We're going to be on the frontier for the next three years. Or at the border, on the edge, at the limit, in the margin, on the boundary, perhaps in no-man's land - maybe at the barrier or on the barricade, or even on the fence (let me remind you that 'fence' is the everyday sense of the French word clôture, now systematically translated 'closure'): and especially, perhaps, on the frontier (or border, edge, limit, margin, boundary, barrier, barricade or fence) between these various, non-synonymous words or concepts. But even though we'll be on the frontier for three years, we'll take things term by term.

One of the questions I'd like us to follow as literally as possible is that of how frontiers or boundaries happen. More naïvely or traditionally, we might ask, what is the nature of a frontier or a boundary? One of the texts we'll certainly be looking at sooner or later is the comment in Marx about exchange beginning accidentally at the frontiers of natural communities. (In due course we'll need to read this against Aristotle's analysis of exchange in the Politics, where this value of the 'accidental' as opposed to the 'natural' also plays a vital role in the argument about exchange.) We might want to wonder what a 'natural community' is, and whether natural communities have so-called 'natural boundaries' (where exchange begins accidentally). It's quite common to talk of coasts, rivers or ranges of mountains as 'natural boundaries': but we might wonder whether there are or ever could be natural boundaries, or whether natural boundaries are only ever called boundaries by analogy with non- natural ones, once they have been crossed. Or are all boundaries natural boundaries in the sense of being boundaries of nature, boundaries to nature, lines where nature ends, the transition or transgression point of nature into one of its others (culture, law, tekhné, politics, etc.)? Maybe every frontier also divides nature and culture.

Here's one description of a frontier happening, or not quite happening:

Remus, the story goes, was the first to receive a sign - six vultures; and no sooner was this made known to the people than double the number of birds appeared to Romulus. The followers of each promptly saluted their master as king, one side basing its claim upon priority, the other upon number. Angry words ensued, followed all too soon by blows, and in the course of the affray Remus was killed. There is another story, a commoner one, according to which Remus, by way of jeering at his brother, jumped over the half-built walls of the new settlement, whereupon Romulus killed him in a fit of rage, adding the threat, 'So perish whoever else shall overleap my battlements'. (Livy, I,6)

From which let's hold on at least to the suspicion that frontiers are constructed against prior violence or discord, and that their construction involves their being crossed before they can prevent crossing, all still in violence. Tracing a frontier is here a violent move in a violent context, and invites the further violence of jealousy, jeering, revenge and threat. Later on, reading Lyotard's The Wall of the Pacific, we'll come back to Rome and its frontiers, and wonder to what extent it can be taken as paradigmatic of frontiers in general.

Here's another, more recent description of a frontier happening, or not quite happening:

Wherever two regions are about to form a boundary (...), the third region (...) establishes a chain of outposts. In order that these outposts do not form bilateral borders with their neighbours, they in turn are surrounded by chains of islands in a structure which is repeated down to infinitely small dimensions...

What may seem almost impossible as a boundary between three 'countries' can be extended without any mathematical difficulty to situations with 4,5,6... competing domains. The boundary is made up entirely of points where 4,5,6... countries meet. (Peitgen and Richter, The Beauty of Fractals, p. 19).

This is from a popularising book about 'fractals'. One of the attractions of fractal geometry has been that it promises mathematical descriptions or models of 'natural' phenomena (coastlines and clouds, roots and branches, weather and turbulence) that had previously looked chaotic from the point of view of Euclidean geometry and Newtonian or even quantum mechanics. And although I hope we might one day look with due modesty at the strictly mathematical aspects of fractals, let's just note here the uncontrolled mixing in this description of 'natural' and 'political' language: there's talk of 'islands' but also of 'countries', of 'competing domains' involving borders with 'neighbours', and more than a suspicion of teleology in the mysterious 'In order that these outposts do not form bilateral borders...'. Where does the competition come from, and what force is preventing bilateralism in the name of a more complex plurality? Perhaps the boundary between the natural and the political here could itself be described in fractal terms, but let us beware of a covert metaphysics informing these descriptions, and the desire we may have to appeal to 'scientific' description as a final arbiter of our problems to come.

I started with a list of related words or concepts - or let's call them terms: frontier, boundary, edge, limit, border, margin. One thing I expect we may spend some time on is pretending to do some 'ordinary language philosophy' around these terms, or trying to establish their 'grammar', in Wittgenstein's sense. We can, I suppose, already invoke Derrida's handy notion of 'non-synonymous substitutions', though we need to recognise that this is also the name of a problem (what determines the substitutions if the terms are not synonymous - i.e. interchangeable salva veritate, in Leibniz's definition?). There seems to be good reason to think of Derrida here, not only in that he makes abundant use of this vocabulary, but because these words or concepts or terms (frontier, border, etc.) seem to share with others, such as difference, the complication involved in also saying something about what it is to be a concept, a word or a term. The term 'term', at any rate, means just that: boundary, border or frontier of territory: a term can be a stone or post (traditionally carved with the image of Jupiter terminus, god of boundaries) marking the limit of possession of a piece of ground. In one conception of philosophy at least, it would be our task to establish as precisely the possible the frontiers between these various concepts - and the establishment of precise frontiers between them would be a condition of their conceptuality. Frege famously suggests that if a concept does not have precise boundaries then it is simply not a concept:

The concept must have a sharp boundary. If we represent concepts in extension by areas on a plane, this is admittedly a picture that lay 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. 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 cannot be recognised as concepts by logic; it is impossible to lay down precise laws for them. 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? (Grundgesetze der Arithmetik, Vol. 2, par.56: Translations, p. 139)

And Wittgenstein equally famously contests this necessity, typically enough by pursuing Frege's analogy or 'picture' (which Frege has said 'may be used only with caution', and to which he himself could not accord conceptual status - Frege's passage is a non-conceptual description of what a concept is or must be): here, for example, in par.71 of the Philosophical Investigations:

One might say that the concept 'game' is a concept with blurred edges. - 'But is a blurred concept a concept at all?' - Is an indistinct photograph a picture of a person at all? Is it even always an advantage to replace an indistinct picture by a sharp one? Isn't the indistinct one often exactly what we need?

Frege compares a concept to an area and says that an area with vague boundaries cannot be called an area at all. This presumably means that we cannot do anything with it. [You'll remember that Frege actually complains about an impossibility of laying down the law for it] - But is it senseless to say: 'Stand roughly there'? Suppose that I were standing with someone in a city square and said that. As I say it I do not draw any kind of boundary, but perhaps point with my hand - as if I were indicating a particular spot.

Or again, a little earlier:

I can give the concept 'number' rigid limits in this way, that is, use the word 'number' for a rigidly limited concept, but I can also use it so that the extension of the concept is not closed by a frontier. And this is how we do use the word 'game'. For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give a boundary? No. You can draw one; for none has so far been drawn. (But that never troubled you before when you used the word 'game'.)

'But then the use of the word is unregulated, the 'game' we play with it is unregulated'. - It is not everywhere circumscribed by rules; but no more are there any rules for how high one throws the ball in tennis, or how hard; yet tennis is a game for all that and has rules too. (68)

And, finally for now:

If I tell someone 'Stand roughly here' - may not this explanation work perfectly? And cannot every other one fail too? But isn't it an inexact explanation? - Yes; why shouldn't we call it 'inexact'? Only let us understand what 'inexact' means. For it does not mean 'unusable'. And let us consider what we call an 'exact' explanation in contrast with this one. Perhaps something like drawing a chalk line round an area? Here it strikes us at once that the line has breadth. So a colour-edge would be more exact. But has this exactness still got a function here: isn't the engine idling? And remember too that we have not yet defined what is to count as overstepping this exact boundary; how, with what instruments, it is to be established. And so on. (par.88)

We shall need to come back to these texts in detail. Let me pick out for now the perception that 'the line has breadth' (whereas the (colour-)edge has none), and the persistent linking, in Wittgenstein at least, of these questions with questions of pointing, of pointing out (in the immediate vicinity of these remarks, 'A rule stands there like a sign-post' (par.85)), and therefore of deictics ('Stand here, stand there'). We shall need to see whether this association of questions of boundaries and questions of pointing is accidental, or whether the two (boundary-posts - terms, as we were saying - , and sign-posts) always go together or get confused. To do this, we shall not only follow all the paradoxical sign-posts and pointing fingers in Wittgenstein in the Tractatus as well as the Philosophical Investigations, but also in the Philosophical Grammar and in On Certainty (though by doing that I think we shall be able to establish some perhaps surprising links between the early and late Wittgenstein), but wonder why the first two examples Heidegger gives of 'signs' in par.17 of Being and Time should be 'signposts' and 'boundary-stones', precisely, or why the one example he chooses for detailed analysis in the same section should be that of an 'adjustable red arrow' sometimes (apparently) fitted to motor cars, so that they can indicate to others which way they are going at a cross-roads (where no doubt there is a signpost to help the driver make up his mind), and why the preliminary examination of the sense of logos in the introduction to Being and Time should stress so much Aristotle's notion of 'apophantic' discourse as 'making manifest in the sense of letting something be seen by pointing it out'. And these questions will rapidly lead us into a detour via Lyotard and Derrida, in an attempt to clarify their apparent conflict over the interpretation of deictic terms, especially in Husserl.

More surprisingly, perhaps, we shall have to take account of arguments in Derrida's new 'Afterword' to Limited Inc, around the status of conceptual boundaries, which we have just seen Wittgenstein suggest need not be rigid or precise. Searle accuses Derrida of hanging on to the Fregean assumption (which Searle rather sarcastically associates with logical positivism, using that well-known anti-deconstruction line which begins 'I find it rather ironic that...') of a need for rigid distinctions, and Derrida retorts in a way which may give us pause:

How can one make the demand for 'rigorous and precise' distinction the property of any one school of thought or of any one philosophical style? What philosophers ever since there were philosophers, what logician ever since there were logicians, what theoretician ever renounced this axiom: in the order of concepts (for we are speaking of concepts and not of the colors of clouds or the taste of certain chewing gums), when a distinction cannot be rigorous or precise, it is not a distinction at all. If Searle declares explicitly, seriously, literally that this axiom must be renounced, that he renounces it (...), then, short of practising deconstruction with some consistency and of submitting the very rules and regulations of his project to an explicit reworking, his entire philosophical discourse on speech acts will collapse even more rapidly. (pp. 123-4)

and only a little later:

I confirm it: for me, from the point of view of theory and of the concept, 'unless a distinction can be made rigorous and precise it isn't really a distinction'. Searle is entirely right, for once, in attributing this 'assumption' to me. I feel close to those who share it. (p. 126)

This is part of a general attack on Searle's concern always to aim for the 'centre' of concepts (of the promise, for example) and leave the margins to look after themselves. As this is a general tendency in much so-called 'analytic' philosophy, we shall have to look at it seriously. The problem is made more acute by the fact that Derrida himself seems on occasion to resort to the same procedure - in 'Signature, Event, Context', for example, he seems happy to isolate 'essential' features of the concept of communication, and elsewhere talks of concepts having a 'nucleus' or core. And even though there is an immediate difference between Derrida's reading off central features of a classical concept (including the classical concept of concept) before doing something else, rather than attempting to establish a legality of a concept for future use, and even though the very concept of 'centre' is famously read in this way in 'Structure, Sign and Play', there is here a difficult set of relationships between what are and are not concepts, what is and is not philosophy, which involve the whole question of deconstruction and which we shall have to treat with care to avoid many current misunderstandings.

Kant and Hegel beckon to us here too. Kant's philosophy is all about drawing frontiers and establishing the legality of territories. In the 'Introduction' to the third Critique, for example, there is a rather more complex use of the spatial analogy we've just seen in Frege:

Concepts, so far as they are referred to objects apart from the question of whether knowledge of them is possible or not, have their field [feld], which is determined simply by the relation in which their Object stands to our faculty of cognition in general. - The part of this field in which knowledge is possible for us, is a territory (territorium) for these concepts and the requisite cognitive faculty. The part of the territory over which they exercise legislative authority is the realm (ditio) of these concepts, and their appropriate cognitive faculty. Empirical concepts have, therefore, their territory, doubtless, in nature as the complex of all sensible objects, but they have no realm (only a dwelling- place, domicilium), for, although they are formed according to law, they are not themselves legislative, but the rules founded on them are empirical, and consequently contingent. (Eng. tr. p. 12)

This quite complex topology is related to a pervasive Kantian language of territory, which is certainly not innocent. Here, for example, from the first Critique, is the opening of Chapter III ('The Ground of the Distinction of all Objects in general into Phenomena and Noumena') of Book II ('Analytic of Principles') of the First Division ('Transcendental Analytic') of the Second Part ('Transcendental Logic') of the first main section ('Transcendental Doctrine of Elements'):

We have now not merely explored the territory of pure understanding, and carefully surveyed every part of it, but have also measured its extent, and assigned to everything in it its rightful place. This domain is an island, enclosed by nature itself within unalterable limits. It is the land of truth - enchanting name! - surrounded by a wide and stormy ocean, the native home of illusion, where many a fog bank and many a swiftly melting iceberg give the deceptive appearance of farther shores, deluding the adventurous seafarer ever anew with empty hopes, and engaging him in enterprises which he can never abandon and yet is unable to carry to completion. Before we venture on this sea, to explore it in all directions and to obtain assurance whether there be any ground for such hopes, it will be well to begin by casting a glance upon the map of the land which we are about to leave, and to enquire, first, whether we cannot in any case be satisfied with what it contains - are not, indeed, under compulsion to be satisfied, inasmuch as there may be no other territory upon which we can settle; and, secondly, by what title we possess even this domain, and can consider ourselves as secured against all opposing claims. (Eng. tr., p. 257)

There is much at stake in this language of boundaries, mapping and possession. We should try to follow it not only in Kant, but in Lyotard's recent readings of Kant (and notably perhaps, in Le différend, his extension of Kant's island analogy to that of the archipelago of discursive genres). Hegel's critique of Kant, for example, is crucially concerned to undermine the legitimacy of this boundary-language, seeing it as the culprit for the diremption in Kant between understanding and Reason and eventually between the concept and the law. Both in the Phenomenology and in the Greater Logic, there are powerful arguments against this Kantian set-up. Gillian Rose's reading of this nexus - including Kant's late distinction between boundary and limit - in her Hegel and Sociology will help us here, and also, perhaps, to explore some of the (bad) arguments about law and post-structuralism put forward in her Dialectic of Nihilism.

This general problem of conceptual boundaries (or frontiers, or edges, or limits) may seem preliminary to any investigation at all of our problem. It looks as though we ought to clarify the conceptual boundaries of the concept of boundary before we try to clarify problems with 'real' boundaries. But I'd like to suggest that we postpone it - probably until next year. Doing this postponement, which implies that we can get along fine for the time being without that clarification, almost certainly commits us to something like the Wittgensteinian argument outlined above. I suggest this partly for 'pragmatic' reasons (the 'Afterword' to Limited Inc also has some interesting remarks about pragmatics), but partly in the spirit of the deconstructive argument (which we shall rehearse in due course) against the possibility of absolutely justifiable starting-points. According to the Grammatology, we must start 'somewhere where we are, in a text already...', and move on following our noses to see where we might be going. Wittgenstein says at the beginning of the 'Lecture on Ethics' that the problem resides in the fact that 'The listener is unable to see both the road he is being led to take and the goal to which it leads' (in this case - but in fact in general - this is true of the speaker as well as the listener): here that necessary contingency pushes me to return rather more literally to Wittgenstein's and Kant's language of spaces and areas with or without frontiers - in other words, to a language of territory. Standing in a city square and saying 'stand roughly there' was one of Wittgenstein's scenarios I just quoted. This suggests problems of space and place which might inspire us to read Heidegger's explication of those terms in 'Building, Dwelling, Thinking', but might also point us toward a whole set of questions we might entitle 'Architecture and postmodernism'. Remember Jameson's distress at the experience of space (and the need for signposts) in the foyer of the Bonaventura hotel, for example. Or, in Robert Venturi's Complexity and Contradiction in Architecture, something of a precursor text for architectural postmodernism, a comment on 'residual space':

Residual space in between dominant spaces with varying degrees of openness can occur at the scale of the city and is a characteristic of the fora and other complexes of late Roman urban planning. Residual spaces are not unknown in our cities. I am thinking of the open spaces under our highways and the buffer spaces around them. Instead of acknowledging and exploiting these characteristic kinds of space we make them into parking lots or feeble patches of grass - no-man's lands between the scale of the region and the locality. (p. 80)

Residual space communicates with the vague boundaries of Wittgenstein's persistent analogy - but rather than pursue the phenomenological flavour of this talk of region and locality, I'd like to exploit its own lack of conceptual clarity by picking on its links with a geo-political sense of region, which rapidly requires clarification of the notion of country and all that that implies - as in the analogical terminology used in the unreflected way I quoted from the authors of book on fractals. Can we separate this geo-political dimension from the most apparently 'abstract' reflection on concepts and the nature of philosophy, once the language of frontiers and borders seems inescapable? (This question will confirm Hegel's identification of a link between boundaries and/or limits and the 'ought' of morality). It also involves the problem of the frontier between 'philosophical' and 'ordinary'(?) language which will again haunt our discussion of Derrida and Searle: in 'La Double Séance', for example, Derrida writes:

When a writing marks and re-marks this undecidability, its formalising power is greater - even if it is apparently 'literary' or seems to come from a natural language - than that of a proposition in logico-mathematical form still short of this type of mark. Supposing that the still metaphysical distinction between natural language and artificial language is rigorous (and here we are no doubt touching on the limit of its pertinence), there would be texts in so-called natural language whose formalising power would be greater than that accorded to certain apparently formal notations. (p. 251)

Note that the metaphysical distinction seems to break down at a limit, which suggests a continuing problem around border-terms. But this will also allow us some literary readings of frontiers, and especially perhaps Kafka's 'Great Wall of China'.)

Deleuze and Guattari, at any rate, seem prepared to claim a priority of the geo-political over the conceptual, at least in its traditional self-conceptualisation:

Thought would in itself already conform to a model borrowed from the State apparatus, fixing it aims and paths, conduits, channels, organs, a whole organon. There would, then, be an image of thought covering the whole of thought, which would be the special object of a 'noology', and which would be like the State-form developed in thought. And this image has two heads which refer precisely to the two poles of sovereignty: [on the one hand] an imperium of true-thinking, which operates by magical capture, grasp or bond, constituting the efficacy of a foundation (mythos); [and on the other] a republic of free spirits which proceeds by pact or contract, constituting a legislative and juridical organisation, bringing the sanction of a foundation (logos)... Remaining with this image, it is clear that it is not a simple metaphor, each time there is talk of an imperium of the true and a republic of spirits. It is the condition of constitution of thought as principle or form of interiority, as a stratum. (Mille Plateaux, pp. 465-6)

And everything they write about territorialisation and de-territorialisation, about nomadism and sedentarism, about smooth and striated spaces, and especially perhaps about war-machines, will concern us too. But let's start with borders and frontiers in this apparently 'literal' sense. Deleuze and Guattari say themselves that 'the most important thing is perhaps frontier-phenomena, where nomad-science exerts a pressure on State science, and where, conversely, State science appropriates and transforms the data of nomad science' (Mille plateaux, p. 449). This isn't just a tribute to 1992, when our three years will be up, but let's pretend that it is for the moment. Nor is it an attempt simply to follow a recent interest in France in questions of nationalism and internationalism, of cosmopolitanism and racism, though we should at least keep an eye on that too. What I propose we do for this year is to look at some of the major texts of the tradition of political philosophy with an eye to frontiers and border-crossings, international relations, war, invasion, foreigners and cosmopolitanism. This should not be essentially a historical investigation (and it certainly won't be exhaustive) - there's no reason to feel that we would be competent to do that - but, in more philosophical vein, more like an attempt to work out some conditions for any such historical approach to get started. If this remark has a good old Kantian-transcendental flavour to it, maybe that's because the two texts I'd like to start with are indeed by Kant: on the one hand the 'Idea for a Universal History from a Cosmopolitan Point of View' of 1784, and on the other, 'Perpetual Peace: a Philosophical Sketch', of 1795-6. And to introduce those texts in a way which suggests that the link with Kant's territorial analogy for the divisions of reason is not innocent, here's a passage from the Metaphysics of Morals (which we should remember is a doctrinal rather than a critical text) which introduces many of the themes that with concern us in the immediate future:

A country (territorium) [the same Latin word used in the Introduction to the third Critique for that part of the general field of Reason accessible to knowledge] whose inhabitants are fellow citizens of one and the same commonwealth by the very nature of the constitution (i.e. without having to exercise any particular right, so that they are already citizens by birth) is called the fatherland of these citizens. Lands in which this condition of citizenship does not apply to them are foreign countries. And a country which is part of a wider system of government is called a province (in the sense in which the Romans used this word); since it is not, however, an integrated part of an empire (imperii) whose inhabitants are all fellow-citizens, but is only a possession and subordinate realm of the empire, it must respect the territory of the ruling state as its motherland (regio domina). (Kant's Political Writings, p. 160)

And as the problem of sexual difference will emerge as a complexity not always addressed and certainly not clarified in the texts we shall read, here is a little more on the maternal and the paternal, from Kant's essay 'On the Common Saying: "This may be true in theory, but it does not apply in practice"' (1793):

The only conceivable government for men who are capable of possessing rights, even if the ruler is benevolent, is not a paternal but a patriotic government (imperium non paternale, sed patrioticum). A patriotic attitude is one where everyone in the state, not excepting its head, regards the commonwealth as a maternal womb, or the land as the paternal ground from which he himself sprang and which he must leave to his descendants as a treasured pledge. (p. 74)

As this maternal womb will not fail to remind some of you of recent work around the notion of chora in Kristeva and Derrida, let me end today by recalling that in Greek one of the primary senses of that word (which does not mean womb) is, precisely, territory, country, homeland. Thus Orestes, his crime finally absolved by Apollo at the end of Aeschylus's trilogy the Oresteia (to which we shall return), pardoned on the grounds that his killing his mother, Clytemnestra, for killing his father, Agamemnon - you remember the story - that this is a lesser crime than was hers in killing his father because a mother's womb is no more than a receptacle for the child who is essentially the work of the father, mother and child being essentially in a relation of stranger to stranger or foreigner to foreigner [xeno xene: there seems every reason in the context to maintain a metaphor of international politics], thus Orestes, who had been deprived of fatherland [gaias patroas] leaves Athens where the trial has taken place, to return to Argos, whence he had been chased by the furies after his crime, to return home [pros domos], but not before pledging a pact of peace, indeed of perpetual peace, for the oath is for 'the fullness of all time to come [apanta pleistere kronos]' between Argos and Athens, your land, your chora.