The Twofold Limit of Objects: Problematising Timothy Morton’s Rift in Light of Eugenio Trías’s Notion of Limit

Jordi Vivaldi 1
  • 1 European Graduate School (EGS), Division of Philosophy, Art and Critical Throught, Saas-Fee, Switzerland
Jordi Vivaldi
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  • European Graduate School (EGS), Division of Philosophy, Art and Critical Throught, Saas-Fee, Switzerland
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Abstract

The ontological abyss that separates real objects from sensual objects is one of the central principles of Object-Oriented Ontology (OOO), which has its most explicit and profuse modulation in Timothy Morton’s notion of rift. This article argues that, despite succeeding in explaining the radical difference that inhabits every object, Morton’s rift fails to explain the object’s unification, rendering the overall theory inconsistent. An alternative approach that accounts simultaneously for disjunction and conjunction between essences and appearances can be found in Eugenio Trías’s philosophy of the limit, a term widely ignored in OOO despite its deeply non-relational conception of the reality of things. The article further argues that the reinterpretation of Trías’s twofold liminal approach in light of OOO successfully addresses the inconsistencies found in Morton’s rift, paving the way for a theory of limits within Harman’s ontological framework.

1 Introduction: the undermined relevance of limits in OOO

The emergence of a new philosophical proposal usually implies a terminological renovation. This process does not necessarily introduce terms ex nihilo; in most cases, it simply centralises expressions with a formerly peripheral presence in the contemporary discourse. Husserl’s emphasis on “intentionality,” Levinas’ insistence on “otherness” and Deleuze’s focus on the “rhizome” are emblematic examples of how neglected terms can be brought to the foreground when new ideas arise. The emergence and consolidation of Object-Oriented Ontology (OOO) in recent years is no exception: under its umbrella, the term “object,” once marginalised by a relational philosophical episteme, has been recovered as a central element in some of the most relevant philosophical debates.1

However, the terminological renovation resulting from the rise of a philosophical alternative is hardly reducible to the centralisation of a single term. A plethora of related expressions arises around it, underpinning its conceptual power. New Materialism is a good example: although the notion of “matter” plays a central role, the term is conveniently flanked by expressions such as “entanglement,” “becoming,” “network,” “assemblage” and “process.” Amid this myriad of orbiting bodies, one shines with a particular force: “relation.” Its presence has been theorised by thinkers such as Karen Barad2 or Rick Dolphijn and Iris van der Tuin, who invoke “a discursive practice centered on the creation of concepts in their relationality,”3 i.e. an affirmative relationality4 that precedes its terms.

OOO advocates for the opposite. An object is “anything that has a unified reality that is autonomous from its wider context and also from its own pieces.”5 This radical withdrawal has led critics to define OOO as a metaphysics of absence, a metaphysics founded on a “deeply non-relational conception of the reality of things.”6 However, paradoxically, the centralisation of the notion of “object” has occurred without the systematisation of a term that is underexplored in philosophies associated with Speculative Realism and which seems fundamental to OOO: “limit.”

The term “limit” arises as soon as we think of an object as demarcated from its environment.7 In the case of OOO, the limit’s role seems even more decisive, since the object’s core is not just individual and separated but also withdrawn and inaccessible. The limit is actually present in OOO’s argumentation through the frequent use of liminal terminology by its thinkers: expressions such as “walled island,”8surface effects”9 or “encrusted qualities”10 are regularly employed in order to emphasise the “metaphysical abyss” that separates real objects and sensual objects within the quadruple object. To my knowledge, there is no systematic treatment of the nature of this metaphysical “wall,” “surface” or “crust” in the work of Graham Harman, something that is crucial in order to illuminate the combination of internal difference and unity that we observe in objects. The broadest development in this direction takes shape in Timothy Morton’s notion of rift, whose opening, suspense and closure account for the object’s birth, persistence and death.

The central argument in this article will be that Morton’s rift succeeds in explaining the radical difference that inhabits the core of every object, but that it fails to explain the object’s unification. The article will propose approaching this problem by way of Eugenio Trías’s notion of limit, the conceptualisation of which as differential sameness and autoreferential difference allows for articulating it as a territory of disjunction and conjunction rather than as a dividing Euclidean line.

Section 2 analyses the centrality of Morton’s rift in Harman’s Object-Oriented Ontology. Section 3 discusses the difficulties of Morton’s rift in accounting for the unified condition of objects in spite of their inner partition. In light of these criticisms, Section 4 briefly presents the philosophical work of Trías and then reconstructs his twofold notion of limit, particularly its territorial constitution and its conjunctive and disjunctive vocation. Section 5 first demonstrates that the core of Trías’s theory can be grafted onto Harman’s ontology with reasonable ease. Then, given this foundation, it proposes an object-oriented approach to the concept of limit, demonstrating that it constitutes an adequate alternative to Morton’s rift.

By way of conclusion, Section 6 discusses how the incorporation of a twofold theory of limits within OOO problematises the logical status of objects argued by Morton on the basis of Graham Priest’s dialetheism.

2 Hide and seek

The central principle of OOO is that objects have a unified reality that cannot be reduced to its parts or to its effects. Although the cosmos may be populated with an infinity of objects, they come in only two kinds: “the real object that withdraws from all experience, and the sensual object that exists only in experience.”11 By no means does this distinction refer to two separate groups of objects, some being sensual and others being real. Instead, it differentiates between two modes of being – sensual and real – which are simultaneously present in all objects.

An object is therefore a unified entity which is withdrawn from all access (real object) yet somehow manifests (sensual object). Withdrawn and manifest. At the very same time. Withdrawn: objects retreat from all relations with other objects, enclosing themselves in a vacuum-sealed region that precludes any attempt at knowledge. Manifest: in spite of their radical distancing, objects allude to their inscrutable reality by appearing in the experience of other objects. Objects play hide and seek.12

In OOO, the true duality does not lie between subjects and objects or between body and mind but between real objects and sensual objects. This duplexity is not the result of a transcendental condition that is external to objects. On the contrary, the difference between the real object and the sensual object is fuelled from the interior of every object. This point is particularly relevant. According to Timothy Morton, a threefold paradox arises: first, an object is at the same time itself and not itself; second, an object is at the same time present and non-present; and third, an object is at the same time part and whole.

An object is at the same time itself and not itself; it cannot be perceived but only perceived-as. Its appearance in the experiential field of another object is always a translation; it is always the result of paraphrasing the object in itself according to the structure of the perceiver. In consequence, and despite being one, the object in itself and the object as it is perceived are neither identical nor deducible one from the other but qualitatively different.

An object is at the same time present and non-present; its manifestation (presence) in the experience of another object is nothing but an allusion to a withdrawn realm (non-presence). Its apparition certifies its disapparition. Its register documents its absence. This mysterious voidness conforms an inscrutable domain that does not lie in any external Platonic world but inhabits the object itself. Objects withdraw, yet they appear.

An object is at the same time part and whole; an object’s composition is made up of other objects, which are parts of the former. However, at the same time, these objects are also wholes in themselves – that is, they can neither be reduced to the object they compose nor to the parts that compose them. We are confronted thus with a strange mereology: objects are wholes constituted by parts but also parts constituting other objects.

This constant interplay between identity and alterity, presence and non-presence and part and whole unveils, according to Timothy Morton, an ontological condition that resonates with Graham Priest’s statements that objects are cracked, objects are double-truthed and objects are dialetheic. Objects are “what they are and what they are not at the same time.”13 This twofold condition produces a rift between appearances and essences, the ontological centrality of which has been lucidly described by Morton in three steps: the aperture of the rift gives birth to an object, the development of the rift sustains an object and the erasure of the rift ends an object.

The rift underpins the object’s autonomy. The tension established by the separation between the real object and the sensual object accounts for all salient aspects of reality, without relying on any external environment. Time, space or causality pours constantly from the object itself, from its internal contradiction – that is, from the rift that arises between the real object and the sensual object. This duel is what makes objects “float, breathe, oscillate, threaten, seduce, rotate, cry, orgasm.”14 Morton’s rift makes it possible to explain reality on the basis of a single object, without requiring other entities in order to function. It is presented as a radical and permanent chorismos, an “irreducible gap between real and sensual objects”15 that makes objects into uncanny and unstable doubles.

3 The problem of unification

Morton’s rift succeeds in accounting for the object’s duality. It establishes an insurmountable abyss between the real object and the sensual object which effectively underpins the object’s irreducibility. Yet, irreducibility is inherently linked with unification: objects cannot be separated into parts without their essence being dismantled. If they could, objects would be reducible to their components, and OOO would not be able to explain emergence. Objects are therefore wholes without parts or, more aptly, wholes without parts whose mere addition would be able to account for the object. In OOO, objects are unified realities; as Harman affirms, “each object is a unified thing, despite its multitude of features.”16 In other words, “objects are units that both display and conceal a multitude of traits.”17 Ian Bogost also emphasises the unified condition of objects by replacing the term “object” with “unit operation.” Bogost’s use of the term unit is indifferent to the nature of what it names, but it emphasises the condition of being “isolated, unitary, and specific, not simply the part of a whole.”18 Like objects, unit operations are enclosed and unified systems – an entire universe’s worth.

However, how can an object be unified and at the same time split by a radical cut between its real object and its sensual object? How can an object be an isolated, single and specific unit and at the same time cracked by a profound and permanent rift? How can one be two?

Morton’s notion of “rift” illuminates the radical difference established within every object, but it fails to explain the object’s unicity. Morton affirms that “a cut between an object and its manifestation to other objects doesn’t mean that the manifestation can be anything at all.”19 In order to underpin this statement, Morton affirms that the violation of the Law of Noncontradiction (LNC) resulting from the object’s contradictoriness does not imply an ex contradictione quodlibet (ECQ). For him, the crucial problem in avoiding the possibility of an object radiating random manifestations is whether trivialism can follow from logical principles that are dialetheistically correct. In this sense, Morton simply writes that “there are good reasons for supposing that ECQ doesn’t hold just because LNC doesn’t hold,”20 and in a footnote he refers to Graham Priest’s In Contradiction: A Study of the Transconsistent, where the author explains these reasons. Whether trivialism follows from true contradictions is an ongoing open debate in which Priest’s theses have come up against solid resistance.21 However, it is not necessary to enter into this debate in order to signal Morton’s failure, which precedes the recognition of a hypothetical object’s contradictory condition. As soon as Morton states that an object is simultaneously p ∧ ¬p because there is a rift between essences and appearances, he is actually laying out, aside from the contradictory status of objects, two crucial points: first, that the real object (p) is that which the sensual object is not (¬p), and, second, that the summation (∧) of both constitutes an object (p ∧ ¬p). This assertion precludes the possibility of affirming the object’s immanent unification; it implies the absolute independence of the real object and the sensual object: if the former (p) has something to do with the constitution of the latter (¬p), then the real object (p) cannot simply be negated (¬p) in order to account for the sensual object of the same quadruple object.

The object’s unification is crucial for at least two reasons. First, in order to establish any fertile tension, dialogue or contradiction between two different elements, there needs to be a certain resistance among them, that is, a common ground where they can enter into friction; resistance between different elements implies that these elements have something in common. They cannot be completely transparent to one another, which is what absolute negation implies (p ∧ ¬p). Without the internal rub between the real object and the sensual object, and in order to account for the integrity of the quadruple object, OOO would need to rely on forces that are external to the quadruple object, drastically harming its autonomy.

Second, if the real object and the sensual object of the same object were completely irrelevant to one another, the different sensual objects related to one real object would not be consistent. Nor would there be consistency between the different sensual objects of the same real object perceived by different observers. The same real object could be arbitrarily perceived as a zebra, as a galaxy or as dinner – in other words, we would be unable to explain permanence, which would defy our most common experience.

Morton’s rift tells us only half the story. It brilliantly accounts for the abyssal difference between the real object and the sensual object, but it doesn’t explain how both elements avoid mutual transparency, that is, how they “resist” each other in spite of their radical distinction. Pure difference is insufficient: there can be no tension, duel or contradiction without resistance. Rather than full transparency, resistance paradoxically demands a certain affinity between the elements at play. Without it, the real object and the sensual object of any object just traverse each other as ethereal phantoms; their existence is mutually irrelevant.

The coexistence of the real object and the sensual object within a single object presents, then, a threefold requirement that challenges Morton’s rift. First, the real object and the sensual object must be radically distinct. Second, they must form a unified object. Third, the object’s distinction and its unification must be immanent to the object, that is, they must not be the result of any external force. As we have seen, Morton’s rift accounts for distinction and immanence, but it fails to explain unification.

This article proposes addressing this threefold requirement through the notion of limit. In spite of some scattered allusions, the limit has not been systematically approached in the context of OOO. This is rather surprising. In a theory of reality that privileges discrete objects over relational networks, it seems reasonable to assume that the notion of limit would enjoy a certain centrality. Although related terms such as “firewalls,” “surfaces,” “crusts,” “rifts,” or “abyss” are recursively used by OOO thinkers, only Ian Bogost and Tristan García have explicitly referred to the notion of limit.

Bogost’s book Play Anything does not approach the limit from an ontological perspective but in the context of play and fun. The limit is not a reductive and coercive fence but a fruitful and pleasurable tool. Its capacity to constrain is fundamental for at least two reasons: first, limits provide definition and therefore permit comprehension; second, limits make space for novelty by setting the convention from which invention arises. If fun “isn’t maximizing pleasure, but finding something new in a familiar situation,”22 then limits set the terms from which originality, in its double sense of original and originating, can take place.

In Form and Object, Tristan García briefly approaches the limit from an ontological register. For García, the limit is an object in between objects. It is contrasted with form, whose ontological brightness eclipses the limit: while a thing “can have as many limits as one wants it to have or as one discovers it to have,” one “does not choose its form.” The limit is contingent, and it is constantly subject to question; limits are plural, limits change, limits are dependent and limits are finite. Instead, García’s form is single, fixed, independent and infinite. The limit is nothing other than “an object that seeks to disappear in between two other objects.”23

Neither Bogost nor Garcia articulate an ontological limit powerful enough to deal with the paradox of having, on the one hand, a “fundamental Rift between withdrawn essence and aesthetic appearance”24 (i.e. between the real object and the sensual object) and, on the other, the requirement of the object’s cohesion “in a unified reality that is autonomous from its wider context and also from its own pieces.”25

In spite of a different terminology, this challenge runs through the work of the Spanish philosopher Eugenio Trías (1942–2013). In Los límites del mundo, Eugenio Trías doubles the limit “in those two extremes that it determines, as that which at the same time joins and disjoins them.”26 By doubling the limit into an obverse and a reverse that frames an inhabitable space, the limit takes on a central role in his ontology, accounting on the one hand for the junction and disjunction of what remains withdrawn and what is manifested, while on the other maintaining the former’s absolute inaccessibility.

4 Doubling of the limit in Eugenio Trías

Given that most of Eugenio Trías’s work is likely unknown to an international audience, a brief clarification of its principal terminology seems appropriate. The aim of introducing Trías’s work is to make space, within the framework of present-day continental philosophy, for an approach that avoids the limit’s reduction to a negative and restrictive entity whose function oscillates between that of complete unification (Hegel) and that of complete separation (Derrida).

Trías’s ontological proposal opposes postmodern discourses. Following decades of postmodern criticism of the universal pretensions of enlightened reason, a number of voices in the late 1980s and early 1990s criticised postmodern discourses for being conservative (Habermas) or for their complicity with late capitalism (Jameson). However, according to Trías, the most remarkable downside of postmodern theses lies in the fact that “with them, the dinner guest is forever hungry and anorexic in relation to his philosophical demands.”27 Trías opposes postmodern thinking due to its lack of interest in orchestrating a proposal that takes on the big ontological questions which concern the human being. In Trías, this proposal gravitates around a single entity: the philosophical idea of the limit.

Trías develops his notion of limit in contrast with modern and postmodern philosophy. According to the Spanish thinker, one of the key characteristics of modern thought consists in having set, as a definitive methodological trait, the concept of limit as the horizon for any philosophical research. Modernity understands the limit as the red light of thinking; it indicates what is impossible by fixing a negative necessity in relation to the ambits of power and linguistic possibilities. The limit is thus not conceived as something but as the negation of something. This approach forces modern thinking to oscillate between the fear of erring (Kant and Wittgenstein) and the Faustian desire to exceed any limit (Hegel). In this context, the limit is understood as negation and contradiction, as a frontier between something and its other. Trías aims to move beyond this modern consciousness, while at the same time avoiding the postmodern enthroning of the fragment, the collage or the puzzle as the locus of being and meaning. The ironic deviations or unexpected combinations characteristic of postmodernity are set aside in order to understand the limit as a place of ontological affirmation. Despite being discarded by modern philosophy, the limit can be found in Kant (“Limitation is nothing other than reality combined with negation”28), in Schelling (“Since the ground of the limit lies neither in self nor thing, it lies nowhere”29), in Hegel (“The limit, besides referring to the unity and being the moment of negation in it, is also, as one, self-referred.”30) and in the later philosophies of Heidegger (“Being is delimited against an Other and thus already has a determinateness in this setting of a limit”31), Jaspers (“The word limit implies that there is something else, but it indicates at the same time that this other thing is not for an existing consciousness”32) and Wittgenstein (“The limits of my language mean the limits of my world”33). It can also be found in the scientific tradition, in infinitesimal calculus or in the calculus of limits. However, it has never been considered in its radicality. It has never been conceived as the cornerstone of a philosophical proposal. By replacing its negative vocation with an ontological affirmation, Trías sanctifies the limit as the territory where first philosophy occurs.

Trías’s originality lies in replacing the usual Euclidean conception of the limit with a Roman approach. From this perspective, the limit is doubled and takes on thickness. Rather than being an infinitesimal line, it becomes a territory, a land and an occupiable space. The limit becomes the limes, the peripheral territory which, in the Early Roman Empire, marked the confines of Roman civilisation. Rather than a wall, the limes was a stretch of land, a narrow and oscillating strip that was inhabitable, susceptible to colonisation, cultivation and worship. The limes was an isthmus; it mediated between the Roman Empire and the tribes, between culture and nature, between civitas and barbarie and between law and anarchy. Between world and mystery. Its inhabitants, the limitanei, were not only Roman soldiers and their families but also members of two other collectives. First, all sorts of merchants were attracted by the territory’s character as a place of encounters. Second, certain Germanic tribes were hired by the Roman Empire to protect the border. Thus, in the long run, the limes became vibrant and eclectic poles of activity, although its horizon was always threatened by the radical otherness of the barbarian troops, whose incursions regularly altered and reshaped the “limits of the limes.” Thus, the limes was an inhabitable oxymoron, a space of junction and disjunction and an unstable land of conflict whose effervescent and compressed diversity could by no means take place within the clinical abstraction of the Euclidean line. Daring dwellers of the world’s confines, the limitanei inhabited the Roman Empire without occupying its interior; they were suspended in a liminal land that belonged to the civitas but referred to the barbarie. The limes was thus a suffocating and malleable territory, an unstable locus adjacent to yet withdrawn from the mysterious barbarian otherness.

This territorial understanding of the notion of limit – i.e. the limes – is the idea with which Trías will shift all philosophical problems. Although this variation includes areas such as ontology, aesthetics, ethics, politics and theology, in this article we are interested in one specific theoretical tool that can help us approach the coexistence of the real object and its sensual object in a way that meets the three requirements previously mentioned: distinction, unification and immanence. This theoretical tool is Trías’s ontological approach to the limit through a method that is twofold. First, in its moment of retreat, the limit unveils its intrinsic determinations, which are the coupling and the disjunction of the terms that it mediates. Second, in its expansive moment, the limit unfolds and projects three enclosures: the hermetic enclosure – that is, the transcendental region that withdraws and can be conceived but not known; the enclosure of appearing – that is, the immanent region that manifests and is present to our experience and the frontier enclosure – that is, a limes that belongs to the first enclosure while referring to the second. In opposition to Morton’s ontological rift, Trías’s limes is a dense zone of affirmation, constituting and mediating both previous enclosures, while simultaneously being the inhabitable locus of the human being.

4.1 The retreat

In the first part of his method, Trías approaches the notion of limit in itself, i.e. in its “nature of differential sameness and autoreferential difference.”34 Disjunction and coupling are the internal engines of the limit; they are derived from its self-reflexive condition and, as we will see later, they unfold its essence in three enclosures. The disjunctive power makes it possible to distinguish each of them, while the unifying coupling redirects them towards a liminar unification in the frontier enclosure.

The limit is what separates the immanent existence from its transcendental causes, but at the same time, it refers this existence to its absent causes. The limit separates and refers. It has a dialectical nature: while preventing the world from finding its foundation, the limit also prevents the world from remaining enclosed in itself. It informs us that there is something beyond it, while simultaneously keeping this beyond eternally withdrawn. That is why Trías asserts that the essence of the limit consists in a double power: the power of disjunction, which separates what appears from what withdraws, and the power of coupling, which unifies and conjugates the two.

Thus, the interior of the limit itself is inhabited by these two powers, which emerge from the spontaneous reflection of the limit in itself, in which its selfness is revealed. It is a selfness that is difference or, more aptly, it is a selfness that is, like Hölderlin’s definition of beauty based on Heraclitus, εν διαϕερον εαυτω, that is, “that which distinguishes one in itself.”35 The limit is, indeed, “itself in its radical internal differentiation.”36 In other words, the limit is at the same time the unifying selfness of that which, itself, by itself, by its differentiating power, separates and splits. That is why Trías’s limit differs both from how it is approached by the Derridean philosophy of différance and the Hegelian philosophy of the Absolute: while the former understands the limit as pure alterity (“différance (with an a) as the displaced and equivocal passage of one different thing to another”37) and the latter as pure identity (“something in its limit both is and is not”38), Trías assumes the equivalent coexistence of alterity and identity as the essential determination of the limit. This ambivalence, a consequence of both the conjunctive power and the disjunctive power, establishes a dialectical relation, which admits two general forms of correlation. The first is the most obvious: it is based on the conflict and clash derived from its contrasting character. However, Trías emphasises a second relation which, assuming this conflictive nature, is able to sublimate it under the notion of the game. Whereas in the fight and the conflict both powers are in relation and empowered by the force of disjunction, in the game exactly the opposite occurs: both forces are equally connected but the conjunctive empowerment prevails.

By virtue of this reflexivity, and because of its nature and condition, the limit is doubled into an obverse and a reverse. However, while in Hegel this reflection produces “a symmetric duplication in which both extremes, in their pure contradictory negativity, are completely identical under the same speculative impulse that presages and prepares the concept of the absolute,”39 in Trías this reflection is asymmetrical – that is, the terms of this doubling are not specular. Trías’s reflection is, in a certain sense, a failed reflection: it does not produce terms which are completely identical in their own contradiction but “shows a fundamental asymmetry integrated within the limit itself.”40

Under this umbrella, the reflexive essence of the limit re-flects in itself in an asymmetric and non-speculative relation to those extreme regions in which it is projected: the enclosure of appearing and the hermetic enclosure. The limit belongs to the former and refers to the latter; it is exposed in the former and indisposed in the latter. It is thus shown in the former as far as it can be manifested, and it is withdrawn in the latter up to where it can be sheltered and guarded. By no means can the limit be traversed. Together with the frontier enclosure, ambit and realm of the limit itself, the unfolding of the limit through the hermetic enclosure and the enclosure of appearing forms the second moment of Trías’s method: its expansive moment.

4.2 The expansion

The limit is always re-flexive. However, it produces an asymmetric doubling: the part related to what the limit is limiting, and the part related to what the limit refers to. Thus, the limit is not a simple, symmetrical and indeterminate “in between;” rather, in opposition to Morton’s isotropic rift, the limit belongs to something in reference to something else. In the twofold formulation of “belonging to” and “referring to” lies the asymmetrical nature of the limit. And according to Trías, what the limit is limiting is also what the limit makes it possible to show, and what the limit refers to is also what constitutes a negative reference, i.e. a shadow, a mystery.

Thus, this reflection expands into the production of a plurality of enclosures. It is important to note that Trías uses the Spanish word cerco, translated here with the term “enclosure.” This word has a double meaning that is crucial. On the one hand, the term cerco refers to a topological delimitation: the tracing of limits in order to separate what is enclosed from a space that remains outside. But on the other hand, cerco refers to a military delimitation, that is, a siege, whose aim is not merely to separate but also to assail, to beset. Both meanings assume an essential plurality – inside and outside, before and after the divisory line, fence or frontier but also a duplicity in opposed powers – the besieged city and the army laying siege. There is not, therefore, a single enclosure but a plurality of enclosures. However, differently from all previous dualist ontologies, the one proposed by Trías does not refer to “two worlds” but to two ambits unfolded by the obverse and the reverse of the limit. Both ambits differ in their accessibility: the first refers to that which can be known, i.e. stated in the form of a “specific proposition whose scientific value can be proven and verified,” while the second refers to that which can only be thought, i.e. “stated in the form of a perplexed question and a hypothetical answer.”41 Yet this dualist ontology is revealed by a third ambit, the frontier enclosure, where both previous ambits come together in their radical difference.

The first ambit is unfolded by the obverse of the limit and is defined by Trías as the enclosure of appearing. It is the world. It is immediate. It is a radical datum. It is what “is there,” what occurs only as experience, resonating thus with Harman’s sensual domain. It is an “interconnected set of physical events, each of them potentially constituting, at the same time, a specific mode of perception in itself, each of them furnished with a scheme or spatio-temporal map that determines measurements, dates, weights, lengths and speeds.”42 The enclosure of appearing is an affirmed plurality of raw facts, a set of immediate “givens” which have been brutally tossed before our experience and whose crude existence elicits the first philosophical emotion: the astonishment of certifying that there is something instead of nothing. However, this datum is “in exile and exodus.” In other words, it is always referred to a limit that is constitutive to it and that precludes a profound and holistic knowledge of what is given.

The second ambit is unfolded by the reverse of the limit, which is defined by Trías as the hermetic enclosure. In order to be postulated, the limit needs to be conceived as belonging to what is given – the enclosure of appearing – and referring to what cannot be simply denied, because its negation would relentlessly imply the instant suppression of the limit. The other that subsists beyond the limit must be conceived, in spite of its radical transcendence, as an affirmation, as a mode of alterity demanded and postulated by the nature of the limit itself. While the enclosure of appearing emphasises the quotidian and the familiar, the hermetic enclosure belongs to the realm of the weird, the inhospitable and the disturbing. Despite the passion aroused by the mystery of its void, the hermetic enclosure is recursively withdrawn from experience, documented by the limit as that which is absent, but at the same time that which in spite of being silent, opaque and closed off from any hermeneutic appropriation, must be decidedly affirmed. The hermetic enclosure resonates with Harman’s real domain in that it can never be reached; its limit can never be crossed. It is the mute referent of any interpretative and philosophical adventure, always “in perpetual escape in relation to our possibilities of thinking, saying, predicating or even symbolizing.”43

The third ambit is constituted by the limit itself, and is defined by Trías as the frontier enclosure. As we will see in what follows, it differs sharply from Morton’s rift. The consideration of the limit as an ontological realm in its own right is one of Trías’s main contributions: “The limit is not just what restricts and brakes, the obstacle and the barrier that resists. It is also a space of liberation, an area in which the frontier inhabitant plays out its being or not being.”44 Indeed, Trías has doubled the limit in those two extremes that determine: the enclosure of appearing and the hermetic enclosure. However, this duplication opens an inner space that is framed by the relative terms that it puts into connection. The limit thus has its own ambit; it is a region of coupling and disjunction that mediates between the measurable world and incommensurable mystery. According to Trías, this daimonic space is the space par excellence of the human being. S/he is its inhabitant, being simultaneously referred to that which appears and that which withdraws, having one foot planted inside and another outside and being in a permanent state of suspension between being and not being. If astonishment is the emotion characteristic of the enclosure of appearing, and passion that of the hermetic enclosure, then vertigo is the emotional register of the limit’s inhabitation: it is the vision into a bottomless abyss, the cracking of all that is firm and the loss of the certainty that could house any conviction. The limes is, thus, in opposition to Morton’s gap, “the land, the ground, the paradoxical space in which our unwelcome human occupation is precariously implanted.”

These three enclosures are the result of the limit’s self-reflexivity. The limit finds, in its own interior, identity and difference: the conjunctive power, which produces a recursive return, and the disjunctive power, which produces a constant distance. Trías’s philosophy assumes the coexistence of identity and difference as the limit’s essential determination. Thus, the limit’s Janus-faced nature “produces an asymmetric doubling: relative to that which the limit is limiting and that to which the limit refers.”45 The first is what the limit projects: the world, being and familiarity. The second is what constitutes a negative reference or a shadow: mystery, nothingness and strangeness.

However, and in opposition to Morton’s rift, at the exact moment where the limit marks the frontier of the world to which it belongs, it necessarily certifies the existence of the beyond to which it refers. As a consequence, the limit produces in the inhabitant of the frontier enclosure “the obligation of finding a possible access to the mystery of transcendence that lies beyond the limit.”46 Trías affirms that a direct access to the hermetic enclosure is categorically impossible. In opposition to Hegel, the limit cannot be traversed. However, its transcendence can be evoked; according to Trías, the symbol, in its religious or artistic conjugation, is the only way to bring about a precarious, indirect and analogue allusion to that mystery. The term “symbol” should be read here in its etymological sense, that is, as “sym-ballein,” which means to throw in conjunction, and in opposition to the “dia-ballein,” which means to throw in disjunction. The symbolic thus opposes the diabolic; the symbol brings together two fragments related to a split unity: the enclosure of appearing, or world, and the hermetic enclosure, shelter of mystery. This combined launching takes place in the frontier enclosure or limes, whose reference to the Latin expression limen (door, access, threshold) emphasises the hermeneutic vocation of the limes, anchored as it may be to an eternal failure.

The symbol is thus suspended between its fully immanent appearing and a mysterious and inaccessible side on which its complete ntelligibility also relies. Trías defines the symbol as that “irruption of the hermetic enclosure through an apparition that shines and sparkles in the frontier of the world.”

5 The object and its limits

The ontological twinning of Trías’s limit pursues multiple aims, but it is relevant to us here for one simple reason: it approaches the limit simultaneously as a disjunctive and coupling device. In Trías’s work, the limit’s identity lies precisely in its inner alterity; its sameness consists in differing in itself and by itself, in being “itself in its radical internal differentiation.” This approach differs from Morton’s rift, the theorisation of which accounts for the abyssal distinction between essences and appearances, but does not account for the object’s required cohesion in order to constitute a unified reality. Trías’s strategy in laying out a notion of limit that simultaneously accounts for coupling and disjunction has three specific peculiarities which facilitate its incorporation into Harman’s fourfold ontological structure.

First, the limit is not understood as (1) the symmetric in between of two entities or (2) the solipsistic extreme of a single entity, but as (3) a vectorised element that belongs to one entity and refers to another entity. This belonging/referring structure has three consequences. First, the limit is not ontologically autonomous but depends on its belonger. In other words, it is its property: the limit is not an object with qualities but the quality/ies of an object. Second, the limit is not isotropic but anisotropic – that is, it is asymmetric, oriented and vectorised; it has a different relation with the two terms that it separates. Finally, in its “referring,” the limit announces to its belonger that, although it cannot be traversed, there is something beyond it. The limit does not provide any information about the specific content of that otherness, but it certifies the existence of that radical alterity. The intelligibility of this proclamation is relevant because it implies an indirect and analogue contact between the elements which the limit, in itself and by itself, separates.

Second, the limit reflects itself, and in this reflection it is doubled into an obverse and a reverse: it becomes a twofold limit. However this twinning is not specular (Hegel) but distorted. It produces two sides that are not symmetric and which refer to two completely different regions: the enclosure of appearing and the hermetic enclosure. These enclosures should also be seen as sieges – that is, they do not only delimit a certain space, but they also enact pressures, either as executors (enclosure of appearing) or as receivers (hermetic enclosure). This pressure implies a certain mutual recognition that results in a cohesive tendency between both enclosures.

Third, the tension established between the obverse and the reverse of the limit separates both sides and opens a third enclosure within the limit itself: the frontier enclosure. Thus, the limit becomes a limes: it is no longer an infinitesimal Euclidean line, but an effervescent inhabitable territory. Occupied by the human being, it is the territory of the symbol, understood, on the one hand, in its etymological register of “sym-ballein” and, on the other, in its artistic or religious conjugation. The limes is thus the locus of the recursive but inevitably failed attempt to penetrate the hermetic enclosure through the symbol by using what is manifested in the enclosure of appearing in order to refer to what withdraws in the hermetic enclosure.

However, in order to graft Trías’s twofold model of the limit onto Harman’s fourfold structure, we need to leave behind certain aspects of the former’s ontological structure. Three of these aspects, especially the last one, are particularly incompatible with OOO. They are the limit’s ontological single centrality, the assumption of the world’s existence, and the ontological privilege of the human being over other beings.

First, Trías’s philosophy conceives the being always as “the being of the limit.” Trías approaches the limit from an ontological and an affirmative point of view, but he also situates it at the centre of any philosophical reflection. Trías’s ontology primarily consists in making the limit, “scarcely thought of, into a true cornerstone.”47 However, OOO’s cornerstone is not the limit but the object. In OOO, to exist means to be an object: more specifically, to be an object’s interior. There is nothing outside objects. In consequence, although this work argues that the notion of limit is fundamental in OOO, it also maintains the notion of object as the cornerstone of OOO’s metaphysics.

Second, Trías defines the limit as the limit of the world. He is very explicit on this point, particularly in the title that he uses for one of his more emblematic books: Los límites del mundo [The Limits of the World]. According to Trías, the limit is “the line and frontier that permits mutual access between these two worlds and at the same time certifies their irremediable distance.”48 The limit is thus “a frontier territory that separates this world from the other world,”49 the locus “where two worlds are intertwined and come together, while simultaneously diverging and differing.”50 However, there is no world in OOO – that is, there is nothing exterior to objects, there is no trascendental environment, no general medium. This means that in order to graft Trías’s model of limit onto OOO, it is necessary to understand Trías’s ontological structure not as an external condition that lays the foundation for objects’ existence, but as interior to objects – i.e. immanent to them produced by every object in itself and by itself.

Third, Trías privileges the human being in relation to all other beings by considering that s/he is the only being inhabiting the frontier enclosure: “we [the humans] are the limits of the world, with one foot planted inside it and the other outside it.”51 Thus, according to Trías, the human is the limit itself, defining and circumscribing both worlds: from his/her limit’s inhabitation, the human “simultaneously contemplates what s/he seems to bid farewell to – home – and what s/he seems hopelessly attracted toward – the abyss.”52 It is a twofold tendency towards the outside (hermetic enclosure) and towards the inside (enclosure of appearing). As the single inhabitant of the limes, the human thus differs both from the animal, who only inhabits “this world,” and from the angel, who only inhabits “that world.”

The ontological singularity that Trías grants to the human being by positioning him/her in a specific locus (the frontier enclosure) is incompatible with the flat ontology professed by OOO, for which “all objects must be given equal attention, whether they be human, non-human, natural, cultural, real or fictional.”53

The tension between Trías’s human ontological privilege and Harman’s flat ontology is particularly relevant, since it might be a decisive objection for the purpose of grafting Trías’s theory of limits onto Harman’s fourfold structure. There is a very precise reason for this: in Trías, the limit is so powerful because it is the exclusive locus of a human whose ontological status has been privileged: the singular fact that the human belongs to the enclosure of appearing, while alluding to the hermetic enclosure, qualifies him/her to navigate between the two waters, although never invading the latter. However, since there is no ontological privilege for the human being in Object-Oriented Ontology, who is responsible for mediation once the limit has been secularised from Trías’s anthropocentrism?

In the light of Trías’s liminal ontology, and paying particular attention to this question, we propose an approach to the notion of limit in OOO that aims to constitute an alternative to Morton’s rift. The main benefit of the former over the latter consists in its capacity to account for both junction and disjunction. Its construction responds to five key categories: the limit’s structure (“belong to” and “refer to”), the limit’s performance (de-finire and per-cipere), the limit’s ontological status (real limit and sensual limit), the limit’s impermeability (blurriness and transparency) and the limit’s décalage (limes and pressures).

5.1 Structure: “belong” and “refer”

In OOO, reality is formed by objects and their qualities (and their interactions), and therefore the limit must occupy one of these ontological categories. In order to ascertain this, it is crucial to determine the formal structure of the limit, that is, (1) whether the limit is in between the two objects, (2) whether the limit is the extreme of one object or (3) whether the limit belongs to one object and refers to another. This conceptualisation is relevant not just to define the limit’s ontological dependence or independence but also to define its symmetrical or asymmetrical condition and its vocation of junction and/or disjunction.

To be in between means to be symmetrically indeterminate – to be ontologically neutral – in relation to two or more objects. The limit is thus detached from any object; otherwise it could not maintain its impartiality. As a consequence, there is only disjunction; the limit is ontologically independent and therefore it is an object among objects. To be the extreme means to de-termine – to be the terminus of – one object. There is nothing but attachment to that object. The questions regarding symmetry/asymmetry and junction/disjunction are impertinent because there is only one object at play. The limit is thus ontologically dependent on that object, and therefore it belongs to the kingdom of qualities. To belong to one object and refer to another one means to de-termine one object – to be the terminus of that object – while evoking that which is not that object, i.e. another object. Since in Trías’s approach, and in opposition to Hegel, the limit is ontologically asymmetrical, it conjures up more objects than the object it belongs to, but it only determines that object. Thus, the limit separates by belonging to one object, but it couples by referring to otherness. The limit is ontologically dependent on that object, and therefore it belongs to the kingdom of qualities.

However, if the limit is “differential sameness and autoreferential difference,”54 if the limit is in itself and by itself internal differentiation, if in its re-flection it separates and divides, then the limit necessarily joins and disjoins, or, more accurately, the limit joins what it disjoins. In the structural formulation “belong/refer,” and in opposition to Morton’s rift, what the limit actively disjoins is the limit’s belonger, and what the limit actively joins is the limit’s reference. At the precise moment where the limit marks the frontier of what it limits, it necessarily certifies the existence of the beyond to which it refers, which is already a form of recognition, i.e. a form of conjunction.

Thus, the “belong/refer” structure prevents what is limited from remaining solipsistic. It precludes its loneliness by a formulation that is ontologically asymmetric: to belong implies a relation of inclusion and to refer implies a relation of allusion. However, asymmetry is the only ontological scenario in which the limit can simultaneously join and disjoin: the symmetry of the in between implies no attachment or full attachment, and the solipsism of the extreme ignores alterity. Thus, by differing from itself through its belong/refer structure, the limit is, at the same time, the unifying selfness of something that, itself, by itself, by its differentiating power, separates and splits.

5.2 Performance: “De-finire” and “Per-cipere

In resonance with Trías’s twinning, in OOO the limit is doubled. In its condition of being “itself in its radical internal differentiation” the limit re-flects, and in this re-flection it produces an obverse and a reverse. However, the limit’s reflection is a failed reflection, that is, it is not specular: rather than producing two symmetrical sides, the limit’s reflection engenders an asymmetrical pair polarised under the Latin terms definire and percipere.

This point is particularly relevant because it provides a response to the problem caused by the tension between Trías’s ontological human privilege and Harman’s flat ontology. In Trías’s framework, the limit is occupied only by the human being, who in his/her ontological singularity is able to mediate between the enclosure of appearances and the hermetic enclosure. However, since in OOO there is no ontological human privilege, who or what is then responsible for mediation once the limit has been secularised from Trías’s anthropocentrism? Answering this question implies identifying one key aspect of Trías’s limit: its double power of junction and disjunction operates through the human. In Trías, the limit is nothing but a locus, a receptacle whose performance depends on the presence of its singular inhabitant, the anthropos.

When we introduce Trías’s limit into OOO, the limit’s conjunctive and disjunctive power are not executed through any singular being occupying its space, but through the impact that the limit has on the limited object. In Trías, the limit, besides joining and disjoining both enclosures by providing locus to the human being, does not have an impact on any object. This is related to the fact that, for Trías, the three enclosures are transcendental regions that are located outside of objects, or more aptly, occupied by objects. However, in OOO the limit is internal to every object, because every object is constituted necessarily by a real object and accidentally by a sensual object. The fact that the limit is internal to every object implies that the limit, in its limiting execution, in its conjunction and disjunction, is affecting the limited object, something that does not occur in Trías’s notion of limit. Thus, whereas for Trías the limit joins and disjoins the enclosure of appearances and the hermetic enclosure through the human who inhabits that liminal territory, in OOO the limit joins and disjoins the real object from the sensual object through its twofold impact on the quadruple object. First, it disjoins the limited object from the limiting objects by defining the former. Second, it joins the limited object to the limiting objects by manifesting the former – that is, by providing the basis for its perception. It is precisely by virtue of these two operations that the limit in OOO joins and disjoins, and not by the occupation of any ontologically privileged entity.

5.2.1 Limit as De-finire

The term definire signifies the act of tracing the borders of something with clarity and precision in order to separate – disjoin – it from its neighbours. Definire is thus de-finire, the establishment of finis, ends. However, the term finis shouldn’t be read here in light of its topological or chronological sense; rather, it should be approached in its semantic register: to define means to specify the qualities of an object that make an object this object and not that object. To define is thus to shed light on the object’s thisness, on “what an object is,” or what Scotus alluded to with the term “haecceity.” Defining consists in tracing an ontological contour in order to limit an object’s in-finite possible variability into one single framework that distinguishes it from all other objects. De-finition implies con-fination; illuminating the object’s thisness means isolating it from its exterior, enclosing it, marking its quantitative and qualitative borders, cutting off continuity’s homogeneity by accounting for the object’s double discreteness: the object’s mathematical countability and the object’s individual distinction.

In this light, the limit should be read as what de-fines the object to which it belongs. In other words, an object is what it is in virtue of the real limit that it assigns to itself. However, the object’s de-finition, that is, the establishment of the object’s thisness, cannot occur in a vacuum. There is no this without that: if it is nothing but thisness, if there is no that beyond this, then it is not this, but it just is. Thus, at the same time that the limit defines its object, it necessarily evokes otherness, i.e. it alludes to another object. This consideration certifies the need for the limit’s “belong/refer” structure: if the limit is the object’s solipsistic extreme, there is no allusion to any otherness, and if the limit is what is in between objects, then the limit would be an object, and by de-fining another object it would be undermining its neighbour’s autonomy. Instead, the belong/refer structure recognises the limit’s definition of its object, while assuming existence as an external reference.

5.2.2 Limit as Per-cipere

The term percipere means “to completely capture,” to enclose. Percipere is thus per-cipere; the term cipere, to capture, indicates the relational and active action of separating something from its background in order to be joined with – perceived by – something else, in other words, bringing something to the foreground of something else by delimiting the former from its exterior. The notion of limit is also crucial to understanding other terms related to perception, like the terms divisare or contemplare. Divisare signifies to separate through vision, and it is used specifically to refer to the act of sighting land from a ship as it is approaches the coast. Divisare is thus di-visare, the association between the notion of separation (“dis-”), i.e. delimitation, and the notion of vision (“-videre”), i.e. a type of percipere. This link between vision and separation can be found, along with other derivative terms such as “division” or “divulgation,” in the word contemplare. In this second case, the root tem means “to cut,” and the word templum signifies that sacred zone that has been cut off and separated from the profane space. Contemplare was the collective activity engaged in by the augurs, who, by observing and delimiting the sky into regions, could register the movements of birds and elucidate the fortune of the city that was about to be founded on the earth. Both terms divisare and contemplare assume the act of separating as a precondition for perception.

The limit is, on the one hand, a condition of perception – i.e. a condition of capture – and, on the other, it is what is being perceived. In other words: we perceive because we delimit, and what we perceive is that which delimits, in other words, the limit of something as being “the limit of something” and not necessarily the something in itself. This perception is physical and/or intellectual: the term comprehendere and its compound hendere, “to catch,” associate the word comprehension with its double sense of intellectual understanding and physical embracing. This consideration certifies the need for the limit’s “belong/refer” structure: if the limit is the object’s solipsistic extreme, there is no allusion to any background from which a figure is cut out at the moment of perception, and if the limit is what lies in between objects, then the limit would be another object in itself. Instead, the belong/refer structure recognises the limit’s relation to its object while assuming the existence of otherness as an external reference.

In its differential sameness and autoreferential difference, the limit has been doubled into the two sides that form any surface. On its reverse side, the limit’s vocation is that of definire: it illuminates the object’s thisness through a process of confinement. On the obverse side, the limit’s vocation is that of percipere: it permits the object’s manifestation through a process of capture. Both sides fuel the disjunctive and conjunctive forces that operate within the limit: while the first tends to separate the limit’s object from its exterior in order to singularise it, the second tends to relate the object to its exterior in order to display it.

5.3 Ontological status: the real limit and the sensual limit

In order to incorporate Trías’s notion of limit into OOO, we need to elucidate the ontological status that the limit should occupy in Harman’s fourfold structure. Since the latter is the result of two intersecting axes, the notion of limit needs to be positioned in relation to two dualisms: objects versus qualities and real versus sensual.

The “belong/refer” formal structure characteristic of the limit implies that, in OOO, the limit pertains, in opposition to García’s limit, to the kingdom of qualities; to belong to something means to be its property, that is, to be its attribute, its quality, to not have an independent existence. Hegel already associated the notion of quality with limit, particularly when affirming that “Quality, in the distinct value of existent, is reality; when affected by a negating, it is negation in general, still a quality but one that counts as a lack and is further determined as limit, restriction.”55

However, as soon as we associate limits with qualities under OOO, three questions arise. First, is the limit one quality of an object, some qualities of an object, or all qualities of an object? Second, is the limit related to real qualities and/or to sensual qualities? Third, are the objects involved in the asymmetrical structure of the limit real objects and/or sensual objects?

As we have seen, the limit has been doubled into an obverse and a reverse, where the former is related to de-finire and the latter to per-cipere. In the first case, if the limit is what provides thisness to an object, the limit must consist in all those qualities that are necessary in order to specify what an object is, and not just one quality or some of them. Since in OOO these qualities are real qualities, we will define this limit as the real limit. The same applies for the second case: if the limit is what captures an object, the limit must consist in all those qualities that are necessary for its manifestation, and not just one quality or some of them. Since in OOO these qualities are sensual qualities, we will define this limit as the sensual limit.

Thus, the limit has been doubled into the real limit and the sensual limit. Each of these limits is not an individual quality of an object, but the unified totality of the real qualities on the one hand, and the unified totality of the sensual qualities on the other. What provides the liminal character (impermeability and belong/refer structure) to each group of qualities – i.e. what converts a complete set of qualities into a limit – is not only the exhaustive summation of these qualities but also their unification as caused by the object they belong to. Strictly speaking, the limit is thus not something that an object has or obtains. Rather, objects “limit” (a verb), in the same sense that objects “time” (a verb) and “space” (a verb) rather than being “in” time or “in” space. Objects are not framed by limits, but radiate limits.

5.3.1 Real limit

The real limit resonates with Morton’s rift by unfolding the disjunctive nature characteristic of Trías’s limit. It is the reverse side of the limit’s doubling. In the real limit, de-limitation implies de-finition, which in turn implies con-finement. By de-fining an object, the real limit con-fines it, that is, the real limit circumscribes it to Trías s hermetic enclosure, the inhospitable and mysterious region where immediate access is roundly denied. The real limit is thus responsible for the object’s specific ethos and singularity, but it is also responsible for the real object’s exodus and exile, for its exitus, for its ungraspable essence and for its recursively withdrawn nature. However, what lies beyond the limit must exist; it must be some-thing rather than no-thing. In opposition to Parmenides, Plato pointed out the need to differentiate between absolute nothingness and relative nothingness – relative to the word, to discourse, to thought. The latter is what lies beyond the limit.

However, the real limit does not just preclude our access to the real object; as a consequence of its defining nature, the real limit is, in itself, also imperceivable.

The real limit is thus absolutely intro-verted; i.e. it completely “verses” towards the interior of the object to which it belongs. It compresses its object, it tightens it and it singularises and encloses it by applying a centrifugal pressure. However, de-finition and con-finement cannot occur in a vacuum; they always occur in reference to something else; otherwise there would be no need for both actions to take place. Thus, the real limit de-fines and con-fines the object to which it belongs, but it does so by necessarily referring to an exterior, that is, to everything that is not the object that it limits. This reference occurs in a tangential but non-partial form. It is tangential because, due to its real nature, it cannot directly manifest its content but can only indirectly allude to it; and it is a non-partial reference because objects have no parts, and therefore the reference must be complete. Tangential and complete, in other words, a silhouette.56 Thus, the real limit results in precise but unmanifested contours in relation to the object to which it belongs, while it is conjugated as bemused but accessible silhouettes in relation to the object to which it refers.

In its de-fining vocation, the real limit relates to the notion of “essence” when it belongs to the real object and it relates to the notion of “eidos” when it belongs to the sensual object. “Essence” and “eidos” are two of the four tensions established in the four-fold logics of the quadruple object. In Harman’s ontological structure, both are the result of contrasting the real qualities, on the one hand, with the real object or the sensual object, respectively, on the other. Both “essence” and “eidos” are actually elements providing de-finition to the real object or the sensual object, which is what the real limit does. While “essence” is what is provided to “an object itself that does not have its own essential features,”57 “eidos” refers to “qualities crucial for the object to be acknowledged as what it is.”58 In both cases, the real limit provides “thisness” to the object (real or sensual) to which it belongs. However, rather than considering merely the set of real qualities, the consideration of them as a real limit – i.e. as the complete and unified set of real qualities that belongs to an object but that refers to another object(s) – permits, as we will see in Section 5.5, the opening of a limes of fusions and fissions which, in its belong/refer structure, joins and disjoins the real object and the sensual object.

5.3.2 Sensual limit

In contrast to the real limit, the sensual limit unfolds the conjunctive nature characteristic of Trías’s limit. It is the obverse side of the limit’s doubling. Rather than accounting for the object’s separation, the sensual limit accounts for the object’s conjunction, for its capturing, that is, for its per-cipere. The sensual limit does not com-press its belonger object, as the real limit does, but ex-presses it – in other words, it pulls it, it applies a centrifugal pressure on the object that it limits towards the objects to which it refers. Ex-pression instead of com-pression. Whereas in the real limit there is a lack of information towards its exterior, the sensual limit displays an excess of information, that is, it is over-formed. Where the real limit manifests less than what it limits, the sensual limit manifests more than what it limits.

The sensual limit is thus absolutely extro-verted, i.e. it completely “verses” towards the objects to which it refers. To put it differently, the sensual limit has no direct contact with the object to which it belongs, but it is completely thrown towards what it refers to, existing only as reference’s experience, that is, existing only under another’s delimitation, under capture and under per-cipere. The sensual limit operates thus as a crust; it is a salient, protuberant and bulky enclosure, an eruption and an efflorescence whose perpetual vibration is caused by the relations in which it necessarily participates in order to exist.

The sensual limit is responsible for the object’s appearance and promiscuity, for the object’s contact and caress and for the object’s friction. Although it displays precise figures for the objects to which it refers, the contact between the sensual limit and the object to which it belongs is (like the real limit with the object to which it refers) tangential and non-partial. The sensual limit becomes a bemused silhouette in relation to the object to which it belongs, while it is conjugated as a precise contour in relation to the objects to which it refers.

In its per-ceptive vocation, the sensual limit results in “space” when it belongs to the real object and it results in “time” when it belongs to the sensual object. “Space” and “time” are two of the four tensions established in the fourfold logics of the quadruple object. In Harman’s ontological structure, both of them are the result of contrasting the sensual qualities, on the one hand, with the real object or the sensual object, respectively, on the other. Both “space” and “time” are actually associated with per-ception, which is precisely what the sensual limit promotes: while “space” relates to the notion of allure, defined as “a special and intermittent experience,”59 “time” refers to “the excess of carnal detail that shifts in each moment without our viewing them as different objects. This is the very nature of perception.”60 In both cases, the sensual limit provides a mode of perception to the object (real or sensual) to which it belongs. However, rather than merely considering the set of real qualities, considering them as a sensual limit – that is, as the complete and unified set of real qualities that belongs to an object but that refers to another object(s) – permits; as we will see in Section 5.5, the opening of a limes of fusions and fissions which, in its belong/refer structure, joins and disjoins the real object and the sensual object.

The real limit and the sensual limit should be read as the obverse and reverse sides of the object’s single limit being unified by the object they qualify. Both limits, respectively, account for the limit’s belong/refer formal structure. On the limit’s reverse side, the real limit de-fines the object to which it belongs; while on its obverse side, the sensual limit is what is per-ceived by the object to which the limit refers. Although, in an ontological sense, the real limit and the sensual limit could be, respectively, read as the inner and outer face of the object they limit, there is no spatial, temporal or causal relation between the two limits: the real limit is neither what lies topologically behind or chronologically before the sensual limit nor its unavoidable cause. Thus, the sensual limit is not a mere deduction, derivation or crystallisation of the real limit – that is, the real limit is not what one finds after traversing the sensual limit. As we have seen, both limits are exhaustive and unified sets of real or sensual qualities that belong to a real or sensual object while referring to the other one. It is important to note that as soon as these two limits are internal to the quadruple object, the belong/refer structure can only compromise the real and sensual object of the same quadruple object: if the limit belongs to the real object, it refers to its sensual object; and if the limit belongs to the sensual object, it refers to the real object. As we have seen, in this belong/refer structure, in addition to joining and disjoining the real object and the sensual object, they establish the four tensions defined by Harman: Time, Space, Eidos and Essence. As we will see in Section 5.5, each real or sensual limit does not perfectly adhere to its real or sensual object; instead, there is a décalage, a misfit that opens up Trías’s limes as a territory of forces and pressures equivalent to Harman’s space of fusions and fissions. However, there is one crucial difference: Trías’s belong/refer structure is present in the real and sensual limit and in this décalage (limes), and therefore it implies the junction and disjunction between the real object and the sensual object, something that does not occur in Harman’s ontography. However, before detailing the role of Trías’s limes in Harman’s ontological structure, something else needs to be said in relation to the nature of the real limit and the sensual limit: both are absolutely impermeable, and there are precise reasons for that.

5.4 Impermeability: blurriness and transparency

The limit's obverse and reverse, respectively, account for the object’s de-finition and per-ception, since each side is the exhaustive and unified conjugation of real qualities (real limit) and sensual qualities (sensual limit). As we have seen, this doubling resonates with the limit’s “belong/refer” formal structure. However, it also accounts for another of its formal peculiarities: its absolute impermeability.

The real limit and the sensual limit are impenetrable. Under OOO, the limit is not an inflexion but an interruption. A limit is not Deleuze’s “ideal genetic element of the variable curve or fold,”61 Caché’s “intrinsic singularity”62 or Klee’s “point-fold.”63 There is no continuity between the terms that the limit couples and disjoins but at best contiguity or adjacency. What lies beyond the limit is not a variation, modulation or derivation of what it encloses. The limit is not an event or an accident but a hiatus that simultaneously secures and refers to strict otherness, an alterity whose radical difference precludes any knowledge of it. However, the impossibility of crossing the object’s limit is conjugated by the real limit and the sensual limit in different ways: while the former destroys its object by blurring it, the latter narcotises its object by making it transparent.

5.4.1 Blurriness

The real limit cannot be crossed because that automatically implies the destruction of the object it encloses; it implies that something is happening, il se passe quelque chose, something has been trespassed. To traverse the limit is the radical happening, the real se passer, in its double French sense of “happening” and “crossing.” In this sense, it resonates with Morton’s rift – in particular when its closure implies the reduction of an object to the sensual object, and therefore its annihilation. However, it differs from Morton’s rift in that destruction, here, does not occur because the real is reduced to the sensual. Instead, what occurs when the object’s real limit is traversed is that the object’s de-finition is pierced, i.e. its unified and exhaustive fabric of real qualities is torn. To penetrate the real limit means, thus, to blur the object’s thisness and to cloud what makes an object this object. It means con-fusing this with that. At the very moment when the limit is traversed, its object dissolves and it becomes whatever, i.e. nothing: its de-finition, its thisness, is immediately blurred into a sort of generic matter that does not exist. The object has been literally undermined; it vanishes.

5.4.2 Transparency

In opposition to the real limit, the sensual limit cannot be crossed because that automatically implies the narcotisation of the object it encloses: it becomes a dormant object completely removed from experience. What occurs when the object’s sensual limit is traversed is that the unified and exhaustive fabric of sensual qualities that enclosed is pierced, and therefore the object can no longer be “under capture” (per-cipere) by another object. What separated the object from its background – that is, the limit that permitted its per-ception, its capture – has been ruptured, opened, and therefore the object can no longer be discerned from its background. By traversing the sensual limit, the object is then con-fused with its background, that is, it becomes transparent, removed from experience.

To cross the real limit or the sensual limit, respectively, implies the immediate destruction or narcotisation of its object. The limit is therefore impenetrable, where by penetration we mean access to that what the limit guards, either because the object does not exist anymore – its thisness has dissolved into the blurriness of whatever – or because the object has become a dormant object – its enclosure has become transparent.

The limit is not crossable, but it is, under certain conditions, occupied. Its relation with the object to which it belongs is not always that of complete adherence; in a local and intermittent manner, a set of décalages generates a space of pressures between the real or sensual limit and the real or sensual object to which they belong. These décalages could be read as the imperfect wrapping of a physical object by a wrapping paper: the misfit zones generated between the limitant paper and the limited object produce a liminal space of pressures, which resonates with Trías’s limes and which accounts, first, for Harman’s fusions and fissions, and, second, for the junction/disjunction of the real object and the sensual object.

5.5 Décalage: the Limes and its pressures

In order to graft Trías’s notion of limit onto Harman’s fourfold structure, a liminal approach to Harman’s fusions and fissions is crucial. This operation demands the introduction of Trías’s limes, i.e. Trías’s frontier enclosure, one of the fundamental contributions of Trías’s theory of limits.

As we saw in Section 5.3, the real limit and the sensual limit, in their constitution as the exhaustive and unified set of real and sensual qualities, produce the different tensions that Harman refers to as space (RO-SQ), time (SO-SQ), essence (RO-RQ) and eidos (SO-RQ). However, this paper does not consider that these tensions are produced by real or sensual objects and real or sensual qualities but rather by real or sensual objects and real or sensual limits. The reason for this substitution lies in the fact that, as soon as the real and sensual objects are tensioned by limits and not by a mere group of qualities, this tension can be articulated through Trias’s belong/refer structure and is therefore capable of simultaneously joining and disjoining the real object and the sensual object through the performances of de-finire (real limit) and per-cipere (sensual limit). It is important to note that this replacement leaves the fourfold structure completely intact, as soon as the qualities acquire their liminal condition by the fact of being considered in their totality and unified by the object to which they belong as a single (real or sensual) mantle.

In Harman’s ontology these tensions are affected by actions of fusion and fission: while fusion affects space and essence by a process of allure and causation, respectively; fission affects time and eidos by a process of confrontation and theory, respectively. When Trías’s liminal theory is grafted onto Harman’s fourfold structure, the two fusions and the two fissions should be read, respectively, as closing and opening a décalage, a liminal zone between the real limit or the sensual limit and the real object or the sensual object. This liminal zone operates as Trias’s limes. For Trías, the limes is the frontier enclosure; and as an enclosure (i.e. as a cerco), it is not a Euclidean border line but a land of forces and pressures, a territory whose belong/refer structure simultaneously conjoins and disjoins the enclosure of appearances and the hermetic enclosure. However, in Trías it is the human being, in its limes’ inhabitation, who mediates this conjunction and disjunction, in the limes associated with the décalages established between the real object or the sensual object and the real limit or the sensual limit; what embodies this mediation is its performance as de-finire and per-cipere by conjugating the limit as contour or as silhouette. While de-finire operates through the tensions of essence (RO-RL) and eidos (SO-RL), per-cipere operates through the tensions of time (SO-SL) and space (RO-SL). In both cases, the relations between the real limit or the sensual limit and the real object and the sensual object are not that of pure adherence or pure distance; rather they are established as four different limes in which fusions and fissions occur by opening or closing this territory of pressures.article image

In each of the four cases – allure, confrontation, theory and causality – what occurs is the separation (fission) or union (fusion) between the real limit or the sensual limit and the real object or the sensual object. This process implies the engagement or disengagement of both limits with both objects, opening or closing a décalage that resonates with Trías’s limes and that represents the colonisation of Morton’s rift. Continuing with the spatial metaphor, under allure, confrontation, theory and causality, the limit is no longer an infinitesimal Euclidean line reducible to its obverse or reverse; rather it acquires thickness: the limit becomes a territory in its own right that occupies Harman’s ontography but that is vectorised by Trias’s belong/refer structure. Thus, under the two fissions and fusions, the limit becomes a limes, a narrow and oscillant strip that is inhabitable, susceptible to colonisation, cultivation and worship. It is a space of pressures, an area of junction and disjunction and an unstable land of conflict and resistance. However, in the two fissions and the two fusions, not all qualities are detached or attached to their object. For example, in most if not all cases of allure described by Harman, “the less essential traits of the object break free more easily into independent life, just as a planet’s outermost moons are those most easily liberated.”64 If the real limit and the sensual limit are the unified and exhaustive fabric made out of real and sensual qualities, the disengagement or engagement between the real limit and the sensual limit does not uniformly extrude or flatten the limit’s obverse or reverse side (real limit and sensual limit). Rather, it only operates with those particular qualities that are relevant: for example, in allure, those qualities that have become sensual objects in their own right.

In spite of its common territorial and autonomous condition, the limes developed here has three main differences from Trías’s frontier enclosure: it is not a constant condition; it is not uniform; and it is not exclusively inhabited by the human. Instead, the limes is an intermittent, scattered and variable widening of the object’s real limit or sensual limit according to the processes of fusion and fission.

Let’s look, for example, at the case of allure. In this case, the pressure responds to the objectification of certain qualities belonging to the unified and exhaustive set of qualities which constitute the fabric of the sensual limit. Under allure, the infinitesimal, flat and smooth limit becomes bulky and thick; its freshly opened inner space is inhabited by those qualities that have been converted into sensual objects in their own right. However, the limes still operates as a limit, with the peculiarity that it couples objects in a deeper and more robust manner. As in Trías, it does not provide access to what remains mysterious and withdrawn, it “makes no attempt to bring the hidden kingdom of objects into direct visibility.”65 Allure doesn’t entail penetrating the limit but rather separating an object from its qualities, that is, disengaging the adherence between the real limit and the sensual limit in order to open a space occupied by those specific qualities converted into sensual objects in their own right. These objectified qualities still belong to their own object and refer to another one, although in allure they invert this structure by pretending to belong to another object and referring to their original one.

Note that the reconstruction of Trías’s limit under the umbrella of OOO leaves the fourfold structure of objects completely intact. It conjures up a limit characterised by four formal principles.

First, the limit belongs to one object and refers to another; this belong/refer structure does not join and disjoin the real object and the sensual object through Trias’s ontological favouring of the human. Instead, it acts through the limit’s derivation as contour and silhouette and its performance as de-finire and per-cipere, which operate through Harman’s four tensions and their derived fissions and fusions.

Second, the limit is doubled into the real limit and the sensual limit; this twofold limit differs from Trias’s obverse and reverse side in two ways: first the limits are internal to each object and not a transcendental condition, and, second, they are not successive – that is, one does not chronologically or topologically follow the other.

Third, the limit is composed of the complete and unified set of real qualities in the real limit, and the complete and unified set of sensual qualities in the sensual limit. Rather than being a receptacle occupied by the human, the qualitative nature of OOO’s limit provides its performativity.

Fourth, the limit, under certain conditions, is spatialised. It expands or contracts as a limes according to the fusions and fissions operated in the four tensions produced by the relation between the real limit or the sensual limit and the real object or the sensual object.

None of these formalisations imply a change in Harman’s fourfold structure. The question is, now, whether this twofold theory of limits is an adequate response to the problems of unification presented by Morton’s rift. As we have previously mentioned, the coexistence between the real object and its sensual object under a single quadruple object presents a requirement that is threefold.

The first demand asks for disjunction. The real limit explicitly accounts for this by being modulated as a contour in relation to the object to which it belongs and as a silhouette in relation to the object to which it refers. The real limit com-presses its object by de-fining its specificity, by contouring its distinction, by providing its thisness. It disjoins the object “to which it belongs” from the object “to which it refers” by the lack of information implied in the process of converting the limit as a contour into the limit as a silhouette. The tensions essence and eidos are involved in this process, together with their respective fusions and fissions, which constitute the two limes associated with the real limit.

The second demand asks for conjunction. The sensual limit explicitly accounts for this by being modulated as a silhouette in relation to the object “to which it belongs” and as a contour in relation to the object “to which it refers.” The sensual limit ex-presses its object by capturing its manifestation from the other objects that are in our field of experience. It joins the object “to which it belongs” to the object “to which it refers” through the excess of information implied in the process of converting the limit as a silhouette into the limit as a contour. The tensions time and space are involved in this process, together with its respective fusions and fissions, which constitute the two limes associated with the sensual limit.

The third demand asks for immanence. The twofold limit described here is not the result of any external force, context or environment. It is not only topologically internal to the quadruple object in its limes spatial register but also constituted by its components: the exhaustive and unified set of its qualities. The limit is therefore radiated by the object, that is, the object “limits” (verb) rather than having a limit or being limited.

Under this view, the metaphysical abyss that separates real objects from sensual objects is not constituted by a single ontological rift placed in between the real object and the sensual object but by a twofold limit that belongs to one of the two objects and refers to the other one while constituting a liminal space (limes) of pressures. Thus, rather than a “cracked” object which is dialetheic and double truthed, what we have is a unified object that is internally constituted by a set of com-pressions and ex-pressions – a liminal composite of forces operating within the quadruple object through a twofold operativity. The limit conjoins the real object and the sensual object by being modulated as a silhouette, while simultaneously keeping its radical disjunction by being modulated as a contour.

Morton’s rift resonates with Hegel’s understanding of the limit. The metaphysical abyss that separates the real object and the sensual object is a locus of contradiction and a paradoxical space in which an object both is and is not. Conversely, the object’s twofold limit builds on Trías’s understanding of the limit as a land of affirmation: it is not a mere negative border or frontier but an ambit of allusions and a territory of pressures.

6 Conclusion

The construction of a liminal approach within the framework of OOO in light of Trías’s ontology provides an adequate alternative to Morton’s rift, increasing the consistency of the overall theory. The fact that Trías’s twofold limit can be grafted onto the quadruple object with reasonable ease underpins the relevance of the notion of limit in OOO. In spite of its absent systematisation in Harman’s fourfold structure, the limit is revealed as a powerful conceptual tool: it accounts for the paradoxical relation of conjunction and disjunction established between the real object and the sensual object within the quadruple object.

The unified distinction conjured up by the twofold limit may also lead us to reconsider the dialetheic conception of objects argued by Timothy Morton on the basis of Graham Priest’s logics of contradiction. Morton writes that once a rift is located between appearances and essences within the object itself, “we shall have to accept some kind of paraconsistent, possibly dialetheic logic, the kind of logic proposed by Graham Priest, a logic that allows things to be what they seem, and not what they seem, simultaneously.”66 This point is crucial in Morton’s approach, because once this inherent instability is accepted, it is possible to understand objects as autonomous, without having to rely on processes or particles to underpin their existence.

However, if objects are unified, and if this unification is not the result of any external force, the sensual object and the real object of a single quadruple object cannot be completely transparent to one another; a certain friction needs to occur. This resistance takes place in the space of pressures opened up by the object’s twofold limit. In this light, being an object no longer implies being riddled with contradiction, i.e. having at least one thing in them (this is Priest’s and Garfield’s delta) “that is 'both in them and not in them.’”

In light of the preceding analysis, objects would not be what Priest and Garfield define as “inclosures,” in the sense of being both closed and not closed, that is, limited and not limited:

The first part is an argument to the effect that a certain view, usually about the nature of the limit in question, transcends that limit (cannot be conceived, described, etc.). This is Transcendence. The other is an argument to the effect that the view is within the limit – Closure. Often, this argument is a practical one, based on the fact that Closure is demonstrated in the very act of theorizing about the limits. At any rate, together, the pair describe a structure that can conveniently be called an inclosure: a totality, Ω and an object, o, such that o both is and is not in Ω.67

As we have seen, objects are limited in a twofold sense: they limit in the real sense (real limit) because they have a specific thisness independent of the observer (contour) – an object is a rabbit but not an orange, and they limit in the sensual sense (sensual limit) because they have a specific manifestation that depends on the observer (silhouette) – an object is perceived-as rather than perceived.

In this context, the notion of limit becomes relevant not only because it permits us to articulate an adequate response to the problems of unification presented by Morton’s rift but also because it enriches a discussion of the logical status of objects. In this sense, a further development in this direction would permit us to construct an argument opposing the contradictory condition of objects defended by Priest’s dialetheism.

References

  • Bennett, Jane. “Systems and Things: A Response to Graham Harman and Timothy Morton.” New Literary History 43:2 (2012), 225–33.

  • Bogost, Ian. Alien Phenomenology, or What It’s Like to Be a Thing. London: University of Minnesota Press, 2008.

  • Bogost, Ian. Play Anything: The Pleasure of Limits, the Uses of Boredom, and the Secret of Games. Philadelphia: Basic Books, 2016.

  • Bono, José Luís Caballero. Ocho filósofos españoles contemporáneos. Barcelona: Diálogos Filosóficos, 2004.

  • Caché, Bernard. Earth Moves: The Furnishing of Territories. London: MIT Press, 1995.

  • Carrara, Massimilano. “Naïve Proof and Curry’s Paradox.” In From Arithmetic to Metaphysics, edited by Ciro de Florio, Alessandro Giordani. Berlin: De Gruyter, 2018.

  • Casati, Roberto and Varzi, Achille C. Parts and Places. Cambridge: MIT Press, 1999.

  • Deleuze, Gilles. The Fold: Leibniz and the Baroque. London: The Athlone Press, 1995.

  • Derrida, Jacques. Margins of Philosophy. Chicago: University of Chicago Press, 1982.

  • Dolphijn, Rick and van der Tuin, Iris. New Materialism: Interviews and Cartographies. Michigan: Open Humanities Press, 2012.

  • Garfield, Jay and Priest, Graham. “Nagarjuna and the Limits of Thought.” Philosophy East and West 53:1 (2003), 1–21.

  • García, Tristan. Form and Object. Edinburgh: Edimburgh University Press, 2014.

  • Harman, Graham. Guerrilla Metaphysics: Phenomenology and the Carpentry of Things. Illinois: Open Court Press, 2005.

  • Harman, Graham. The Quadruple Object. Winchester: Zero Books, 2011.

  • Harman, Graham. Object-Oriented Ontology: A New Theory of Everything. London: Pelican, 2018.

  • Hegel, Georg Wilhelm Friedrich. The Science of Logic. Cambridge: Heidelberg Writings, 1996.

  • Heidegger, Martin. Introduction to Metaphysics. London: Yale University Press, 2000.

  • Hölderlin, Friedrich. Hyperion. Berlin: Tredition Classics, 2012.

  • Jaspers, Karl. Philosophy (Volume II). Chicago and London: The University of Chicago Press, 1970.

  • Kant, Immanuel. Critique of Pure Reason. Cambridge: Cambridge University Press, 1998.

  • Morton, Timothy. Realist Magic: Objects, Ontology, Causality. Michigan: Open Humanities Press, 2013.

  • Trías, Eugenio. Los límites del Mundo. Barcelona: Ariel Filosofía, 1985.

  • Trías, Eugenio. La razón fronteriza. Barcelona: Destino, 1999.

  • Trías, Eugenio. Ciudad sobre ciudad. Barcelona: Destino, 2001.

  • Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. London: Edinburgh Press, 1922.

Footnotes

1

Philosophy is not the only field that has been impacted by the emergence of Object-Oriented Ontology; other such disciplines include architecture and the arts.

2

Barad’s differentiation between “inter-action” and “intra-action” is a good example.

3

Dolphijn and van der Tuin, New Materialism: Interviews and Cartographies, 126.

4

“In an affirmative approach, a dualism does not only involve a binary opposition, a relation structured by negativity according to which different-from is necessarily worth-less-than. The starting point is that related terms belong to one another. Only when this sense of belonging is affirmed are we able to work towards an absolute concept, once liberated from the condition which made difference an entirely relative maximum.” “A relationality in the negative, dualistic sense presupposes the terms of the relation in question, whereas the creation of concepts entails a traversing of dualisms, and the establishment of a relationality that is affirmative – i.e., structured by positivity rather than negativity.”

Dolphijn and van der Tuin, New Materialism: Interviews and Cartographies, 126.

5

Harman, The Quadruple Object, 116.

6

Ibid., 187.

7

Casati and Varzi, Parts and Places, 71.

8

Harman, The Quadruple Object, 112.

9

Ibid., 210.

10

Ibid., 29.

11

Ibid., 49.

12

Bennet, New Literary History, 225.

13

Morton, Realist Magic, 201.

14

Ibid., 36.

15

Ibid., 192.

16

Harman, The Quadruple Object, 7.

17

Ibid., 7.

18

Bogost, Alien Phenomenology, 25.

19

Morton, Realist Magic, 98.

20

Ibid., 31.

21

Carrara, “Naïve Proof and Curry’s Paradox”, 61–8.

22

Bogost, Play Anything, 176.

23

García, Form and Object, 138.

24

Morton, Realist Magic, 76.

25

Harman, The Quadruple Object, 116.

26

Trías, Los límites del Mundo, 118. In this article, all translations from Trías are my own.

27

Ibid., 121.

28

Kant, Critique of Pure Reason, 215.

29

Schelling finds that the self limits the thing, and the thing limits the self, but their common limit cannot lie any more in one than in the other.

30

Hegel, The Science of Logic, 167.

31

Heidegger, Introduction to Metaphysics, 99.

32

Jaspers, Philosophy, 179.

33

Wittgenstein, Tractatus Logico-Philosophicus, 74.

34

Trías, Los límites del Mundo, 121.

35

Hölderlin, Hyperion, 95.

36

Trías, Ciudad sobre ciudad, 123.

37

Derrida, Margins of Philosophy, 17.

38

Hegel, The Science of Logic, 99.

39

Trías, Ciudad sobre ciudad, 89.

40

Ibid., 89.

41

Trías, Los límites del Mundo, 212.

42

Ibid.

43

Trías, La razón fronteriza, 33.

44

Ibid., 47.

45

Trías, Los límites del Mundo, 218.

46

Bono, Ocho filósofos españoles contemporáneos, 323.

47

Trías, Los límites del Mundo, 287.

48

Ibid., 289.

49

Ibid., 298.

50

Ibid., 299.

51

Ibid., 289.

52

Ibid., 300.

53

Harman, Object-Oriented Ontology, 9.

54

Ibid., 382.

55

Hegel, The Science of Logic, 48.

56

In Guerrilla Metaphysics, Graham Harman uses the term silhouette in this sense, when he mentions that “none of these objects [the spiraling interplay of objects wrapped in objects wrapped in objects] is ever accessible to us. I never see Arkhytas, but only silhouettes and adumbrations of his unified reality.” Harman, Guerrilla Metaphysics, 158.

57

Harman, The Quadruple Object, 105.

58

Ibid., 104.

59

Ibid., 105.

60

Harman, The Quadruple Object, 102–3.

61

Deleuze, The Fold, 14.

62

Caché, Earth Moves, 16.

63

Deleuze states that for Paul Klee the point as a “nonconceptual concept of noncontradiction” moves along an inflection. “It is the point of inflection itself, where the tangent crosses the curve. That is the point-fold;” Deleuze, The Fold, 15.

64

Ibid., 164.

65

Ibid., 143.

66

Morton, Realist Magic, 99–100.

67

Garfield and Priest, “Nagarjuna and the Limits of Thought,” 1–21.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Bennett, Jane. “Systems and Things: A Response to Graham Harman and Timothy Morton.” New Literary History 43:2 (2012), 225–33.

  • Bogost, Ian. Alien Phenomenology, or What It’s Like to Be a Thing. London: University of Minnesota Press, 2008.

  • Bogost, Ian. Play Anything: The Pleasure of Limits, the Uses of Boredom, and the Secret of Games. Philadelphia: Basic Books, 2016.

  • Bono, José Luís Caballero. Ocho filósofos españoles contemporáneos. Barcelona: Diálogos Filosóficos, 2004.

  • Caché, Bernard. Earth Moves: The Furnishing of Territories. London: MIT Press, 1995.

  • Carrara, Massimilano. “Naïve Proof and Curry’s Paradox.” In From Arithmetic to Metaphysics, edited by Ciro de Florio, Alessandro Giordani. Berlin: De Gruyter, 2018.

  • Casati, Roberto and Varzi, Achille C. Parts and Places. Cambridge: MIT Press, 1999.

  • Deleuze, Gilles. The Fold: Leibniz and the Baroque. London: The Athlone Press, 1995.

  • Derrida, Jacques. Margins of Philosophy. Chicago: University of Chicago Press, 1982.

  • Dolphijn, Rick and van der Tuin, Iris. New Materialism: Interviews and Cartographies. Michigan: Open Humanities Press, 2012.

  • Garfield, Jay and Priest, Graham. “Nagarjuna and the Limits of Thought.” Philosophy East and West 53:1 (2003), 1–21.

  • García, Tristan. Form and Object. Edinburgh: Edimburgh University Press, 2014.

  • Harman, Graham. Guerrilla Metaphysics: Phenomenology and the Carpentry of Things. Illinois: Open Court Press, 2005.

  • Harman, Graham. The Quadruple Object. Winchester: Zero Books, 2011.

  • Harman, Graham. Object-Oriented Ontology: A New Theory of Everything. London: Pelican, 2018.

  • Hegel, Georg Wilhelm Friedrich. The Science of Logic. Cambridge: Heidelberg Writings, 1996.

  • Heidegger, Martin. Introduction to Metaphysics. London: Yale University Press, 2000.

  • Hölderlin, Friedrich. Hyperion. Berlin: Tredition Classics, 2012.

  • Jaspers, Karl. Philosophy (Volume II). Chicago and London: The University of Chicago Press, 1970.

  • Kant, Immanuel. Critique of Pure Reason. Cambridge: Cambridge University Press, 1998.

  • Morton, Timothy. Realist Magic: Objects, Ontology, Causality. Michigan: Open Humanities Press, 2013.

  • Trías, Eugenio. Los límites del Mundo. Barcelona: Ariel Filosofía, 1985.

  • Trías, Eugenio. La razón fronteriza. Barcelona: Destino, 1999.

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  • Wittgenstein, Ludwig. Tractatus Logico-Philosophicus. London: Edinburgh Press, 1922.

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Open Philosophy is an international Open Access, peer-reviewed academic journal covering all areas of philosophy. The objective of Open Philosophy is to foster free exchange of ideas and provide an appropriate platform for presenting, discussing and disseminating new concepts, current trends, theoretical developments and research findings related to the broadest philosophical spectrum.

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