We are, then, going to be spending time on the frontier.1 On the frontier, which is also to say on the border, the extremity, the limit, the marches, the confines, on the edge, the periphery, around the rim, on the boundary, the shore, the threshold, the end. And perhaps especially on the frontier one can imagine passing between these various words and concepts, or rather these terms (a term is a frontier). According to one traditional (philosophical) approach to philosophy, our task here would consist in establishing as precisely as possible the frontier between these diverse words and concepts (in order to determine, for example, whether we are really dealing with different concepts or the same concept under different names), and doing so successfully might be thought to be a condition of their conceptual status, if they are to achieve such status. For, or so one might think, a concept is only a concept if it can be precisely and completely delimited. I am borrowing the formula for this eminently philosophical demand not from, say, Descartes or Kant, but, for strategic reasons to do with the style or manner of philosophy being practiced here, from Gottlob Frege. Here, in the Grundgesetze der Arithmetik:
The concept must have a sharp boundary [der Begriff muss Scharf begrenzt sein]. If we represent concepts in extension by areas [Bezirke] on a plane, this is admittedly a picture [ein Gleichnis] that may be used only with caution, but here it can do us good service. To a concept without sharp boundary there would correspond an area that had not a sharp boundary-line all round, but in places just vaguely faded away into the background [stellenweise ganz verschwimmend in die Umgebung überginge: note that here the boundary or frontier of the concept apparently separates it from an Umgebung, a milieu, an environment or a fringe-area that are apparently imprecise, a wasteland rather than other concepts, perhaps even a liquid medium in which the concept might be swimming]. This would not really be an area at all; and likewise a concept that is not sharply defined is wrongly termed a concept. Such quasi-conceptual constructions [solche begriffsartige Bildungen] cannot be recognized as concepts by logic; it is impossible to lay down precise laws for them [note this language of legislation: the point for Frege, very Kantian here, is to delimit a territory with a view to legislation]. The law of excluded middle is really just another form of the requirement that the concept should have a sharp boundary. Any object δ that you choose to take either falls under the concept or does not fall under it; tertium non datur. E.g. would the sentence “any square root of 9 is odd” have a comprehensible sense at all if square root of 9 were not a concept with a sharp boundary? Has the question “Are we still Christians?” really got a sense, if it is indeterminate whom the predicate “Christian” can truly be ascribed to, and who must be refused it?2
This demand of Frege’s, repeated from beginning to end of his work,3 this demand that is the demand of philosophy itself, this demand that is legitimate if ever a demand were legitimate—drawing a clear frontier is the beginning of legitimacy—has several immediate and paradoxical consequences:
1. If one is to speak clearly and be recognizable by logic, and indeed to mean anything at all, one must have concepts with sharp frontiers.
2. The need or obligation in which we find ourselves to draw or find such sharp frontiers assumes that in fact we find cases where such frontiers have not been traced, pseudo-conceptual constructions that must be got rid of.4
3. As every concept must have such a frontier to ensure its definition, every concept presupposes the frontier, and so there can be no concept of frontier that does not presuppose that its object is already known.
4. Which is why we have to speak in images (bildlich), metaphorically rather than conceptually.
5. Which means that not only do we not have a sharply defined concept of what a frontier is, but nor do we have a sharply defined concept of what a concept is in general (not having a concept of frontier, but rather a metaphorical illustration, although the frontier defines the concept: so the concept as such, and not just the frontier, is being defined metaphorically).
6. Which means that in the end it remains indeterminate to what the concept “concept” can be assigned in truth, given that the non- or quasi-conceptuality of the frontier means that the concept “concept” is not clearly defined and remains a quasi-concept. The definition of the concept “concept” cannot be complete, because it depends on the definition of the frontier that delimits it—and the frontier defining the concept cannot be defined, not being a concept but the preconceptual condition of any concept.
Frege’s philosophical difficulties repeatedly confirm this slightly brutal analysis. For example, in “On Concept and Object” (1892), written in response to a certain Kerry:
Kerry contests what he calls my definition of “concept.” I would remark, in the first place, that my explanation is not meant as a proper definition. One cannot require that everything shall be defined, any more than one can require that a chemist shall decompose every substance. What is simple cannot be decomposed, and what is logically simple cannot have a proper definition [was logisch einfacht ist, kann nicht eigentlich definiert werden]. Now something logically simple is no more given to us at the outset than most of the chemical elements are; it is reached only by means of scientific work. If something has been discovered that is simple, or at least must count as simple for the time being, we shall have to coin a term for it, since language will not contain an expression which exactly answers. On the introduction of a name for something logically simple, a definition is not possible; there is nothing for it but to lead the reader or hearer, by means of hints [durch Winke anzuleiten; to lead by allusions, pointers, insinuations, almost winks, the wink of a slightly secret and perhaps shameful complicity] to understand the word as is intended. (Kleine Schriften, 167–68/182–83; my emphasis)5
Because “concept” is the name of something logically simple, it cannot be defined, and we cannot know whether it has a clear-cut frontier. It will be objected that this is a straightforward consequence of what is sometimes called Frege’s Paradox—namely, that because in Frege “concept” (or “function”; it is by an extension of the mathematical notion of function that Frege develops his concept of concept) always names a predicate (i.e., an incomplete or unsaturated expression of the type “. . . is the capital of the German Empire” [Frege’s example]), one cannot name a concept without transforming it into what Frege calls an object (an object being what is properly named by a name, and a name what properly names an object), which object is, precisely, the other of the concept or function. There is between object and concept a clear frontier that means one cannot directly address the concept without transforming it into an object:
It must indeed by recognized that here we are confronted by an awkwardness of language, which I admit cannot be avoided, if we say that the concept horse is not a concept, whereas, e.g., the city of Berlin is a city, and the volcano Vesuvius is a volcano. Language is here in a predicament [ein Zwangslage] that justifies the departure from custom. The peculiarity of our case is indicated by Kerry himself, by means of the quotation-marks around “horse”; I use italics to the same end. There was no reason to mark out the words “Berlin” and “Vesuvius” in a similar way. In logical discussions one quite often needs to say something about a concept, and to express this in the form usual for such predications—viz. to make what is said about the concept into the content of the grammatical predicate. Consequently, one would expect that what is meant by the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or, more precisely, an object must go proxy for it. (170–71/185–86)
So if one wishes to insist on the clear-cut definition of the concept, we must first find the definitional frontiers of the object. But this is no more possible on the side of the object, if we are to believe Frege, than on the side of the concept:
When we have thus admitted objects without restriction as arguments and values of functions, the question arises what it is that we are here calling an object. I regard a regular definition [ein schulgemässe Definition] as impossible, since we have here something too simple to admit of logical analysis. It is only possible to indicate [hinzudeuten] what is meant. Here I can only say briefly: An object is anything that is not a function [i.e., a concept], so that an expression for it does not contain any empty place. (134/147)
So we will never have a definition of the concept or of the object. This turns out to be part of the very logic of definition: In a little text on formal theories in arithmetic (1885), Frege, seeking “a certain sharpness of delimitation, a certain logical completeness [eine gewisse Schärfe der Abgrenzung, eine gewisse logische Vollkommenheit],” intends to show that arithmetic can be entirely derived from logic, that (for once) “there is no sharp boundary [keine scharfe Grenze] between the two” (103/112). In the course of this argument, Frege devotes a development to the question of definition, precisely:
In the case of any definition whatever we must presuppose as known something by means of which we explain what we want understood by this name or sign. We cannot very well define an angle without presupposing knowledge of what constitutes a straight line. To be sure, that on which we base our definitions may itself have been defined previously; however, when we retrace our steps further, we shall always come upon something which, being a simple, is indefinable, and must be admitted to be incapable of further analysis. And the properties belonging to these ultimate building blocks [Urbansteinen] of a discipline contain, as it were in a nutshell [im Keime, in germ, as seeds], its whole contents. [. . .] Now it is clear that the boundaries of a discipline are determined by the nature of its ultimate building blocks. (104/113–14)
The frontiers of a science are thus traced, in their necessary clarity (if we are trying to say there is no such frontier between arithmetic and logic, this is in order to assert that, precisely, they are not separate sciences), by the ultimate blocks that are their basis. These blocks, assumed to be simple,6 which can only be simple, are precisely what cannot be defined, and they condemn us, even in logic, to metaphors and hints or winks, and thus to nonsimplicity.7
The impossibility of arriving at a clear definition of the frontier, and thus of the concept of concept, means that no more can one be certain of the frontiers of a science, which inherit the lack of sharpness that thus affect its constitutive elements, the building blocks that contain the germ (note that Frege, condemned to metaphor, does not wield it with any great care or logic). As Jacques Derrida has taught us, the foundation of an institution, its very institution, the institution of the institution, including the institution of a science, and even of a science of logic, cannot be understood by that institution, can only be violent with respect to that institution.8 What I am trying to show here is that the frontier is the enduring (uncrossable) trace of that violent institution of the institution in general, and that this violence marks all concepts with the trace of a constitutive nonconceptuality. Frege, who is a bit disgusted by all this, can only give hints, slightly shady winks, base himself on a common precomprehension of the language, or else speak metaphorically to get across the frontier and get us to logic, conceptuality, and clarity. At the root of Fregean logicism, and of all the philosophy of language that is inspired by it, there is, then, a constitutive and unthought murkiness (unthought and unthinkable in the terms of such a philosophy), a nonlogical frontier of logic, a frontier that cannot be traced clearly, a poorly defined zone that is named, for want of anything better, by “image,” “metaphor,” or “indication.” Even a logical notation, such as the Begriffschrift proposed by Frege in 1879, which is at the root of all subsequent logical notations, necessarily has its roots in this zone. All of Frege’s philosophy (and therefore a few others’ too) tries desperately to repress this nonlogical “origin” of logic behind dogmatic demands and stipulations—whence its deep-seated moralism. This murkiness that defines the definition itself and makes it indefinite, and is, therefore, the indefinite definition of definition, the quasi-conceptual nature of conceptuality, undermines all the bases of this philosophy, up to and including the famous and untenable distinction between Sinn and Bedeutung, and condemns Frege to the very fiction and metaphor he tried so hard to avoid. If, as Derrida claims in Schibboleth, the indecision of the frontier between the philosophical and the poetical is what most provokes philosophy to think,9 then it must be said that the philosophy that appeals more or less directly to Frege is the philosophy that most firmly tries to block thinking. Not only do we not find a concept of frontier in Frege, but we find in him and his successors that the essential lack of that concept means there is no concept of concept either, nor indeed of anything else. We will, then, never know if we are still Christians, or even, it seems, if that question has any meaning. We will never cross the frontier into absolute clarity.
Having got stuck here, how are we going to move forward? Our book on the frontier really is on the frontier, and even on the frontier of the frontier, apparently unable to define its object, to draw a frontier that would allow us to cross over and get started. (For the more sharply a frontier is drawn, the easier it is to cross, according to a law we would need to formalize—or that is the law of formalism itself.)
As we have seen, in attempting to approach our object philosophically, we have rapidly run up against an impossibility, or even a petitio principii: Not being able to define the concept of frontier without presupposing the possibility of drawing nonconceptualizable frontiers around it condemns us to a mode of indirectness that shows up right here, from the start, in the form of an inevitable resort to what philosophy would call analogy, image, or metaphor. This “metaphor” of the frontier is not neutral or innocent but immediately leans toward a geometric or cartographic, and ultimately geopolitical, language. Rather than remaining stuck on the metaphor of conceptual frontiers, why not turn to the apparently literal sense of that metaphor? If we cannot make the conceptual frontier literal, and if it will remain forever metaphorical, might we not, instead, pursue the “literal,” geopolitical frontier?
There are two ways of proceeding here, and we need to distinguish them at least provisionally, to draw a frontier between them. The first would consist in claiming a certain failure of philosophy: having failed to produce a concept of the frontier, philosophy sees conceptuality itself collapse. According to this first way of proceeding, if we want to pursue our inquiry, we would need to drop philosophical demands as illusory and be content with an empirico-positive study of frontiers. We cannot follow that route here, because in spite of all the interesting things that might be said within the framework of such a study (especially, perhaps, at the present moment) it would sooner or later come up against the fact that it cannot fail to presuppose that it knows what a frontier is, that therefore it has a concept of the frontier, when it claims to draw its whole supposed legitimacy from the fact that no such concept can be produced. Which means it is indulging in what Derrida might call “transcendental contraband.”10
The second way of proceeding, the one we will follow here, consists not in forgetting philosophy but in retreating more modestly—and provisionally—from logic or pure or fundamental philosophy in order to move toward a philosophy that claims to deal directly with the region in which we have located the “literal” sense of the frontier (i.e., political philosophy). This retreat can only be provisional, because we shall see that the very project of delimiting something like a “region” presupposes frontiers that will constantly refer us from politics to logic, from a logic of politics to a politics of logic, in a movement that can come under neither logic nor politics, at least as they are usually understood.
What do we find in political philosophy as to the frontier? Basically, not very much. Let me put forward the hypothesis that, in general, political philosophy tries to think the State or the polis in the singular. This object must be delimited and defined, thus surrounded by a frontier, but to the extent that the object is usually presented as essentially singular, this frontier is more often presupposed than thought. In classic political philosophy, it appears that we first try to define or deduce the State (Plato and Aristotle would be the obvious loci classici), and if one asks questions about the relations this State can have with other States, this is done later, as though it were a secondary problem. Rousseau’s Social Contract, for example, seems to be coherent in spite of the absence in the main text of any reflection on the frontier of the State and, therefore, its relation with other States.11 Here, via analysis of some texts of Kant’s, I will be trying to show that, in fact, the problem of the frontier is the primary problem of political philosophy, that this problem entails the thought of what I shall call an “absolute exteriority,” and that it cannot be resolved dialectically. We shall never cross over this frontier.
1. In the French text I was able to write “nous allons passer du temps à la frontière,” which can also be read quite pertinently as meaning “we are going to move from time to the frontier,” which captures one distant aspiration of the book—namely, to insist on the resistance of spatiality to its philosophical sublation into time.
2. Gottlob Frege, Grundgesetze der Arithmetik (Hildesheim, Germany: Georg Ohms, 1962), vol. 2, §56; partial translation in Translations from the Philosophical Writings of Gottlob Frege, ed. Peter Geach and Max Black (Oxford: Blackwell, 1970), 139. I address Wittgenstein’s comments on this demand of Frege’s in Frontiers: Kant, Hegel, Frege, Wittgenstein (CreateSpace, 2003), 372–75.
3. I quote Frege’s papers from Kleine Schriften, ed. Igancio Angelelli (Hildesheim, Germany: Georg Ohms, 1967), tr. Hans Kaal as Collected Papers on Mathematics, Logic and Philosophy, ed. Brian McGuinness (Oxford: Blackwell, 1984). In the text “On the Law of Inertia” (1891), for example, “If something fails to display this sharp boundary [diese scharfe Begrenzung], it cannot be recognized in logic as a concept”; in “Function and Concept” (1891), he states that “as regards concepts we have a requirement of sharp delimitation [scharfe Begrenzung]” (135/148), or “If something fails to display a sharp boundary, it cannot be recognised in logic as a concept” (122/133), and constantly warns against any “blurring” of boundaries. Thus in a polemical exchange from 1906 with a certain Korselt, “I have been at pains to draw sharp boundaries; Mr Korselt, it seems, diligently blurs them once again” (281/293), or more generally, and crucially for Frege’s uncompromising realism, he is determined to “prevent the blurring of the boundary between psychology and logic” (343/352).
4. Frege goes so far as to make of this the motor of the history of science, while contesting the role of contradiction in this respect. According to Frege, a concept can perfectly well involve a contradiction without for all that ceasing to be a concept or calling for any development or sublation. Recall that in The Foundations of Arithmetic it is the contradictory concept “not equal to itself” that helps Frege define the zero, from which all the rest is supposed to follow. This idea is developed in “On the Law of Inertia”:
The concept of not being identical with itself contains a contradiction and remains none the less what it is and always was, and still does not look as if it was about to develop further. It has a good claim to being recognized in logic as a concept, for its boundary is as sharp as it can possibly be; and one can make good use of it in defining the number 0, as I have shown in my book, The Foundations of Arithmetic. In our case too, it is not contradictions in the concept of motion that are the driving force behind its development. Contradictions have indeed appeared; but it is not as if they had been created by combining mutually contradictory characteristic marks in the definition; they have, rather, been created by treating as a concept something that was not a concept in the logical sense because it lacked a sharp boundary. In the search for a boundary line, the contradictions, as they emerged, brought to the attention of the searchers that the assumed boundary was still uncertain or blurred, or that it was not the one they had been searching for. So contradictions were indeed a driving force behind the search, but not contradictions in the concept; for these always carry with them a sharp boundary: it is known that nothing falls under a contradictory concept; it is therefore impossible to doubt whether or not a given object falls under the concept, once the contradiction in it has been recognized. The real driving force is the perception of the blurred boundary [die Wahrnehmung der verschwommenen Begrenzung]. (Kleine Schriften, 123/134)
5. See too, a little later: “Kerry holds that no logical rules can be based on linguistic distinctions; but my own way of doing this is something that nobody can avoid who lays down such rules at all; for we cannot come to an understanding with one another apart from language, and so in the end we must always rely on other people’s understanding words, inflexions, and sentence-construction in essentially the same way as ourselves. As I said before, I was not trying to give a definition, but only hints [Winke]; and to this end I appealed to the general feeling for the German language [das allgemeine deutsche Sprachgefühl]. It is here very much to my advantage that there is such good accord between the linguistic distinction and the real one” (169–70/184–85; neither the first nor the last German philosopher to find to his satisfaction that his language accords so well with reality). This problem returns constantly: “I admit that there is a quite peculiar obstacle in the way of an understanding with the reader. By a kind of necessity of language, my expressions, taken literally, sometimes miss my thought; I mention an object, when what I intend is a concept. I fully realize that in such cases I was relying upon a reader who would be ready to meet me half-way [ein wohlwollendes Entgegenkommen des Lesers]—who does not begrudge a pinch of salt [einem Körnchen Salz]” (177/193). See too the paper “What Is a Function?” (1904): Frege has just said that functions, unlike numbers, are unsaturated, and he continues: “Of course this is no definition; but likewise none is here possible. I must confine myself to hinting at what I have in mind by means of a metaphorical expression [Ich muss mich darauf beschränken, durch einbildlichen Ausdruck auf das hinzuweisen, was ich meine], and here I rely on my reader’s agreeing to meet me half-way” (280/292). I have tried to show elsewhere that this type of appeal to the reader condemns philosophy to what it calls “metaphor”; see my “Lecture—de Georges Bataille,” in my Géographie et autres lectures, 5–32 (Paris: Hermann, 2011).
6. But this cannot be demonstrated just because of the impossibility of definition—the same impossibility that is supposed to confirm the simplicity in question. This is why the Wittgenstein of the Tractatus makes of this type of simplicity a logical necessity: There must be simples, even if we are not in a position to describe their nature. These simples in the Tractatus (2.02) are strictly logical and not to be confused with any empirical simple, as some positivists have thought.
7. Frege’s frustration is, in fact, a frustration with language itself. In the first of the Logical Investigations (entitled simply “Thoughts”), we find the following: “I am not here in the happy position of a mineralogist who shows his audience a rock-crystal [or perhaps a pinch of salt]: I cannot put a thought in the hands of my readers with the request that they should examine it from all sides. Something in itself not perceptible by sense, the thought, is presented to the reader—and I must be content with that—wrapped up in a perceptible linguistic form. The pictorial aspect of language [die Bildlichkeit der Sprache] presents difficulties. The sensible always breaks in and makes expressions pictorial and so improper. So one fights against language [there is “ein Kampf mit der Sprache”], and I am compelled to occupy myself with language although it is not my proper concern here. I hope I have succeeded in making clear to my readers what I mean by ‘a thought’ ” (350n4/360n6).
8. See, for example, Jacques Derrida, Force de loi: le “fondement mystique” de l’autorité (Paris: Galilée, 1994), tr. Mary Quaintance as “Force of Law: The ‘Mystical Foundation’ of Authority” in Acts of Religion, ed. Gil Anidjar, 231–98 (London: Routledge, 2002), 242; and “Mochlos, ou le conflit des facultés,” in Du droit à la philosophie, 397–438 (Paris: Galilée, 1990), 435, tr. Jan Plug as “Mochlos or the Conflict of the Faculties” in Eyes of the University: Right to Philosophy 2, 83–112 (Stanford, CA: Stanford University Press, 2002), 109–10.
9. Jacques Derrida, Schibboleth: pour Paul Celan (Paris: Galilée, 1986), 80, tr. Thomas Dutoit as “Schibboleth: For Paul Celan” in Sovereignties in Question, 1–64 (New York: Fordham University Press, 2005), 44.
10. This is not only the case with the so-called human sciences, in that philosophy falls very easily into this trap. This seems to be notably the case with Foucault, who can in principle say everything except how it is possible for him to say what he says. The case of Deleuze seems more complex. In the zone of our immediate preoccupations, one can find a very interesting exploitation of a “political” language in the conceptual domain: “Thought as such is already in conformity with a model that it borrows from the State apparatus, and which defines for it goals and paths, conduits, channels, organs, an entire organon. There is thus an image of thought covering all of thought; it is the special object of ‘noology’ and is like the State-form developed in thought. This image has two heads, corresponding to the two poles of sovereignty: the imperium of true thinking operated by magical capture, seizure or binding, constituting the efficacy of a foundation (mythos); a republic of free spirits proceeding by pact or contract, constituting a legislative and juridical organization, carrying the sanction of a ground (logos). [. . .] But confining ourselves to the image, it appears that it is not simply a metaphor when we are told of an imperium of truth and a republic of spirits. It is the necessary condition for the constitution of thought as principle, or as a form of interiority, as a stratum” (Gilles Deleuze and Félix Guattari, Capitalisme et Schizophrénie: Mille plateaux [Paris: Minuit, 1980], 465–66, tr. Brian Massumi as A Thousand Plateaus: Capitalism and Schizophrenia [Minneapolis: University of Minnesota Press, 1987], 374–75; the translation makes the passage a little more assertive than the original, in which the verbs in the first two sentences quoted above are in the conditional). And more generally, everything that is described in terms of territorialization and deterritorialization, and even nomadism, goes in the direction of what we are proposing here. But Deleuze clearly gives priority to one of the terms in these descriptions. So politics (the State form) is supposed to be the key to the concept, and within this “politics,” the nomad always has a privilege (a privilege one might find a little “romantic”) over the sedentary.
11. The final chapter of the work, entitled simply “Conclusion,” reads as follows in its entirety: “After setting down the true principles of political right and trying to found a State on its basis, it would remain to buttress the State by its external relations; which would include the right of nations, commerce, the right of war and conquests, public right, leagues, negotiations, treaties, etc. But all this forms a new object too vast for my short sight; I should always have fixed it nearer to myself” (tr. Victor Gourevitch in The Social Contract and Other Later Political Writings, 39–152 [Cambridge: Cambridge University Press, 1997], 152). See the commentary by Peggy Kamuf in Signature Pieces: On the Institution of Authorship (Ithaca, NY: Cornell University Press, 1988).