We prove that if $A$, $B$ are noncomputable c.e. sets, $A<_{sQ_{1}}B$ and [($B$ is not simple and $A\oplus B\leq _{sQ_{1}}B$) or $B\equiv _{sQ_{1}}B\times \omega $], then there exist infinitely many pairwise $sQ_{1}$-incomparable c.e. sets $\{C_{i}\}_{i\in \omega }$ such that $A<_{sQ_{1}}C_{i}<_{sQ_{1}}B$, for all $i\in \omega $. We also show that there exist infinite collections of $sQ_{1}$-degrees $\{\boldsymbol {a_{i}}\}_{i\in \omega }$ and $\{\boldsymbol {b_{i}}\}_{i\in \omega }$ such that for every $i, j,$ (1) $\boldsymbol {a_{i}}<_{sQ_{1}}\boldsymbol {a_{i+1}}$, $\boldsymbol {b_{j+1}}<_{sQ_{1}}\boldsymbol {b_{j}}$ and $\boldsymbol {a_{i}}<_{sQ_{1}}\boldsymbol {b_{j}}$; (...) (2) every c.e set in $\boldsymbol {a_{i}}$ is a maximal set; and (3) every c.e. set in $\boldsymbol {b_{j}}$ is a non-maximal hyperhypersimple set. We prove that a noncomputable c.e. $sQ$-degree contains either only one or infinitely many c.e. $sQ_{1}$-degrees. The $sQ_{1}$-degrees of c.e. cylinders are dense upper semilattice. (shrink)

How a human observer perceives duration depends on the amount of events taking place during the timed interval, but also on psychological dimensions, such as emotional-wellbeing, mindfulness, impulsivity, and rumination. Here we aimed at exploring these influences on duration estimation and passage of time judgments. One hundred and seventeen healthy individuals filled out mindfulness (FFMQ), impulsivity (BIS-11), rumination (RRS), and depression (BDI-sf) questionnaires. Participants also conducted verbal estimation and production tasks in the multiple seconds range. During these timing tasks, subjects (...) were asked to read digits aloud that were presented on a computer screen. Each condition of the timing tasks differed in terms of the interval between the presentation of the digits, i.e., either short (4-s) or long (16-s). Our findings suggest that long empty intervals (16-s) are associated with a relative underestimation of duration, and to a feeling that the time passes slowly, a seemingly paradoxical result. Also, regarding more mindful individuals, such a dissociation between duration estimation and passage of time judgments was found, but only when empty intervals were short (4-s). Relatively speaking, more mindful subjects showed an increased overestimation of durations, but felt that time passed more quickly. These results provide further evidence for the dissociation between duration estimation and the feeling of the passage of time. We discuss these results in terms of an alerting effect when empty intervals are short and events are more numerous, which could mediate the effect of dispositional mindfulness. (shrink)

In a time interval of four years, from 1982 to 1986, Louis Althusser wrote a number of short papers, which were all published posthumous. Short papers are typical for Althusser’s work, much more than every other art of writings, but the main characteristic of his last papers lies neither in their form nor in the method – it lies rather in a radically new approach to the politics. During the sixties, Althusser holds a point of view according to which the (...) dialectical materialism represents the philosophical core of the Marxism and the historical materialism corresponds to its science. In the eighties, he changes this theoretical approach in favour of a “philosophy of the encounter”, which in his opinion reflects the non-teleological principle of materialism in far more exact way, than the dialectical materialism which becomes logocentric and idealistic. Dialectical materialism will be completely rejected, and a new term will step into its place: the aleatoric materialism, a materialism of contingency and emptiness that radically rejects any precedence of the sense over the phenomena. The following text pursues this radical late turn in Althusserian understanding of philosophy, primarily in its relation to politics and ideology. (shrink)

This paper describes a cubic water tank equipped with a movable partition receiving various amounts of liquid used to represent joint probability distributions. This device is applied to the investigation of deductive inferences under uncertainty. The analogy is exploited to determine by qualitative reasoning the limits in probability of the conclusion of twenty basic deductive arguments (such as Modus Ponens, And-introduction, Contraposition, etc.) often used as benchmark problems by the various theoretical approaches to reasoning under uncertainty. The probability bounds imposed (...) by the premises on the conclusion are derived on the basis of a few trivial principles such as "a part of the tank cannot contain more liquid than its capacity allows", or "if a part is empty, the other part contains all the liquid". This stems from the equivalence between the physical constraints imposed by the capacity of the tank and its subdivisions on the volumes of liquid, and the axioms and rules of probability. The device materializes de Finetti's coherence approach to probability. It also suggests a physical counterpart of Dutch book arguments to assess individuals' rationality in probability judgments in the sense that individuals whose degrees of belief in a conclusion are out of the bounds of coherence intervals would commit themselves to executing physically impossible tasks. (shrink)

ABSTRACT: It is characteristic of a continuum that it be “all of one piece”, in the sense of being inseparable into two (or more) disjoint nonempty parts. By taking “part” to mean open (or closed) subset of the space, one obtains the usual topological concept of connectedness . Thus a space S is defined to be connected if it cannot be partitioned into two disjoint nonempty open (or closed) subsets – or equivalently, given any partition of S into two open (...) (or closed) subsets, one of the members of the partition must be empty. This holds, for example, for the space R of real numbers and for all of its open or closed intervals. Now a truly radical condition results from taking the idea of being “all of one piece” literally, that is, if it is taken to mean inseparability into any disjoint nonempty parts, or subsets, whatsoever . A space S satisfying this condition is called cohesive or indecomposable. While the law of excluded middle of classical logic reduces indecomposable spaces to the trivial empty space and one-point spaces, the use of intuitionistic logic makes it possible not only for nontrivial cohesive spaces to exist, but for every connected space to be cohesive.In this paper I describe the philosophical background to cohesiveness as well as some of the ways in which the idea is modelled in contemporary mathematics. (shrink)

This work treats the correlative concepts knowledge and opinion, in various senses. In all senses of ‘knowledge’ and ‘opinion’, a belief known to be true is knowledge; a belief not known to be true is opinion. In this sense of ‘belief’, a belief is a proposition thought to be true—perhaps, but not necessarily, known to be true. All knowledge is truth. Some but not all opinion is truth. Every proposition known to be true is believed to be true. Some but (...) not every proposition believed to be true is known to be true. Our focus is thus on propositional belief (“belief-that”): the combination of propositional knowledge (“knowledge-that”) and propositional opinion (“opinion-that”). Each of a person’s beliefs, whether knowledge or opinion, is the end result of a particular thought process that continued during a particular time interval and ended at a particular time with a conclusive act—a judgment that something is the case. This work is mainly about beliefs in substantive informative propositions—not empty tautologies. We also treat objectual knowledge (knowledge of objects in the broadest sense, or “knowledge-of”), operational knowledge (abilities and skills, “knowledge-how-to”, or “know-how”), and expert knowledge (expertise). Most points made in this work have been made by previous writers, but to the best of our knowledge, they have never before been collected into a coherent work accessible to a wide audience. -/- Key words: belief, knowledge/opinion, propositional, operational, objectual, cognition, . (shrink)

The four essays collected in this dossier are directed upon the contemporary understandings of blackness, as an ontology, a phenomenology, or a historicity. In the order of their presentation they encompass and situate what seems first to limit black being or overflow it, but which, when questioned, that is, disclosed, or unconcealed, does not fit into this logos, nor is ordered by it, even making what is most discernable about blackness in its past, future, or present, seem imaginary, moored in (...) a non-present,and presence, but in ways which make the non-being that marks blackness as sign, affect, or speaking being, unthinkable except as an appearing, a manifestation, an identity.As a dossier directed upon the present philosophical understanding of blackness, each paper seeks to unanchor blackness from the meanings and presuppositions that it normally calls forth. Beyond what is discernable, or ready-made, each paper addresses structures that make (and have made) blackness discernable as the always given to be seen, as meaningless speech, as pathology, as a concept beyond reason.The dossier opens with a question: what kind of disturbance does blackness present to being? Why does it seem to madden reason, or call forth frenzy? In Calvin Warren’s essay, “The Karen Call,” what comes into correlation with blackness are various kinds of emergency that structure white thought and presence but that belie witnessing and intelligibility, and in whose chain of significations can be discerned an ontological privilege that constitutes the world. To appear emergent, it seems, all blackness has to do is become one with the myth that bans or compromises it; a manifestation in which subject-object relations are already polarized by the dangers that deploy it in dramas of emergency. Once blackness becomes emergent, there is no escape, for it comes up against what Warren, reading Heidegger against the grain, suggests is a racial destiny of Being. To appear black is forthwith to resemble an es gibt that is indissociable from threat, falsehood, fantasy, and obliteration. To that extent, blackness attests to a kind of ontological emergency without surcease or hope, and one whose trace remains in every moment or glimpse; whose technical modality and structure always returns us to the call that is neither speech nor gaze, word nor symbol, but represents an extimacy that is undeconstructable, beyond utterance, meaning, or reparation.Such extimacy seems to induce a crisis in the philosophical notion of being itself. In Axelle Karera’s essay, “Paraontology,” the question asked is why blackness cannot be contained or fitted into ontology itself; or, if philosophy is ontology, why does blackness seem to signify an irreducible resistance to it?How does such resistance occur? If blackness can only be presented as “paraontology,” a word that seems to shelter ontology at the same time as it presents the search for a new order of being, what does the para teach us about blackness as disorder, resistance, or identity? What is its philosophical genealogy and affiliation, and why does the para itself seem to never get beyond its own conciliation, or filiation to philosophy, whose ordering and racist historicity thereby remains the seme and mark of the para as interval, trope, and index? Or, put more simply, can blackness ever resist its own resistance as trope, conjuncture, or representation? Retracing that genealogy through the work of Oskar Becker, Karera uncovers a surreptitious repetition in black uses of the word, in whose weave can be discerned a fascist interference that not only undermines the fugitivity of the resistance so claimed, but one that unwittingly repeats a fascist ontology of world, history, and being.1 It’s a startling, deeply disturbing claim. But the apparent echoing of the Heideggerian bell in black significations of ontology suggests that what is being reabsorbed here is not so much a radical difference but a concept that remains justified and in fee to, pardoned and annulled by, a white notion of being. What, then, can it mean to think blackness as para? Nothing more than a philosophical confusion that confuses l’être qui fuit, that is, the lack that Lacan says cannot be completed or resisted, for an appositional fantasy of displacement. Here everything that is deemed black has to be made meaningful in apposition to ontology, but everything that is black must also, it seems, always return apposition to the white para of ontology; to be black and appositional would, it seems, produce only the disavowal of the philosophical genealogy that always already determines it.One would be right to distrust such claims—the moralism of the refusal, and the scandal of the faux resistance by which the para hides behind its own whited-out screen.In the third contribution to the dossier, the question asked is what would it mean for blackness to repair itself, to let go or retrieve and so redeem its own historical conjuncture? How do we refer to an irreparable past, that is, a past that keeps on coming back, but one that has no sign or signified, no memory that can recapture or reveal it, or simply rejoin us to it without remainder? Rinaldo Walcott’s essay, “‘Retrospective Significance,’” revisits the reparations debate as a question of black being. Instead of repair, he finds desolation and emptiness, or what he calls a staggeringly incoherent rhetoric of coherency. It’s a paradox that addresses what it means to remember or to forget a nothing; if blackness is nothing, how does one reconnect with it, bond with it, compensate it in its historic devastation? What would it mean to receive meaning from such devastation, to express it if this nothingness is absolute, or absolutely valueless? If ontology is a structure, then blackness, Walcott suggests, expresses nothing less than a “slave-ness” that continues to confront and disturb us absolutely, irrevocably. As such slave-ness is the trace that remains as a sign of the irreparable. As a trace, and not a sign, slave-ness becomes the primordial signifier of being, nation, history, and diaspora. But it is what makes it irrecuperable that defines its value and difficulty for the very language of reparation. Walcott pursues this difficult, enigmatic thread through the work of black thinkers on diaspora and identity. He concludes: black being cannot be dissociated from the disturbance it offers value, conscience, and any thought of alterity.The final and fourth contribution returns to the question of blackness as the trace or thread (the monstration) of being. How does one follow the thread (montrer) of blackness if it is always already withdrawn from being? David Marriott’s essay, “Ontology and Lalangue,” evokes Lacan’s concept of lalangue in pursuit of this enigmatic equivocation between letter and signifier, philosophy and psychoanalysis. Showing how both discourses have sought to master this exorbitance as master and/or free it as slave, I show how blackness is extinguished by the very words used to precipitate it into being. The slavish audacity of this lalangue is then shown to disarticulate, or more exactly, withdraw from ontology, but only so that whiteness can be presented and proclaimed all the more as the un-representable truth and logic of Dasein. This way of excluding blackness while preserving whiteness is not only central to philosophical and psychoanalytic understandings of language, Marriott argues, but this way of manifesting itself without manifesting itself is also crucial to the racialization of the logos as such.What is essential here is the way a meaning that is beyond meaning or representation is inserted into a problematic of mastery and servitude that advances-conceals a racial genealogy but in ways that makes the being of blackness an enigma. As such, blackness becomes an exorbitance that is always effaced in its monstration. More, its revelation must necessarily be unrecognized as the very locus of knowledge and truth. In that sense, what would it mean to figure, or to speak, this n’est pas without the consolation of being, meaning, truth, or logic? What would it mean to represent it as situated or defined by the language of ontology? Is black speaking being always in a relationship to and simultaneously the manifestation of a lalangue of lalangue? (shrink)

How are the various classically equivalent definitions of compactness for metric spaces constructively interrelated? This question is addressed with Bishop-style constructive mathematics as the basic system – that is, the underlying logic is the intuitionistic one enriched with the principle of dependent choices. Besides surveying today's knowledge, the consequences and equivalents of several sequential notions of compactness are investigated. For instance, we establish the perhaps unexpected constructive implication that every sequentially compact separable metric space is totally bounded. As a by-product, (...) the fan theorem for detachable bars of the complete binary fan proves to be necessary for the unit interval possessing the Heine-Borel property for coverings by countably many possibly empty open balls. (shrink)

In modern physics, the constant "c" plays a twofold role. On the one hand, "c" is the well known velocity of light in an empty Minkowskian space—time, on the other hand "c" is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space—time intervals. We ask for the interrelations between these two, at first sight different meanings of "c". The conjecture that the value of "c" has any influence on (...) the structure of space—time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space—time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space—time can be reconstructed already on the basis of a restricted classical ontology (Mittelstaedt, Philosophie der Physik und der Raum-Zeit, Mannheim: BI-Wissenschaftsverlag, 1988 and Mittelstaedt, Kaltblütig: Philosophie von einem rationalen Standpunkt, Stuttgart: S. Hirzel Verlag, pp. 221-240, 2003), and that without any reference to the propagation of light. However, the space—time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with "c" but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of "c" and for a dualism of space—time and matter. (shrink)

In modern physics, the constant “c” plays a twofold role. On the one hand, “c” is the well known velocity of light in an empty Minkowskian space–time, on the other hand “c” is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space–time intervals. We ask for the interrelations between these two, at first sight different meanings of “c”. The conjecture that the value of “c” has any influence on (...) the structure of space–time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space–time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space–time can be reconstructed already on the basis of a restricted classical ontology, and that without any reference to the propagation of light. However, the space–time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with “c” but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of “c” and for a dualism of space–time and matter. (shrink)

continent. 1.3 (2011): 208-212. … intervals of destructuring paradoxically carry the momentum for the ongoing process by which thought and perception are brought into relation toward transformative action. —Brian Massumi, Parables for the Virtual: Movement, Affect, Sensation 1 Facing a blank canvas or blank page is a moment of pure potential, one that can be enervating or paralyzing. It causes a pause, a hesitation, in anticipation of the moment of inception—even of one that never comes. The implication is that (...) the blank is yours in that moment, and it calls on you to act on it, to think into it, to create on it. Each blank canvas gives you time, of an undefined length, to transform that canvas’ inherent potential into a work. This two-dimensional plane of potential can be projected into a space, which the body can then occupy. When you “destructure” a space in the same way, prepare it to be a blank, much as you build a canvas, you allow your entire body to enter the space of potential, and you rest in anticipation of work, like the hand poised above the page. Artists have found that the deliberate creation of that space of potential through sealing the space and painting it white, thereby erasing details and distractions, can be such a transformative experience as to help define their whole practice. The cessation of distraction, the absence of indicator that a “blanked” workspace provides allows for a new presence of mind, it gives them the room, literally, to move into their work, and from there to move their work into the world. The workspace for the artist, the studio, is often perceived as a lab-like condensation of the gallery or museum, the traditional and idealized white cube. Similarly, with the blank page, a concrete relation between space and time comes forward as the intentional simplification of the architecture changes behavior and perception within the space. The work of “blanking” the studio space is a meditative reduction, an erasure, and in a way, an attempt at drawing away from the world beyond the studio - the sealed space is meant to recede from reality, to become abstracted by its willed lack of details and distractions. Within that space the time for a new beginning is made more present, more attainable, and the focus it fosters becomes another tool to aid creation. At the formative moment of his artistic practice, Tom Friedman used the blank of his studio, saturated in white, sealed off from the world, to fight velocity. He describes how he projected his vision of the end goal, the museum - a place he believes to be defined by slow contemplation - onto his own studio experience. He then sat and reflected on common objects, one by one, framed by the blank box he had created. The domestic objects he brought into the space to study foreshadow his mature works, where often the quotidian object has a single additional element – his intense labor. Friedman makes discrete objects through absurdly intense and focused labor, epitomized, perhaps by his 1,000 hours of Staring , made from 1992-97: Tom Friedman. 1000 Hours of Staring (1992-1997) His labor, to use his own words, is his way to “bring all of who you are to the experience.” Friedman shares his labor, allows the slow, deliberate pace of his work born in the studio to penetrate the museum. Nothing seems effortless, or a gesture, the labor is apparent, displayed, and tangible. He gives us the labor, the personal investment in the physical that saved art for him, that divorced the work from the language he cites as a factor of alienation. When we see his work we do not see words, we see acts, we see objects. He has forced the studio as workspace into the exhibition space, as he stuffs hundreds of more hours of labor into his shows with each new piece, filling the space with material and labor, material and labor – his involvement, his investment, is his gift to us as the viewers, as he introduces the laborious and contemplative pace he feels belongs to the museum. He saves us also from the alienation of language, which first drove him into the sealed studio and away from the discourse of his school. He presents us with his real, the object which stands in stark contrast to the white slate of the studio, the sealed white box he started from, where his individual, self-contained objects begin and end, completed through the intensity of isolation, first of the individual artist, and then of the material he chooses to slowly, slowly, slowly work: Tom Friedman. Untitled (1992) In his in-depth analysis of galleries as a blank white cube, Brian O’Doherty emphasizes the religious connotations implied in the strict laws of the exhibition space and the valuation, aesthetics and elements of control he feels it imposes upon the work. Like Friedman, he recognizes the power of the restricted space – indicating the “perceptual fields of force” – that act on any object introduced into it. Going beyond Friedman’s assessment of the space as highly utilitarian for focusing his perception, O’Doherty emphasizes the rejection of the physical body of the artist or observer, saying that the cube allows for only observation - eyes and mind. He later parallels the picture frame as a psychological container for the artist with the room as the same for the observer. In both cases, this is an emphasis on the alienating nature of the relationship – just as the artist is kept out of the frame by the picture, in the gallery the art forces the body of the spectator out, calling for a self-referential purity. Patrick Ireland. White Cube (1998) O’Doherty makes a point of saying that the installation shot of the gallery without figures is “one of the icons of our visual culture.” In recent years, however, installation shots have begun to include figures, in some cases they are essential to understanding the scale and even the nature of the work, specifically with work that captures the experience of the space and the way that it varies from a white cube. The work of Olafur Eliasson is a case in point, as the Danish artist uses elements of scientific and natural phenomena to alter perception within the controlled gallery environment, tweaking and redirecting O’Doherty’s “perceptual fields of force” to make points about the act of seeing, or seeing yourself seeing, to quote the artist. This indicates a shift in the role of the artwork, not to exclude the body and stand discretely and self-sufficiently, but to include it, to manipulate it and to make the observer aware of the nature of that manipulation and the work’s ability to manipulate. Olafur Eliasson. 360º room for all colours (2002) So though in O’Doherty’s analysis, the intense blankness of the gallery pushed the observer out in favor of the artwork’s isolation, artists can replicate this inhumane sterility in their own workspace to focus their work on the influence of the gallery right from inception. This can be interpreted as an almost opposite understanding of the purpose of sealing and whitewashing the workspace as stated by Friedman. He sought a refuge from the critical language of the art school, and a space that, like the museum, gave him a protracted sense of time, and, he felt, welcomed him in, “to bring all of who you are,” as opposed to O’Doherty’s feeling that the museum was asking you, at least in body, to leave, and allow the work to take on its own life. Friedman does not seem to imply the tension with the cube and critical stance that O’Doherty prioritizes. Where Friedman finds a refuge, O’Doherty defines an opponent. In a third position, Robert Irwin describes his sealed studio space as “the world.” Though he made the same effort as Friedman to seal out all influences and distractions, he implies that he is in dialogue with the world through his own concentration and perception. This is reminiscent of the nature of the monad, as interpreted by Deleuze, a unity that envelops a multiplicity, a sealed container that contains the universe. He went through the same ritual described by Friedman, sealing up the space, painting it white, and then forcing himself to remain inside, staring at his own work, training his concentration relentlessly. But he found that the room became the distraction: …he became aware that a thin crack along the wall a few yards away from the canvas likewise exerted its presence; that when he plastered that crack over and repainted the wall, the canvas itself presented an entirely new aspect.2 The context was in a relentless dialogue with the work, and trying to neutralize that dialogue, to mute the conversation between space and object, became part of his ritual as he “fixed” his space each day in the hope of total concentration on the work. Ultimately, Irwin shaped the trajectory of his art by relinquishing the studio, establishing a post-studio practice, where the work is conceived and created out in the world, in dialogue with the world and reflective of the conditions it finds surrounding it. The white cube failed to ever achieve neutrality, his heightened concentration prevented him from ever neutralizing the space, so, instead of continuing to try to maintain the charade of a perfect blank, he acknowledged the unstoppable voice of place and turned all his efforts onto the object and the world, as a constant dialogue. Some artists push their studio space far from purity, domesticating it like a lair or a living room, and others destroy it, fill it with chaos or detritus, blacken or clutter it so as never to be starting from a blank, and thereby try to avoid the anxiety of facing that void. Similarly artists may never prepare a white canvas, a clean page, a marble block, or other form that is intentionally lacking, in order to try to escape the dialogue with emptiness. But Irwin, like O’Doherty, found an opponent in the white cube, and he learned not to fight it, rather he ended the conflict by making it an ally, an interlocutor, a collaborator. We can vainly strive to start from nothing, to find the lull, the clearing, and to always consider what we do in balance with the empty set. Somehow that intangible cloud of hazy nothingness, that softness of a lapse continually offers a place to bounce off of, to react to, to wrestle with, to rest with, in tension, or a place to begin. Robert Irwin. Excursus: Homage to the Square3 (1998) NOTES 1 Massumi. Parables for the Virtual: Movement, Affect, Sensation. p271. 2 MOMA, NY. Eliasson, 360 ? Room for All Colours . Installation. 2002. (shrink)

For Vajrayana Buddhism, the now is an interval, a boundary, a point of tension and suspension with an atmosphere of uncertainty. It is a bifurcation point of variable length; its name is “bardo.” The bardo is immersed in the conventional, or “seeming” reality. It emerges from what is called the “unstained” ultimate or primordial emptiness or “basal clear light.” Further, the ultimate is not the sphere of cognition. Cognition, including cognition of time, belongs to conventional reality. Buddhahood, in contrast, is (...) a condition of uncompounded knowledge where basic mind blossoms without temporal or other cognitive distinctions, unmade, unfabricated, luminous and pristine. Cyclical existence involves both the ultimate and the conventional as it moves through six bardos—all of which are the effulgent of the basal clear light—until Buddhahood. The six are: the bardo of this life ; the bardo of dream; the bardo of meditation; the bardo of dying; the bardo of dharmata ; and the bardo of existence. Each realm is both ultimate and conventional, and has specific initiation-based yogas to investigate these differences. The process of transition from one to the next involves at least three bodies, one mind, and aspects of speech. In each bardo, the character of the now as embodiment and temporal knowing varies yet a complete and consistent cross-bardo yogic wisdom leads to its total cessation in the basal clear light; the now is extinguished. The author presents, from the viewpoint of a knowledgeable practitioner of over 30 years, an essay on Vajrayana Buddhist time, drawing implications for Fraser’s time typology. The essay will draw from English translations of significant older, tantric texts on dream yoga, deity yoga, the Chod, tantric time, the bardo of death, and empowerment. Useful practices that can be applied by the audience to test the tradition and author’s assertions will be suggested. (shrink)

continent. 1.3 (2011): 201-207. “Poetry is experience, linked to a vital approach, to a movement which is accomplished in the serious, purposeful course of life. In order to write a single line, one must have exhausted life.” —Maurice Blanchot (1982, 89) Nikos Karouzos had a communist teacher for a father and an orthodox priest for a grandfather. From his four years up to his high school graduation he was incessantly educated, reading the entire private library of his granddad, comprising mainly (...) the Orthodox Church Fathers and the ancient classics. Later on in his life he sold the library for money, only to buy a little more time before he went broke again: “I carry sorrow like a cage/ I got no birds/ as I come back from her hair/ I see the profit emptied/ cool from terror.” (1993, Ι, 101) Nowadays—and ridiculously recently—we are more than apt to speak of a certain insouciance pertaining to the Greek form of expenditure: expenditure without any type of investment, sometimes not (even) symbolic. In the vaults of the European unconscious, this imprudent stance still conjures a “capital punishment” in the form of de-capitation, reflecting back the fear of excess and the terror of its consequences.1 Thus the Greek way of living is very close to what a stranger could have termed as “the Greek way of dying.” Yet, what is not often understood is that the Greek esprit , the same one that invented the maxim μηδ?ν ?γαν (“nothing in excess”), does not experience death solely as an imminent fear of bankruptcy. For it miraculously combines its unconditional acceptance with the promise of a resurrection that is always there in the scents of Spring, from Dionysus to the orthodox Christ: “Everyone resurrects himself through dying [….] Resurrection is the switching of mortalities.” (2002, 94) Hence, if an entire library was imprudently traded for a plate with seven olives, a sliced tomato and some fresh goat cheese, let us not be fooled: this is not the meal of the pauper, but that of “an aristocrat from God” (1993, II, 491) feeding his eloquent loudmouth, ridiculously cut open in an otherwise rock-solid caput . *** To speak of the Greek experience is to speak about a half-dead language that still utters in life what is seemingly excluded from it and thus forbidden to be talked about: death. Death as anything that is out of this world, as something that will never return . Still, along with an experience of death that recently waned as a worn-out academic fashion, the Greek experience is dead too. Nearly 2300 years of written words separating Homer from the fall of Byzantium equal 500 books on a library traded for money: “I am with the killed. Hence my deepest solitude. I do not feel this tremendous macho society, beyond from the fact that it is a ruthlessly consuming one. It is me who pays all the time .” (2002, 57) Let us do the math and see how much this dealing with the Greek experience is costing the poet and how much dealing with the Greek experience might cost us today. *** “I do not guarantee a single word.” (Karouzos, 1993, II, 454) Through its various dialects and forms, the Greek language speaks through an incessant historical dissemination. Anyone who is aware of this terrifying polymorphy and still calls himself a poet, must stand against a white sheet of paper, pen-in-hand, with a very particular duty: to be as fully inconsistent as possible. In the formally ironic uniqueness of the poem, the poet functions as “a band-aid for lesser and greater antinomies.” (1993, I, 251) Of course these antinomies are not exhausted in language—they are historical, political and, alas, existential. Yet, beyond appearances , it is language that ruthlessly encodes them through history, submitting the poet to the temptation of placing them one next to the other on a single white sheet. The closer their neighboring, the greater the scattering of the writer in the ironic uniqueness of the paper. In a work where poetic license is described as a “freedom-impasse” (2002, 51), this task is undertaken in full conscience of its personal consequences: “what I am interested in is to escape my individuality (envisioning the non-ego) […] Nevertheless, my dissociations never achieve duration.” (2002, 74-75) Hence, though poetry is the “deserted direction of will,” (1998, 62) the stance of the poet is not that of a Nietzschean “great man.”2 Whereas drunkenness provides a thread between the poem and the excess it both presupposes and infuses (“Poetry always enlarges. ‘Drunkenness’ is nothing more than that,” (2002, 85)), whereas language flashes in loudmouth spurts of déraison (“When I am alone I do something else. I utter words. For example, while having my ouzo and listening to music I am most likely capable of randomly shouting ‘Electricity!’” (2002, 138)), the poet never gives in to the double affirmation that would eventually risk the “element of pleasure in discourse.” (2002, 80)” It is exactly because the gap of the antinomies is so vast that poetry is not meant to be written with a hammer. Neither does writing consist in a reevaluation of those elements. In short, poetry is not an affirmation of difference, but the surprising beauty of chiming antinomies. We might never transcend them, but it is up to us to put them together. Yet again, this voisinage is not to be identified with the necessity of chance as an eternal return.4 On the contrary it is a return from that very return : Let us treat Yes as a No to No and No as a Yes […] And let us not forget that this pissed affirmation crumbled down Nietzsche’s intellect in the dark paths of this world. (2002, 88) This return from the “vicious circle” should in no way be taken as a form of artistic prudence. Rather it can be seen as a dribble of demonic inconsistency as Dionysus transforms himself into a Christ that is in turn de-theologized: “Who can forbid that? Every man is capable of his own theology, nothing can stop him.” (2002, 73-74) This is a turn towards an existential vision of the world, historically coinciding with a particular political defeat of the Left, to which the poet devoted all his life: after the defeat of the popular front I raised the question “why do we exist?” while others were asking “why we failed.” (2002, 57)5 But most of all it is a return to poetry that exceeds the existential question itself, going beyond the issue of faith. Poetry comes in as a question of return after a defeat that is confessed in full profanity. Though it accepts the necessity of the defeat, it does not affirm it. Though it negates it, the negation is not in the name of a promise to be delivered in the kingdom of heavens. Following a historical and existential defeat, poetry is born post mortem . It signals a return to Christ as “groundless religiousness in the surprise of the real as such” (2002, 72) which is at once a return to the refuge of childhood. It is not a question of endurance towards an eternal return. Rather it is a question on the possibility of an existential return. Returning in a world as someone who cannot enjoy any returns exactly because he is averse to guarantees. A return without returns. *** PHOTOCOPY OF HAPPINESS When I was young I used to pin down cicadas and step on ant nests. I used to stand there silent for hours. With threads I decapitated bees. Now I am a dead man breathing. (Karouzos, 1993, II, 336.) The return to the “paradise of childhood” (2002, 68) constitutes the devouring refuge of its own memory when defeat becomes the synonym of adulthood. The political struggles of a young communist in a country torn up by a civil war right after World War II fraught with incarcerations and exiles. Historically they resulted in the defeat of the communist movement in Greece and opened up a long turbulent road that would peak in the dictatorship of 1967. Existentially they led to a series of disillusionments: mental breakdown, divorce, abandonment of studies in law school. To the question “why do we exist” the answer was poetry. Still this exposé should not be read as a sweeping chronography of a man. For it actually happens to coincide with the historical fate of a nation that after its modern constitution never stopped dreaming of the glories of its past youth, in a present that was (and is) sweepingly disappointing. But isn’t this return to youth finally a way of compensating for a loss of youth that necessarily results in a losing adulthood? Will Greeks, the eternal children of Plato and Nietzsche, ever learn? How to return without dying, how to remember without wasting time? WE ARE IN THE OPEN MEANING Living the coldest mauve night right across Parthenon I went to take a piss on some foliage and I was enjoying the foliage as it was steaming. (Karouzos, 1993, II, 340) Beyond the historical tragedies of modern Greece and away from any personal disappointments, the relation that this land holds with language and history is mediated through the Greek light—whose omnipresence is the very condition of its transcendence. All historical contradictions from Dionysus to Christ took place under this light; all those disseminated dialects were spoken beneath its warmth. To paraphrase Lévinas,6 light is both the condition of the world and of our withdrawal from it—a withdrawal towards the invisibility of God, of the dead, of meta-physics, resulting from the temptation that all is still here, behind this light the visibility of which they once evaded: “birds, the allurement of God.” (1993, I, 17) Under that luminous sky, if Greeks can do anything at all, it is to envision a return that will never come. All they can do is write poetry—which is doing nothing; other than lending an ear to a disseminated language whispering a unity that cannot be promised, as an adulthood in defeat is ready to recognize. Trying “to trap the invisible in visibility” (1993, II, 483) they forget that they have grown up and one day they die—with the promise of return. Hence an additional meaning must be given to this return to childhood. It does not signal salvation but rather its promise. To the ears of an aged continent it means that the return to/of poetry is a losing game, a return without returns. “Europe, Europe… you are nothing more than the continuation of Barabbas.” (1993, I, 295) *** “Life is not there to verify theories.”7 The records show that Karouzos was finally given a second-class pension from the Greek government, at the time when he was being recognized by the literary press as one of Greece’s major contemporary poets. Being neither a bourgeois nor a nobelist, he proclaimed himself to be an anarcho-communist, unconditionally faithful to the utopia of a classless society. He also drank, heavily. “Capitalism made an animal out of man/ Marxism made an animal out of truth/ Shut up.” (1993, II, 369) Perhaps one of the most scandalous divides of our times has been the one between the living and the dead, the latent prohibition that the living should not be concerned with the dead based on the mere impossibility of the dead to be concerned with the living in the first place. What adds to this scandal is that this divide abuses anything that cannot return to us by subsuming it under the same futility. Hence death is no longer “loss” in the usual sense. It no more refers to the things we lost but to our “loss” (of time, money and well-being) as we insist to dwell on them. Death is a waste —of time. It is this waste that we find in the insouciance of Greek expenditure; the waste in dealing with a language that most of its historical part is no longer spoken (a dead language); the waste in translating a poet who is ex definitio untranslatable; the waste of his vision, his money, his life. The waste of dealing with anything that cannot return and that cannot bring in any returns . But it is also the waste of life that poetry itself presupposes, the waste of dealing with invisibility, with anything that is out of this world and thus invokes the fear of death that is in turn—and surprisingly— nowhere to be found. Instead of death, what is there, beyond the light, is the being without us (to recall the Lévinasian il y a ), the mumble of our own nothingness which constitutes the price to be paid for writing poetry under an evergreek light. To understand this to-and-fro, is to realize that poetry is something out of this world that nevertheless takes place in this world, by virtue of this world. But to ridiculously equate this to-and-fro with death as non-existence, is to exile poetry along with its own possibility from this same old world: I do not believe that poetry will ever disappear from this world. […] But I am also sure that it does not have many chances of playing, as you say, a redemptive role in our vertiginous technological future. Without being endangered as a creative need, it will be placed on the side of history. (2002, 32) It is mainly there that we would like to locate the meaning of Nikos Karouzos’s poetry today. If we are willing to include the Greek original it is because we consider that it will be both a waste of time for us to do so (since most of you cannot read Greek) and because it might induce you to the even larger waste of learning it. We would additionally be glad if this small introduction served as an equally wasteful, academically useless piece of reading, gesturing towards a taboo of investing in anything Greek—that is in anything dead among the living, in anything that will never come back and maybe was never here in the first place. This is the only way to reserve for ourselves the possibility of poetry and preserve the light of its promise. “To return: that is the miracle.” (1993, I, 17) Athens, Greece July 10, 2011 NOTES 1 “ Capitale (a Late Latin word based on caput “head”) emerged in the twelfth to thirteenth centuries in the sense of funds, stock of merchandise, sum of money or money carrying interest.[…] The word and the reality it stood for appear in the sermons of St. Bernardino of Siena (1380-1444) ‘… quamdam seminalem rationem lucrosi quam communiter capitale vocamus ’, ‘that prolific cause of wealth that we commonly call capital’” (Braudel, 1992, 232-233). 2 “A great man – a man whom nature has constructed and invented in the grand style – what is he? First : there is a long logic in all of his activity, hard to survey because of its length, and consequently misleading; he has the ability to extend his will across great stretches of his life and to despise and reject everything petty about him, including even the fairest, ‘divinest’ things in the world.” (Nietzsche, 1968, 505, §962) 3 Cf. Deleuze, 1986, 186-9. 4 “Return is the being of becoming, the unity of multiplicity, the necessity of chance: the being of difference as such or the eternal return.” (Deleuze, 189)5 In this 1982 interview Karouzos refers to the defeat of the communist movement in Greece after the civil war of 1946-1949 between the Governmental Army and the Democratic Army of Greece, the military division of the Greek communist party. Karouzos’s father was a member of the communist National Liberation front (EAM) members of which formed the mainl resistance movement (ELAS) in Greece during WWII. The poet was a member of the United Panhellenic Organization of Youth (EPON), which was a youth division of EAM. After the end of the war, ELAS was called to disarmament in view of the formation of a National Army. The members of EAM resigned from the government of national unity and a series of protests led to a 3 year civil war between ELAS and the Government Army. After the defeat of ELAS the Communist party was outlawed and many communists were exiled in deserted Greek islands. Karouzos, who took action in the Greek resistance and was active during the Greek civil war, was exiled in Icaria on 1947 and in Makronisos on 1953 where he was called two years earlier to do his military service. 6 “Existence in the world qua light, which makes desire possible, is then, in the midst of being, the possibility of detaching oneself from being. To enter into being is to link up with objects; it is in effect a bond that is already tainted with nullity. It is already to escape anonymity. In this world where everything seems to affirm our solidarity with the totality of existence, where we are caught up in the gears of a universal mechanism, our first feeling, our ineradicable illusion, is a feeling or illusion of freedom. To be in the world is this hesitation, this interval in existing, which we have seen in the analyses of fatigue and the present.” (Lévinas, 1988,43-4) 7from a TV interview. THE POETRY OF NIKOS KAROUZOS From Redwriter [ Ερυθρογρ?φος ], in Collected Works, Vol . II, Athens: Ikaros. 1993, 463-4. [Athens: Apopeira, 1990, 9-10.] JESUS ANTI-OEDIPUS* Why were we once saving till the fifth day the Paschal lamb? The scriptures say: with this victim’s meat we ought to cleanse all of our senses. To give life to the whitest wave miraculous odors in the extension of the chest. Ideals to death. For us to witness the illustrious dawns of Absinthe and for the soul to be a deeply carved ornament on the fore we named will. Then many deer running amidst the evergreen growth with watery hymns, then, the unintended angels descending with heights spiraling in their momentum offer themselves to the luminous Adventure. Whence the need for speech and our sufferings covered with flags like the glorified dead. An incorporeal finger pointing at the flamboyant and fragrant holocausts within the tired horizons and the exhausted breadths with joys of the mistletoe on fire and shivering all of the green-leaved love. Something would have chirped again had we not driven it away— maybe the ewe’s grass. Something would have called us to the eternal resurrection— maybe the grace of spring. But now our heart is fiercely blinded, withdrawn to the appearances of Hades. Silence and ice incessantly cover the Infant Spirit in thatched times. While the cherry trees are dreaming faintly glowing in absolute darkness there’s nothing the Babylonians can contemplate in labs with automatic colored lights. How to rejoice now in the fifth day of the lamb? We have forked the stars. We’ve gradually become supposedly sublime with plucked chimeras in our hands. Avenged relentlessly by science. *Though the poem appears in a 1990 collection, it was actually written in 1968. Hence the reader must be aware in not associating Karouzos’ Anti-Oedipus with the famous 1972 work of Deleuze and Guattari, given that the former precedes the latter. ΙΗΣΟΥΣ ΑΝΤΙ-ΟΙΔΙΠΟΥΣ Γιατ? κρατο?σαμε κ?ποτε ?ς την π?μπτη μ?ρα το πασχαλιν? πρ?βατο; Τα κε?μενα λ?νε: μ’ αυτο? του θ?ματος το κρ?ας ?πρεπε να καθαρ?σουμε ?λες τις αισθ?σεις. Για να δ?σουμε κ?μα στη ζω? λευκ?τατο θαυμ?σιες ευωδι?ς στην ?κταση του στ?θους. Ιδανικ? στο χ?ρο. Για να βλ?πουμε τα λαμπρ? χαρ?ματα του ?ψινθου και να ’ναι η ψυχ? στ?λισμα βαθυχ?ρακτο της πλ?ρης που την ε?παμε θ?ληση. Τ?τε πολλ?ς δορκ?δες τρ?χοντας αν?μεσα στην καταπρ?σινη φ?ση με τους υδ?τινους ?μνους, τ?τε, κατεβα?νοντας οι αθ?λητοι ?γγελοι με κυλινδο?μενο το ?ψος στην ορμ? τους χαρ?ζονται της αστραφτερ?ς Περιπ?τειας. ?θεν η μιλι? γι’ αυτ? χρει?ζεται και τα δειν? σκεπ?ζονται ωσ?ν τους τιμημ?νους νεκρο?ς με σημα?ες. Ασ?ματο δ?χτυλο δε?χνει τα φλογ?δη και μοσχοβ?λα ολοκαυτ?ματα στους κουρασμ?νους ορ?ζοντες στα εξουθενωμ?να πλ?τη καθ?ς αν?βουν οι χαρ?ς του νερα?δ?ξυλου και τρ?μει ολ?κληρη η πρασιν?φυλλη αγ?πη. Κ?τι θα κελαηδο?σε π?λι αν δεν το δι?χναμε— μπορε? της προβατ?νας το χορτ?ρι. Κ?τι θα μας καλο?σε στην απ?ραντη αν?σταση— μπορε? του ?αρος η χ?ρη. Μα η καρδι? μας ?γρια τυφλ?θηκε π?ρασε στα φαιν?μενα του ?δη. Σιγ? και π?γος αδι?κοπα σκεπ?ζει στους αχυρ?νιους καιρο?ς το Ν?πιο Πνε?μα. Την ?ρα που ονειρε?ονται οι βυσσινι?ς και λ?μπουν αμυδρ? μεσ’ στο απλ?τατο σκοτ?δι τ?ποτα δε στοχ?ζονται οι βαβυλ?νιοι στα εργαστ?ρια με τ’ αυτ?ματα χρωματιστ? φ?τα. Π?ς να χαρο?με πια την π?μπτη μ?ρα του προβ?του; Φουρκ?σαμε τ’ αστ?ρια. Γ?ναμε σιγ?-σιγ? δ?θεν υπ?ροχοι με μαδημ?νες χ?μαιρες στα χ?ρια. Μας ν?μεται σκληρ? η επιστ?μη. From: Redwriter [Ερυθρογρ?φος], in Collected Works, Vol. II, Athens: Ikaros. 1993, 472. [Athens: Apopeira, 1990, 18.] DIALECTΙCS OF SPRING Christ the straight angle; Christ the Pythagorean theorem. Christ the infinitesimal calculus from above the blessed Sets Christ. Christ the tessellation of massive particles Christ the zero mass. Hence we spray numbers and fields of lust. We are carabineers of diseased logic plus something— Observed means observer and Hekate The darkness luminous and light in the dark Astarte banqueters demons from today. ΔΙΑΛΕΚΤΙΚΗ ΤΟΥ ΕΑΡΟΣ Χριστ?ς η ορθ? γων?α· Χριστ?ς το πυθαγ?ριο θε?ρημα. Χριστ?ς ο απειροστικ?ς λογισμ?ς ?νωθεν ?λβια Χριστ?ς τα Σ?νολα. Χριστ?ς η ψηφιδογραφ?α στα μαζικ? σωμ?τια Χριστ?ς η μ?ζα μηδ?ν. ?ρα ψεκ?ζουμε αριθμο?ς και πεδ?α λαγνε?ας. Ε?μαστε τυφεκιοφ?ροι νοσο?σης λογικ?ς και κ?τι-- παρατηρο?μενο σημα?νει παρατηρητ?ς και Εκ?τη σκ?τος το π?μφωτο και φως εν τ? σκοτ?? η Αστ?ρτη συνδαιτημ?νες δα?μονες απ’ ?ρτι. From: Redwriter [Ερυθρογρ?φος], Athens: Apopeira, 1990, 18. [1993, II, 472]. CREDO (as we are used to say in Latin) Α I believe in one Poet expelled from heavens / fugitive from the god and vagabond, Empedocles / and here on earth / exile on the earth etc. of Baudelaire /. Β I believe in one Computer inside thunder and through matter. Γ Suffering undefiled / substantive / the Poet uplifts himself slow-burning suicidal implying lengthy sleeps. Δ Cutting down on prospective mistakes. Ε Of all things visible and invisible officiating the onion-peelings. Ζ The Poet has nothing / see the departed /. Η I believe in one Poet that says: madness I enjoy; he ridicules existence; let me light up from my mana. Θ Syntax he doesn’t care about when musicality commands him. Along with still more licenses, and Ts are played according to the concept sound anywhere. E.g. the winters here, he winters there; it will not come—I will not rest, etc. etc. Ι The Poet exercises thought until it’s stripped down. Κ And if he’s Greek he must always study the fineness of Attica, in light, mountains, fields and sea. For this fineness teaches language. Λ And if he’s deeply destined the Poet expresses the unexplainable of the explained; he happens to be a rightful heir to the scientist and his predecessor. Μ On the froth he does not last; the Poet blusters at the bottom of the pot. Ν Flamebred and never redeemed. Ξ The Poet must sometimes say: what a consumption of presence — be a bit lonely for a change! Ο The Poet is twilit. Π He is susceptible of deaths and resurrections. Ρ He looks from the corner of his eye and exists in a glance. Σ He follows behind the mother. Τ Eveningless when it comes to age. Υ I believe in one Poet who says: let the purities coincide. Until the Corinth of the Universe or even further. Φ In a higher despair. Χ In a brighter quintessence. Ψ In one sensation that lifts off. Ω Forgiving everyone. CREDO (ως ε?θισται να λ?με λατινιστ?) Α Πιστε?ω εις ?να Ποιητ?ν εκτ?ς ουρανο? / φυγ?ς θε?θεν και αλ?της, Εμπεδοκλ?ς / και επ? της γης / εξ?ριστος π?νω στη γη κ.λπ. του Βωδελα?ρου /. Β Πιστε?ω εις ?να Υπολογιστ?ν εντ?ς κεραυνο? και δια της ?λης. Γ Υποφ?ροντας ?χραντα / ουσιαστικ?ν / ο Ποιητ?ς ανατε?νεται βραδυφλεγ?ς αυτ?χειρας εξυπακο?οντας πολ?ωρους ?πνους. Δ Τα υποψ?φια λ?θη λιγοστε?οντας. Ε Ορατ?ν τε π?ντων και αορ?των ιερουργ?ντας την αποκρομμ?ωση. Ζ Ο Ποιτ?ς ?χει τ?ποτα / βλ?πε τους αναχωρ?σαντες /. Η Πιστε?ω εις ?να Ποιητ?ν που λ?ει: η τρ?λα μ’ αρ?σει· γελοιοποιε? την ?παρξη· ας αν?ψω απ’ τη μ?να μου. Θ Συνταχτικ? δεν το γνοι?ζεται στην προσταγ? της μουσικ?τητας. Μαζ? και μ’ ?λλες ακ?μη λευτερι?ς, και τα νυ πα?ζονται κατ? την ?ννοια ?χος οπουδ?ποτε. Π.χ. τον χειμ?να εδ?, το χειμ?να εκε?· δε θ? ’ρθει – δεν θα καταλαγι?σουμε, κ. λπ. κ.λπ. Ι Ο Ποιητ?ς γυμν?ζει τη σκ?ψη σε απογ?μνωση. Κ Κι αν ε?ναι ?λληνας οφε?λει να σπουδ?ζει π?ντοτε της Αττικ?ς τη λεπτ?τητα, σε φως, βουν?, χωρ?φια και θ?λασσα. Διδ?σκει γλ?σσα η λεπτ?τητα το?τη. Λ Κι αν ε?ναι βαθι? πεπρωμ?νος ο Ποιητ?ς εκφρ?ζει το ανεξ?γητο του εξηγητο?· τυγχ?νει ν?μιμος δι?δοχος του επιστ?μονα και προκ?τοχ?ς του. Μ Στον αφρ? δεν ?χει δι?ρκεια· στο πατοκ?ζανο μα?νεται ο Ποιητ?ς. Ν Φλογοδ?αιτος και ποτ? ξελυτρωμ?νος. Ξ Ο Ποιητ?ς κ?ποτε πρ?πει να λ?ει: μεγ?λη καταν?λωση παρουσ?ας – γενε?τε και λ?γο μοναξι?ρηδες! Ο Ο Ποιητ?ς ε?ναι αμφ?φλοξ. Π Επιδ?χεται θαν?τους και αναστ?σεις. Ρ Ακροθωρ?ζει και υπ?ρχει σε ξαφνοκο?ταγμα. Σ Ε?ναι ουραγ?ς της μητ?ρας. Τ Αν?σπερος απ? ηλικ?α. Υ Πιστε?ω εις ?να Ποιητ?ν που λ?ει: να συμπ?σουν οι αγν?τητες. Μ?χρι την Κ?ρινθο του Σ?μπαντος ? μακρ?τερα. Φ Σε αν?τερη απελπισ?α. Χ Σε φαειν?τερη πεμπτουσ?α. Ψ Σε μια α?σθηση που πτηνο?ται. Ω Συγχωρ?ντας τους π?ντες. From Large Sized Logic [ Λογικ? μεγ?λου σχ?ματος ], Athens: Erato, 1989, n.p. [1993, II, 521-3]. (shrink)

Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set $D\in$ d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that (...) there exists a d.r.e.d such that R d] has a minimum element $>$ 0. The most striking result of the paper is the existence of d.r.e. degrees for which R[d] consists of one element. Finally we prove that for some d.r.e. d R[d] can be the interval [a,b] for some r.e. degrees a,b, a $<$ b $<$ d. (shrink)

Almost all the original philosophers, from Socrates to the verificationists of the present day, have tried to provide some universally applicable method of eliminating confusion and error from our discourse: this provision of a method of ‘correcting the understanding’ is at least one, and perhaps the principal, of the continuous threads which can be traced in Western philosophy. There was the Socratic method, which requires us to look for real definitions of our fundamental abstract terms: the Cartesian methods of rejecting (...) as possible candidates for knowledge any propositions which do not consist of clear and distinct ideas: the Humean or Empiricist method of dismissing as nonsense any non-tautologous statement which cannot be justified as referring to the order of our sensations: Kant's transcendental method of critical philosophy, whichit would certainly be imprudent to characterize in a phrase, but which was equally intended to be a safe protection against empty metaphysics and meaningless questions: lastly, the verification principle, which provides a general method of determining which of our statements conform to some scientific standard of intelligibility, and which are to classed as tautologies or as playing with words. New movements in philosophy have in general been new methods of correcting the understanding, methods which are further generalized and applied in the interval before another great philosopher appears with another general method of showing that all previous metaphysics is nonsense. (shrink)

An excerpt from Sergei M. Eisenstein's memoirs describing a night visit to the museum of Chichén Itzá in Mexico is set forth as a real life example reflecting, both from a visual and theoretical perspective, the architecture of Aby Warburg's Bilderatlas Mnemosyne and his concept of Denkraum. Drawing upon Warburg's own writings and F. T. Vischer's theory of symbol, the paper looks at Eisenstein's experience at the museum as highlighting the dynamic relation between man's religious/magical and scientific/rational psychic poles, and (...) the in-between space of thought inherent to the concept of Denkraum and visually represented by the empty dark intervals separating the images in the Bilderatlas. Adding significance to its argumentation, the paper also hints at an affinity between Eisenstein's film montaging and Warburg's image assembling criteria. (shrink)

The East has seen totality in a far more consistent and systematic way than the West; and India more so than any other civilisation in the East. When the Swami Siddheswarananda came to France to lecture on Vedic philosophy, he entitled his address, Outline of a Philosophy of Totality’. The expression could have been applied to the philosophies of India as a whole. But the world of thought, coextensive with culture, is far broader than philosophy. It is no exaggeration to (...) assert that India is the land of totality par excellence. Is it not even, according to one dictum, bigger than the world …? The notion of totality, implicit or conscious, poetic or theoretical, original or final, is present throughout Indian culture, both in its religion and in its arts, both in its customs as in its language. The Mahabharata, the largest epic poem ever conceived, proclaims: everything in the Mahabharata can be found elsewhere, but what is not in the Mahabharata cannot be found anywhere. Whilst the absolute beginning of a piece of Western music is in keeping with a dramatic time analogous to that of the Creation, Indian music seems to come from the eternity of a universe without transcendence. The body takes on a cosmic meaning through dance. By performing the tandava, the cosmic dance, Shiva Nataraja (‘Lord of the dance’) endlessly creates and destroys worlds. Indian art is an art of proliferation: both the reiteration of motifs sculpted in architecture and the litanies and metaphors spun out in epic poetry are symbolic attempts to capture the totality of the world. Every single element, being, movement or thing within this continuous space and time points towards all the others. The texts describe the sky of Indra with its web of pearls arranged in such a way that when one looks into one, one sees all the others reflecting in it; in the same way, each object of this world is not merely itself but comprises every one of the others and actually is all the others. The culture of India is one of plenitude, presence and continuity. At the opposite extreme, Japan developed a culture based upon the values of emptiness, absence and the interval. When a guru speaks, Valmiki and Vyasa know that it will take them many scores of verses. A Zen master's reply to his disciple takes up a single-line anecdote, or a word, or even a silence. At the other extreme, hundreds of statues line the gopuram of the temple at Madurai: not all of the thirty-three million gods ‘recognized’ in the writings are there, of course, but at least their unbelievable abundance gives us a plausible image of them. (shrink)

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical (...) situations involving more than one maximal value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A, where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U- uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U = 1/h 0 h log [1+]d, where h is the largest membership value obtained by any element of A and is the measure of the -cut of A defined by the Lebesge integral of its characteristic function. (shrink)

The Choquet expected utility model deals with nonadditive probabilities (or capacities). Their dependence on the information the decision-maker has about the possibility of the events is taken into account. Two kinds of information are examined: interval information (for instance, the percentage of white balls in an urn is between 60% and 100%) and comparative information (for instance, the information that there are more white balls than black ones). Some implications are shown with regard to the core of the capacity and (...) to two additive measures which can be derived from capacities: the Shapley value and the nucleolus. Interval information bounds prove to be satisfied by all probabilities in the core, but they are not necessarily satisfied by the nucleolus (when the core is empty) and the Shapley value. We must introduce the constrained nucleolus in order for these bounds to be satisfied, while the Shapley value does not seem to be adjustable. On the contrary, comparative information inequalities prove to be not necessarily satisfied by all probabilities in the core and we must introduce the constrained core in order for these inequalities be satisfied. However, both the nucleolus and the Shapley value satisfy the comparative information inequalities, and the Shapley value does it more strictly than the nucleolus. (shrink)

We introduce a novel expansion of the four-valued Belnap–Dunn logic by a unary operator representing reductio ad contradictionem and study its algebraic semantics. This expansion thus contains both the direct, non-inferential negation of the Belnap–Dunn logic and an inferential negation akin to the negation of Johansson’s minimal logic. We formulate a sequent calculus for this logic and introduce the variety of reductio algebras as an algebraic semantics for this calculus. We then investigate some basic algebraic properties of this variety, in (...) particular we show that it is locally finite and has EDPC. We identify the subdirectly irreducible algebras in this variety and describe the lattice of varieties of reductio algebras. In particular, we prove that this lattice contains an interval isomorphic to the lattice of classes of finite non-empty graphs with loops closed under surjective graph homomorphisms. (shrink)

Following up on previous results by Falmagne, this paper investigates possible mechanisms explaining how preference relations are created and how they evolve over time. We postulate a preference relation which is initially empty and becomes increasingly intricate under the influence of a random environment delivering discrete tokens of information concerning the alternatives. The framework is that of a class of real-time stochastic processes having interlinked Markov and Poisson components. Specifically, the occurence of the tokens is governed by a Poisson (...) process, while the succession of preference relations is a Markov process. In an example case, the preference relations are the various possible semiorders on the set of alternatives. Asymptotic results are obtained in the form of the limit probabilities of any semiorder. The arguments extend to a much more general situation including interval orders, biorders and partial orders. The results provide (up to a small number of parameters) complete quantitative predictions for panel data of a standard type, in which the same sample of subjects has been asked to compare the alternatives a number of times. (shrink)

This paper presents a theory of empty names that is consistent with direct-reference theory and Millianism.

This paper begins with a response to Josh Gert’s challenge that ‘on a par with’ is not a sui generis fourth value relation beyond ‘better than’, ‘worse than’, and ‘equally good’. It then explores two further questions: can parity be modeled by an interval representation of value? And what should one rationally do when faced with items on a par? I argue that an interval representation of value is incompatible with the possibility that items are on a par (a mathematical (...) proof is given in the appendix). I also suggest that there are three senses of ‘rationally permissible’ which, once distinguished, show that parity does distinctive practical work that cannot be done by the usual trichotomy of relations or by incomparability. In this way, we have an additional argument for parity from the workings of practical reason. (shrink)

What are the meanings of empty names such as ‘Vulcan,’ ‘Pegasus,’ and ‘Santa Claus’ in such sentences as ‘Vulcan is the tenth planet,’ ‘Pegasus flies,’ and especially ‘Santa Claus does not exist’?Our view, developed in Adams et al., consists of a direct-reference account of the meaning of empty names in combination with a pragmatic-implicature account of why we have certain intuitions that seem to conflict with a direct-reference account.

Emptiness means that all entities are empty of, or lack, inherent existence - entities have a merely conceptual, constructed existence. Though Nagarjuna advocates the Middle Way, his philosophy of emptiness nevertheless entails nihilism, and his critiques of the Nyaya theory of knowledge are shown to be unconvincing.

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

A logic of intervals is proposed akin to the one published by Hamblin (Hamblin (1969) and (1971)). Like Hamblin's, the present system is also based on a single primitive. However, the work presented here differs from Hamblin's in a number of respects. Most importantly, the present system is explicitly based on mereological ideas in such a way that not only are the two notions of abutment and temporal order involved in Hamblin's primitive two-place relation "abuts at the earlier end" (...) distinguished ; the temporal ordering itself is built up from a symmetric mereological primitive. The present system is shown to be complete. (shrink)

This paper focuses on empty mind, transitional space and the dissolving of the self object function.

What are the meanings of empty names such as ‘Vulcan,’ ‘Pegasus,’ and ‘Santa Claus’ in such sentences as ‘Vulcan is the tenth planet,’ ‘Pegasus flies,’ and especially ‘Santa Claus does not exist’?Our view, developed in Adams et al., consists of a direct-reference account of the meaning of empty names in combination with a pragmatic-implicature account of why we have certain intuitions that seem to conflict with a direct-reference account.

The problem of empty terms is one of the focal issues in analytic philosophy. Russell’s theory of descriptions, a proposal attempting to solve this problem, attracted much attention and is considered a hallmark of the analytic tradition. Scholars of Indian and Buddhist philosophy, e.g., McDermott, Matilal, Shaw and Perszyk, have studied discussions of empty terms in Indian and Buddhist philosophy. But most of these studies rely heavily on the Nyāya or Navya-Nyāya sources, in which Buddhists are portrayed as (...) opponents to be defeated, and thus do not truly reflect Buddhist views on this issue. The present paper will explore how Dignāga, the founder of Buddhist logic, deals with the issue of empty subject terms. His approach is subtle and complicated. On the one hand, he proposes a method of paraphrase that resembles Russell’s theory of descriptions. On the other, by relying on his philosophy of language—the apoha theory, he tends to fall into a panfictionalism. Through the efforts of his follower Dharmakīrti, the latter approach would become more acceptable among Indian and Tibetan Buddhists. Dignāga’s Chinese commentators, who were free from the influence of Dharmakīrti, dealt with the empty term issue in three ways: (1) by adhering to Dignāga’s method of paraphrase; (2) by allowing exceptions for non-implicative negation; and (3) by indicating the propositional attitude of a given proposition. Among these, the third proved most popular. (shrink)

This is an entry on Empty Names for the Routledge Companion to the Philosophy of Language, edited by Delia Graff Fara and Gillian Russell.

John Stuart Mill (1843) thought that proper names denote individuals and do not connote attributes. Contemporary Millians agree, in spirit. We hold that the semantic content of a proper name is simply its referent. We also think that the semantic content of a declarative sentence is a Russellian structured proposition whose constituents are the semantic contents of the sentence’s constituents. This proposition is what the sentence semantically expresses. Therefore, we think that sentences containing proper names semantically express singular propositions, which (...) are propositions having individuals as constituents. For instance, the sentence ‘George W. Bush is human’ semantically expresses a proposition that has Bush himself as a constituent. Call this theory Millianism. Many philosophers initially find Millianism quite appealing, but find it much less so after considering its many apparent problems. Among these problems are those raised by non-referring names, which are sometimes (tendentiously) called empty names. Plausible examples of empty names include certain names from fiction, such as ‘Sherlock Holmes’, which I shall call fictional names, and certain names from myth and false scientific theory, such as ‘Pegasus’ and ‘Vulcan’, which I shall call mythical names. I have defended Millianism from objections concerning empty names in previous work (Braun 1993). In this paper, I shall re-present those objections, along with some new ones. I shall then describe my previous Millian theory of empty names, and my previous replies to the objections, and consider whether the theory or replies need revision. I shall next consider whether fictional and mythical names are really empty. I shall argue that at least some utterances of mythical names are. (shrink)

Abstract: In this paper I offer an account of a particular variety of perception of absence, namely, visual perception of empty space. In so doing, I aim to make explicit the role that seeing empty space has, implicitly, in Mike Martin's account of the visual field. I suggest we should make sense of the claim that vision has a field—in Martin's sense—in terms of our being aware of its limitations or boundaries. I argue that the limits of the (...) visual field are our own sensory limitations, and that we are aware of them as such. Seeing empty space, I argue, involves a structural feature of experience that constitutes our awareness of our visual sensory limitations, and thus, in virtue of which vision has a field. (shrink)

Three views of psychological emptiness, or xū, can be found in the Zhuāngzĭ. The instrumental view values xū primarily as a means of efficacious action. The moderate view assigns it intrinsic value as an element of one Zhuangist vision of the good life. The radical view also takes it to be an element of the ideal life, but in this case the form of life advocated is that of the Daoist sage, who transcends mundane human concerns to merge with nature (...) or the Dào. The instrumental and moderate views articulate a relatively commonsensical position, on which the agent continues to pursue at least some characteristically human projects. On the radical view, by contrast, the agent ceases to exercise agency and lives a life hardly recognizable as human. The three views thus signal a tension in Zhuangist ethics, and the unattractiveness of the radical view poses a potential obstacle to the application of Daoist ideas in contemporary ethical discourse. The paper argues that there are principled grounds within Zhuangist thought for detaching the instrumental and moderate views from the radical view and rejecting the latter. (shrink)

This paper considers the problem of assigning meanings to empty natural kind terms. It does so in the context of the Twin-Earth externalist-internalist debate about whether the meanings of natural kind terms are individuated by the external physical environment of the speakers using these terms. The paper clarifies and outlines the different ways in which meanings could be assigned to empty natural kind terms. And it argues that externalists do not have the semantic resources to assign them meanings. (...) The paper ends on a sceptical note concerning the fruitfulness of using the Twin-Earth setting in debates about the semantics of empty natural kind terms. (shrink)

In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding (...) the possible observation—as well as conceptual overthrow—of this geometric ether. (shrink)

Carter (Noûs 55(1):171–198, 2021) argued that while most simple positive numerical sentences are literally false, they can communicate true contents because relevance has a weakening effect on their literal contents. This paper presents a challenge for his account by considering entailments between the imprecise contents of numerical sentences and the imprecise contents of comparatives. I argue that while Carter's weakening mechanism can generate the imprecise contents of plain comparatives such as `A is taller than B', it cannot generate the imprecise (...) contents of comparatives that quantify the difference between their arguments, such as `A is exactly n times as tall as B'. I then propose an alternative theory on which intervals serve as both thick degrees on a scale and denotations of numerical expressions. I argue that the alternative theory can account for the imprecise contents of both forms of comparatives as well as the data that motivate Carter's theory. (shrink)

Philosophers and theorists have long been puzzled by humans' ability to talk about things that do not exist, or to talk about things that they think exist but, in fact, do not. _Empty Names, Fiction, and the Puzzles of Non-Existence_ is a collection of 13 new works concerning the semantic and metaphysical issues arising from empty names, non-existence, and the nature of fiction. The contributors include some of the most important researchers working in these fields. Some of the papers (...) develop and defend new positions on these matters, while others offer important new perspectives and criticisms of the existing approaches. The volume contains a comprehensive introductory essay by the editors, which provides a survey of the philosophical issues concerning empty names, the various responses to these issues, and the literature on the subject to date. (shrink)

When it comes to empty names, we seem to have reached very little consensus. Still, we all seem to agree, first, that our semantics should assign truth to negative singular existence statements in which an empty name occurs and, second, that names are used in such statements. The purpose of this paper is to show that ruling out that the names are mentioned is harder than it has been thought. I will present a new metalinguistic account for negative (...) singular existence statements in which an empty name occurs, and I will show that the account can deal both with the objections to the traditional metalinguistic account and with other objections that seem to target my new proposal. (shrink)

Sometimes a fact can play a role in a grounding explanation, but the particular content of that fact make no difference to the explanation—any fact would do in its place. I call these facts vacuous grounds. I show that applying the distinction between-vacuous grounds allows us to give a principled solution to Kit Fine and Stephen Kramer’s paradox of ground. This paradox shows that on minimal assumptions about grounding and minimal assumptions about logic, we can show that grounding is reflexive, (...) contra the intuitive character of grounds. I argue that we should never have accepted that grounding is irreflexive in the first place; the intuitions that support the irreflexive intuition plausibly only require that grounding be non-vacuously irreflexive. Fine and Kramer’s paradox relies, essentially, on a case of vacuous grounding and is thus no problem for this account. (shrink)

Millianism is the view that the semantic content of a proper name is its semantic referent. Empty names, names with no semantic referents, raise various problems for Millianism. To solve these problems, many have appealed to pragmatics, thus ‘Pragmatic Millianism’. Pragmatic Millianism employs the relation of association between names and descriptions as well as some pragmatic processes to substitute empty names with descriptions associated with. The resultant content should account for the intuitions raised by utterances of sentences containing (...) empty names. Here, I will try to argue against this picture: Names are associated with descriptions of different kinds in a number of ways. The complex nature of this relation is overlooked by Pragmatic Millianism. Neither the relation of association nor the pragmatic processes responsible for substituting a description or a cluster of descriptions for an empty name guarantee the fullness of what is pragmatically imparted. The moral is this: Regarding empty names, Pragmatic Millianism should be avoided. (shrink)

This volume collects Jay Garfield 's essays on Madhyamaka, Yogacara, Buddhist ethics and cross-cultural hermeneutics. The first part addresses Madhyamaka, supplementing Garfield 's translation of Fundamental Wisdom of the Middle Way, a foundational philosophical text by the Buddhist saint Nagarjuna. Garfield then considers the work of philosophical rivals, and sheds important light on the relation of Nagarjuna's views to other Buddhist and non-Buddhist philosophical positions.

Data envelopment analysis is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units. However, the existing DEA models cannot tackle the newly confronted applications with imprecise and negative data as well as undesirable outputs simultaneously. Thus, we introduce undesirable outputs into modified slack-based measure model and propose an interval-modified slack-based measure model, which extends the application of interval DEA in fields that concern with less undesirable outputs. The novelties of the model are that it considers the (...) undesirable outputs while dealing with imprecise and negative data, and it is slack-based. Furthermore, the model with undesirable outputs is proven translation-invariant and unit-invariant. Moreover, a numerical example is provided to illustrate the changes of the lower and upper bounds of the efficiency score after considering the undesirable outputs. The empirical results show that, without considering undesirable outputs, most of the lower bounds of the efficiency scores will be overestimated when the DMUs are weakly efficient and inefficient. The upper bound will also change after considering undesirable outputs when the DMU is inefficient. Finally, an improved degree of preference approach is introduced to rank the DMUs. (shrink)

I argue that there are no plausible non-representational explanations of episodes of hallucination. To make the discussion more specific, I focus on visual hallucinations in Charles Bonnet syndrome. I claim that the character of such hallucinatory experiences cannot be explained away non-representationally, for they cannot be taken as simple failures of cognizing or as failures of contact with external reality—such failures being the only genuinely non-representational explanations of hallucinations and cognitive errors in general. I briefly introduce a recent computational model (...) of hallucination, which relies on generative models in the brain, and argue that the model is a prime example of a representational explanation referring to representational mechanisms. The notion of the representational mechanism is elucidated, and it is argued that hallucinations—and other kinds of representations—cannot be exorcised from the cognitive sciences. (shrink)

This paper excavates the practice-oriented background and therapeutic significance of emptiness in the Madhyamaka philosophy attributed to Nāgārjuna and Sengzhao. Buddhist emptiness unravels experiential and linguistic reification through meditation and argumentation. The historical contexts and uses of the word indicate that it is primarily a practical diagnostic and therapeutic concept. Emptiness does not lead to further views or truths but, akin to yet distinct from Ajñāna and Pyrrhonian skepticism, the suspension of assertion. This sense of emptiness as a practice can (...) be traced in the intercultural transmission of Madhyamaka from Nāgārjuna, its paradigmatic philosopher, to Sengzhao 僧肇, its first pivotal indigenous Chinese representative. (shrink)

In my dissertation (UCLA 2002), I argue that, by appropriating Fregean resources, Millians can solve the problems that empty names pose. As a result, the debate between Millians and Fregeans should be understood, not as a debate about whether there are senses, but rather as a debate about where there are senses.