by guest contributor Audrey Borowski
Paradox features prominently in Leibniz’s thought process, and yet has failed to receive much attention within mainstream scholarship. The French philosopher Gilles Deleuze, however, devoted his book The Logic of Sense to the analysis of paradox. I undertake to shed light on Leibniz’s deployment of paradox through the prism of Deleuze’s reflection. Deleuze greatly admired Leibniz, and even dedicated a book to the latter’s “art of the fold”—his particular treatment of and extensive recourse to continuums—in 1988. And yet Deleuze’s connection to Leibniz may run still deeper.
For Deleuze, paradox designated that which ran counter to common opinion (doxa) in its dual incarnations, good sense and common sense. He defined it in the following manner: “The paradox therefore is the simultaneous reversal of good sense and common sense: on one hand, it appears in the guise of the two simultaneous senses or directions of the becoming-mad and the unforeseeable; on the other hand, it appears as the nonsense of the lost identity and the unrecognizable” (Logic of Sense, 78). In this manner, paradox ushered in a novel type of thought process, one which broke free from the strictures of simple causality implied by good sense and proved deeply unsettling by constantly oscillating between two poles, “pulling in both directions at once” (Logic of Sense, 1). Paradox was to be distinguished from contradiction: while the former applied to the realm of impossibility, the latter was confined to the real and the possible from which it was derived. Paradox operated on a different conceptual plane; it lay beyond the framework of pure signification altogether.
For evoking impossible entities, paradox has too easily been dismissed as philosophically suspect. Yet, far from entailing error, paradox suggests a “certaine valeur de vérité,” a particular type of truth inherent to language: after all, “It is language which fixes the limits… but it is language as well which transcends the limits and restores them to the infinite equivalence of an unlimited becoming” (Logic of Sense, 2-3). In this manner, a squared circle, for instance, possessed sense even though it lacked signification. While they lacked real referents—and thus failed to exist—paradoxical entities inhered in language: they opened up an uncanny wedge between language and existence.
In fact, Leibniz had previously cultivated to perfection the dissolution of seeming contradictions into productive tensions. He formulated his mathematical “Law of Continuity” most clearly in his Cum Prodiisset in 1701, in which the rules of the finite were found to succeed in any infinite continuous transition. By virtue of this reasoning, rest could be construed as “infinitely small motion,” coincidence as “infinitely small distance” (GM IV, 93), elasticity as “nothing other than extreme hardness,” and equality as “infinitely small inequality” (and vice versa) (GP II, 104-5). In fact, Leibniz’s epistemological project essentially hinged on a process of reconfiguration: whereby finite and infinite were no longer pitted against each other, but correlated through the recourse to “well-founded fictions” which were not rigorously true: whilst they were uniquely “apt for determining real things” (GM IV, 110), they constituted finite ideal projections of which they were “none in nature” and which strictly speaking “[were] not possible” (GM III, 499-500). Reality was henceforth accessible primarily through fiction.
With his infinitesimals, Leibniz tread an ambiguous middle ground, whose lack of empirical counterpart or referent earned him much criticism from a number of contemporary mathematicians. French mathematician Jean le Rond d’Alembert conveyed the sense of dismay which Leibniz’s constructions elicited even more than fifty years later: “a quantity is something or it is nothing: if it is something, it has not yet disappeared; if it is nothing, it has literally disappeared. The supposition that there is an intermediate state between these two states is chimerical” (d’Alembert (1763), 249–250). Simply put, an intermediate state between “something or nothing” was simply inconceivable.
And yet, according to Deleuze, such absurd mental objects, whilst they lacked a signification, had a sense: “Impossible objects —square circles, matter without extension, perpetuum mobile, mountain without alley, etc.—are objects ‘without a home,’ outside of being, but they have a precise and distinct position within this outside: they are of ‘extra being’—pure, ideational events, unable to be realised in a state of affairs” (Logic of Sense, 35).
In Deleuze’s account, paradox stood not only as that which destroys “good sense as the only direction,” but also as that “which destroys common sense as the assignation of fixed identities” (Logic of Sense, 3). It emerged as the unforeseeable or the “becoming mad” and acted as the “force of the unconscious” which threatened identity and recognition. This was perhaps all the truer in Leibniz’s deployment of paradox in his metaphysics. Leibniz’s concept of “compossibility,” whereby the world was only made up of individuals that could logically co-exist, went beyond mere adherence to the principle of non-contradiction.
In the preface to his New Essays on Human Understanding, Leibniz defined his principle of continuity. According to it, “nature never makes leaps.” The world was organized according to an infinitely divisible continuum, in which everything was interconnected and change took place gradually. In it, “diversity [was] compensated by identity” (Elementa juris naturalis, 1671 (A VI, 484) in the image of the monad, that foundational spiritual entity which acted as a “perpetual living mirror of the universe,” albeit from its own particular perspective (Monadology, § 57, 56). In this manner, reality folded and unfolded indefinitely and rationally in an “uninterrupted” process of continuous transformation, whereby one state naturally “disappeared” into the next, a sufficient reason “always subsist[ing]… whatever alterations or transformations might befall” throughout the transition (New Essays). Each state was simultaneously the product of “that which had immediately preceded it” and “pregnant with the future”. Simply put, “something also was what it wasn’t” (Belaval (1976), 305).
Leibniz consecrated a thoroughly fluid and dynamic outlook, one in which truth was “hallucinatory” and lay in the very act of vanishing itself (Deleuze, The Fold: Leibniz and the Baroque). It could no longer be reduced to the fixed identities of “common sense,” but was essentially diachronic, governed as it was by “logic of becoming“:”The paradox of this pure becoming, with its capacity to elude the present, is the paradox of infinite identity (the infinite identity of both directions or senses at the same time- of future and past, of the day before and the day after, of more and less, of too much and not enough, of active and passive, and of cause and effect.)” (Logic of Sense 2).
According to Deleuze’s critique of the “regimes of representation” in Difference and Repetition, Leibniz had made representation infinite instead of overcoming it, thereby producing a “delirium” which “is only a pre-formed false delirium which poses no threat to the repose or serenity of the identical” (63). In The Fold, Deleuze asserted that “one must see Leibniz’s philosophy as an allegory of the world, and no longer in the old way as the symbol of a cosmos” (174).
In this manner, fixed identity had given way to infinite iteration in the shape of a “continuous metaphor” (metaphora continuata). This infinite deferral of proper meaning made incessant creation possible; truth was “infinitely determined,” each viewpoint becoming “the condition of the manifestation of truth” (Deleuze, Lecture on Leibniz, 16 December 1986). Leibniz’s philosophy of “mannerism” consisted in “constructing the essence from the inessential, and conquering the finite by means of an infinite analytic identity” (Difference and Repetition 346). Truth lay in infinite variation itself, each moment eliciting a different modality of an essentially elusive essence that could never be directly grasped or circumscribed.
Leibniz turned paradox into a marvelously fruitful tool, emblematic of the audacity and subtlety which drove the endless twists and turns of his broader thought process. Far from being the mark of a flawed system, it ensured that the system would remain contradiction-free by bringing about the “coincidence of opposites” (The Fold 33) in the process, confirming Leibniz as the quintessential philosopher of the Baroque age.
Ultimately both Leibniz and Deleuze inveighed against the poverty of the conventional thought process and set out to open up new horizons of thought by recovering the genetic force of paradox. Paradox threatened to overturn the very foundations of philosophical reason. And yet, by unsettling and challenging us, it forced us to think.
Audrey Borowski is a DPhil student in the History of Ideas at the University of Oxford.