The remainder equations were introduced by S. O. Hansson. In this paper, we will give an exhaustive characterization of the set of solutions for remainder equations. Moreover, solutions to some unsolved problems proposed by Hansson are reported.

The remainder set A⟂B of a set of sentences A modulo a set of sentences B is the set of all maximal subsets of A not implying any element of B. A remainder equation is an expression containing remainder sets, such as {A} = B⟂X, in which at least one set is unknown. Solutions to some classes of remainder equations are reported, and some unsolved problems are listed.

Friendly Remainders draws on Adorno's concept of the negative dialectic, examining its importance in Adorno's thought and its critical application to musical forms. Moving beyond a positivist view where musical object and appreciation operate as a synthesis, the negative dialectic method focuses on divergence and dissonance in musical forms and in society. Contradictions and divergent details and concepts become "remainders," friendly because of the fresh perspective they offer on musical forms. Dineen examines these contradictory remainders in subjects such as the (...) fascist element in Wagner's character, the torpor of Schoenberg's twelve-tone method, the self-contradiction implicit in Beethoven's Late Style, Frank Zappa's attempt to define himself as a "serious" composer, the reactionary stasis in Marilyn Manson's DVD "Guns, God and Government World Tour," and the death motive in John Coltrane. Friendly Remainders takes seriously the project of making Adorno accessible, asking the same questions of classical and popular music - taking the measure of Mahler as much as Manson - for the value of the critical insights they provoke. (shrink)

Hegel’s idealism is generally perceived as a system of rational sublation (Aufhebung) of all empirical contingencies: nothing resists notional mediation which, in a movement of negation of negation, establishes a rational totality. Already Schelling opposed to this complete sublation an “indivisible remainder” of empirical contingency. However, a close reading of Hegel makes it clear that the concluding moment of a dialectical movement of sublation is an empirical remainder which totalizes it, like the body of Christ in Christianity. And (...) the same goes for the process of “negation of negation”: it concludes with a failure of negation, and its ultimate form is a failed suicide where the subject survives as a living dead. Such a reading of Hegel makes him a thinker of our time which is the time of a failed negation: most of us live as survivors of our death, with life dragging on in depressive apathy. (shrink)

The line separating the “good life” and the savagery that the “good life” requires, or, perhaps what might be articulated as the line between the space of biopolitics and the space of necropolitics, is maintained in the present through both practices of global policing and imperial war. These practices of policing and war produce the very global refuse that constantly threatens the “good life”—actively wasting the lives and livelihoods of people and non-human lifeworlds Western colonialism established as the raw materials, (...) instruments, and objects of its civilizational goal—against which violence acts to protect a fundamentally human life worth living. At the same time, through capital-intensive projects of “saving” the very targeted populations it destroys, permanent war also produces the subordinated life that will come to serve as the means of maintaining and upholding that “good life.” Beyond this mode of colonial inhabitation, however, subsist other ecologies of life-making practices on the part of those deemed disposable, a planetary remainder which might well be our only hope for a possible future. (shrink)

The Invisible Remainder' begins with a detailed examination of the two works in which Schelling's speculative audacity reached its peak: his essay on human freedom and his drafts on the 'Ages of the World.

The debt and responsibility toward what thus withholds itself in any heritage will become clearer once we focus on the irreducible remainder in the double memory of Europe, in particular, within its Greek memory. Indeed, in the context of Derrida elucidation in “Faith and Knowledge” of the notion of the “most barren and desert‐like” abstraction, two names are invoked, the Greek name “khōra,” and the Jewish name of the “messianic”. This chapter reconstructs, at least in a very succinct manner, (...) the arguments that impel the invocation of these two names. Like “the messianic without messianicity” in one part of the double memory of Europe, khōra in its Greek part is an immemorial remainder that withdraws from what it renders possible. According to “Faith and Knowledge,” “this Greek noun [khōra] says in our memory that which is not reappropriable, even by our memory, even by our ‘Greek’ memory. (shrink)

In a very late essay on remains, one might say a throw away essay, Derrida doggedly tracks the relation of a certain desire to remains, linking it to sacrificial economy and to a hierarchical ontological order. If our concern is a thinking of desire as it pertains to remains, why should we not turn first, or perhaps exclusively, to Derrida's monumental works on the subject of remains, specifically Glas and Cinders, jettisoning the little-known essay we have not yet named? Certainly (...) Derrida has said much in these well-known works about desire and remains, consumption and excretion, fire and ashes. So, why devote all one's attention, as we will do in this paper, to what might be said to be a morsel of an essay, which has remained largely unread and hence falls outside of Derrida commentary? The essay in question is his 2002 ‘Remains – the Master, or the Supplement of Infinity’, a homage to Charles Malamoud, a French ethnologist and scholar of Indian and Oriental religions whose work, especially his 1989 Cooking the World, was influential on Derrida's thinking concerning the ‘rhetorics of cannibalism’ and ‘eating the other’ and featured prominently in his seminars from 1989–1991 on the aforementioned themes. In ‘Remains – the Master’, a dense and rich essay, Derrida analogically links two vastly different cultures – the Brahmanic of India and the Greco-European – in terms of a ‘law of remainders’, which for both traditions, he claims, is an organizing principle of humans, gods, and the whole of the world. In his essay Derrida returns to or, more accurately, remains with a thinking of ‘the French word “reste”, the remnants [restance] of “reste”’, which, as Derrida notes, is ‘difficult to translate in an exhaustive or transparent manner,’ that is, ‘without remainder’. However, what this paper will follow is the circulation of remainders in the Vedic tradition, as analysed by Derrida and Malamoud. In doing so, we can begin to not only translate the notion of Malamoud's ‘cascade de restes’ from one culture, logic, and idiom to another but understand how for Derrida this ritual downpour of remainders not only institutes a hierarchy of remainders but also produces ipseity. (shrink)

This introduction to this special section on race considers the case for the thesis advanced by Ash Amin in his article ‘The Remainders of Race’ that the conjuncture of vernacular and biopolitical racism has resulted in an upsurge in racism. It draws from three responses to that article by Abdou-Maliq Simone, Denise Ferreira da Silva and Ali Rattansi to problematize explanations for racism which appeal to ideas of human sorting instincts and other universalisms. It examines efforts to combat racism through (...) multiculturalism and non-racial policies implemented in different parts of the world. The role of biopolitics and of neoliberalism in inflecting such policies is highlighted. Lessons are drawn for the analysis of racism from Foucault’s critique of political economy and the functioning of the discourse of ‘race war’ in legitimizing the power relations sustaining systematic inequality in society. The implications for a new politics of the commons are then drawn out. (shrink)

This article approaches the question of what musters, or should muster, as global theory for these times through the lens of mediatization. Emergent globalities – states of global (perhaps glocal) becoming – are seen as constituted by world-making practices that are obviously, per­haps paradigmatically, referenced in processes of digital communication within and across borders. This is no hymn to “mere connection”, but a sustained attempt to marry process and consciousness with a proper regard for the vagaries of human interaction with (...) the structures of indifferent technology and indifferent globalities. (shrink)

This article responds to Srinivas Aravamudan's call to revisit the notion of the trace from the standpoint of the Anthropocene. A Derridean understanding of the trace shows how postcolonial difference challenges the humanist distinction between human and nature by questioning the distinction between life and death that is central to metaphysics. This discussion thus reframes the prospect of extinction signaled by the Anthropocene by means of a return to a Marxist, feminist, psychoanalytic and deconstructive trajectory within postcolonial thought.

Revision operation is the consistent expansion of a theory by a new belief-representing sentence. We consider that in a paraconsistent setting this desideratum can be accomplished in at least three distinct ways: the output of a revision operation should be either non-trivial or non-contradictory (in general or relative to the new belief). In this paper those distinctions will be explored in the constructive level by showing how the remainder sets could be refined, capturing the key concepts of paraconsistency in (...) a dynamical scenario. These are preliminaries results of a wider project on Paraconsistent Belief Change conduced by the authors. (shrink)

Prompted by the speed with which, in certain historical moments, the hard-won achievements of anti-racism can be comprehensively undone, this article reflects on the mechanisms that keep racial coding and judgement close to the surface, ready to spring into action. It reads the intensity of race in a given present in terms of the play between vernacular legacies of race-coded reception of visible difference and the conjunctural mobilizations of race by biopolitical regimes — state-regulated systems of governing populations — to (...) maintain collective order. The article explains the contemporary trend in the West towards the ‘racialization of everything’ as the product of mutually reinforcing mischief between vernacular and biopolitical racism. It closes with a discussion of the implications of such conjunctural tightness, one which questions the effectiveness of humanist arguments that have come to the fore in recent years focusing on practices of recognition and reconciliation. (shrink)

This book disentangles two terms that were conflated in the initial Anglo-American appropriation of French theory: deconstruction and poststructuralism. Focusing on Sartre, Derrida, Foucault, and Baudrillard (but also considering Levinas, Blanchot, de Man, and others), it traces the turn from a deconstruction inflected by phenomenology to a poststructuralism formed by the rejection of models based on consciousness in favor of ones based on language and structure. The book provides a wide-ranging and complex genealogy of French theory from the 1940s onward, (...) placing particular emphasis on the largely neglected early work of the theorists involved and on deconstruction’s continuing relevance. The author argues that deconstruction is a form of radical, antiscientific modernity: an interdisciplinary reconfiguration of philosophy as it confronted the positivism of the human sciences in the 1960s. By contrast, poststructuralism is a type of postmodern theory inflected by changes in technology and the mode of information. Inasmuch as poststructuralism is founded upon its “constitutive loss” of phenomenology (in Judith Butler’s phrase), the author is also concerned with the ways phenomenology (particularly Sartre’s forgotten but seminal Being and Nothingness) is remembered, repeated in different ways, and never quite worked through in its theoretical successors. Thus the book also exemplifies a way of reading intellectual history that is not only concerned with the transmission of concepts, but also with the processes of transference, mourning, and disavowal that inform the relationships between bodies of thought. (shrink)

But if, with Jonathan Lear, we scrutinize these thinkers' attempts to explain human behavior in terms of a higher principle--whether happiness or death--the ...

In his essay ‘Ethical Consistency’, Bernard Williams famously introduced the concept of a moral remainder, which points to the phenomenon of an in itself defensible decision that may nonetheless re...

This paper reads Antigone from the perspective of the Chorus. Whereas most interpreters read Antigone from the perspective of Creon and Antigone’s respective laws, I maintain that the protagonists represent laws that are distinctly apolitical. Alternatively, I argue that the Chorus make the polis—past, present, and future—the center of their thought and action and are therefore uniquely political. Through close attention to the Chorus’s composition as a body that is both one and many at the same time, and by tracing (...) their evolving position throughout the action of the drama and in their choral odes, I argue that they model a reflective and political orientation to judgment rooted in plurality, tradition, and innovation. (shrink)

This article tries to show the irreducible connection between vulnerability and violence. This connection leads us back to the ethical level of experience. If vulnerability makes violence irreducible, then at least two reactions to violence are possible. On the one hand, a reaction is possible in which one attempts to negate vulnerability in order to close down the very thing within us that allows violence to enter. This negative reaction is actually the worst violence. On the other hand, a reaction (...) is possible in which one attempts to affirm vulnerability, even though its affirmation opens us to the violence that will happen. Affirming vulnerability is the least-violent reaction. If the formula for the worst violence is apocalypse without remainder, then the least violence is the maintenance of the remainder. The maintenance would happen only by not possessing the remainders, which places us in a new situation of poverty. (shrink)

ABSTRACTThe target article presents a new version of if-thenism: call it IF-thenism. In this commentary I discuss whether IF-thenism can solve a problem that besets classic if-thenism. The answer will be that it can, on certain assumptions. I will briefly examine the tenability of these assumptions.

A History of Civilization in France, England, and Germany from 1756, and in the Remainder of Eruope from 1715, to 1789.

In the multiplying uncertainties of urban life, entrenched, mediated positions are increasingly difficult to sustain — a dynamic which simultaneously intensifies and counters a racialized biopolitics. In such contexts, is it possible for racial significations to become ironic instruments in the everyday experimentations of residents trying to figure out new ways of both engaging and retreating from each other, of trying to figure out new calibrations of collectivity that enhance the value of differences, not only as markers of navigation, but (...) as a means of curtailing the increased urban emphasis on individual competence and eligibility? (shrink)

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...) and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

John Dewey and Ludwig Wittgenstein offer devastating critiques of the dominant model of human action that each inherited in their own time. Dewey, very early in his philosophical career, ostensibly put the stimulus–response mechanical understanding of action to rest with his “reflex-arc” concept article. Wittgenstein famously redescribed action as moves within language games that interconnect to constitute an interpretively open-ended form of life. In each case, these fundamental insights serve as heuristics, guiding our intellectual activity with regard to understanding our (...) practices, and as reminders in approaching problems. Several scholars have interpreted Dewey and Wittgenstein as allies in a grand project of... (shrink)

This article takes up Hortense Spillers’ conception of ‘ungendered’ flesh and Saidiya Hartman’s notion of the ‘position of the unthought’ occupied by the figure of the Black-qua-Slave in order to explore their resonance for considering the interrelations between anti-black racial antagonism, ontological positioning and hegemonic renderings of gender formation and sexual taxonomies. Examining the performance and reception of the recent Broadway revival of Hedwig and the Angry Inch starring Taye Diggs as a case study, it asks what role race, and (...) specifically (anti-)blackness, plays in the representation, recognition and intelligibility of proper, (non-)normative gendered corporealities within the dominant imaginary and collective unconscious. (shrink)