HUME'S REPLY TO BAYLEAN SCEPTICISM

HUME’S REPLY TO BAYLEAN SCEPTICISM TODD RYAN Trinity College, Hartford Commentators have long been aware of the pervasive influence of Pierre Bayle on Hume’s philosophical thought. As early as 1941 Kemp Smith identified four main areas in which Hume’s Treatise of Human Nature bears the impress of his French predecessor. Among these were the theory of space and time, the nature of animal souls and Spinoza’s substance monism. Norman Kemp Smith, The Philosophy of David Hume (London: MacMillan, 1941), 325-338. Each of these has received some measure of critical attention in the intervening years. However, with regard to the fourth—scepticism—it is fair to say that Richard Popkin’s observation that there has been as yet “fairly little work done on assessing the actual amount of influence, and the relationship between these two major sceptics” continues to hold true. Richard Popkin, “Bayle and Hume” in Richard A. Watson and James E. Force, eds., The High Road to Pyrrhonism, San Diego: Austin Hill Press, 1980, 149. While acknowledging certain differences in methodology and temperament, Popkin himself saw Hume as in essential agreement with Bayle with regard to both the scope of sceptical doubt in general and the force of Bayle’s sceptical arguments in particular. According to Popkin, Hume “saw that the sceptical arguments that he and Bayle had set forth ‘admit of no answer and produce no conviction’…” Ibid., 155. In this paper I wish to challenge that assessment by showing that despite Hume’s admonition that “if we are philosophers, it ought only to be upon sceptical principles (T 1.4.7.11)”, Hume was not a sceptic in the Baylean mold, nor did he consider as answerable those sceptical arguments most characteristic of Bayle. David Hume, A Treatise of Human Nature, eds. David Fate Norton and Mary Norton (Oxford: Clarendon Presss, 2007), cited by (T book.part.section.paragraph). Appreciation of this point will help shed light on the character and limits of Hume’s own brand of scepticism. Of course, I cannot offer a definitive account of Humean scepticism within the scope of this paper. Instead, I shall pursue the more limited aim of establishing what kind of sceptic Hume was not. More specifically, I shall argue that Hume rejects the sceptical position to be found in the Dictionary as well as the more nuanced view Bayle articulates in his final works. 1. BAYLE AND SCEPTICISM In remark B of the article “Pyrrhon” Bayle offers what purports to be an account of a conversation between two abbés, one of whom, commonly referred to as the “abbé pyrrohnien,” argues that by virtue of his commitment to Christian dogma, the orthodox believer is more vulnerable to Pyrrhonian attack than were ancient dogmatists. According to the abbé pyrrhonien a satisfactory response to scepticism would require that one be in possession of a sure criterion of truth. To this he adds that the most plausible—perhaps the sole—candidate for such a criterion is évidence, roughly, self-evidence. The abbé proceeds to argue that a number of évident principles are logically inconsistent with, or even flatly contradict, the truths of Revelation, and that therefore the orthodox Christian must hold that some self-evident propositions are false. The abbé pyrrhonien then offers a long list of évident principles of logic, metaphysics and morality, each of which is shown to be false by the light of Revelation. Thus, for example, the logical principle that two things that do not differ from a third do not differ from one another is contradicted by the doctrine of the Trinity, whose three distinct persons are held to be one and the same God. Similarly, the doctrine of original sin contradicts the self-evident moral principle that it is unjust to hold a person morally responsible for a crime in which he had no part. The moral Bayle ostensibly draws from the discussion is that it is wrong “to waste time disputing with the Pyrrhonists or to imagine that their sophisms can be easily eluded by the mere force of reason; that it was necessary above all to make them feel the infirmity of reason so that this feeling might lead them to have recourse to a better guide, which is faith.” Pierre Bayle, Dictionnaire historique et critique, 4 vols. (Amsterdam, Leiden, The Hague and Utrecht, 1740) [= DHC] art. “Pyrrhon”, rem. B, 733b. Translations from the Dictionnaire are from Richard Popkin, Historical and Critical Dictionary (Indianapolis: Hackett Publishing, 1991) [=P]. Hence, P, 204.   However, the dogmas of revealed religion are not the only source of difficulty for the first truths of philosophy. On the contrary, Bayle insists that irresolvable conflicts among self-evident principles can be found even within the domain of the strictly philosophical. Doubtless the most familiar of these alleged conflicts concerns the composition of extension. I shall return to this case presently. However, the difficulty surrounding the continuum is by no means unique. Among the many instances of irreconcilable conflicts adduced by Bayle, of particular interest is the difficulty concerning the nature of mind or thinking substance. In a discussion in the Réponses aux questions d’un Provincial in which he emphasizes the difficulty of achieving knowledge of the nature of God by sole means of unaided reason, Bayle advances a version of the argument that Kant would later dub the “Achilles of all dialectical inferences”. At its heart, the Achilles is an attempt to secure the immateriality of the mind on the grounds that material substance is by its very nature composite and therefore lacks the essential unity that is an indispensable condition of coherent thought. Bayle offers an extended version of the Achilles argument in rem. C of article “Dicéarque”. For a discussion of Bayle’s version of the Achilles, see my Pierre Bayle’s Cartesian Metaphysics (New York: Routledge, 2009), Chapter 2. Earlier, in the Nouvelles de la République des Lettres, Bayle had gone so far as to declare that the version of the Achilles formulated by the Abbé Daigneau amounted to “as sure a demonstration as those of geometry." Pierre Bayle, Œuvres diverses de Mr. Pierre Bayle, 4 vols., LaHaye 1727-1731, Reprint Hildesheim 1966, 5 vols., 1964-1968 [= OD], vol. I, 110b. The complete quotation runs as follows: “It can be said without hyperbole that this is as sure a demonstration as those of geometry, and if everyone does not see the self-evidence, it is because they are either unable or unwilling to rise above the confused notions of their plodding [grossière] imaginations." However, despite what he takes to be the mathematical certainty of the argument itself, Bayle goes on to raise a series of difficulties for its conclusion, namely that the mind is an immaterial, and therefore unextended, substance. Chief among these is the implication that mental substance cannot be spatially located. Bayle goes on to develop a second difficulty for the conception of thinking substance as an immaterial, non-spatial entity. According to Bayle, such a view renders inconceivable the possibility of causal interaction between mind and body. For according to Bayle, only extended objects are capable of occupying a place, from which it follows that immaterial substances of the kind established by the Achilles would be quite literally nowhere. As Bayle observes, proponents of Cartesian substance dualism must hold that “created spirits are nowhere and that it is the greatest of all absurdities to suppose that our soul is locally united with our body, or that it exists in our body." “les esprits créés ne sont nulle part, et que c’est la plus grande de toutes les chimères que de suposer que notre âme soit unie localement avec notre corps, ou qu’elle existe dans notre corps (OD III, 941a).” Thus, the true nature of the soul represents an antinomy for human reason, since the immateriality and simplicity required for thought undermine our clear and distinct notion that everything that exists, exists in a determinate location. As Bayle puts the point, “into what confusion are we not thrown, if we say that there is no local connection between souls and bodies? Is evidence, or even some minimally distinct notion, to be found in the discourse of one who speaks in this manner?” “dans quel embarras ne se précipite-t-on point si l’on dit qu’il n’y a nulle liaison locale entre les âmes et les corps? L’évidence, ou pour le moins quelque notion un peu distincte, accompagne-t-elle le discours de ceux qui parlent ainsi? (OD III, 940b)” Bayle sometimes suggests that the difficulty posed by immaterial, unextended substance is that we cannot form an adequate idea of a being that is incapable of spatial location. Such a being, he alleges, “n’a nulle convenance avec nos manières de penser: il met notre esprit à la gêne: une substance qu’on ne peut placer dans aucun lieu, quelle prise peut-elle donner à nos conceptions? " (OD III, 941b). However, perhaps the most compelling case of conflict between the évidents principles of reason—and the one upon which Bayle most insists—concerns the problem of the continuum. In the article “Zénon d’Elée” Bayle argues that there are only three possible positions concerning the composition of extension. Either it is composed of mathematical points, or it is composed of physical points (atoms), or it is infinitely divisible. However, each of these alternatives can be shown impossible. The arguments Bayle deploys against each are familiar, and we need not enter into the details here. Briefly, extension cannot be composed of mathematical points, because by definition such points have no magnitude, and not even an infinite collection of entities of zero magnitude can constitute an extended being. Atoms, or physical points, cannot be the ultimate constituents of extension, because they are impossible objects in so far as they are said to be extended, yet indivisible. For, according to Bayle, everything that is extended is composed of really distinct parts into which it can be separated, if not physically, then at least conceptually. Therefore, the very characterization of atoms as extended, indivisible beings is contradictory. Finally, Bayle adduces a number of arguments against the infinite divisibility of extension. To take just one example, if extension is infinitely divisible, it must be composed of an infinite collection of really distinct parts. However, an infinite number of really distinct parts, each occupying a distinct spatial location cannot be fitted into any finite volume. Consequently, an infinitely divisible substance that is nevertheless finite in extent is likewise impossible. Although Bayle’s announced conclusion is that the existence of extension is impossible, he sometimes suggests that what these arguments show is rather that extension cannot exist independently of the mind, or as he himself puts the point, that “this extension exists only mentally [mentalement].” DHC, “Zenon d’Elée", rem. G, 540b ; P 363. Unfortunately, Bayle does not fully explain this ambiguous and rather puzzling claim. What exactly does it mean to say that extension exists “mentally”? On at least one occasion the context suggests that Bayle is speaking of visual perceptions—that is, the visual extension of phenomenal space. Thus, he observes The human mind is a certain terrain [fonds] where a hundred thousand objects of different color, different shape, and different location are brought together; for we can see at once from a hilltop a vast plain dotted with houses, trees, flocks, and the like. But it is far from being the case that all these things are of such a nature as to be able to be disposed in this plain. Not even two of them could find room there. Each requires an infinite space, since it contains an infinity of extended bodies. DHC, “Zenon d’Elée”, rem. G, 540b; P 363. Bayle’s insistence on the impossibility of locating the objects of visual perception in a finite region of physical space suggests that the claim that extension can exist “only mentally” is best understood to mean that considered as a sensible quality extension is essentially perception-dependent. On other occasions, however, Bayle’s remarks suggest a rather different reading. In the article “Zénon, Philosophe Épicurien” Bayle returns to the impossible existence of extended objects. Here he draws attention not to visual percepts, but to our concept of extension. Bayle acknowledges that “of all human knowledge, mathematics is the most evident and certain” DHC, “Zenon, philosophe Epicurien”, rem. D, 547b; P 389. owing to the concept of extension, which numbers among our clearest and most distinct ideas. Cf. “L’esprit de l’homme n’a point d’idées plus nettes ni plus distinctes que celles de la nature et des attributs de l’étendue. C’est là le fondement des mathématiques” (DHC, “Leucippe” rem. G, 102-103). However, he goes on to argue that despite the self-evidence of mathematics, there is an irreparable and most enormous difficulty with mathematical objects—they are chimeras that cannot exist. Mathematical points, and therefore lines and geometrical surfaces, globes, and axes are fictions that can never have any existence. DHC, “Zenon, philosophe Epicurien”, rem. D, 547b; P 390. We need not rehearse Bayle’s argument for the impossibility of concrete geometrical objects in detail. The crucial point for our purposes is that according to this alternative formulation, to say that extension can exist only mentally is to say that although we have a perfectly adequate concept of extension qua object of geometry, nevertheless that concept is of such a nature that it cannot be instantiated in the physical world. In his final works, the Réponses aux questions d’un Provincial and the posthumous Entretiens de Maxime et de Thémiste, Bayle offers a definitive statement of his position with regard to scepticism and reason. Bayle had been attacked by Jean Le Clerc and Isaac Jaquelot, both of whom portrayed Bayle as arguing that God’s actions violate our notions of goodness and holiness and that therefore God can be neither good nor holy. Le Clerc dismisses the fideistic dénouement that Bayle habitually appends to his sceptical discussions, arguing that on Bayle’s view there is no rational justification for belief in the existence of a supremely good being. In response, Bayle denies that his fideism removes all rational grounds for religious belief. He portrays the epistemic position of the orthodox believer as follows: in light of Revelation, the Christian is faced with a conflict between two évidents principles. On the one hand, we know that God is supremely perfect, from which it follows that whatever God does is rightly done. Furthermore, because a supremely perfect being can neither deceive nor be deceived, his word, as contained in Scripture, must be accepted as true. On the other hand, reason is in possession of a host of évidents moral principles which we are unable to reconcile with God’s actions. Consequently, we cannot understand how God can be either good or holy. As a result, the orthodox Christian is in an epistemic position similar to that in which we find ourselves when confronted with a paradox. That is, he has a pair of apparently impeccable arguments for logically inconsistent conclusions. According to Bayle, the way out of this dilemma is to reject those moral principles that would lead us to condemn God’s actions, despite the self-evidence of the principles themselves. However, Bayle insists that to do so does not constitute a complete abandonment of reason, or even of self-evidence as a criterion of truth. This is for two reasons. First, the Christian believer need not reject all self-evident principles as false, but only those that conflict with the truths of Revelation. Moreover, even these problematic moral principles are not to be rejected wholesale and in every context, but only in the specific case in which we are tempted to use them to evaluate the rightness of God’s actions. In other, non-paradoxical contexts (for example, in assessing the morality of human actions), the principles retain full validity. Second, Bayle insists that this partial abandonment of certain évidents principles is not done blindly or arbitrarily, but rather is in accordance with reason itself. Speaking of the choice to accept Revelation at the expense of the evident principles of morality, Bayle affirms that nothing would so conform with reason than such a preference, since it would be based on a metaphysical axiom as evident as the proposition, the whole is greater than its part. “rien ne sera plus conforme à la raison qu’une telle préférence, puisqu’elle sera fondée sur un axiome de métaphysique aussi évident que cette proposition: le tout est plus grand que sa partie (OD III, 767a).” According to Bayle, the rational preference of Revelation to self-evident moral principles rests on what we might call the Principle of Divine Veracity—the self-evident truth that a supremely perfect being can neither deceive nor be deceived, which is “the most evident notion of the human mind”. OD III, 770a. Underlying this account of the relation of faith and reason is the claim that while both the Principle of Divine Veracity and the first truths of morality are self-evident, they are not equally so. The former is more évident, and therefore more certain than the latter. It is for this reason that in cases of conflict between Revelation and the evident principles of morality, the rational course is to reject the latter. Against the objection that such conflicts between self-evident principles are impossible, and that therefore his true intention in insisting upon the irrationality of faith is to show the absurdity of Christianity itself, Bayle reiterates his view that the same kinds of conflicts arise with regard to purely philosophical questions. Bayle offers several examples of strictly philosophical or metaphysical questions in which our evident rational principles are found to be mutually inconsistent. Most prominent, as we might expect, is the case of the composition of the continuum. Thus, in response to Le Clerc’s complaint that Bayle places reason and Revelation in opposition to one another, Bayle observes: Mr. Le Clerc speaks as one persuaded that the teachings of the natural light always agree with one another and are so tightly bound together that we cannot accept one part of them and reject another. This shows that he has little familiarity with the subject…for, far from supporting one another, they often come into conflict. Would you like insoluble arguments for infinite divisibility? The natural light will furnish you with them. Would you like others against infinity divisibility? It will furnish you with those as well. Cf. OD III, 771a where Bayle maintains that “…there are philosophical questions concerning which reason cannot be reconciled with itself.” In support of this claim he cites disputes concerning the composition of the continuum and the definition of motion. Nevertheless, Bayle insists that the result of this conflict is not global scepticism, since the same resolution to which he had recourse with respect to the dogmas of religion, is equally available in the case of purely philosophical conflicts. That is, in cases where one of the conflicting metaphysical principles is more évident, or more certain than the other, it is rational to embrace that proposition and to abandon the other. It is by this means that one can affirm the infinite divisibility of extension, despite the insoluble objections to which it is subject. As Bayle puts the point, “thus, by the idea of extension, we affirm its infinite divisibility, even though we can conceive no agreement between an extension of three feet and its infinite number of parts, and even though we succumb to innumerable objections against infinite divisibility”. “c’est ainsi que par l’idée de l’étendue l’on embrasse sa divisibilité à l’infini, quoi que l’on ne puisse concevoir aucun accord entre une étendue de trois pieds et l’infinité de ses parties, et quoi que l’on succombe aux objections innombrables qui attaquent la divisibilité à l’infini (OD III, 773b)”. It is worth noting that Bayle makes precisely the same move with regard to the antinomy concerning the immateriality of the soul. Speaking of his critic Jacques Bernard, Bayle asserts that he was misled when he was told that M. Bayle maintained that all evident propositions are equally evident. I reply that this proposition [thèse], bodies are incapable of thinking, appears sufficiently evident for M. Bayle to judge it to be certain. But he does not believe that it is as evident as the proposition [proposition], two and two make four. “on l’a trompé, lorsqu’on lui a dit que M. Bayle soutenait que toutes les propositions évidentes étaient également évidentes. Je lui réponds que cette thèse, les corps sont incapbles de penser, paraît assez évidente pour M. Bayle pour la juger certaine, mais qu’il ne la croit pas aussi évidente que cette proposition, deux et deux font quatre (OD III, 1071a).” For Bayle the demonstration of the immateriality of the soul is évident, but not to the same degree as certain other truths of reason, such as mathematical truths. The problem, it would seem, lay not with the Achilles argument itself, which as we have seen, Bayle considers “a geometrical demonstration”. Rather, the conclusion lacks the maximal degree of self-evidence, because it is contradicted by several other maxims, which themselves enjoy some measure of self-evidence. For a more detailed discussion of the argument for the immateriality of the soul, see my “Bayle’s Critique of Lockean Superaddition” Canadian Journal of Philosophy 36 (4), December, 2006. In sum, Bayle’s view as he presents it in his final works is that human reason is subject to a number of contradictions in which two or more self-evident principles are found to be logically inconsistent. However, in at least some cases a rational choice can be made among the conflicting principles, because évidence is a matter of degree. In cases of conflict, the rational course is to accept that principle which is more self-evident, while acknowledging that its epistemic certainty is diminished by the existence of countervailing principles. I examine Bayle’s characterization of “rational fideism” in greater detail in “Évolution et cohérence du fidéisme baylien: le paradoxe du ‘fidéisme raisonnable’” in Hubert Bost and Antony McKenna, eds, Les “Éclaircissements” de Pierre Bayle (Paris: Honoré Champion, 2010), 447-457. Bayle’s position is perhaps best described not as Pyrrhonism, but rather as a kind of probabilistic scepticism with respect to self-evident principles. 2. HUME AND BAYLEAN SCEPTICISM Perhaps the deepest and most abiding problem in Hume scholarship concerns the nature and extent of Hume’s scepticism and how, if at all, it can be reconciled with his ambition to found a new “science of man.” Fortunately, answering this question is not my present task. Instead I shall pursue the more limited goal of demonstrating that whatever the precise nature of his scepticism, Hume clearly and deliberately rejects the kind of logical conflict among principles of reason upon which Bayle builds his own scepticism. Although, characteristically, Hume does not mention the French philosopher by name, at several junctures Hume directly confronts the sceptical strategies employed by Bayle and goes out of his way to reject them. Naturally, the most straightforward method of attacking this form of scepticism would be to consider one by one the sceptic’s arguments in order to show that in each case the alleged paradox admits of a satisfactory resolution. And, in fact, Hume makes extensive use of this strategy. Consider, for example, his response to Bayle’s paradox concerning the immateriality of the soul. Recall that according to Bayle we are in possession of an argument as certain as a geometrical demonstration that the mind is an unextended, immaterial substance. However, this conclusion is held to be inconsistent with our self-evident belief that everything that exists must be spatially located, which an immaterial substance cannot be. Of course, Hume is not committed to the Cartesian account of mind as res cogitans. Nevertheless, the paradox still threatens, albeit in slightly different form. For Hume’s account of extension turns on the claim that only visual and tactile perceptions can compose our ideas of extension, because only they admit of spatial arrangement. From this it follows that other perceptions such as tastes and smells (as well as the passions) neither are nor can be spatially located. Further, because for Hume such perceptions are distinguishable and separable one from another, each is a distinct entity, capable of independent existence. Having established these points to his satisfaction, Hume immediately turns to address Bayle’s worry. A further piece of internal evidence that Hume was familiar with these sections of Bayle’s Réponse aux questions d’un Provincial occurs in Section XII of the Enquiry. There Hume wryly observes that no philosophical position has been subject to more withering criticism than that of speculative atheism, despite the fact that its critics are wont to deny the very possibility of being a sceptical atheist, thus acting in the manner of “knights errant” of medieval legend (EHU 12.1). This observation is drawn directly from the Réponses aux questions d’un provincial where Bayle makes a similar comparison between the theological opponents of atheism and “un preux chevalier” (OD III, 925). Hume writes: ‘Twill not be surprizing after this, if I deliver a maxim, which is condemn’d by several metaphysicians, and is esteem’d contrary to the most certain principles of human reason. This maxim is that an object may exist, and yet be no where: And I assert, that this is not only possible, but that the greatest part of beings do and must exist after this manner (T 1.4.5.10; Hume’s italics). Thus, Hume attempts to undo the sceptical impasse to which Bayle had claimed reason is led, by dogmatically rejecting one of the clear and distinct principles that gave rise to the alleged conflict. With regard to the composition of extension Hume again attempts to dissolve the sceptical paradox set up by Bayle. Briefly, Hume develops a theory of minima sensibilia in an attempt to recast the theory of mathematical points so as to render it impervious to the objections put forward by Bayle. Recently, scholars have devoted considerable attention to Hume’s positive account of space and time as a response to Bayle’s arguments in “Zenon d’Elée”. For this reason, I shall not dwell on the details of Hume’s account. However, it is fair to say that, by narrowly focusing on Hume’s positive account of space as his main strategy for responding to Bayle’s sceptical challenge, commentators have largely failed to engage Hume’s more general reasons for rejecting the kind of scepticism advanced by Bayle—reasons that arguably run deeper than his particular solution to the problem of the continuum. It is with this more general response to Baylean scepticism that I shall be interested. Moreover, Hume’s ultimate commitment to the account of space presented in Book I, Part 2 of the Treatise is difficult to assess, since while it survives in essentials into the Enquiry concerning Human Understanding, it is there relegated to a footnote in which it is offered less as a definitive solution to the problem of the continuum than as a promising, but undeveloped “hint”. This response consists of three parts. First, Hume rejects Bayle’s contention that our geometrical concepts fail to correctly represent concrete physical extension. Recall that Bayle sometimes argues that while we have a clear and distinct idea of extension and this idea suffices to secure the certainty of geometrical truths, when applied to extended matter it leads to contradiction. Bayle’s conclusion is that no physical object can exist in conformity with the geometer’s idea of extension. The concept, while clear and distinct in itself, cannot be instantiated. Now, Hume is well aware of Bayle’s position, which he characterizes as follows: the objects of geometry, those surfaces, lines and points, whose proportions and positions it examines, are mere ideas in the mind; and not only never did, but never can exist in nature. They never did exist; for no one will pretend to draw a line or make a surface entirely conformable to the definition: They never can exist; for we may produce demonstrations from these very ideas to prove, that they are impossible (T 1.2.4.10). Hume decisively rejects these sceptical worries. He writes: But can anything be imagin’d more absurd and contradictory than this reasoning? Whatever can be conceiv’d by a clear and distinct idea necessarily implies the possibility of existence; and he who pretends to prove the impossibility of its existence by an argument deriv’d from the clear idea, in reality asserts, that we have no clear idea of it, because we have a clear idea. ‘Tis in vain to search for a contradiction in any thing that is distinctly conceiv’d by the mind. Did it imply any contradiction, ‘tis impossible it cou’d ever be conceiv’d (T 1.2.4.11). Bayle’s argument fails because it violates the Conceivability Principle according to which whatever is clearly and distinctly conceivable is possible. Hume lays down the general principle, which he characterizes as an “establish’d maxim in metaphysics,” that “whatever the mind clearly conceives includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible (T 1.2.2.8; Hume’s italics).” He goes on to argue that we have the idea of a finite extension that is composed of indivisible parts, and which therefore is not infinitely divisible. Applying his Conceivability Principle, Hume concludes that it is possible that a finite extension be actually composed of such parts, and consequently any attempt to prove its impossibility must be fallacious. Thus, in opposition to Bayle, Hume is prepared to dogmatically assert clear and distinct conceivability as a sure criterion of possibility. Notice, in passing, that this response seems to beg the question against Bayle, since it assumes rather than proves that no clear and distinct idea can be such that its instantiation is impossible. Second, not only does Hume refuse to allow that a clear and distinct idea might contain within itself characteristics that preclude its instantiation, he likewise denies that any two clear and distinct ideas can be mutually inconsistent. Hume makes this point most clearly in Section XII of the Enquiry concerning Human Understanding, where after rehearsing several sceptical arguments against “all abstract reasoning”, Hume observes: Yet still reason must remain restless and unquiet, even with regard to that scepticism, to which she is driven by these seeming absurdities and contradictions. How any clear, distinct idea can contain circumstances, contradictory to itself, or to any other clear, distinct idea, is absolutely incomprehensible; and is, perhaps, as absurd as any proposition, which can be formed. So that nothing can be more sceptical, or more full of doubt and hesitation, than this scepticism itself, which arises from some of the paradoxical conclusions of geometry or the science of quantity (EHU 12.20). David Hume, An Enquiry concerning Human Understanding, ed. Tom L. Beauchamp (Oxford: Clarendon Press, 2000), cited by (EHU Section.Paragraph). Although his discussion in the Enquiry is characteristically more circumspect than the corresponding passages in the Treatise, Hume’s suggestion is that the sceptic’s attempt to show that some self-evident propositions are mutually inconsistent is more absurd than any alleged paradox to which the defender of “abstract reasoning” might be subject. The result, he suggests, is that no such sceptical worry can be sustained. The third component of Hume’s reply to Bayle’s sceptical methodology concerns the means by which the French philosopher sought to escape the paradoxes of reason. Earlier we saw that in his final works Bayle attempts to avoid the conclusion that the logical conflict of self-evident principles completely undermines reason by offering a kind of probabilism with respect to évidents principles and demonstrations, according to which it is more reasonable to endorse those principles that possess a higher degree of self-evidence. Not only does Hume reject the suggestion that clear and distinct propositions might be mutually contradictory, he further argues that the sort of probabilism envisaged by Bayle has no place in the domain of demonstrative knowledge. Hume writes: ‘Tis not in demonstrations as in probabilities, that difficulties can take place, and one argument counterballance another, and diminish its authority. A demonstration, if just, admits of no opposite difficulty; and if not just, ‘tis a mere sophism, and consequently can never be a difficulty. ‘Tis either irresistible, or has no manner of force. To talk therefore of objections and replies, and ballancing of arguments in such a question as this, is to confess, either that human reason is nothing but a play of words, or that the person himself, who talks so, has not a capacity equal to such subjects (T 1.2.2.6). Thus, Hume refuses to allow that the certainty that attends a demonstrative argument might be the product of weighing its self-evidence against the self-evidence of opposing principles. The upshot of these three considerations is that for Hume neither the alleged paradoxes nor Bayle’s proposed resolution of them are philosophically acceptable. Now, it might be objected that there is at least one case in which Hume is prepared to allow the possibility that two clear and distinct propositions might be logically inconsistent. In the famous revisitation of his theory of personal identity in the Appendix to the Treatise, Hume expresses dissatisfaction with his account on the grounds that it rests on two principles which he can neither reject nor fully reconcile. He writes: In short there are two principles, which I cannot render consistent; nor is it in my power to renounce either of them, viz. that all our distinct perceptions are distinct existences, and that the mind never perceives any real connexion among distinct existences (T App. 21; Hume’s italics). Here Hume explicitly acknowledges his inability to reconcile the two evident propositions, and professes to adopt a sceptical position in response: For my part, I must plead the privilege of a sceptic, and confess, that this difficulty is too hard for my understanding. I pretend not, however, to pronounce it absolutely insuperable. Others, perhaps, or myself, upon more mature reflection, may discover some hypothesis, that will reconcile these contradictions. (T App. 21). However, it is far from clear that Hume is really allowing the possibility that two clear and distinct propositions might be absolutely inconsistent. For one thing, commentators have long puzzled over why Hume believes the two to be inconsistent at all, given that the one appears to be a direct corollary of the other. This has led Richard Popkin to suggest that Hume must hold not that the two principles are mutually inconsistent, but rather that that they jointly conflict with our common sense belief in the continued existence of a single self. But this latter can scarcely be taken for a self-evident truth. Richard Popkin, “Hume’s Pyrrhonism and Critique of Pyrrhonism” in Richard A. Watson and James E. Force, eds., The High Road to Pyrrhonism, San Diego: Austin Hill Press, 1980, 112-113. More importantly, Hume does not explicitly declare the two propositions to be absolutely irreconcilable. He simply reports that he himself has so far been unable to render them consistent. Indeed, he goes on to express hope that either he or others may in the fullness of time succeed in doing so. Thus, we need not interpret Hume’s dissatisfaction as an admission that two clear and distinct propositions might ultimately prove to be inconsistent. By way of conclusion, I would like to briefly examine the most obvious, yet most important question raised by the preceding discussion. That question, simply put, is this: why does Hume dogmatically rule out the very possibility of Baylean scepticism? After all, Hume willingly qualifies his own philosophy as sceptical, not only in the conclusion to Book I of the Treatise, but also in the final section of the Enquiry concerning Human Understanding. Hume’s curt dismissal can seem all the more surprising in light of Treatise 1.4.1, a section which bears the title Of Scepticism with regard to reason. As is well known, Hume there develops an argument purporting to establish that (1) all demonstrative knowledge reduces to mere probability, and (2) “by all the rules of logic” the certainty of probabilistic beliefs ought to diminish to zero. The implication would seem to be that we have no epistemic justification for virtually any belief whatsoever. Or, as Hume himself formulates the conclusion, “all is uncertain, and…our judgment is not in any thing possest of any measures of truth and falsehood (T 1.4.1.7; Hume’s italics).” But if according to Hume’s own sceptical argument, reason left to its own devices would so thoroughly undermine itself that “all is uncertain”, why should he show such determined hostility to Bayle’s scepticism with regard to reason? One possible answer concerns the theological use to which the difficulties surrounding the composition of the continuum had frequently been put. As Several commentators have remarked, one of Hume’s aims in Treatise 1.2 is to undermine the sort of fideistic defense of the Christian mysteries to be found not only in Bayle, but also such works as the Port Royal Logic. See for example Lorne Falkenstein, “Space and Time” in Saul Traiger, ed, The Blackwell Guide to Hume’s Treatise (Blackwell: New York and Oxford, 2006), 59-76 and Marina Frasca-Spada, Space and the Self in Hume’s Treatise (Cambridge: Cambridge University Press, 1998). It is true that in the Treatise Hume characterizes belief in the infinite divisibility of matter as arising not out of concern for Christian apologetics, but the “mutual complaisance” between paradox-mongering philosophers and their admiring disciples (T 1.2.1). However, the polemical uses which Hume’s opponents had made of our inability to comprehend the structure of even the least parcel of matter were not far from his mind. This is made clear by Hume’s introduction of the corresponding discussion in the Enquiry. There he observes: No priestly dogmas, invented on purpose to tame and subdue the rebellious reason of mankind, ever shocked common sense more than the doctrine of the infinite divisibility of extension, with its consequences; as they are pompously displayed by all geometricians and metaphysicians, with a kind of triumph and exultation (EHU 12.18). Doubtless, Hume’s rejection of Bayle’s brand of scepticism is motivated in part by the desire to remove one of the central arguments that defenders of orthodox Christianity had invoked in defense of the mysteries of faith. Still, this cannot be the whole story. For by the Conclusion to Book I of the Treatise Hume’s sceptical arguments against the epistemic justification of virtually all beliefs—especially those concerning things outside “the sphere of common life”—leave him in a position to offer nothing more than prudential reasons for preferring philosophy to “superstition” (T 1.4.7.13). Thus, it is difficult to see how these considerations alone can warrant dogmatically rejecting Baylean scepticism. To appreciate Hume’s strictly philosophical reasons for doing so, it is important to note a crucial difference between Hume’s own sceptical attack on reason and the arguments put forward by Bayle. Hume’s argument in Treatise 1.4.1 neither assumes nor implies that reason in itself is inherently flawed. On the contrary, he assures us at the outset of the discussion that in every demonstrative science, the rules are “certain and infallible” and that it is only our occasional misapplication of those rules that serves as grounds for scepticism. For Hume, comparisons of ideas are inherently infallible. The problem is rather that the operation of our rational faculties may be interfered with from the outside, by which means error is introduced. Hume’s scepticism with regard to reason, then, is based not on a direct attack on our rational faculty, but on a second-order judgment based on past experience that such causal interference may have occurred in any particular operation of that faculty. Moreover, even if acceptable, what the argument of 1.4.1 shows is that we have no epistemic justification for any of our rational beliefs. What it does not show is that reason is inherently defective in the deeper sense that even under ideal operating conditions it sometimes yields beliefs that are logically inconsistent, and which therefore cannot all be true. Yet this, as we have seen, is precisely what Bayle’s arguments had attempted to prove. In a review of Bayle’s Continuation des Pensées Diverses, Jacques Bernard had argued that it is one of the foundational principles of reason that when a belief is founded on clear and evident reasons, we must consider it certain, even if it is accompanied by “great difficulties”, which take their rise from the narrow limits of our mind. He insists that to do otherwise would inevitably lead us to “the most excessive Pyrrhonism” (OD III, 691b). For his part, Bayle accepts Bernard’s maxim and attempts to show how, by weighing their various degrees of évidence, we can have rational grounds for continuing to believe self-evident principles even when they conflict with other évidents principles. However, as we have seen, Hume rejects the suggestion that in demonstrative reasoning, one self-evident principle can be “counterbalanced” by another. As a result, he must believe with Bernard that to allow the possibility of an irresolvable conflict between our clear and distinct ideas would inevitably lead to radical Pyrrhonism—that is, to a scepticism far more destructive than the “mitigated” version that he himself endorses. Perhaps it is for this reason that Hume refuses to countenance even the possibility of the sort of scepticism upon which Bayle had so forcefully insisted.