had appeared in French translation as early as 1688 in Jean LeClerc's Bibliotheque Universelle, although Bayle shows no signs of familiarity with the work at this early date. However, Bayle followed closely the debate between Locke and Stillingfleet through accounts that appeared in the Histoire des ouvrages des savans in 1697 and 1698, as well as two articles in the Nouvelles de la Republique des Lettres in 1699. Later, Pierre Coste, Locke's translator and a close friend of Bayle, sent the latter a copy of his French translation of the Essay, which first appeared in 1700. We also know that Bayle read Book I of the Essay as part of his preparations for writing the Continuation des Pensees Diverses. For a complete account of Bayle's familiarity with Locke's writings, and of the personal relations between the two, see P.J.S. Whitmore, ‘Bayle's Criticism of Locke,’ in Pierre Bayle, le philosophe de Rotterdam, Paul Dibon, ed. (Amsterdam: Elsevier Publishing 1959) 81-96.

31 Although Bayle cites no specific texts in support of his reading, one likely source is Locke's discussion of our idea of matter qua matter in Book II, Chapter XXIII ‘Of Our Ideas of Substances.’ There Locke ascribes to matter the same qualities mentioned by Bayle, observing that, ‘Our Idea of Body, as I think, is an extended solid Substance, capable of communicating Motion by impulse…’ (Essay Il.xxiii, 22). Locke goes on to suggest that none of these constitutes the real essence of matter, in so far as none of them is explanatorily basic. He summarizes his position by emphasizing our complete ignorance of the real essence of matter (and mind) and by characterizing extension and mobility — precisely as Bayle suggests — as mere properties of matter: ‘The substance of Spirit is unknown to us; and so is the substance of Body, equally unknown to us: Two primary Qualities, or Properties of Body, viz. solid coherent parts, and impulse, we have distinct clear Ideas of …’ (Essay II.xxiii.30)’ Some indirect evidence that Bayle may have been aware of this passage is that in a letter of 1703, Bayle indicates that Coste had cited two passages from Locke's Essay and solicited Bayle's opinion of them. Although Coste's letter is lost, we know from Bayle's response that the second passage concerned Locke's account of substance. See Bayle to Coste, July 20,1703 (OD IV, 831b).

32 ‘[Locke] ne croioit pas que nous conussions la nature des substances. II avoiioit que 1 ‘etendue impenetrable, la divisibilite, la mobilite etoient des proprietez, de la matiere, ou de la substance corporelle, mais non pas 1'essence ou Vattribut constitutif de la substance de la matiere. II croioit done que ces proprietez-la subsistoient dans un sujet que nous ne connoissons pas’ (Bayle, OD III, 941b).

33 ‘Dieu doit etre une nature intelligente: tout ce qui est compose de parties est incapable d'intelligence: tout ce qui est materiel est compose de parties: il faut done que Dieu soit immaterial’ (Bayle, OD III, 940a).

34 Bayle discusses these difficulties at much greater length in Dictionnaire, art. Rorarius.

35 Gianni Paganini argues that this latter discussion influenced Hume's discussion of mind-body dualism in the Treatise. See Gianni Paganini, ‘Hume et Bayle: conjunction locale et immaterialite de l'ame,’ in De Vhumanisme aux Lumieres. Bayle et le protestantisme. Melanges en Vhonneur d'Elisabeth Labrousse, Magadelaine, Pitassi, and McKenna, eds. (Paris: The Voltaire Foundation 1996) 701-13.

36 ‘Nos qui nullum discrimen agnoscimus inter attributum necessario conjunctum, et attributum essentiale, dicimus proprium quarto modo esse attributum essentiale et identificatum realiter cum differentia’ (Bayle, ODIV, 224). Interestingly, Bayle illustrates this claim with the example of divisibility with respect to extension, arguing that divisibility, which is a proprium quarto modo of matter does not differ from extension, and is therefore really identical with the essence of material substance — that is, with extension itself.

37 Bayle, OD III, 941-2

38 Thomas Lennon, ‘Bayle, Locke and the Metaphysics of Toleration’ in Oxford Studies in the History of Philosophy, vol. 2: Studies in Seventeenth-Century European Philosophy, M.A. Stewart, ed. (Oxford: Clarendon Press 1997), 182-3.

39 Here I must disagree with Thomas Lennon who reads Bayle as ascribing to Locke a bare substratum view of substance. In general, Bayle's metaphysical arguments always presuppose the Cartesian ontology of substance according to which a substance is identical with its primary attribute. Indeed, Bayle seems to treat this view as a philosophical commonplace. Thus, Bayle observes that Spinoza ‘admits, along with all other philosophers, that the attribute of a substance does not differ actually from that substance’ (Bayle, Dictionnaire, art. Spinoza, rem. N, 259; P 302-3). However, on Bayle's view the question of whether Locke holds a bare substratum view of substance in general, or instead takes it to be a natured particular is largely irrelevant. For once one denies that extension is the essence of matter, it must be an accident. Thus whatever the nature of material substance, be it bare particular or natured particular, it is essentially unextended. Hence there is no longer any conceptual impossibility in claiming that matter is capable of thinking.

40 ‘exigentia extensionis affixa substantiae in communi non praebet ullam ideam distinctam, sed conceptum vagum, confusum et manifeste falsum, nisi redigas…exigentiam ad meram potentiam passivam, quae cum nihil distinctius significet quam non repugnantia omni enti possibili conveniens, inepta est prorsus ad constituendam differentiam specificam materiae’ (Bayle, OD IV, 116).

41 Bayle had offered a similar line of reasoning in the Dictionary: ‘…If it [an alleged third kind of substance] is not extended, I would like to know on what basis it is distinguished from mind; for it is like mind in being an unextended substance, and we cannot comprehend how this classification can be divided into two kinds, since the specific attribute that may be given to one would never be incompatible with the other. If God can join thought to one unextended being, he could also join it with another unextended being, there being nothing but extension that seems to us to make matter incapable of thought’ (Bayle, Dictionnaire, art. Rorarius, rem. G, 82; P 233; slightly emended)

42 OD IV, 942a

43 Thomas Lennon, ‘Mechanism as a Silly Mouse: Bayle's Defense of Occasionalism against the Preestablished Harmony/ in Causation in Early Modern Philosophy, Steven Nadler, ed. (University Park, PA: Pennsylvania State University Press 1993), 179.

44 ‘Combien seroit-il plus avantageux a la Religion de s ‘en tenir au principe des Cartesiens que l'etendue, et la matiere ne sont qu'une seule et meme substance*.’ (Bayle, OD III, 942b)

45 ‘[beaucoup d’] attention pour trouver l'attribut de corps dans l'idee de l'etendue; il faut pour cela livrer combat… aux prejugez populaires touchant le vuide….A cela se joignent quelques raisons de mecanique, qui font trouver a de grands esprits, que s'il n'y avoit point de vuide, il n'y auroit point de movement…. C'est ainsi que la revelation naturelle sur Yidentite du corps, et de l'etendue, s'est obscurcie’ (Bayle, OD III, 545a). In the article ‘Zeno of Elea’ Bayle reports having heard from a mathematician familiar with Newton's work that ‘the falsity and impossibility of this proposition [that motion is possible in a plenum] had not only been proved, it has been mathematically demonstrated.’ He goes on to argue that modern mathematicians thus stand in opposition to our clearest and most distinct idea, that of extension (Bayle, Dictionnaire, art. Zeno of Elea, rem. I, 545; P 379). Cf. Bayle, Dictionnaire, art. Leucippe, rem. G.