Śūnyatā and the Zeroing of Being A reworking of empty concepts

by Fabio Gironi

Introduction

This paper discusses the historical development of the number and concept of zero, followed by some considerations of its treatment in contemporary mathematics, as well as an examination of its less evident semiotic properties. I then re-examine the concept of śūnyatā, identifying its central

meontological significance in Nāgārjuna's thought. I next examine the idea of the trace in the thought of Jacques Derrida, viewing it as another actor in the assemblage of concepts which I attempt in this paper Finally, I undertake a synthetic reading of these three voids—of zero, of śūnyatā and of the trace— aimed at a speculative rearrangement of these heterogeneous concepts, in a philosophical exercise which I see as both a possible and necessary evolution of 'comparative philosophy'.

The problem of ’objective scholarship‘ and of hermeneutical procedures needs to be tackled briefly and so I would like to start by subscribing to Huntington’s remarks on the topic:

[F]or us, meaning is necessarily embedded in the symbolic forms of our culture and our time. In response to the reader who condemns all such attempts to interpret a text on the ground that the text itself does not employ our linguistic and conceptual structures, I can only throw my hands up in despair of

ever understanding any ancient way of thinking. At some point we simply must acknowledge that no translation and no textcritical methodology can be sacrosanct. Translation and all other forms of hermeneutical activity rest firmly on the preconscious forms of linguistic and cultural prejudices peculiar to our historical situation. The most vital challenge faced by scholars is certainly summed up in their responsibility to make their…presuppositions entirely conscious and to convey through

their work a sense of wonder and uncertainty of coming to terms with the original text. (1989, xiii)

I intend to take responsibility for my linguistic and conceptual choices, and to acknowledging my means and my ends, as my argument proceeds. This said, in order to avoid the criticism that I offer an ahistorical, decontextualized analysis, I should clarify what ‘crosscultural philosophical speculation’ means. This article is not to be understood as an historical account of possible interactions between Nāgārjuna's thought and mathematics. Nor do I intend to give a historical genealogy of the social, cultural, doctrinal and

political influences active on Nāgārjuna.1 I believe (as the Madhyamikas do) that both natural and social affairs can (and should) be analysed and explained on a multiplicity of ontological levels: absolute reduction is impossible. I do not claim that my analysis is the only possible way to understand Nāgārjuna (or zero, or Derrida's thought) but I do claim that to prioritize one (any) explanatory level over another, instead of joining them all for a

more complete vision, is a mistake. Hence, what this paper aims at is precisely to extrapolate three concepts ('emptiness', 'zero', 'trace/void') out of their usual disciplinary contexts in order to let them 'encounter' each other on a philosophical ground articulated by their own mutual interaction. As my title suggests, the paper is a reworking of concepts. This is meant neither as a work in Buddhist studies, nor as a history of mathematics nor as an apology for the pre-eminence of contemporary continental philosophy.

I do not wholeheartedly accept the label 'comparative philosophy', inasmuch I do not believe that our current understanding of 'comparative' work is satisfactory. I hold that the comparative' stage is, indeed, a stage of a cross-cultural philosophical work, and not an endpoint. The contextualized and

textually/philologically accurate recovery of the evolution of an idea in a given culture—which can then engender a constructive (albeit limited) philosophical comparison between similar concepts from other contexts—is one possible enterprise. Another, different kind of work, however, is the philosophically accurate reemployment of ideas on new philosophical grounds.2 This is certainly a

1A more than comprehensive survey of these influences can be found in Walser 2005. 2 It would seem that I still take for granted the possibility of singling out a philosophical plane. For an interesting discussion around the validity of our category ‘philosophy’ in cross-cultural context see the debate (regarding Chinese philosophy,

speculative enterprise, but it is profoundly different from an uncritical appropriation of an alien concept in order to force it into one's cognitive categories or symbolic forms. No philosopher is context-free but my aim is not to rekindle the fire of western philosophy with de-contextualized raw conceptual materials from the Buddhist tradition, nor to steal concepts from the field of mathematics and clumsily rearrange them to fit my philosophical project, but rather to envision a way to create a new philosophical set of coordinates by forging new alliances between ideas.

Around the problem of interpretation of ancient texts, Hayes claims that [o]n looking at trends in twentieth-century scholarship on Nāgārjuna, one can discern two fairly distinct styles, which seem to correspond to the traditional approaches known as exegesis and hermeneutics. Roughly speaking, the former attempts to discover what a text meant in the time it was written, while the latter attempts to find the meaning of a text for the time in which the interpreter lives. (1994, 362)

I do not think that this distinction, one that implicitly assigns to exegesis the status of superior objectivity, can be formulated and established in such a clear-cut way, as if bracketing off one’s cultural conditioning would immediately reproduce the original meaning of a text. This implies both the actual possibility of achieving absolute detachment from one’s cultural milieu and the presupposition that there is one meaning underlying the text under

examination, a meaning that in hermeneutics would, by implication, be ignored or at least downplayed. This prejudice emerges even more clearly when Hayes comments contemptuously on deconstructionist scholarship, defining the deconstruction as ‘an act of playing with the written symbols in deliberate disregard of what the author’s intention may have been in first inscribing them’ (Hayes 1994, 347). This definition can surely be applied to something, but this would be, plainly, bad scholarship.3 In the specific

but relevant to any kind of comparative enterprise) between Carine Defoort (2001, 2006) and Rein Raud (2006a, 2006b). I am here attempting to bypass the problem by employing an understanding of ‘philosophy’ disengaged from its conventional Greek understanding and oriented towards the unstable construction of a network of concepts. 3 Such an understanding of deconstruction is the heritage of decades of hermeneutically lazy Derridean epigones, that kept alive the myth of Derrida as an

case of this paper, the possible accusation of dissolving the 'intrinsically Buddhist' nature of the concept of emptiness raises another set of issues, which closely touch the discussion around the trope of 'authenticity' in Buddhist studies. As it has been recently observed (Garfield 2010b; Quli 2009), Buddhist scholarship has been the stage for a resurgence of the talk of authenticity against modernized versions of Buddhism. Quli (2009, 5) urges us to acknowledge that

this nostalgia [for original 'eastern' Buddhism], with its characteristic trope of decay and distortion, goes hand-in-hand with the tendency to discount hybrid identities. Indeed, this tendency to reject the hybrid as inauthentic is an extension of the colonial search for pure races and pure cultures, and as such is part and parcel of what anthropology identifies as “salvage studies”.

Therefore Quli (2009, 6-7), referring to the social phenomenon of westernized Buddhism, argues that [t]o more deeply understand Buddhists in the global ecumene, we must abandon nostalgic notions of “pure” cultures and traditions and recognize the presence

of multiple and hybrid identities—such as both Asian and American, or Asian and Western. Many Buddhist scholars have relied on an unarticulated Western Self/Asian Other dichotomy, manifesting in a “hierarchy of field sites” that discourages studies of Western Buddhism, including both Asian Americans and non-Asian American converts, continuing to cultivate those old colonial fantasies of pure cultures and pure traditions.

Translating this argument from the sociological analysis of Buddhist individuals to a philosophical analysis of Buddhist concepts, we could say that, not only is the quest for pure and original Buddhist thought an impossible one but that this theoretical nostalgia ends up denying the possibility of developing hybrid thought. This term indexes more or less precisely what I am trying to accomplish in this paper: the construction of a theoretical site (an empty site, the place of a rupturing event in the sense

intellectually dishonest obscurantist. It would suffice to read what Derrida himself has to say on the practice of ‘deconstructing texts’ to understand that to accuse it of ‘disregard of the author’s intention’ means to miss the mark completely: Derrida indeed claims that ‘texts are not to be read according to a hermeneutical of exegetical method which would seek out a finished signified beneath a textual surface. Reading is transformational’ but he immediately underlines that ‘this transformation cannot be executed however one wishes. It requires protocols of reading’. (Derrida 1981, 63).

described by Alain Badiou)4 where different concepts can be joined together by forming new and unprecedented assemblages,5 establishing a thought which is indescribable according to the rules of any of its previous situations/contexts. To 'always historicize' means to appreciate the contextual fabric in which textual documents (like philosophical treatises) are woven. This however, should not translate into a practice of historical purification. Nāgārjuna's context is not our context and we should be able to regulate our

interpretation of this thought according to his own concerns. And yet, at the same time, one can't help but wonder: how do we set the spatio-temporal limits in order to define different 'contexts'? To what extent does our interest in preserving 'pure Nāgārjunian thought', 6 an ostensibly noble move

motivated by a a refusal of violent appropriation, also performatively establishes the impossibility of a hybridization of contexts, concepts and intellectual lineages? The Buddhist and Western traditions will forever remain locked in their academic compartments—only to meet in sporadic 'comparative' exercises—as long as we refuse to envision the possibility of a synthesis which is not an appropriation, an encounter which is not a reduction, and the creation of a hybrid conceptual topology.

Williams (1991, 194) observes that '[i]t is simply fallacious to think that because absolute objectivity is a myth, reading Mādhyamika through the eyes of Wittgenstein is no different from the attempt to understand Mādhyamika on its own terms in its own historical context. Both historical scholarship and appropriation are possible'. I agree: both are legitimate enterprises. But my approach attempts a third way, different from both text-historical scholarship (which in seeking the original context of a text’s production, must recognize its own cultural emplacement) and hermeneutical interpretation (which should refrain from wholesale appropriation of an alien context by carefully placing its

4 See Badiou 2006. Badiou’s mathematical ontology is an implicit influence in my interpretation of ‘voids’ in this paper. 5 My employment of the term ‘assemblage’ is informed by the Deleuzian work of Manuel De Landa (in particular, 2006). An assemblage is a construction where the single parts do not

merge seamlessly under the imposition of the whole, but indeed constrain what can be built, resisting inadequate appropriations. Yet, out of such an assemblage the ‘emergent property’ of a new intercultural philosophical thought can proceed. 6 Tuck (1990, 15) observes that ‘for an interpreter to believe that he can accurately reconstruct the intentions and beliefs of the original author without betraying his presence is nothing less than belief in his own scholarly omnipotence’.

objects—texts and authors—in a coherent historical perspective). Thus, if as Keenan observes, ‘the difficulty in understanding Nāgārjuna, or for that matter any ancient thinker, results from the difficulty in understanding the inter-textual web of meanings within which he thought and wrote’ (1985: 367), this difficulty cannot be overcome by employing the romanticised trope of ’objective scholarship’, able to lend its ear to the faint voice of Nāgārjuna himself and to transcribe it literally in its singular significance. The only

possibility of moving closer to the possible meanings of Nāgārjuna’s work for us is precisely to pluralise and disseminate it, Such a gesture does not enact historical violence but instead remains cognisant of the historical conditions of the writer whilst simultaneously maintaining the possibility a live exchange7 between two cultures and periods. In the special case of Nāgārjuna, these methodological considerations are complicated by his own philosophy, since Nāgārjuna wants to be elusive, he wants to bewilder and to escape the very linguistic categories that he consistently uses as a kind of Wittgensteinian ladder; he wants to explode and dissolve meanings and being. Reading his work outside of the confines of any closed conceptual totality seems the best way to regard its meaning.

The historical development of zero

In order to ‘explain’ the number zero I will briefly trace its history and present its various forms and uses: sign (digit, numeral), place-holder (mark for an empty place) and number (integer).

The origin of the zero is in the invention of the positional system of mathematical notation. The introduction of such a method allowed computations to be carried out at a much faster rate and with a sensible economy of space. Instead of having a dedicated symbol for units, tens,

7 I believe that this approach allows us to avoid the danger of interpretative utilitarianism which Inada (1985, 220) warns us against: ‘to extract concepts from the corpus of Nāgārjuna’s philosophy, nay the whole of Buddhism, merely to suit one’s purposes’.

hundreds and so on, the positional system allowed mathematicians to determine the value of a symbol in a string of numbers due not only to its shape, but also to its position. A clear example is to compare the way the contemporary positional notation system writes the number 111, thus repeating the same symbol but differentiating its different roles according to the position it occupies, and the way in which the Romans would have written it—CXI—using three

different symbols, indicating hundreds, tens and units (and the difference appears more striking when we consider bigger numbers: our 448 becomes CDXLVIII). The credit for the invention of the positional system of notation has been given to several cultures as ‘[p]resent evidence indicates that the principle of place value was discovered independently four times in the history of mathematics’ (Joseph 1991, 22) in the Babylonian, Chinese, Indian and Mayan civilizations.8

The use of positional notation gave rise to the necessity for a symbol to denote a ‘space intentionally left blank’, where one of the columns would remain empty, in order to avoid confusion (1 1 can easily be confused with 11, unless we mark the absence of a value in between with another special symbol, as in 101). While the Babylonians used two slanted wedges to signify ‘nothing here’, the Indians used a small dot (bindu) that later evolved into an empty circle9 that became known as śūnya.10 In its first appearance, zero thus played a marginal role, being a mere placeholder, a necessary mark but without the dignity of a real number: its use was limited to the practical context of counting-board calculations. As Ifrah suggests,

To the Babylonians the zero sign did not signify ’the number zero‘. Although it was used with the meaning of ’empty‘ (that is, ’an empty place in a written number’) it does not seem to have been given the

8 The debate on mutual influences between these cultures (excluding the Mayan due to its geographical isolation) has been as lively as it has been inconclusive due to the relative lack of historical evidence. The most common view gives temporal priority to the Babylonian(see, for example, Ifrah 1988, 382). 9 Whether the use of the same symbol in Greece, within the context of astronomical notation, is due to cultural importation or is an original

invention, probably deriving from the letter omicron, first letter of the word ouden (nothing) is not of direct concern here. As Seife (2000, 39) claims ‘[z]ero never worked its way into ancient Western numbers, so it is unlikely that the omicron is the mother of our 0’. 10 Śūnya was the main, but not the only name for this symbol, others being kha and ākāśa, both linked to the concept of ‘sky’ hence ‘space’, ‘openness’ and also ‘infinity’.

meaning of ’nothing‘ as in ’10 minus 10‘, for example; those two concepts were still regarded as distinct.

(1988, 382) But this separation of concepts would not last long in India,11 where zero matured. In the subcontinent a decimal place-value notation developed during the first five centuries CE through the adoption of three successive types of numerals: initially the Kharosthi (circa 4th century BCE–2nd century CE) and the Brahmi (3rd century BCE), then, as an evolution of the Brahmi, the Bakhshali (3rd–5th century CE) and the Gwalior (8th century CE), the

latter being the very direct source, through the Arab manipulation and export, of modern western numeral symbols. In the Bakhshali manuscript, retrieved near the village of Bakhshali in north-west India and dated to the first five centuries CE, it is possible to find a fully developed place-value system with a dot as a sign for an empty position. But the earliest appearance of the śūnya symbol as the empty circle, is to be found in the Gwalior inscription, found near Lashkar in central India with an inscribed date, commonly reckoned to correspond to 870 CE (see Menninger 1968, 400), where in the

number 270 we find the circular zero in a final position, even if slightly smaller and elevated compared to the other two digits. But is completely new in India, as opposed to the Babylonian use of zero, is the evidence of the manipulation of zero not merely as a place-holder, but as an independent number.

The first certain description of zero that matches (with some imperfections, as we will see) our current understanding of zero as an integer on the number line, can be found in the work of the seventhcentury Indian mathematician Brahmagupta (598-668 CE). In his Brahmasphutasiddhanta (628 CE) the author not only deals with negative values but, for the first time, enunciates rules for the basic arithmetical operations with zero, śūnya: addition, subtraction,

multiplication, division, raising to powers and extraction of roots. Of all these operations Brahmagupta makes a ‘mistake’ (for contemporary mathematics) only concerning the division by zero, to which he basically gives no result, tautologically claiming that the quotient of any number and zero is a fraction with zero as a denominator. The correction of the problem was attempted by successive mathematicians such as the twelfth-century Bhaskara II (1114–1185 CE), who interestingly proposed

11 For a comprehensive history of Indiam Mathematics see Plofker 2007.

a n/0 = ∞ solution.12 Emancipated from its role as a mere place holder, zero had therefore now acquired the fully-fledged status of a number that could be manipulated within arithmetical operations.

From Brahmagupta onwards zero as a number developed until the contemporary era, travelling west with other Indian numerals in the work of Arab mathematicians. It took several centuries for these symbols to reach the West: they were introduced into European culture only in the eleventh century with the publication of the Liber Abaci by the Italian merchant and mathematician Leonardo da Pisa, better known as Fibonacci (c. 1170–c. 1250 CE).13 Fibonacci

was a reader of Arab mathematical treatises, including that of the Persian mathematician AlKhwarizimi (780–850 CE), who in turn had studied Brahmagupta’s Arabic translations at the Abbasid court of Baghdad. The very word we use today in English and in other European languages are distortions of the original śūnya: the Arabs translated it as sifr, and Fibonacci translated the Arabic word with the Italian zefiro—from which are derived the English ‘cipher’ and the French ‘chiffre’—which were successively deformed into zevro, or zero.

The introduction of zero into European culture was anything but painless. The feelings of awe, scepticism and rejection towards this new number are well summarised in Menninger’s vivid description:

What kind of crazy symbol is this, which means nothing at all? Is it a digit or isn’t it? 1,2,3,4,5,6,7,8 and 9 all stand for numbers one can understand and grasp—but 0? If it is nothing, then it should be nothing. But sometimes it is nothing, and then at other times it is something: 3 + 0

12 ‘Bhaskaracharya seemed to have known the importance of zero, not just in positional notation, but also as a number. He has special verses describing the peculiar properties of zero. He lists eight rules such as a + 0 = 0, 0·2 = 0, √0 = 0, a x 0 = 0 etc. The interesting aspect of this verse is the definition of infinity or Khahara as a fraction whose denominator is zero. In other words, a/0 = ∞’ (Nagaraj 2005, 17). In contemporary mathematics this formula is

admitted only in the context of inversive geometry, where the inverted image of zero as a center is a point at infinity. 13 In the first chapter of the Liber Abaci Fibonacci introduces the new numerals and the zero: ‘Novem figure indorum he sunt 9 8 7 6 5 4 3 2 1, cum his itaque novem figuris, et cum hoc signo 0, quod arabice zephirum appellatur, scribitur quilibet numerus, ut inferius demonstratur’. Note that if the other numerals are called ‘figuris’, only the zero is merely a ‘signo’. It will be also known as ‘nulla figura’, no number, from which our current word ‘null’ is derived. It is thus evident how at the moment of its introduction in European culture, zero was not yet understood as a number like others.

= 3 and 3 – 0 = 3, so here zero is nothing, it is not expressed, and when it is placed in front of a number it does not change it: 03 = 3, so zero is still nothing, nulla figura! But write the zero after a number, and it suddenly multiplies the number by ten: 30 = 3 x 10. So now it is something— incomprehensible but powerful, if a few ’nothings‘ can raise a small number to an immeasurably vast magnitude. Who could understand such a thing? And the old and simple one-place number 3000 (on the counting board) has now become a four-place number with its long tail of ‘nothings’—in short, the zero is nothing but ’a sign that creates confusion and difficulties‘ as a French writer of the 15th century put it—une chiffre donnant umbre et encombre.

Thus the resistance to the Indian numerals by those who used the counting board for calculations took two forms: some regarded them as the creation of the Devil, while others ridiculed them. (1969, 422) 14

Europe was still conceptually dependent on Aristotle—whose philosophy rejected the possibility of absolute void (nature itself was said to abhor vacuum) and infinity—and was preoccupied, theologically, with the fullness of being, relegating nothingness to the realm of Satan. To examine here in detail the reasons for the West’s aversion towards zero would lead us too far from our path, but this hostility should be kept in mind when we look back to India and ask: why did zero not encounter hostility, but on the contrary, managed to achieve an independent status and was elaborated as a concept there? I will argue that it is not surprising that a culture that nourished the Buddhist doctrine of śūnyatā welcomed and developed this mathematical void.

Zero’s role in mathematics

Descriptions of zero in contemporary mathematics raise some provocative problems. By definition, zero is the integer that precedes 1, it is an even number, and it is neither positive nor negative. It is also a real and a rational number. Arithmetically, most of the rules firstly enunciated

14 Eventually, the superiority of the Hindu numerals for computations over the cumbersome manipulation of the abacus or counting board—especially for the bookkeeping of the mercantile classes in Renaissance Italy—won over scepticism. Thus, today we use a deformation of the ancient Brahmi numerals, zero included.

by Brahmagupta are still valid: zero is a neutral element with respect to addition15 and subtraction, while the product of any number and zero is zero, collapsing any number back on itself. When it comes to division, there is an even odder result—one that Brahmagupta did not identify— for the quotient of any number and zero is meaningless.16 Moreover, in its interaction in the decimal place-value system, there are three possible roles for zero:

It must be noted that in a fully developed place-value system of numeration, the zero must be able to play all the following three roles successfully:

medial or internal, which is the classical role of a blank space, e.g. as in 205, 2005, etc.

final or terminal, which is more stringent role, e.g. in 250, 2500, etc.

initial, which is a rather superfluous role ordinarily, e.g. 025 = 0025 = 25 in value. But in computer age this role is also important. (Gupta 2003, 22)

Thus far, then, what can we detect about the concept and use of zero? Necessary and futile at the same time,17 interacting in a peculiar

15 In mathematics, an additive identity is an element which when added to another element, leaves that element unchanged. The number zero is the most familiar additive identity. 16 There are a few mathematical forms called undefined or indeterminate, and all those forms—interestingly—involve zero and infinity: ‘Whatever the context in which it is used, division by zero is meaningless. [Any result] is unacceptable mathematically and division by zero is therefore declared to be an invalid operation….On the other hand, in higher mathematics we often encounter the socalled “indeterminate forms”….Such an expression has no preassigned value; it can only be evaluated through a limiting process….The seven

indeterminate forms encountered most frequently in mathematics are 0/0, ∞/∞, ∞(0), 1∞, 00, ∞0 and ∞ - ∞’ (Maor 1987, 7–9). Maor here implicitly refers to L’Hopital’s rule, used to convert an indeterminate form into a determinate one through the determination of limits. Without entering into the mathematical details, I should note that in these cases zero and infinity seem to run parallel and opposite to each other, carving the very theoretical limits of

mathematics. Further, in the case of division, zero annihilates the meaningfulness of numbers. If 6 x 0 = 0 and 8 x 0 = 0, then 6 x 0 = 8 x 0. And if we were to divide both these equations by zero (6 x 0/0 = 8 x 0/0) the zeros would cancel out and the result would be a nonsensical 6 = 8. Zero uncovers the common emptiness of significance of all numbers. 17 Even with a large number (say 300000) the zeros have no role in themselves. They are auxiliary since they support the 3 in increasing magnitude. Without the initial 3

way with other numbers, in its position at the center of the number line— squeezed on its side between the positive and the negative infinity of numbers—in mathematics zero remains the one number without repetition, neither positive nor negative, the beginning of the positive line and the end of the negative.18 That empty circle is all that remains when the numbers annihilate each other, and it is what made them possible in the first place. Zero stands

at the same time inside and outside the number line—being anywhere where nowhere is—and it threatens its meaning. In spite of this, it is the very condition for its beginning. It indicates that nothing is present there, not merely as a vacant place, an omission, but an actual warning of the absence of anything at all that can be signified within the mathematical system. Rotman gives an insightful interpretation of zero’s strange role:

[A]sa numeral, the mathematical sign zero points to the absence of certain other mathematical signs, and not to the non-presence of any real ‘things’ that are supposedly independent of or prior to signs which represent them. At any place within a Hindu numeral the presence of zero declares a specific absence:

namely the absence of the signs 1,2,…,9 at that place. Zero is thus a sign about signs, a meta-sign, whose meaning as a name lies in the way it indicates the absence of the names 1,2,…,9….Zero points to the absence of certain signs either by connoting the origin of quantity, the empty plurality, or by connoting the origin of ordering, the position which excludes the possibility of

predecessors….It is this double aspect of zero…that has allowed zero to serve as the site of an ambiguity between an empty character…and a character for emptiness, a symbol that signifies nothing….In short: as a numeral within the Hindu system, indicating the absence of any of the numerals

1,2,3,4,5,6,7,8,9, zero is a sign about names, a meta-numeral; and as a number declaring itself to be the origin of counting, the trace of the one-who-counts and produces the number sequence, zero is a meta-number, a sign indicating the whole potentially infinite progression of integers. (1987, 12–14)

they would be nothing. Still, without them, the 3 would not achieve its expansion. It is this hybrid role as a necessary yet diaphanous entity that I will elaborate further in the third part of this paper. 18 In geometry this property is even more striking: firstly, (0,0) is the coordinate of the origin of the Cartesian axes on a plane. The axes both begin and encounter at the point of zero, and zero is the only fixed point that enables the whole system of

coordinates to have any meaning and practical value; secondly, the basic element of Euclidean geometry, the point—the basic building block of a line, in turn the building block of a 2-dimensional figure and so on—is a zero-dimensional object. The line acquires a measurable length out of an infinite series of points of length zero.

For now, we can formulate the following observations about this double aspect of zero differentiating itself from all the other number signs.19 Zero allows us to manipulate it as a number and use it within the context of a calculation, accompanied by—and somewhat disguised among—the other, more familiar

numbers: never quite the same as the others, signalling their absence and creating the possibility for the appearance of any other number: if 2 implies the repetition of 1, hence presupposing 1, doesn’t 1 presuppose 0? But if we pluck it out of the operation, and look at it, trying to grapple with its meaning, our critical

19 What does a number sign stand for? A Set Theory answer, for example, would be that the numeral 2 corresponds to the set of all sets with two elements. The analysis of zero within the categories of Set Theory is a source of other interesting observations: in Set Theory, one of the fundamental pillars of

mathematics, sets are abstract objects whose definition is given by the entities they contain, and that can be used to define all other concepts in mathematics. The contained entities are elements, or members of a set. One of the fundamental axioms of Set theory is the existence of an Empty Set, denoted with the symbol Ø or { }. This set has the unique property of being the only set with no members.

It is thus said that the empty set has cardinality (the number of its elements, denoted, for any set A with |A|) zero. More precisely, Halmos defines the empty set thus: ‘The empty set is a subset of every set, in other words Ø ⊂ A for every A. It is to be proved that every element in Ø belongs to A; since there are no elements in Ø, the condition is automatically fulfilled’ (Halmos 1960, 8). Every set has in itself the empty set. The powerset—the set of all

subsets of a given set—always includes the empty set. This can lead to the statement that all the elements of the empty set are also elements of any set A. This statement is true, but it is a vacuous truth. We can observe how zero and the empty set are not quite the same thing: even if empty, the empty set is still something, precisely a set with the characteristic of

having no members. As a matter of fact, the very first axiom of a Set Theory is ‘there exists a Set’: given that this set is not ulteriorly characterised, it is the empty set. On the other hand, we have already observed how sets are determined by their elements. The set of all cats with white paws exists due to the existence of these cats; if there are 300 white-pawed cats, the cardinality of such a set will be 300. Therefore the set of all winged cats is an

empty set and at the same time is the empty set. The cardinality of Ø is always 0. The empty set defies the distinction between plurality and singularity. Any set of nonexistent entities is the one and same empty set. It is therefore the one entity that we can deduce the existence of without using any existential premises. If we were to attack the axiom of the existence of an empty set, we would bring down the whole structure of Set Theory, thus making impossible any sort of countability, and even mathematics itself. Indeed, natural numbers are defined as the set of their predecessors, starting with the empty set. For a thorough set-theoretical approach to śūnyatā, see Priest 2009.

gaze falls on its openness; our categorisations encounter no ground, instead whirling down a hole, a singularity, where all shrinks to zero. Zero’s role seems to be consistently elusive, hybrid, never completely nothing but yet never something. Its thin circle ambiguously divides an empty interior and an exterior vacuum, creating emptiness out of nothingness. Differently to what we observe on white pages on some books—‘This page was intentionally left blank’—the zero signals absence without claiming it, without breaking its silence. It is as if zero held a secret, a cipher, that cannot be kept hidden nor uttered: how can we conceptualize this ‘nothing’ that is repellent to reification, this symbol referring to a chain of absences? All these remarks and questions gently allude towards the two next points of this paper: Nāgārjuna’s śūnyatā and the poststructuralist analysis of the metaphysics of presence.

Śūnyatā

To introduce the concept of śūnyatā in Nāgārjuna’s philosophy it is best to begin with possible translations of the term. We have already seen that śūnya meant ‘zero’ for Indian mathematicians, but that was not the only meaning of the term. According to Sathyanarayana Śūnya (skt.) is derivable from śūna, which is formed from the root ‘śvi’ (cl.1, ‘bhvādi’, parasmaipadi) also taking the forms ‘śū’ or even ‘śvā’. The root means ‘to swell’ (morbidly), ‘to enlarge’; and by semantic extension, ‘hollow’. It is in this last sense that the word ‘śūnya’ has now established itself to mean empty, void, vacant, vacuity, absence, free from, nonentity, nonexistence, cypher (zero), nought and space.

(2003, 264) Therefore, śūnyatā is the abstract noun of śūnya, hence emptiness, voidness, absence, and so on. Indeed, the most common translation of this term amongst scholars is emptiness. Nonetheless, since this term has an often derogatory meaning in contemporary English usage, śūnyatā has been interpreted in various ways with scholars seeking to escape the semantic baggage of the word ‘emptiness’. A small sample indicates the efforts that have been made to avoid the conflation of śūnyatā with emptiness: Stcherbatszky notoriously translates it as ‘relativity’, Sprung

and Magliola use ‘devoidness’ while McCagney even attempts ‘openness’. Even if we were to consider, evaluate and use some of these alternative translations, in the present paper I will simply use ‘śūnyatā’ keeping implicit and silent the semantic dissemination of the term. As for the problem of Nāgārjuna’s textual sources, my guide texts will be the Mūlamadhyamakakārikā20 (MMK) and the Vigrahavyāvartanī21 (VV), the two most reliable and rich textual sources of his thought.

Let us quote Nāgārjuna:

For him to whom emptiness is clear,

Everything becomes clear.

For him to whom emptiness is not clear,

Nothing becomes clear.

(MMK, xxiv.14)

This passage makes clear that the first step for any Buddhist philosopher (and in fact for anyone who wants to understand the nature of reality) is to grasp the meaning of this doctrine. Thus, in this section I want to limit myself to considering the concept of śūnyatā both as expounded in Nāgārjuna’s texts and as understood and re-elaborated by scholars and interpreters, proceeding in a relatively non-systematic way (a complete and exhaustive exposition

of the doctrine of śūnyatā would require more spacethan I can dedicate to it here),22 drawing its fundamental lines by grounding my observations in Nāgārjuna’s texts and on interpretations of it, and keeping in mind my purpose of a synthesis of śūnyatā with the concept of zero and the self-devoiding structure of the trace. The fundamental novelty of Nāgārjuna’s anti-foundationalism, over and against the context of early and abidharmic speculation, is that all entities lack self-existence (sva-bhāva)23—they are therefore śūnya—and that this property of being śūnyatā, characterizes everything (including

20 Jay Garfield’s translation (1995). 21 Kamaleswar Bhattacharya’s translation (1986). 22 This task has been brilliantly accomplished by several scholars, in particular Garfield 1995, 2003; Huntington 1989; Siderits 2003; De Jong 1972, May 1978 and Tola and Dragonetti 1981. 23 Svabhāva is commonly translated as ‘inherent existence’. For a thorough examination of the meanings of this term in Indian philosophy see Westerhoff 2009. Journal of Indian Philosophy and Religion, Vol.15 (2012)

the abidharmic dharmas), not just the self, or compounded phenomena such as King Milinda’s chariot. All things lack objective existence, essence is nowhere to be found. To postulate a stable essence would crystallize the world into an immutable, static reality that in fact denies the very conventional observation of an ever-changing world:

If there is essence, the whole world

Will be unarising, unceasing,

And static. The entire phenomenal world

Would be immutable.

(MMK, xxiv.38) On the other hand, to postulate śūnyatā allows pratītyasamutpāda (another concept philosophically renewed by Nāgārjuna) to work, as long as we avoid any reificationist tendency regarding śūnyatā itself. Indeed, we must immediately notice one thing: śūnyatā is not an entity. It is the ultimate state of being of all things, but not a thing in itself, neither an immanent nor a transcendent entity—it is pure form. Given that, according to Mādhyamika

thought, all things are relationally linked within the causal chain of pratītyasamutpāda—hence lacking svabhāva —they share a devoid nature: That nature of the things which is dependent is called voidness [[[śūnyatā]]], for that nature which is dependent is devoid of an intrinsic nature (yaś ca pratītyabhavo bhavati hi tasyāsvabhāvatvam).

(VV, xxii) Therefore, śūnyatā is the nature of things that consists in being devoid of (independent) nature. It self-denies itself and the other at the same time, because there is no other (since otherness, like difference, is dependent on a self-existence that is rejected) and no self. It is the principle of dissolution of the ontological and cognitive illusion of an essence that was always already non-existent, and that held within itself the germ of its

dissolution, in a non-place within the non-existent structure of its non-essence. In other words, śūnyatā is śūnya, an iconic statement of the emptiness of emptiness. To be consistent with its own claims, śūnyatā must negate itself, must not present itself as an ultimate principle, nor as anything close to a self-subsisting reality; it must, therefore, denounce its own emptiness: not a nature, nor an attribute, since all attributes of things are non-existent, not finding any selfsubsistent substratum to hold on to, anywhere. Emptiness must be empty.

But this is not nihilism:24 śūnyatā is not nothingness, but emptiness. It signals the absence of something, not the absolute25 presence of nothing. Of course, from the ultimate standpoint, there could not be anything there instead of a vacuous space, because nothing exists in the first place, but this constitutes no logical problem. Consider the statement ‘My room is empty of winged cats’: what I am predicating here is an absence. But—as far as I am

aware—no winged cats can be found anywhere. The statement is not quite the same as ‘In my room there is nothing’, or even worse ‘In my room there is nothingness’. Of course, nihilism can be even more successfully challenged by referring to the logical tool of the two truths: if śūnyatā is the a-metaphysical pivot of Nāgārjuna’s philosophy, the doctrine of the two truths is certainly the main a-logical one. Just as he warned about the centrality of the understanding of emptiness, so he does for the two truths:

Those who don’t understand

The distinction between these two truths

Do not understand

The Buddha’s profound truth.

(MMK, xxiv. 298) The fact that ultimately all is śūnya, does not correspond to a nihilistic outlook on the phenomenal world since, conventionally, things do exist. In order to understand this double level of truth, can we establish a logical priority between śūnyatā and pratītyasamutpāda? Herein lies the

core of Nāgārjuna’s thought. What he often seems to claim is that, being co-dependently arisen, hence caused by something else (relationally existent), things are therefore empty. And this is indeed a common explanation of śūnyatā. But this is a shortcut that betrays Nāgārjuna’s real message. It is because things lack a stable, recognisable,

24 Nihilism was one of the major accusations—from other contemporary Buddhist schools—that Nāgārjuna took pains to refute. Nonetheless, nihilistic interpretations of Nāgārjuna’s philosophy have been proposed several times in the history of Mādhyamika scholarship: see in particular Wood 1994 and Burton 1999. Moreover, the label of nihilism has been used and abused since the very first encounters the West had with the philosophy of Buddhism. See Droit

2003. 25 In the early decades of Mādhyamika scholarship, an absolutist interpretation of śūnyatā, based on a Kantian reading of Nāgārjuna, was often adopted. See, in particular, Murti 1987 and Stcherbatsky 1989. For a critique of the Kantian interpretation see Della Santina 1986.

fixed self-existence (they are empty of it) that they actually can conventionally be seen as arising and ceasing. Śūnyatā is always before: before arising, before movement, before time, before any kind of conventional designation, definition or signification. It gives conventional rise to conventional entities that enjoy a conventional existence, only to—simultaneously—deny them. Hence, śūnyatā is always after as well, that which remains after we simplify and cancel out all the rest. Commenting on MMK, xxiv.18,26 Garfield exposes this paradoxical process neatly:

Nāgārjuna emphasizes here the double edge of the ontology of emptiness. Even though it is in virtue of the fact that conventional entities are constantly arising and ceasing that they are empty, their emptiness entails that they do not, from the ultimate standpoint, arise, cease or abide at all. This is an

eloquent statement of the interpenetration of the ultimate and the conventional truths: The very ground on the basis of which emptiness is asserted is denied reality through the understanding of emptiness itself. (1995, 264) Śūnyatā, to extend Garfield’s metaphor, is indeed like a doubleedged sword, but a sword that cuts itself. It defies the basic logical rule of a referent and a

signifier, being both—or better, neither—at one and the same time. This is the meaning of the two truths: in the conventional field, the movement of signification—if frail and diaphanous—still works; but ultimately it is an impossibility, because there is nothing to be signified, nor any actor capable of signifying. The articulation and conceptual mapping of reality structured into binaries— ultimate/conventional, nirvāna/samsāra, subject/object, and so

on—is the one obstacle to be overcome by the understanding of śūnyatā.27 Yet this does not mean favouring the ultimate term over the other, because this would lead into the paradoxical ontological primacy of śūnyatā, and the whole system would indeed be exposed to the accusation of nihilism; to deny the existence of an entity does not imply the affirmation of its contrary. The two truths must walk together, if in a peculiar way. The

26 ‘Whatever is dependently co-arisen That is explained to be emptiness. That, being a dependent designation, Is itself the middle way’. 27 This is indeed the core of Nāgārjuna’s soteriological message. Streng (1973, 35) correctly notes that: ‘If one assumes that each opposite term refers to a different eternal quality or essence, and then desires one and hates the other, he fails to perceive the this is an empty, relative distinction’.

conventional world is like a phantom limb: it is absent but it feels like it is there; to perceive its conventional ‘presence’ correctly is to acknowledge its absence,28 its ultimate truth, and its absence relies on the illusion of presence in an endless repetition a swapping of roles.

In a fertile interpretation, May too comments on MMK, xxiv.18, but here he translates upādāya prajñapti with ‘metaphorical designation’,29 so that in his view The term upādāya prajñapti stresses the close dependence of any signifier upon the signified: the mode of existence of signifiers, especially verbal ones, has always been felt by the Buddhists as a particularly striking example of dependent, non-absolute existence. Metaphorical designations are most

strikingly empty: the very nature of metaphorical designation is Emptiness. From a more metaphysical point of view, we can also say that the whole world is a metaphorical designation. It designates something; it hints at something. And at what? At its own emptiness. He who knows how to interpret empirical existence correctly, sees everywhere its Emptiness thoroughly. (1978, 241)

The entirety of reality is a conventional signifier, a signifier that signifies emptiness, being already in itself the same emptiness signified. The process of signification comes to a grinding halt when it realises that it never even started. What makes the metaphorical designation possible is the one shared ‘lack’ that is possessed by all phenomena: śūnyatā. If it is true that ‘[u]nderstanding a metaphor consists in shuttling conceptually between two

things and situations’ (Steenburgh 1965, 685), then the Mādhyamika philosopher will understand the metaphor of śūnyatā by constantly shifting between a conventional and an ultimate world.30 And since there is nothing that ‘is’ not śūnya, and therefore nothing that ‘is’ not a metaphorical designation of itself, any attempt at signification/being will necessarily be constrained by ontological precariousness. 28 The metaphor of the phantom limb appears extremely suggestive in this context if we consider that—just like the conventional world—the main feedback that a phantom limb gives

to the patient under this neurological illusion, is one of pain, of suffering. See Ramachandran and Hirstein 1998. 29 For a thorough critique of nominalist and conventionalist interpretations of MMK xxiv.18 see Berger 2010. For a survey of other possible metaphorical meanings of śūnyatā see Cooper 2002. 30 For an examination of the cognitive role of conventional and ultimate truth in post- Nāgārjunian Mādhyamika see Garfield 2010a.

question arises: what kind of language can we employ in order to talk about emptiness? How can our language, based on and enclosed in basic principles of signification, say anything meaningful about emptiness? In fact, how can it say anything meaningful at all? The problem of language and of meaningful philosophical statements is of course a major problem for the Mādhyamika school, a problem regarding which scholars have been debating from the Indo-Tibetan tradition of commentaries on Nāgārjuna’s works (taking shape in the opposition between the prāsaṅgika and the svatantrika schools)31 to contemporary scholarship on Mādhyamika philosophy. This was partly possible due to different interpretations of some passages of Nāgārjuna’s works, such as

The victorious one have said

That emptiness is the relinquishing of all views.

For whomever emptiness is a view,

That one has accomplished nothing.

(MMK, xiii.8)

I prostrate to Gautama

Who through compassion

Taught the true doctrine,

Of the relinquishing of all views.

(MMK, xxvii.30)

31 The existence of the two opposing schools derives from the need of Mādhyamika philosophers to confront themselves, in the process of defending their doctrine, with other contemporary philosophical schools of India (and Tibet), both Buddhist and non-Buddhist (for a study on the validity of the

distinction between prasaṅgika and the svatantrika see Dreyfus and McClintock 2003). The doctrine of śūnyatā is not an external, isolated and higher critique of the philosophical systems of second-century India, but an internal one. Mādhyamika sprang out of Mahāyāna Buddhism, a movement that historically configured itself as a reaction to the academic scholasticism of abhidharmic speculation. The final goal of such a philosophy is to attain a

return to practical life. As Keenan (1996, 60) observes: ‘The teaching of emptiness developed from the exigencies of practice and is aimed at the furtherance of such practice. It is not a transcendental philosophy that filters all religious truth claims and practices through disinterested models of analysis. Nor is it a sectarian doctrine that crunches the views of others through a biased model of captious criticism’. For a specific examination of the influences on Nāgārjuna’s philosophy of the practical concerns and methods of the Yoga tradition see Mason 1997.

Between these two verses the main point of contention has concerned whether ‘all views’ means ‘all wrong views’ or ‘all views altogether’. Given that the former interpretation coincides more exactly with the logic of emptiness, it appears a more compelling explanation. That ‘emptiness is the relinquishing of

all views’ is not the absolute silence of an intellect mesmerised by the supreme comprehension of Absolute emptiness, nor the nihilistic claim of a ‘religion of abandonment’—the two fallacious extremes, essentialism and nihilism, that the Middle Way intends to avoid—nor again a sceptical claim about

the non-knowability of some reality out there. On the contrary, it is the failure of the power of signification.32 Views, which are linguistically and conceptually formulated, must necessarily refer back to something, have a ground, a starting point, a conceptual substance. Once this origin is eroded inside out by its own śūnyatā, nothing else stands,33 not even śūnyatā, being itself śūnya. The rules of language are broken, or bent, to

32 With this claim I seem consciously to adopt what Huntington (1989, 30) defines as the ‘linguistic interpretation’ of Mādhyamika. Huntington stresses the importance of the practical and contextual employment of language: ‘If the meaning of a word or concept derives entirely from its usage in a historically bound social context, where it must be understood as indicative of a certain attitude toward some actual possible state of affairs in the world, then any

reference to an exclusively private object like a thing-in-and-for-itself (a dharma) or an isolated, inviolate “I” (an ātman) would be senseless. Such private objects are by definition excluded by any sociolinguistic matrix….Metaphysical language is incapable of justifying its claim to capture truth in a complex of ontological and epistemological propositions, for the objects to which it refers are entirely

without practical consequences and are thus devoid of all reality’ (Huntington 1989, 32). Siderits (1988; 2003) shares a similar interpretation (that he defines ‘semantic interpretation’ as opposed to a ‘metaphysical’ one) when he claims that ‘a semantic interpretation of emptiness takes the doctrine to concern not the nature of reality, but the nature of truth. Specifically, it takes the claim that all things are empty to mean that the ultimate truth is

that there is no ultimate truth— there is only conventional truth….Thus, to say that all things are empty is, on the semantic interpretation, to say that no statement can be ultimately true’ (Siderits 2003, 11). For a possible application of the linguistic analysis to Tibetan Buddhism see Napper 2003. For an

explicit Wittgensteinian interpretation of Mādhyamika’s use of language see Gudmunsen 1977. For a critique of the possibility of a linguistic interpretation see Williams 1991. 33 See MMK, iv.8: ‘When an analysis is made through emptiness, If someone were to offer a reply, That reply will fail, since it will presuppose, Exactly what is to be proven’.

accept a discourse that is always metaphorical, groundless, fictional,34 and hence open to an endless play of signification, arising from śūnyatā and shouting (or whispering) back its fall back into śūnyatā.

The impossibility of claims makes the problem of a true claim a trivial one, and in fact it brings into question the concept of truth altogether. No correspondence theory is possible: the truth of śūnyatā is its constant disappearance. Ontology and logic are forced to break their self-preserving partnership: the one hollowed, only provisionally presenting a multiplicity of conventional beings; the other dissolved, dissipated.

The paradox of a conventional/ultimate designation and an expressibility of this reality evacuated of meaning/essence and stability/safeness is exquisitely outlined by Garfield and Priest:

We can think (and characterize) reality only subject to language, which is conventional, so the ontology of that reality is all conventional. It follows that the conventional objects of reality do not ultimately (nonconventionally) exist. It also follows that nothing we say of them is ultimately true. That is, all things are empty of ultimate existence, and this is their ultimate nature and is an ultimate truth about them. They hence cannot be thought to have that nature, nor can we say that they do. But we have just done so. (2003, 13)

Our language would then need a new form, new rules and grammar, wherein any existential statement, the verb ‘to be’ must be cancelled out, but provisionally kept: ‘there is a world’, ‘object x exists’. Since śūnyatā is the ‘nature’ (and crossing out the verb here indicates consistency with the śūnyatā of śūnyatā itself) of all things, ‘to be’, for any-thing, is to be śūnya, 'void' is the ‘proper name’ of being.

I agree with Loy (1984) when he emphasizes the central thrust of Mādhyamika as being a reflection on nonduality, and who warns against reading Nāgārjuna only through a sterile ‘neonominalistic’ standpoint. Of course, Nāgārjuna’s śūnyatā is not only an aseptic tool used to obtain the relinquishment of all views; his whole project is an anti metaphysical

34 I borrow Crittenden’s (1981, 326-327) term: ‘There is nothing in the nature of fictional entities which determines which is the right logic of fiction or what fictional reality really is. Clearly there is no “essential reality” (svabhāva) reflected in fiction and there ought not to be any taken as reflected in literal discourse either; describing reality as fictional can be taken as calling attention to the arbitrariness of the rules of ordinary factual language’.

enterprise aimed towards a soteriological goal.35 This means an informed return to conventional reality, one free from reification, subject/object distinction and from any gesture that secretly hides cryptometaphysical presuppositions. Thus, as Garfield argues,

Nāgārjuna replaces the view shared by the metaphysician and the person in the street, a view that presents itself as common sense, but is in fact deeply metaphysical, with an apparently paradoxical, thoroughly empty, but in the end commonsense view…of the entire phenomenal world. (1995, 122–123)

This is thus a commonsense view that is a second view over reality, a recovery of the residue of emptiness, a view always provisionally accepted and never assumed as self-existing.

The goal of śūnyatā is thus freedom from (reificationist, totalizing) metaphysics and from a strictly referential theory of meaning,36 towards the everyday reality of a phenomenal world and of the language used to describe it, that—being śūnya—result as having a logically indeterminable character. The multiplicity of the phenomenal world is grounded on (or better a presentation of) the emptiness at its core. McCagney’s attempt to reinterpret śūnyatā as

‘openness’, as a boundless and indeterminate arena of ever-changing events is helpful in this respect: The term śūnyatā functions by pointing to the incoherence of assuming that events are determinate or definable. If events were inherently one thing or another and so could be fixed in a term, they would also be unchanging and ordinary experience as well as the Middle Way and the Eightfold Path would be impossible. To assign a determinate, fixed

35 Siderits examines the possible connection between the ‘semantic interpretation’ of emptiness and the practical, everyday soteriological goals of Madhyamika by pointing out how śūnyatā frees us from a ‘grand narrative’ of the self and of truth. He claims that ‘[w]hat is at stake is the thought that there is the right way for a life to go, and that my life might go that way. For this depends on the notion of a truth that is somehow “bigger than all of

us”, that reveals the larger scheme wherein our lives must fit if they are to have value and purpose. On the semantic interpretation of emptiness, the truth that liberates is the insight that there can be no truth apart from the contingent institutions and practices of social existence. It liberates because it undermines the last vestige of clinging, the belief that there is a mind-independent ultimate truth’ (Siderits 2003, 18). 36 See Matilal 1973, 59.

meaning to śūnyatā utterly misses the point….Śūnyatā is like space [[[ākāśa]]],37 there is nothing to cling to, nothing to grasp. (McCagney 1997, 95-101)

The metaphor of openness paints a fertile image of a space to be filled, an absence as a condition for any presence, a playground for any signification: freedom and ‘evental’ novelty is possible only in indeterminacy. However, śūnyatā cannot be a playground. It can be the space of signification, but not the origin of signification, nor the condition for any phenomenal entity. Śūnyatā is not a super-signifier, nor the sign of all signs, but (and we already

gesture towards zero) we could say that it works as a meta-sign declaring the emptiness of other signs/phenomena that are always already empty. Compare the definition of zero as a meta-sign with this statement by Robinson about śūnyatā:

Emptiness is not a term in the primary system referring to the world, but a term in the descriptive system (metasystem) referring to the primary system. Thus it has no status as an entity, nor as the property of an existent or an inexistent. (1967, 43)

On the other hand, the impossibility of thought is necessary for getting rid of any metaphysical imprint, one that might force us always to think about something. In this way, śūnyatā becomes as an impossible concept to grasp as zero and infinity are. An empty world is a state of affairs that holds as long as we do not look for an end, for a limit, or indeed a beginning, because that limit will always escape our conceptual view, and we will always find ourselves frustratingly in the same place, no matter how fast we run. In the same way, it is impossible to ‘think nothing’ as a beginning.

This relinquishment of concepts and views does not mean (once again) that the emptiness of reality cannot be affirmed, accepted and handled, or that a nihilistic stance should be adopted. Just as we can still count even when knowing that doing so is an infinite process of numbering empty signs, so we can talk or live with an empty language in

37 McCagney justifies her interpretation claiming that ‘Nāgārjuna has adopted this sense of ākāśa as the vast, luminous and open sky’ and that he ‘has adopted the more encompassing sense of śūnyatā as openness used in the Aṣṭasāhasrikā Prajñāpāramitā in which it is synonymous with space’ (1997, xx; 58). The reader will recall that ākāśa was another word commonly used for zero.

an empty world. This ‘worldview’38 will therefore keep this contradiction within itself, being a faint remainder of a collapse of dualities.

Tracing voids

It is time now to pick up both the threads of the discussion so far and try to merge them into one coherent line of thought. Williams makes an excellent point when he observes that

the appropriation of Buddhist thought might not involve only relating it to western philosophy….When expressed in its broadest sense, [one] not culturally determined, the principal message of Mādhyamika is to “let go of holding”….To adopt Mādhyamika for the West is not the same as expressing it in terms of contemporary Western philosophy. (1991, 194–195)

Even though Williams refers to a more ‘religious’ form of adoption (he subsequently uses the example of the penetration of Buddhism into China), this observation should push us towards the main problem: if on the one hand an objective and ‘authentic’ retrieval of Nāgārjuna’s own thought is impossible and, on the other, the very nature of Mādhyamika is to resist any kind of assimilation, coalescence, or appropriation by other ‘views’, what can we say about it?

38 Kakol has commented on the Mādhyamika worldview defining it as an ‘open worldview’ or a ‘cosmological worldview’: ‘Closed views are complete but inconsistent whereas open views are consistent but incomplete.…Open views are either positive process-like views (creative synthesis or inclusive transcendence) or negative Mādhyamika-like “views” (negative dialectics or athesis)….[Worldviews] that ground intrinsic values in concrete events and in

creative emptiness, can be called cosmological as they do not ground values in a transcendent absolute beyond the intersubjective cosmos as do the ontological worldviews, which tend toward an ideological and idealist “misplaced concreteness” in that they value the static and eternal over the dynamic and fleeting, being over becoming (and Being over beings), and the ontological over the cosmological (their so-called “ontological difference)’ (2002, 216; 218–219).

I would like to tackle this question through an examination of an influential contemporary trend in Mādhyamika scholarship: the deconstructivist approach,39 a broad label that expresses any kind of interpretative move that generally follows Jacques Derrida’s philosophical project. Even if this kind of interpretation does not remain immune from excessive claims—‘without Derrida it is difficult for a ”moderner” to understand Nāgārjuna!’ (Magliola 1984, 93)—the choice of a deconstructive approach could possibly address the impasse that I earlier described. Derrida states , for example, that

Deconstruction is neither a theory nor a philosophy. It is neither a school nor a method. It is not even a discourse, nor an act, nor a practice. It is what happens, what happens today.

We can see a parallel here in intention between Derrida and Nāgārjuna,40 since both Nāgārjuna’s and the deconstructivist project, are presented as a view on reality that are not intended as new and systematic worldviews. Therefore, to read Nāgārjuna deconstructively means to collate certain terms which in

both cases are meant to be used in a nonsystematic way as a means of evaluating everyday reality. Here I will not be trying a precise point-to-point comparison. In conformity with the concerns I outlined at the beginning of the paper, I will limit myself to appropriating some Derridean terminology as a tool for expressing the connections between zero and śūnyatā. This does not necessarily imply that I am

drawing a ‘doctrinal’ parallel between Derrida and Nāgārjuna, for in fact neither of them proposed any doctrine, but rather between methods. Indeed, one point of similarity between the two philosophers is their forceful denial that they are creators of a ‘new position’ and further, they appear to have a

shared interest precisely in the lack of fixed positions. Therefore, it is not a matter of ‘comparing doctrines’ but a question of the methodology of deconstruction of doctrines. In fact, more than any doctrinal convergences, what really allows us to align the two is their role as internal dissidents within the well-established metaphysical traditions that produced them. What Vattimo observed of Derrida could be applied to Nāgārjuna as well:

39 This label can be reasonably applied to scholars like Magliola, Loy, Mabbett, Le Roux, Wang and—more tenuously—Huntington. 40 For an exhaustive enumeration of points of contact between Nāgārjuna’s and Derrida’s works see Mabbett 1995. For a criticism of Derrida from a Nāgārjunian standpoint see Magliola 1984 and Loy 1987, 1993.

If a real leap out of metaphysics it is not possible…the thought that feels itself summoned to perform such a duty has to configure itself as necessarily ‘parasitic’ towards the tradition from which it is trying to set itself free. (2002, xiii; my translation)

One of the main Derridean concepts I will employ here is that of trace, introduced best in Derrida’s own words: The trace is not only the disappearance of origin—within the discourse that we sustain and according to the path that we follow it means that the origin did not even disappear, that it was never constituted except reciprocally by a nonorigin, the trace, which thus becomes the origin of the origin. From then

on, to wrench the concept of the trace from the classical scheme, which would derive it from a presence or from an originary nontrace and which would make of it an empirical mark, one must indeed speak of an originary trace or arche-trace. Yet we know that that concept destroys its name and that, if all begins with the trace, there is above all no originary trace. (1997, 61)

Derrida sketches this idea within the framework of his critique of the metaphysics of presence—a nostalgia for origins, a rooting in a unitary spring of being, a call for bright sameness, and above all of Being as presence—that is the leitmotif of European philosophy. Against and within this all-inclusive

project, Derrida claims, the trace can always be found, taking shape in any of the many external, exiled concepts that western metaphysics has kept at bay, quarantined at the margins of its self-sustaining presence. If in the linguistic analysis operated over and against the Saussurean structuralist project or in the deconstruction of the classical texts of western philosophy, the trace always makes

its appearance in Derrida’s works, often defined as the non-concrete absent presence that threatens projects of unification; it is the locus of difference, the one non-entity defying the matrix of all the binary oppositions that structure metaphysics: the opposition inside/outside. While feared as an internal

stranger or underplayed as an unnecessary supplement, the aporetic trace is, according to Derrida, really the ‘original’ opening of meaning, the infinite seed of an endless proliferation. Yet, the presence of the trace in the past of an origin was never a present presence. The trace is that which originates without carving its presence on the static surface of being; it is the mere and scandalous lack of being, the presence of an absence. It is impossible to

trace the trace. As a matter of fact, as Derrida notes, ‘The trace itself does not exist. (To exist is to be, to be an entity, a being present, to on)...Although it does not exist, although it is never a being-present outside of all plenitude, its possibility is by rights anterior to all that one

calls sign’ (Derrida 1997, 167, 62) and again, ‘The trace is nothing, it is not an entity, it exceeds the question What is? And contingently makes it possible’ (Derrida 1997, 75). The trace is the non-present possibility of linguistic signification (including mathematical, in the form of zero) and of every order of being.

Indeed, the structure of the trace is not to be limited, as poor readings of Derrida suggest, to textuality: as the recent work of Martin Hägglund (2008) has convincingly shown, the structure of the trace is a feature of reality as a whole, at work in the animate as well as in the inanimate: Derrida is offering an insight into the ‘autoimmune’ nature of the real, not merely providing a methodology for the deconstruction of philosophical texts. For

Derrida, Hägglund clarifies, the trace is an ‘ultratranscendental condition’ and ‘[e]verything that is subjected to succession is subjected to the trace, whether it is alive or not’ (Hägglund 2009, 239-240): all that which is originated is always already undermined by the trace/emptiness as its ownmost way of being.

Derrida’s insistence on the ubiquity of this structure of self-voiding is what led Alain Badiou (2009a, 546) to describe his philosophy as motivated by a ‘passion of Inexistance’. Badiou offers a reading of Derrida, obviously influenced by his own theoretical preferences (and, interestingly in the context of my exposition, by his mathematical ontology), which effectively highlights how it is possible to employ Derrida’s conceptual resources to understand

emptiness as the zeroing of being. According to Badiou (2009b, 140) Derrida’s desire is to ‘locate, touch, clasp, even for less than an instant, the non-existent of a place, the vanishing of a vanishing point. Inscribe this ex-scription’. For Badiou, the absent presence of the inexistent is the claim which Derrida sets against the history of metaphysics, since

[t]he metaphysical error par excellence is to have identified the nonexistent with nothingness. Because the point is that the non-existent is....The non-existent is nothing. But being nothing is by no means the same as non-being. To be nothing is to non-exist in a way specific to a determinate world or place....[N]o stable opposition can really succeed in describing the precise status of the non-existent in terms of a binary opposition. (Badiou 2009b, 140-141)

This inexistent, this pre-originary différance, this trace, is therefore what Derrida’s deconstructive process attempts to ‘performatively’ say (for the inexistent is always below the threshold of representation), just as Badiou’s mathematical ontology identifies the ‘empty set’—the void always presupposed by a presented situation—with proper name of ‘being’.

In its singular role as self-voiding parasite of (or organizing structure of, if ‘conventionally’ seen) reality, the trace is a vanishing ground always to be replaced and re-said in a play of difference. It is, however, no replacement for a metaphysical principle: the trace does not posit. Precisely

responding to a reading of his work seen as simply identifying a new set of transcendental conditions, and indeed of creating a new onto-theology ‘grounded’ on the trace Derrida asked rhetorically:

[H]ave I not indefatigably repeated—and I would dare say demonstrated—that the trace is neither a ground nor a foundation, nor an origin, and that in no case can it provide for a manifest or disguised ontotheology?

(Derrida 1981, 52) If thus correctly interpreted as the ‘ultratranscendental’ structuring/voiding principle of reality (a dual role which I see as mirroring the double register of a conventional/presented and of an ultimate/beyond representation level of being), the trace—I believe—is the conceptual link that allows us to connect zero and śūnyatā, or better to create a mirror of their own elusive nature.

We have seen how zero, as a fully-fledged number on the number line holds a particular role: it is the origin of the series of numbers and it is the opening of the possibility of denumeration; at the same time it is excluded from the possibility of full signification, kept aside, to be handled with care as the number that is able to implode the system of mathematics. Consider again the example of the basic arithmetical operations with zero: zero is the

elusive origin and its clandestine nature within the number system is signalled when a number tries to interact with it. If in subtraction and addition zero can be considered merely a neutral element, ignored by the integrity of the number (just an empty supplement that can be ignored, as in 05), when a number needs to be multiplied—that is repeated zero times—it is annihilated by zero, as if the emptiness of its ‘presence’ is finally exposed, unable to subsist without differential repetition. Finally, to try and divide any number by

zero leads to an impossible result, an undecided result. An answer within the system cannot be found. Not only does zero erase; it completely deconstructs. As Seife (2000, 23) remarks: ‘Multiplying by zero collapses the number line. But dividing by zero destroys the entire framework of mathematics’. When considering its double role as a place-holder and as a mark of emptiness, we can legitimately call zero a supplement, another term derived from Derridean/Badiouian vocabulary, if we consider that Derrida claims that

the supplement supplements. It adds only to replace. It intervenes or insinuates itself in-the-place-of; if it fills, it is as if one fills a void. If it represents or makes an image, it is by the anterior default of a presence. Compensatory and vicarious, the supplement is an adjunct, a subaltern instance which takes-(the)-place. As substitute, it is not simply added to the positivity of a presence, it produces no relief, its place is assigned in the structure by the mark of an emptiness. (1997, 145)

Zero would thus be the supplement within the system of mathematics, a system that, through the infinity41 of numbers extending along the number line, merely presents a presence of being, whilst grounded on the void—the counting of no-thing—that zero represents.

To link together śūnyatā and zero we must consider the historical route of zero. It can be argued that the Indian mathematicians who developed the concept of zero did so at least three centuries after the development of the Mādhyamika school, and a millennium after the birth of the Buddha. It seems reasonable to expect high-caste individuals such as Brahmagupta and Bhaksara to be aware—even if only tangentially— of the intellectual trends and debates that were running through the subcontinent, particularly during the first five centuries CE that saw the rise and expansion of Mahāyāna Buddhism. The scholastic conflicts between Buddhism and other realist Indian philosophical schools (and within Buddhism itself) must certainly have been known by the Indian

41 See the remarks Derrida (1997, 71) makes about infinitist metaphysics: ‘Only infinite being can reduce difference in presence’.

educated elites, and the emphasis of Buddhism on emptiness42 must certainly have made its way into their intellectual milieu. The emancipation of zero in Indian mathematical thinking was possible thanks to the presence of an existing concept of emptiness within its cultural ground.43 The subsequent exportation of zero in the West was not simply the assimilation of an alien concept, but a hard encounter with an external enemy, one that

nonetheless was already the internal enemy of western metaphysics since the days of Parmenides: the trace of absence. If we accept this train of thought, the connection between critiques of metaphysics of presence and Nāgārjuna’s project stands out clearly: if zero, a concept developed in the mathematics of Nāgārjuna’s cultural world, was only slowly, and then grudgingly assimilated by the West it is because Europeans saw it as symbol of the dissolution of the mind’s very integrity.44 And Europeans were correct to fear the corrosive power of

42 I am thinking here specifically of its development from the reductionism of early Buddhism and the dharmas theory of the Abhidharmists to the radical emptiness presented in the Prajñāpāramitā sutras, philosophically perfectioned by Nāgārjuna) 43 I am not trying to suggest that emptiness was the main concept of Indian philosophical speculation. It is enough to mention schools like the Nyāya or Advaita Vedanta to prove this statement wrong. What I am

claiming is that—differently from other cultures—the idea of emptiness (and not mere a nihilistic nothingness) had in India the legitimate status of a respectable philosophical concept. Others dare to take this further than me: ‘…it is quite probable that Bhāksara II’s concept of śūnya was built up against the background of Nāgārjuna’s philosophy’ (Mukhopadhyaya 2003, 202) and ‘Although it is asserted that the discovery of zero in mathematics in India came late, probably in the fifth to sixth century A.D…there are many elements of mathematical logic in Buddhist logic which antedates the above discovery by

several centuries at least’ (Matsuo 1987, 34). 44 One can think, for example, of the difficulties that both Newton and Leibniz encountered, as late as the seventeenth century (hence several centuries after the Hindu numerals with zero were adopted in Europe) with mathematical nothingness, leading to the ‘creation’ of infinitesimals. Moreover, it is worth considering a fundamental difference between Indian and European mathematics. As Raju interestingly

notes: ‘Formal mathematics concern proofs, while computational mathematics concerns algorithms. Formal mathematicians tend to look with contempt upon computational mathematicians: of what use is a computation without a convergence proof? Computational mathematicians tend to reciprocate this contempt. Of what use is it to have an existence proof, if there is no way to calculate the quantity alleged to exist?....It is my contention that Indian mathematics was oriented towards calculation rather than proof: it was more computational than

zero, since the full philosophical implication of describing something as śūnya implies precisely the demolition of any essentialist, reificationistic and eternalistic ontology, or indeed onto-theology. Hence, the ‘dangerous supplement’ that Derrida has identified and Nāgārjuna’s main concept of śūnyatā can be seen to function similarly conceptually, and an analysis of zero—the supplement within the mathematical system—shows it to us, since this supplementary role is caused by its character of hinting back to a transcendental lack, a peculiar character that has its historical roots in an Indian-derived thought of emptiness.

To understand the real danger of such a supplement we can turn again to Derrida

Why is the supplement or surrogate dangerous? It is not, so to speak, dangerous in itself, in that aspect of it that can present itself as a thing, as a being-present. In that case it would be reassuring. But here, the supplement is not, is not a being (on). It is nevertheless not a simple nonbeing (mēon), either. Its slidings slip it out of the simple alternative presence/absence. That is the danger. (2004b, 112

What was a danger for Greek metaphysics is the very state of affairs of the whole of reality for Nāgārjuna. It is śūnya that is situated between the oppositions, between presence and absence, between being and nonbeing: between ‘present/being’ on one side and ‘absence/nonbeing’ on the other Nāgārjuna places śūnyatā. In the metaphysics of presence, this becomes a hybrid, half-caste, undecidable place of void: in other words, unrecognizable as a term of

the situation. The way of this ‘being between’ though, is not merely an equilibrium between extremes but a complete emancipation from polarity, an authentic third alternative. On a conventional level, the Middle Way is the way in-between extremes (hence recognising, but defying the law of the excluded middle) but still engaged with the task of not falling into them (conventionally

formal….This is not to say that Indian mathematicians were unconcerned about methodology: in the manner of computational mathematicians they were concerned about rationale and efficient algorithms, but this rationale was not proof. It could not have been “proof” because the various notions of “valid argument” in Indian traditions were certainly not identical to the notion of “valid argument” in the Greek or western tradition….[W]estern philosophy has characteristically taken mathematics and logic to represent certitude’ (Raju 2003, 175). Raju goes on to claim how the limited and strict rules of western binary logic, always oriented towards certitude, fail when applied to other cultural contexts.

recognising them). On the ultimate level the Middle Way is a complete erasing of the oppositions, ontologically (hence completely deconstructing the structure of the excluded middle), and of discriminative knowledge, epistemologically. There are simply no more oppositions, no binary logic to move

within.45 This happens because no fixed totality (as a self-essence or as a differential principle) can be named: the logical methods employed must be consistent with a ‘reality’, the law of which is not the permanence and self-presence of being, but pratītyasamutpāda, dependent co-arising. Faure summarises this idea thus:

Despite appearances to the contrary, Nāgārjunian logic is not the same as ours, in particular in the following respect: Instead of fixing the terms of the interrelatedness, it draws attention to their constant fluctuation. Whereas in a tautology or an algebraic equation, the terms must turn out to be equal, in Buddhist logic, no terms ever do. The fundamental difference (always supposing that there is a ‘foundation’) is that Buddhism by and large values orthopraxy (correct practice) more highly than orthodoxy (correct opinion) and, in particular, ritual more highly than doctrine. (2004, 96)

Here to value orthopraxy amounts to employing a logic that observes the everyday flowing of pratītyasamutpāda, of dependent entities lacking any self-nature. Hence the formal, binary structure of the alter is broken, introducing an ever-irreducible aliud, whose difference from it is not to be found in the not-sameness of any self-existing nature of the entities under consideration, but in the universal lack of selfsameness (śūnyatā) that characterises everything in the first place. If selfindividuation is impossible, difference is impossible as well,46 except if

45 What in English is commonly called the ‘law of the Excluded Middle’ (P v ~P) was in Latin known as the principium tertii exclusi (principle of the excluded third), or tertium non datur (the third is not given). Now, in our context, the two versions are not quite the same. We could therefore say that Nāgārjuna does refer to the law of the excluded middle when talking conventionally about his doctrine. But ultimately he rejects the principle of the

tertium non datur. Not only does Nāgārjuna want to find a middle way between oppositions, but he also ultimately wants to destroy (deconstruct) the members of the opposition itself, finding a non-position outside the opposition, not merely in the middle of it. When we break the 1-2 binary opposition any other third option is really a multiplicity of options. 46 The long passage (MMK, xiv.5–7) that Nāgārjuna dedicates to the problem of difference provides a wonderful example of his dialectical method and of what I will

we interpret difference outside dichotomies (where ‘different from’ would be the basis of any proposition) but in a free-playing sense as absolute difference.47 When the problem of existence and essence is at stake, when the ‘question of being’ is asked, it is precisely the fourth leg of the tetralemma, the most absurd and metaphysically meaningless of the four that gets closer to the state of any phenomena, it being śūnya: neither existent nor nonexistent.48

The anti-ontological (and deconstructively argumentative) spirit of Mādhyamika is non-committal, 49 but as I mentioned before, the negation of thesis A does not imply the affirmation of thesis B (what the Indian philosophical tradition refers to as a prasajya negation). In other words we might say that the

radical shift of a philosophy of emptiness is from the logical-metaphysical structure of the reified opposition ‘either/or’ to the empty opposition of the ‘neither/nor’, the logic of the undecidable which does not simply stand between an opposition, but which defies the opposition, being always in itself double-faced, unstable, unrepresentable in the closed totality of a situation. This undecidable50 placement is what

soon define as the logic of the neither/nor applied to ontological problems. Consider, as a way of comparison, Frege’s statement about zero (quoted in Rotman 1987, 7): ‘Since nothing falls under the concept “not identical with itself”, I define nought as follows: 0 is the number which belongs to the concept “not identical with itself”. Zero in a logical system covers the role of an impossible nonidentity with itself, which is to say ‘empty of self-

nature’. 47 One of Nāgārjuna’s statements (MMK, vi.4) on the problem of identity seems to play on the same note of the double semantic role that Derrida gives to his word différance (to differ and to defer): ‘In identity there is no simultaneity. A thing is not simultaneous with itself. But if there is difference, How would there be simultaneity?’ 48 I shall quickly observe how this neither/nor way of proceeding is not equivalent to the ‘neti, neti’

mantra of Advaita philosophers: the problem here is not one of progressive negation of all possible positive attributes (apophatic theology) but a radical deconstruction of any possible predication, both positive and negative. 49 As Nayak (1979, 479) puts it: ‘Nāgārjuna’s critical insight is a consistent denial of all “-isms” in philosophy’. 50 Alain Badiou’s own employment of the term ‘undecidable’ is equally applicable in this case: for Badiou an event takes place in the void of a situation precisely because

is what associates zero—the trace that makes possible what at the same time makes impossible (the number line and their power of full meaning and signification)—and śūnyatā, the fundamental nature of things that consists in not having any nature. These two concepts that I have tried to place in proximity share one common focus or center of gravity—an empty one— that is never stable, but which in their endless shifting make possible the play51 between them.

In order to clarify my discourse and to delineate more precisely the convergence of śūnyatā and zero in escaping dichotomizing thought, one more concept can be introduced: the hole.52 Moving on three levels (metaphysical, mathematical and linguistic) we could compare 1) the metaphysical juxtaposition of ‘emptiness’ (lack of anything at all) with ‘hole’ (nothing amid something) with 2) a mathematical one between zero as a numeral and zero as a place-holder and 3) with the role, in a structuralist analysis of linguistic systems, of a a Derridean ‘undecidable’ and a mere blank space between linguistic signs..53 This might be simplified graphically:

Zero as a Numeral Zero as a Undecidable Blank Space

occupies an undeicidable site from the standpoint of the situation itself. See Badiou 2006: 181. 51 We might recall here how Derrida (2004b, 352) defined centred self-presence as excluding any possibility of play. 52 The discussion that we find in analytic philosophy around the metaphysical status of holes is a most stimulating one, and relevant to the central theme of this paper: how can we define a hole without tautologies and without referring to

surrounding matter that marks it precisely as a hole? Do holes exist or are they merely a negative part of matter? For a complete discussion about holes see Casati and Varzi 1994, and Lewis 1983. For an analysis of the perceptual status of holes see Bertamini and Croucher 2003. 53 Indeed, hole is another term employed by Derrida to indicate that trace at the center of every structure: ‘If the center is indeed “the displacing of the question” it is because

the unnamable bottomless well whose sign the center was, has always been surnamed; the center as the sign of a hole that the book attempted to fill. The center was the name of a hole’ (Derrida 2004a, 375).

If, as I argued, Nāgārjunian śūnyatā represents a ‘concept’ which escapes the binary logic of being/nonbeing, and the number zero shares this property of being a hybrid, neither positive nor negative, so in linguistic systems those signs having impossible placement and logically aporetic role are defined

‘undecidables’. On the other hand, the concept of hole, the place-value zero and the blank space in a linguistic continuum are the metaphysical, mathematical and linguistic equivalents of a lack which necessitates a presence, a One, in order to be apparent, and hence whose existence is parasitical on the host system. Śūnyatā and zero are logical undecidables, and not mere negative counterparts (nothingness) to be opposed in any system of binary oppositions.

If zero is a meta-sign for the absence of other signs (that ultimately have no real referent at all) then it is not a representative of nothingness, but of emptiness. And representing a lack that turns back on itself, a lack of a lack, zero is a metaphorical designation, and it is in itself empty. In the same way, śūnyatā hints at a multiplicity of phenomena that nonetheless do not add up to a totality of being, but to an infinity of devoid phenomena.

Conclusion

I would like to conclude with a summary of what I have—and what I have not—proposed thus far, and with a final note.

After an account of the historical development of zero, in the first section of this paper, and an evaluation of Nāgārjuna’s śūnyatā, in the second, I have tried to threading together these two ‘concepts’ with several terms that share a family resemblance, borrowed from a Badiouian reading of Derridean

vocabulary: trace, supplement, undecidable. However, to describe these as ‘parallelisms’ (or comparisons) fails to express correctly the relation that binds these concepts: what is at stake at the core of this exercise is not only a new evaluation of Nāgārjuna’s philosophy, but a recognition of its possible role for a contemporary attempt to redefine ‘comparative’ philosophy. To ‘actualise’ Nāgārjuna does not mean to read into his words our words, but to use his words to enrich the possibility for philosophy as a whole to formulate new questions.

What I have in mind here is the necessity of probing how our ontological commitments condition the development of any intellectual product. In other words, a ‘theory’ of emptiness and co-dependent truth such as Nāgārjuna’s, by deconstructing the totality of a plenary being and the stiffness of a uniquely determined meaning, indexes the possibility of a new, unconstrained and indefinable space of action for thought, beyond already charted territories. This is the liberating power of emptiness.

I have not attempted a consistent and intentional parallelism between the philosophy of Nāgārjuna and the philosophy of Derrida, nor have I tried to imply that the history of mathematics is directly indebted to Nāgārjuna for the invention of zero. The latter is at best unprovable and the former is an enterprise that, while certainly an interesting intellectual exercise which might force us to develop a better understanding of both the philosophers, is

often spoiled by the tendency of using the one to correct the other. In its ‘meshing-up’ approach, my work here has been an attempt to suggest a new philosophical ground by weaving together different concepts and heterogeneous traditions of thought. As such, and only as such, it is philosophical speculation. This understanding of philosophy as an always unfinished and vibrant process of translations and reassociations is best expressed, I believe, by Bruno Latour, when he asks:

how will we define this freedom to go from one domain to another, this scaling up of the networks, this surveying? Philosophy is the name of this trade, and the oldest traditions define philosophers as those who have no specific field, territory, or domain. Of course, we can do without either philosophy or philosophers, but then there might be no way to go from one province to the next, from one network to another. (Latour 1988: 189)

The goal of this experiment has therefore been to offer an example of this 'leaping' across networks, performatively gesturing towards an understanding of philosophy as a process of mediation between disciplines, facilitated by a meontology which, by undermining metaphysical totality, offers an empty ‘ground’ for the unpredictable arrival of novelty. And, perhaps, to introduce a novel way to conceive the encounter between different intellectual traditions.

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