The notion that logic is a domain inhospitable to the prevarications of natural languages is an assumption that has long been held by philosophers and literary theorists alike. Of the logician, W.V. Quine once wrote that “he does not care how inadequate his logical notation is as a reflection of the vernacular, as long as it can be made to serve all the particular needs for which he, in his scientific program, would have otherwise to depend on that part of the vernacular.”1 Seeking, for his part, to disambiguate the roles of linguistic structure and the tendencies of speech in sense-making, Paul de Man noted that “rhetoric radically suspends logic and opens up vertiginous possibilities of referential aberration.” 2 Since Aristotle, it might be said, the means by which one determines the truth or falsity of a statement has necessarily excluded terms that sidestep, by virtue of their sheer utterability, the requirement to point decidedly to a referent. Yet what if, in the long history of this inheritance, such terms were never merely unruly elements that qualified for expulsion but, in fact, were inadvertently invited into the house of logic, registering their presence in language even as reason denied their admissibility into its lexicon of existence and possibility?
It is the great merit of Daniel Heller-Roazen’s extraordinarily rich and ambitious book, No One’s Ways, to have not only posed this very question but to have tracked its career through the centuries from the perspective of one such excluded element, the deceptively innocuous particle “non-.” From the earliest constructions of propositional logic, terms such as “non-man” have been consigned to the domain of the “indefinite”: not a name for something, yet not quite the same as a negation either, such non-words have had to inhabit a region beyond the purview of the syllogistic proof, since they invoke neither something nor its logical negation, but rather everything besides the definite thing. Eventually, these indefinite terms acquired a new identity—the “infinite name”—under which the indefinite expanse of possible non-significations is simultaneously refused and affirmed, denied and contained, for fear that the “anything but” would undermine the “everything” that a “thing” can be said to be. Going far beyond a simple reconstruction of the history of logic and its companion disciplines, No One’s Ways proffers a wholly new look at the logics of exclusion from the standpoint of an equivocation that underlies the very construal of that logic. This equivocation, it argues, is traceable from the very first treatises devised for the purpose of securing logic’s borders against the possibility that infinitization would fracture the unicity of the predicative statement. Moreover, inasmuch as we, as speaking beings, are endowed with the sheer grammatical capacity to enunciate the name of anything that is not some definite thing, this threat cannot not persist. For Heller-Roazen, much of the history of philosophy, ranging from Aristotle’s medieval interpreters to Leibniz and Kant and through the German Idealists and their epigones, can thus be recast as a preoccupation with controlling the extrinsic and intrinsic partitioning that the infinite name promises to visit upon what is.
Indeed, Heller-Roazen writes, “whenever thinking encounters ‘non-being’ or ‘non-art,’ the ‘non-event’ or a ‘non-person,’ the question of infinite naming arises anew” (250). The persistence of this question therefore also serves as an appeal to examine the singularity of no one’s forays into other domains, an appeal which is taken up by Julie Orlemanski in the first response of this forum. Reflecting on the possibilities of infinite self-naming that remain just beyond the purview of the philosophical investigations thereof, Orlemanski speculates on the applicability of Heller-Roazen’s study to one such domain: disability studies. Disability per se is not thematized in No One’s Ways, and as Orlemanski points out, Aristotle himself mobilizes the example of sightlessness as an illustration of mere privation in the Categories and the Metaphysics. But disability also falls within the remit of the third species of “non-” terms, specifically indefinite verbs, which do not so much exclude sight as demarcate a limit beyond which the affirmation of whatever is non-seeing or non-recovering is itself without limit. As Orlemanski asks, might disability studies therefore be another as yet unrecovered chapter in the story of infinite naming? Could disability prove to be another refuge of “non-man” where physical existence manages to evade judgment, whether medical, legal or political?
One of the major claims that is reasserted in various ways throughout Heller-Roazen’s book is that the very process by which an edifice has been constructed for logic and in the name of logic itself produces that which requires bracketing out in order for logic to maintain its definition. In De Interpretatione, for instance, Aristotle summons the indefinite name as something he would soon take leave of for the sake of his science; as Heller-Roazen writes, it is as though Aristotle intended for non-words to persist, inasmuch as they sound out the condition of being without perceptible boundary, in the very architecture of certainty, determinacy, well-ordered contrariety, and reference. In other words, indefiniteness serves the science of definition; the science of sense relies, in a sense, on its own admission of non-sense into the territory of sense-making. Moreover, at a crucial juncture in the reception of Aristotle, indeterminate terms come to signify not just a single uncertainty, but an infinite range of excess signification. This leaves its mark all the way through to the twentieth century. As Juliette Kennedy remarks in the second response of this forum, a straight line might indeed be drawn from Boethius, who was the first to bring the infinite into view in the designation of “indefinite,” to Russell, who similarly affirms a range of non-denotable non-designations by virtue of his pinning reference down to a knowledge of the particular. But, for Kennedy, Heller-Roazen’s account thereby also leads directly into the mathematical controversy that was generated from Cantor’s discovery of the transfinite numbers. This was, in her words, a rediscovery of the question of whether objects with infinite names were also legitimate objects of mathematical propositions. In mathematics, actual infinites might be said to behave like the infinite name inasmuch as they, too, make intuitable an infinite array of items that sit within a range of denotability. Unlike the grammarians and logicians, however, Cantor regarded the infinite not as an indefinite morass of ontologies or interpretations, but as complete and ramified into a single ontology. Thus, Kennedy asks, might it not be the case that the centuries-old quarrel between logic and grammar encounters a solution in mathematics—or, conversely, that one of modern mathematics’ most radical advances was made with the help of the very problem that inaugurates the story of logic and its uneasy, fricative relationship with natural language?
Indeed, one of the most intriguing proposals of Heller-Roazen’s study is that logic, language and mathematics are not just proximate domains but share permeable borders across which they can, given the opportunity, affect one another. At stake in this notion is not just that modern mathematics, in virtue of its new valuation of its symbols, begins to behave like a natural language, but that mathematics changes the very nature of symbolization, language’s position in relation to thought, and therefore naming itself. As Markus Hardtmann remarks in the third response of the forum, it is no accident that the variable gains in importance in the history of logic just as the infinite name recedes from view. Switching the focus from ω to x, Hardtmann argues that Frege’s introduction of the function-argument analysis of predication represents a turning point in the history of logic, not least because the statement “there is an x, such that not f(x)” is simply not mappable onto “x is a non-man”; in modern logic, notation takes leave of grammar altogether. The x in modern formal logic is no longer the x of classical logic, for the specific reason that it no longer needs to refer to the meaning of a specific term, a res, or thing; in other words, x is no longer a name but a variable. And in the event that x denotes “any” term without ranging across the border into the domain of “everything” a thing is—simply because such a border is no longer relevant in the context of a function—are we not, Hardtmann asks, in need of revisiting what it is we might still mean by name, or sign, or indeed signification?
The question of what is left of the name after nominalism is also the question that, for Heller-Roazen, inaugurates the defining event of contemporary philosophy, namely the “parting of the ways” of logical positivism and phenomenology circa 1929, which is the moment with which No One’s Ways culminates. At the same time as Carnap and others were occupied with emancipating logic from the constraints of natural languages, Heidegger sought a “prelogical foundation” (227) in the consciousness that makes predicative assertion possible in the first instance. And though Heidegger, like Carnap, remained unconcerned with the destiny of the grammatical particle “non-“, this very insensitivity on the part of philosophy demonstrates, for Heller-Roazen, that the afterlife of the particle would hereafter persist in language. In the fourth and final response of the forum, Eleanor Kaufman explores the ramifications of this insight for our understanding of how the particle ne operates in Lacanian ontology inasmuch as it appears in language in a negative yet non-negating function. This ne, Kaufman notes, is prelogical yet discursive; it operates in speech, not on the level of the unconscious. Indeed, inasmuch as it articulates negation it seems to undermine negation per se; the Lacanian ne has, in this sense, a unique approximation to the real. Might there be an affinity between Lacanian non-being and the non-words uncovered by Heller-Roazen in his history of the infinite name? And if so, might this imply that there is something like an “unconscious” to logic—that the “unconscious,” too, is an infinite name, something non-identical with itself that needs to be summoned in order for discourse to constitute itself?
Tracking down the multifarious ways in which non-being makes an appearance within the logical and discursive structures that have been erected on the promise of its disappearance might seem like an infinite task but is precisely the achievement of No One’s Ways. As the following exchanges attest, the history of this apparently unremarkable fact of natural grammar named “non-” has proven to be precisely the incitement for thinking in the name of which Heller-Roazen introduces his project. I hope you will agree.