Leibniz’s Anti-scepticism

Abstract

Leibniz never addressed systematically the sceptical issue in its various historical and conceptual dimensions. Nevertheless he progressively met different challenges and arguments throughout his innumerable readings, correspondences and writings displaying different faces of scepticism: the Academic negative meta-dogmatism of Francisco Sanches; Simon Foucher’s middle way; the three related figures of the libertine misosopher, of the fideist after Bayle’s manner, and of a fictitious ‘Sceptician’; and eventually, at the end of his life, Sextus Empiricus’ neo-pyrrhonism. Yet the meaning of his opposition to scepticism is not the same in all those cases: on the one hand, he claims that metaphysical and epistemological sceptical challenges can be refuted by rational arguments; on the other hand, he acknowledges the practical difficulties to overthrow the more dangerous moral and religious scepticism.

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It is in no way astonishing that Gottfried Wilhelm Leibniz returned frequently to the issue of scepticism in his innumerable writings: an insatiable scholar, he sought to become familiar with all disciplines, subjects, and doctrines, and professed to “despise nothing but divinatory arts”¹; as a key figure in the Republic of Letters, he corresponded with over a thousand European personalities, among them such prominent sceptics as Simon Foucher, Pierre-Daniel Huet, and Pierre Bayle²; and, above all, as a tireless philosopher and convinced that “what is soundly philosophical stays out of controversy”,³ he could not help but take seriously the sceptical challenge. With this stated, the question to be determined is what Leibniz knew about scepticism, how he understood it, and where he stood on it. After all, corresponding with sceptics does not necessarily mean addressing scepticism – quite the contrary, in Leibniz’s case. In his scattered first mentionings of scepticism, before he had personally met a few self-declared sceptics in Paris, one finds nothing but a broad identification with an extravagant challenge of all knowledge claims. The label “sceptic”, or its usual counterpart at the time, “pyrrhonist”, is also sometimes associated with “atheist”, and later even with “libertine”.⁴ The young Leibniz refers to Francisco Sanches’s famous writing Quod nihil scitur (That nothing is known), expressing the sceptical motto in full that runs “Nihil scitur, ne hoc quidem, quòd nihil scitur” – nothing is known, not even that nothing is known – which even doesn’t need to be refuted for Leibniz.⁵ This negative meta-dogmatism, which recalls the New Academics, Leibniz links to the pyrrhonian opinion that “there is such a divorce between senses and reason that one of the two must necessary deceive.”⁶ Without considering the historical differences between the two, he opposes a twofold answer to the “sceptical challenge”. As regards reason, he considers it obvious that rigorous demonstrations supported by accurate definitions are “necessary to set up the severity of sciences against the Pyrrhonians”, provided that one does not “throw Pyrrhonians a line” and take dubious foundations for granted.⁷ As for the senses, here Leibniz thinks the sceptics raise a much more legitimate gnoseological question, as the many cases of sensory illusion demonstrate, and thus he states that “all the difficulties raised by the pyrrhonians are confined to such truths as arise from senses.”⁸

If one leaves aside the trite remark that scepticism is, in a sense, always at stake in every philosophical investigation, one has to examine the few cases in which Leibniz understood himself to be dealing explicitly with scepticism: namely, (1) his discussions with Simon Foucher, (2) those with a fictitious ‘Sceptician’ and with Bayle, and (3) those about Sextus Empiricus.

1 Leibniz and Foucher’s Scepticism

Leibniz’s first discussions about certain sceptical assertions occur in his correspondence with Simon Foucher, whom he met during his stay in Paris (1672–1676).⁹ First of all, it must be underlined that only some of Leibniz’s propositions address scepticism in the traditional sense, and not the whole of his correspondence. A commonly held sophism is that Leibniz was sympathetic to sceptical theses because he had engaged in a friendly correspondence with the well-known sceptic Foucher and had displayed agreement on several points. But a closer look discloses both a non-conventional scepticism on the part of Foucher, and a clear-cut dismissal of traditional sceptical arguments by Leibniz.

During his lifetime, Simon Foucher was known as a sceptic. In the titles of his writings he made explicit reference to the “Academics” against Descartes and Malebranche,¹⁰ and since his first writing had made regular mention of “the Academics and the Pyrrhonians” and had defended the view that there is no knowledge of things outside us,¹¹ it was assumed that Foucher was referring to the “New Academics”, and it was said of him that he “renewed the spirit of his famous predecessors by suspending his judgment on all things”.¹² Yet Foucher rejected such a narrow interpretation, and even composed a refutation of these accusations of scepticism.¹³ His History of the Academics finally wiped out any ambiguity about his interpretation: by “the Academy” he meant the old and new historical Platonic schools as a whole, which differ only in their places, persons, or circumstances, he claimed, and not in their doctrine, means, or scope.¹⁴ Neither the Academics nor the Pyrrhonians, he wrote, actually challenge the truth, pointing out that the Academics do admit truths in geometry and mechanics, and that they do acknowledge what is sharply distinguished and fully demonstrated.¹⁵ Foucher explicitly does not look for historical accuracy, but wants to draw from all the objections raised by Plato and Sextus Empiricus “some general principles that one considers then as the sole objects of examination”.¹⁶ Renewing sceptical demands while also making knowledge-claims, Foucher unconventionally declares himself “an Academic after the manner of Plato” – or “Academico-Platonicus”.¹⁷

With this general sketch of Foucher in mind, one can understand how Leibniz cannot help but agree with an author who intends to “promote a demonstrative philosophy displaying both indisputable principles and conclusions”¹⁸; how he cannot help but approve of the “five Academic laws”¹⁹; how he cannot help but welcome the diagnosis of a lack of clarity and distinctness marks by Descartes²⁰; and why he cannot help but encourage Foucher to “draw from the Ancients what is most useful and most proper to the taste of our time, and reconcile and correct them by joining some of [your own] many sound thoughts to them.”²¹ Leibniz appreciates Foucher’s efforts to interpret the Academics “reasonably”²² – that is, to present them as casting upon everything not a destructive doubt, but a “reasonable doubt” which paves the way for indisputable principles and conclusions.²³ In a letter to Foucher published in 1692 by the Journal des Sçavants, Leibniz follows this track in confessing that “one should not despise the difficulties raised by Sextus Empiricus against the dogmatists, since these serve to take them back to principles.”²⁴ Obviously one should not infer from these non-sceptical statements any Leibnizian sympathy for scepticism; indeed, when it comes to those arguments in the correspondence which Foucher has drawn from the ancients against the Cartesians, Leibniz shows himself to be cordially reluctant to support them.

As Leibniz says in his first letter, two of Foucher’s propositions in the Critique caught his attention:

• (a) that “one understands perfectly the thing being considered when one can prove everything that we assert about it”;

• (b) that there are no “truths which affirm that there is something outside us”.²⁵

Leibniz repeatedly asserts that proposition (a) makes sense only if one recalls that every demonstration is based on undemonstrated assumptions (for instance, the principle of contradiction) – so that one can speak of “hypothetical truths” in mathematics.²⁶ To prove everything that is asserted does not mean that everything, in a demonstration, is demonstrated. As obvious as it is to Leibniz that to demand a demonstration of absolutely everything would entail an infinite regress, and thus would prevent any demonstration at all, he rightly discerns a possible equivocation in Foucher’s writing. In his Critique, Foucher suspects that there are no necessary truths, cursorily leaving aside “the case of mathematics, which is a separate issue.”²⁷ Leibniz reads this as an implicit acknowledgement that all truths are hypothetical truths and makes clear that “even the truth of hypothetical propositions is something which is outside us, and which does not depend on us” and is not a devised “chimera”.²⁸ Yet, in his rejoinder to Malebranche’s reply of the following year, Foucher does speak of mathematical truths as being “grounded on mere assumptions which do not instruct us on what is real outside of us”, or indeed as being mere contrived abstract ideas which “are not truths properly speaking, at least not the truths that philosophers ought to search.”²⁹ Leibniz, baffled, writes on his own exemplar: “Why not?”³⁰ Thereafter he regularly reminds Foucher of the necessity of certain assumptions, not only for the sake of the advancement of the sciences, but also, as the old Aristotelian argument goes, for the sake of words’ making sense.³¹ Leibniz rightfully discloses a true sceptical temptation in Foucher’s curious middle way: for although Foucher does admit some first principles to be true, his only examples pertain to the essence or existence of God, and he seems to challenge the truth of any other principle, and thus the possibility of discovering truth at all.³² This is most clear in proposition (b)’s more detailed discussion regarding the knowledge of an external world of things.

In the fifth and sixth assumptions of his Critique, Foucher argues that we never know or perceive immediately the things themselves, but only their ideas: and since ideas have no resemblance to what they represent – for, as the argument curiously goes on, un-extended ideas cannot resemble extended things – we must conclude that we have neither any trustworthy nor any truth-worthy knowledge of the external world.³³ Yet Foucher does not question the existence of the world itself, and takes it for granted that our sensory appearances are caused by certain things. This very assumption of the causal existence of our appearances lays the cornerstone for Leibniz’s answer: the very genuine evidence which we cannot help but admit is not that of the world’s existence as such, but the fact that we have various representations. This leads him to distinguish “two general truths which speak of the actual existence of things” and which determine the “Leibnizian cogito”: “the first, that we think, and the second, that there is a great variety in our thoughts”.³⁴ The manifold content of our representations assures us of the existence of an external world at second hand when we consider two further arguments: First, and according to the rule that everything remains in its present state until acted upon, a mind in itself might not account for its own changes in general, or for having this rather than that representation in particular. Second, the connection, order, and consistency manifested by our appearances gives us the moral assurance of an external world:

The more we see some connection in what happens to us, the more we are confirmed in our opinion about the reality of our appearances; and it is also true that the more we examine our appearances closely, the more we find them well-sequenced, as microscopes and other aids in making experiments have shown us. This constant accord engenders great assurance, but it will only be a moral assurance, after all, until somebody discovers the a priori origin of the world that we see and pursues the question of why things appear the way they do back to the ground of essence.³⁵

The Leibnizian cogito excludes self-deception, but does not rule out the possibility of a permanent deceiver who makes us consider dreams as realities and turns our life into one long, well-ordered dream-sequence – although this would amount to a very implausible permanent “beatific vision”.³⁶ Therefore one must rely on the ever-greater consistency of our empirical knowledge to assert, against Foucher, our confidence in gaining an ever-more-distinct knowledge of external things – the limit of such knowledge being the regulative concept of their a priori essences. Thus, although there is no metaphysical assurance of the world’s actual existence, from a practical point of view its existence is beyond doubt. The argument is obviously meant not only for Foucher, but for Descartes.

Notoriously, Descartes had decided to “apply [himself] seriously and freely to the general overthrow of all [his] former opinions” after observing that his senses sometimes deceive him, and moreover that “there are no certain marks distinguishing waking from sleep.”³⁷ Leibniz undermines these two points in the aforementioned letter, as he would in all later references to Descartes’s doubt. A few deceptive sense-judgments cannot overthrow the whole bulk of concordant sensory statements, he says, and will never actually make me doubt of things. Also, we do have a criterion for waking representations: not their distinctness, as Descartes had assumed in the Sixth Meditation ³⁸ (for they remain confused in spite of all progress of sciences³⁹), but their coherence together. Connections between phenomena, common agreement about them, and the validity of the principle of sufficient reason for them, are together enough to distinguish real phenomena from disordered and imaginary ones.⁴⁰ Thus Leibniz supplants Descartes’s concept of certainty: what is “certain” is no longer that which is indubitable or safe from any possible theoretical doubt, but is that which is corroborated and confirmed by my practice of the world.⁴¹ Descartes wanted to doubt freely and seriously, but an arbitrary doubt is not a serious doubt for Leibniz – which is to say, it is not a doubt at all:

It would certainly be insane to seriously doubt that there are men in the world when we do not see any. To doubt seriously is to doubt as regards practice. We might say that ‘certainty’ is the knowledge of a truth such that to doubt it in practice would be insane.⁴²

Having no reasonable practical reason to doubt, Descartes’s practice of doubting is rejected as wholly inconsistent: his feigned doubt leads to nothing but to a feigned argumentation, and may reveal a deceiving attitude, if not “a great disorder of mind”.⁴³

In short, Leibniz sets a radical anti-sceptical standard in asserting the need to rely on given fundamental truths and principles, and in rejecting any practically inconsistent doubt. In spite of Foucher’s efforts, he remains unconvinced that the Academics could provide us with a useful principle, and urges that they be read “reasonably”.⁴⁴ His portrait of the sceptic remains that of an “all-purpose doubt-maker” bent on foiling all projects.⁴⁵ Leibniz will find further occasions to diffract this portrait, and thus to refine his anti-scepticism.

2 Leibniz, the Sceptic, the Misosopher, the Sceptician and Bayle

It must be pointed out that Leibniz’s correspondences with renowned sceptics have very little to do with scepticism. When we look at his exchanges with the three sceptical musketeers, Foucher, Huet, and Bayle, at most we find requests for clarifications of his propositions, and the explanations he provides them in return. His correspondence with Foucher, to put it briefly, and if we set aside the preliminary discussion, covers various mathematical and physical problems until Leibniz puts forward his views on animal bodies and opens a line of discussion later to inform his New System of Nature.⁴⁶ His few letters with Huet are safe from any single skirmish. They find their anchorage points in Huet’s attempt to demonstrate formally the truth of the Christian religion, and in his criticism of the Cartesian philosophy.⁴⁷ Leibniz basically agrees with him, always confessing his admiration for his immense erudition, and standing on his side in the Quarrel of the Ancients and the Moderns. As for Bayle, their discussion really begins with the review of the New System which appeared in Bayle’s Dictionary (article “Rorarius”, remark H). Bayle finds Leibniz’s hypothesis of the spontaneity of the soul too weakly justified for a discussion, “so long as one does not know distinctly the soul’s substantial core and the way it turns itself from one thought to another.”⁴⁸ Yet this does not mean that he rejects Leibniz’s hypothesis outright as belonging among the undifferentiated bulk of doubtful opinions: on the contrary, he praises Leibniz’s “openings” (ouvertures) for their overcoming the usual objections, or for saving us from confusion, and he encourages Leibniz to “carry on with spreading the most subtle truths of philosophy”.⁴⁹ To confirm the point, then: there is nothing in Leibniz’s correspondence with these “sceptics” but a friendly, cordial exchange of objections and answers, and one that hardly ever goes into scepticism.

Thus, one should not infer from the “aura of sweetness” that pervades Leibniz’s “idyllic relationship” with such “sceptics” that he had any particular interest or sympathy for scepticism per se.⁵⁰ Nor should one suppose that these figures had raised any great objections to Leibniz, and nor, either, that Leibniz was particularly solicitous of such objections, inspired as he was more by a conciliatory spirit of “variety, of pluralism, of tolerance”, than by a polemical spirit of controversy.⁵¹ So these “sceptics” are nothing but philosophical correspondents among others – after all, Leibniz was one to constantly dispatch his views, searching high and low for objections, having no intellectual counterpart in Hanover⁵² – and they certainly had less of an influence on his re-phrasing of old problems and new ideas than, say, the non-sceptical Arnauld or Des Bosses had. These “sceptics” may hit upon certain “areas of agreement” with him,⁵³ but they hardly meet one specific sceptical “area of discussion” according to him, namely the claims about sensory knowledge. Leibniz does acknowledge the formal usefulness of deflationist doctrines about sensory knowledge, and even planned to devote a chapter to it in his numerous drafts for a Philosophical Encyclopedia and General Science⁵⁴; but he does not consider scepticism to be a necessary dialectical step towards truth: well-formulated objections are always welcome, but one need not go through a “pyrrhonian crisis” or an “hyperbolic doubt” to grasp primary truths or establish the principles of certainty in metaphysics, logics, physics, or, especially, in morals.⁵⁵ For, besides the gnoseological sphere, Leibniz has by then singled out the moral and religious sphere as the genuine sceptical “area of discussion”, and had identified two opponents in that sphere: the misosopher and the sceptician.

He did so in a 40-page dialogue between two characters, a hermit Father and a marquis, which he wrote towards 1680.⁵⁶ The hermit Father avows a religious anti-scepticism, having “always recognized in scepticism the source of the incredulity and lack of attachment to spiritual matters to be noticed among society people” (2256). As for the marquis, who obviously belongs to this social circle, he displays two forms of scepticism successively. At first he is said to be “infected with the ordinary scepticism of those living in grand style, disregarding any application to what does not obviously concern the senses or the present interest” (2246). Believing that men are entangled in endless disputes and doubts, that their reason does not partake in truth, nor that it “establish[es] something solid in practice”, he has decided once and for all to cease any further investigation, and to conduct himself according appearances, “following customs in morals and faith in religion” (2249). Although portrayed as a grand-style sceptic, the character of the marquis actually embodies the average everyday sceptic who conveniently follows everyone else’s habits and opinions while assenting to none of them, and who has abandoned the search for certainties and grounds, “having been delivered from this kind of disease by Montaigne and Le Vayer” (2252).⁵⁷ Convinced by his reading of great sceptical works, or lazily giving way to the “unreflected scepticism” of everyday life, his scepticism falls short of the meditation and application that must also come with it.⁵⁸ His indifference is thus only a step away from turning into a veritable misosophy, and his pyrrhonian pragmatic fideism from turning into a libertine eschewal of morals.⁵⁹ This kind of sceptic poses a fundamental and perhaps insurmountable practical challenge: that of converting he who refuses to converse.

The hermit, Leibniz’s spokesman, quickly overcomes this prejudicial objection only by reminding he who is about to “sink in an unfortunate scepticism” (2252) of the practical consequences of such indifference. Those who brilliantly oppose one appearance to the other, says the hermit, forget that “a conclusion may have an influence in the practice of [their] lives”, and that, unfortunately for them, “this faint tranquility as regards one’s misery or felicity will be paid for dearly” (2250, 2255). This aspect of the argument is close to Pascal’s wager against the libertines: one cannot suspend one’s judgment and remain theoretically indifferent in matters where one’s own practice of life is already involved – that is, in matters into which we have already “embarked”.⁶⁰ Convinced by this argument as he seems to be, the marquis then becomes the spokesman for a second type of scepticism, becoming a “sceptician” (Scepticien) – a radical philosophical sceptic – who agrees to enter into an obligational dispute, and now regards his former customs and faith as having been mere chimeras (2256).

The starting point of the hermit’s argument is that “we are all ignorant, that our reasoning rests only on assumptions, that we lack the principles to judge things, that there is no rule for truth, that everyone has a particular sense of it, and that there is hardly a common one” (2257). To put it briefly, the hermit’s strategy amounts to letting very few principles be acknowledged in mathematics, in ordinary reasoning, or in common experience: the principle of contradiction for all conceptual truths, and the assumptions of internal immediate experiences (‘I am’, ‘I feel’, ‘I think’, ‘I want’) for judging of appearances (2262). Having thus left the minimum about still to be proven, the transition from necessary mathematical demonstrations to moral assurance about contingent appearances is carried out by way of a broad concept of order: axiomatic order in mathematics, orderly argumentative form in all types of everyday reasoning, order in natural matters, and, hence, order in moral matters (2272). Here the concept of an “order of things” has a twofold meaning. First, closer attention may disclose unseen regularities between appearances and reveal a serial order of things, just as in mathematics the series of the differences between two successive square numbers reveals a secret regularity, or just as the registering of all things should be the very secret to achieving an ars inveniendi.⁶¹ Second, every individual appearance comes within the order of those things that depend on the relative weight of corroborating appearances. Leibniz the hermit does not take the pyrrhonian view that contrary opinions, regardless of their respective degrees of probability in practice, have a counter-balancing equivalence; instead, from these respective degrees of probability he infers either a moral assurance or a moral void, which “will necessarily unbalance the scales” (2263). Consider, for instance, the assumption (a) of a contingent world without Providence, versus the assumption (b) of a providential Creation. “The appearance of the first is to the other like that of a grain of sand to a world” (2263); “the appearance of this assumption is infinitely small, that is, morally void; and we also have a moral assurance that Providence governs all things” (2268). So the hermit treads an anti-sceptical path in the direction of legitimizing the notion of degrees of probability; it ends as the edifying story of the marquis’s conversion (2282). This is not the most relevant yet.

One must say that the dialogue rests on a weak argumentative device: that the “everyday sceptic” consents to reflection to get rid of his fideism and turn himself into a sceptician. So far Leibniz has dismissed the libertine misosopher, who is beyond redemption, and the sceptician, who is suitable for an anti-sceptical conversion, but not the fideist marquis as such, who has not yet fallen in with misosophy, or taken the sceptician’s disguise. As one knows, the discussion about fideism takes place in the dialogue with Pierre Bayle and finds a condensed expression in Leibniz’s Discours preliminaire de la conformité de la foy avec la raison, which, along with the Essais de Theodicée, appeared in 1710.

Whether Bayle was actually a fideist – as Leibniz assumes – or not, and in which sense this fideism leads to scepticism are debated questions that we cannot address here. What I do want to point out is Leibniz’s general intention in the Discours, which is to overcome the fideist’s sharp separation of faith from reason (a sign of their difference being reason’s inability to solve the problem of evil) which leads to the doctrine of a twofold truth. In overcoming this separation, and in showing the conformity of faith with reason, Leibniz’s purpose is also to prevent the fideist from falling into misosophy. His first step is to draw the distinction between necessary truths (whose contradiction is impossible) and contingent truths (whose contradiction is possible; they may be unlikely, but they are not impossible). The contradiction of necessary truths is against reason; the contradiction of contingent truths may be above reason, but is not against it.⁶² Contrary to the Dialogue, where the hermit could state that “all appearances plea for Providence” (2265), in the Discours Leibniz must defend the more difficult case of Christian religion, for “everyone agrees that appearances are against the Mysteries”.⁶³ The line of defence, inspired by juridical proceedings, is to grant a presumption of truth in those contingent matters, as long as the contrary is not formally proven: the presumption is supported by “motives of credibility”, and the burden of proof is put on the contradictor’s shoulders.⁶⁴

We have now seen that Leibniz went on to cast the portrait of the sceptic in the faces of the misosopher, the fideist, and the sceptician respectively. Whether or not these types rely on reason Leibniz answers differently in each case; but in all of them he sees a common practical scope, and one that he resists, and which informs his anti-scepticism.

3 Leibniz Reads Sextus Empiricus, at Last

Leibniz certainly does not ignore the other faces of scepticism: he knows the difference between negative meta-dogmatism and the suspension of judgment, and also the distinction between Campanella’s manner of scepticism versus that of Montaigne. Yet the labels “scepticism” and “pyrrhonism” remain rather equivalent under his pen, for he is not dealing with historical refinements, but mainly with their common practical stake. Only in one text does Leibniz tackle historical pyrrhonism as such.

In Specimen animadversionum in Sextum Empiricum, percurso libro Pyrrho­niarum Hypothesium (sic) primo datum (Some observations on the first book of Sextus Empiricus’s Outlines of Pyrrhonism), provisionally dated to around 1711, Leibniz surveys “the very principles of the [pyrrhonian] sect”.⁶⁵ Although he had already mentioned Sextus Empiricus a few times in his previous writings,⁶⁶ this survey probably testifies to a closer reading of this “fundamental” and “instructive” entry into the principles of pyrrhonism.⁶⁷ Whether these observations were intended to be a first sketch of the refutation of scepticism he allegedly had promised Fabricius cannot be determined,⁶⁸ but Leibniz does praise the usefulness of such an edition: “One reports that you think of publishing Sextus Empiricus. This subtle and erudite author deserves it: I have already written some observations, although merely philosophical ones (sed non nisi philosophoumena), on his principles.”⁶⁹ In fact, his Observations challenge the three constituent concepts of pyrrhonism: isostheneia, epokhê, and ataraxia.

Following the chapters’ order of the Outlines, Leibniz first questions the alleged zetetic aspect of the doctrine:

[Sextus] says that the sceptics deny having discovered the truth, that they have not yet lost their hope of discovering it: but if there is truly an isostheneia, which the author names in chapter 4 and develops in chapter 6, and which is an equivalence of reasons between two contradictories, then I do not see how there may subsist any hope of discovering the truth, unless the sceptics understand this balance as applying to the reasons hitherto known (48–49).

Some have remarked that Leibniz’s reading may be too inaccurate to really challenge Sextus’s conception of equipollence (isostheneia), for Sextus does not speak of two contradictories but rather only of “conflicting accounts” which are equal only insofar as “being convincing or unconvincing [such that] none of the conflicting accounts takes precedence over any other as being more convincing.”⁷⁰ Although it is true that Sextus does not speak of a balance (aequilibrium) of accounts, nor speaks of “an equipollence between what is and what is not” (aequipollentia inter Est et Non), it does not follow that Leibniz missed the point and failed in his refutation.⁷¹

On the contrary; Leibniz does understand that this balance should only concern “the reasons acknowledged thus far”; what he rejects is that an equivalence of accounts entails their indifference to truth or to likelihood. For Sextus, the relative weight of opposite accounts is irrelevant so long as one given account does not definitively overcome the others: truth is actually a question of “what is and what is not”, not a question of likelihood. This all-or-nothing strategy, and the identification of an account’s balance (or equivalence) and its equipollence (or equipotence) regarding truth in a bivalent logic are precisely what Leibniz rejects. First, one cannot conceive that a balance of all given accounts will last forever – otherwise, this would imply, without any likelihood (ab omni verisimilitudine), that God “would be urged to measure jointly all opposite accounts that men have acknowledged thus far, such that these accounts are always equal” (49). Second, even if an account is equivalent to all others, this does not put it in balance with them as regards truth, or mean there is an equipollence between its affirmation and its negation. Here Leibniz gives a trivial example: if we consider three equivalent accounts, one of them being true, but our having no reason to prefer any one of them above the others, each of them has a two in three chance of being false (49). One can justify his treating the concept of “equipollence” (or, again, “equipotence”) as a 50–50balance if one remembers its original meaning in physics: perfect quantitative equality between a full cause and its complete effect.⁷² Leibniz eventually overcomes the unlikely isostheneia doctrine: if one is looking for a “more convincing account”, then one should be considering their respective degrees of probability (49). Without making it explicit here, Leibniz reproaches Sextus for having demanded of contingent matters what applies only to necessary truths: a rationally grounded conviction that is safe from any probability. Leibniz is always a believer that contingent matters should be decided by their presumption or degree of probability – “not by counting reasons, but by weighing them”⁷³ – and had, in fact, planned to establish a full-fledged logic of probability within the Scientia Generalis.

Given such premises, it is not surprising that the rest of Leibniz’s observations in this work are mainly concerned with the epokhê, or, as he re-describes it, with the justification and limitation of doubt (dubitatio).⁷⁴ He starts by gathering up all of those cases that Sextus had exempted from doubt:

The author restricts quite a lot the sceptic’s doubt to certain limits, and wants certain truths perceived through senses to be accepted, so that one does not say ‘I think I am heated’, but rather ‘I am heated’: the sciences do not deal with such things anyway. I notice here that the limits of doubt are not sufficiently defined, for not all perceptions which apparently come from the senses are always certain, just as those manifested in dreams are not. […] The author also confesses that sceptics subscribe to a reason in accordance with phenomena (chap. 8), and hence live according to senses and customs. […] Moreover, when he admits reasons in accordance with phenomena, he [actually] admits reasons besides phenomena: a phenomenon is one thing; the consequences rationally derived from it are another. He even admits arts (chap. 11), in which reasons and not phenomena are often at stake (49–50).

Part of this first step of Leibniz’s argumentation is also to show that Sextus acknowledges, whether deliberately or not, the practical necessity of relying on some accounts, be it in the area of feelings, customs, or expertises. Practical life constantly demands that we favour one thing over another: Sextus may differentiate between things and phenomena; he may hold that there is a balance between phenomena; but he has to rely practically on them, and in so doing “abolishes the equipollence of accounts by the act itself” (50). Sextus, for his part, would actually not disagree with this examination of the practical level, but he would not regard it as a refutation of scepticism in its various modes.

As for the second step, this includes giving a brief descriptive summary of the ten modes of scepticism as given in Chap. 14 of the Outlines, followed by a concluding remark that applies to them all:

All of this is either irrelevant or badly put together. That various things must appear to us according to the variety which is either in us or in the appearances’ external causes does not stand against the truth of things, since one can account for the differences between these appearances themselves in such a way that one can predict and produce many others from these – for instance, in predicting or bringing about a change in things. It is therefore pointless to assert that we cannot know the nature of things, for it belongs to the nature of one thing that such and such things are bound up with these and these others in our impressions. However, it is very true that certain qualities are not permanently tied in the things, but arise from the union of the thing itself with our senses: heat is of a such kind, for the same thing often appears to us hot or cold according to the diversity of our state – but even then, nothing prevents some root of appearances to be in the nature of the thing and to affect the perceiver according to his own state (51).

Here Leibniz is confronting the core of the ten modes, namely the difference between a thing (res) in itself, gifted with a nature (phusei), and its appearance (apparitio) to us, or rather to oneself in one’s present state (nomô). That we only deal with appearances, and that these may sharply vary with our different states, is in no way a sufficient ground for abandoning any knowledge or truth-claim. To assume that the transitory, superficial, phenomenal level of those things that we know has nothing to do with the permanent, substantial reality of those things in themselves is to err: for we do not perceive a pointillist haze of isolated impressions, but rather phenomena which display a connection to each other – a connection that one can trace even in the ever-smaller constituent phenomena that we are able to discover, and that may be sometimes described in terms of laws. Leibniz frequently uses the distinction between mere phenomena, which are a succession of impressions having mostly no connection and which are not directly grounded in natural things (dreams, for example, or the distorted reflections of a mirror), and real phenomena, which do show a connection to each other, and hence to an actual natural ground or “root” of appearances (radix apparitionis), and which he accordingly calls “well-ordered” or “well-grounded” phenomena.⁷⁵ In short, there are no real phenomena without something phenomenalizing, and their connections are the very object of scientific knowledge. Leibniz also retains the sceptic’s distinction between phusei and nomô, but overhauls it in such a way that it does not justify any epokhê, but, on the contrary, supports our knowledge claims.

Already this examination of the concepts of isostheneia and epokhê undermines the pyrrhonian justification of ataraxia, or the soul’s absence of disturbance, but Leibniz goes on to find two more logical inconsistencies in it: First, in taking epokhê to be doubt, as Leibniz translates it, one must come to the conclusion that “he who permanently doubts is permanently torn between hope and fear and subdued on both sides, [unlike] he who can take firm decisions and hold to them without being disturbed by some event or being forced to change his resolution” (49). The absence of disturbance actually lies on the side of firm knowledge, not on the sceptical side – and this makes it irrelevant whether epokhê means doubting or suspending one’s judgement. Second, to think that a proper representation may, as such, moderate one’s affections is, for Leibniz, altogether illusory; on the contrary, one should take pains and pleasures as the occasion to act in order to avoid this and obtain that. The sceptic, just like the dogmatist, fears and hopes; but tranquility can only be gained by acting: “Reason prescribes that he who does what is in his power should act tranquilly” (51).

By the end of the Observations, Leibniz has replaced pyrrhonism’s three concepts with the anti-sceptical concepts of degrees of probability, knowledge of well-founded phenomena, and acting within one’s power. If Leibniz does still mention Sextus Empiricus as a noteworthy commentator,⁷⁶ this seems only to be a way to point at the usefulness of scepticism for an anti-sceptical program.

Leibniz progressively confronts the different faces of scepticism: Academic, negative, meta-dogmatist; Simon Foucher’s middle way; the three related figures of the misosopher (the libertine), the Bayle-style fideist, and the fictitious ‘sceptician’; and ultimately the neo-pyrrhonist Sextus Empiricus. His discussions leave no doubt as to his anti-scepticism, if one understands this properly not as an outright banishment of an absurd doctrine unworthy of refutation, but as a theoretical overcoming and a practical resistance to these scepticisms. In asserting that one can indeed grasp fundamental truths without going through a dialectical “pyrrhonian crisis”, and in refuting deflationist theories about sensory knowledge, Leibniz declares himself confident as regards this task of a theoretical overcoming. Yet he clearly identifies both the moral and religious scope of these scepticisms and the practical difficulties of overthrowing them when they are rooted in the ineradicable resistances of one’s life-practice – that is, when they come to the limit of reason. It was perhaps this enduring, unreflected, sceptical resistance that Leibniz meant to invoke by the so far unpublished verses he would write on the occasion of Bayle’s death – verses in which Bayle can say that he may not be defeated since he is leaving his sceptical spirit:

Verses on the death of Mr. Bayle. / After the famous Pyrrho and the great Diagoras, / After his fellow Protagoras, / After Epicurus and others, / I followed the plan to establish here below / This incomparable science, / Of which Hobbes, Spinoza and Vanini after them have, / not without success, planted a seed. / Fortified with the spirit of their lessons, / I raised doubt after doubt, / Driven by the passion / To put to rout / The Doctors and Religion. / I have contradicted all at my ease; /And among the various doubts / That were always dear to me, / There is but one that displeases me: / Death is calling me and I am unsure / That this great way is the right one. / O what a dreadful uncertainty! / Jean le Clerc triumphs over it, and Jacquelot laughs at it, / Their victory, however, is doubtful. / If I leave this place, I leave my spirit.⁷⁷