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.

Something remarkable is happening in the cognitive sciences. After a quarter of a century of cognitive models that were inspired by the metaphor of the digital computer, the newest cognitive models are inspired by the properties of the brain itself. Variously referred to as connectionist, parallel distributed processing, or neutral network models, they explore the idea that complex intellectual operations can be carried out by large networks of simple, neuron-like units. The units themselves are identical, very low-level and 'stupid'. Intelligent (...) performance is derived from the pattern of connection strengths between units, and the fundamental cognitive activity is pattern recognition and completion. Connectionism and the Mind provides an introduction to this newly emerging approach to understanding the mind. The first few chapters focus on network architecture, offering accessible treatment of the equations that describe learning and the propagation of activation. Furthermore, the reader is walked step-by-step through the activities of networks engaged in pattern recognition, learning, and cognitive tasks such as memory retrieval and prototype formation. The remainder of the book addresses the implications of connectionism for theories of the mind, both philosophical and psychological. Foe example: What Role is played by pattern recognition and completion as basic as cognitive functions? Connectionist models have particular strength in learning and pattern recognition; should they be limited to those functions, or can they provide an overall account of cognitive functioning? In particular, can connectionist models provide an adequate account of the ability to employ linguistic and other symbol systems, or must an adequate system incorporate symbol processing as a basic cognitive capacity? Finally, Connectionism and the Mind examines the relation of connectionist models to philosophical accounts of propositional attitudes, and to a variety of other inquiries in cognitive psychology, linguistics, developmental psychology, artificial intelligence and neuroscience. (shrink)

This chapter focuses on the ontological nature of the past and our experience of the present in relation to the actual. It is argued that philosophers mistakenly equate the real with the actual. The actual is what is presented to us in experience, but what is presented to us in experience is confined to the present; so one might think that it follows that only the present is real. This presentist theory is subsequently rejected. Past, present and future are real (...) and certain mental acts such as memories of the past and expectations of the future have as their content objects at those times; these objects are just as real as the objects of present experiences. This paves the way for a distinctive brand of eternalism that is defended in the remainder of this chapter. (shrink)

There are a number of problematic features within the current treatment of time in physical theories, including the “timelessness” of the Universe as encapsulated by the Wheeler–DeWitt equation. This paper considers one particular investigation into resolving this issue; a conditional probability interpretation that was first proposed by Page and Wooters. Those authors addressed the apparent timelessness by subdividing a faux Universe into two entangled parts, “the clock” and “the remainder of the Universe”, and then synchronizing the effective dynamics (...) of the two subsystems by way of conditional probabilities. The current treatment focuses on the possibility of using a realistic clock system; namely, a coherent-state description of a damped harmonic oscillator. This clock proves to be consistent with the conditional probability interpretation; in particular, a standard evolution operator is identified with the position of the clock playing the role of time for the rest of the Universe. Restrictions on the damping factor are determined and, perhaps contrary to expectations, the optimal choice of clock is not necessarily one of minimal damping. (shrink)

What I suggest we can see in this brief overview of the literature is an extensive interpenetration on both sides of these debates between scientific, political, and social values. Important shifts in political and social values were of course occurring over the same period, some of them in parallel with, and perhaps even contributing to, these transitions I have been speaking of in evolutionary discourse. The developments that I think of as at least suggestive of possible parallels include the progressive (...) encroachment of public values into the private domain of post-World War II American life, the cold war, the rise of consumerism, and the flowering of what Christopher Lasch calls a “narcissistic individualism.”35 In popular language, the 1960s gave birth to the “me” generation. Perhaps the most tantalizing analogue is suggested by Barbara Ehrenreich's argument for the emergence of a new meaning of masculinity — an ideal of masculinity measured not by commitment, responsibility, or success as family provider, but precisely by the strength of a man's autonomy in the private sphere, his resistance to the demands of a hampering female.36 It is tempting to speculate about possible connections between changes in scientific discourse and developments in the social and political spheres, but such connections, however suggestive, would clearly have to be demonstrated.For now, however, I want to focus on another kind of change —a transformation not so much in the social or political sphere as in the scientific sphere. I make this turn, or return, in support of a more complex account of scientific change that incorporates reverberations within the scientific communty along with social and political changes.In the 1960s, all of biology was undergoing a major transformation in direct response to the dramatic successes of molecular biology. These successes seemed to completely vindicate the values on which the molecular revolution was premised — namely, simplicity and mechanism. Following the victory of Watson and Crick, and of others after them, the fever of that endeavor swept through biology leaving in its wake a new standard of science, and of scientific discourse — one predicated on clarity, simplicity, and analyzability; on the definition of legitimate questions as those capable of clear and unambiguous answers. Every biological discipline felt it — even evolutionary biology, which in some respects was at the furthest pole. Perhaps precisely because it seemed conceptually so remote, evolutionary biology may have felt it most of all. Lewontin inadvertently provides us with some direct support for this view. Indeed, he begins his introduction to Population Biology and Evolution with the following remarks: The twenty years since World War II have seen a vindication in biology of our faith in the Cartesian method as a way of doing science. Some of the most fundamental and interesting problems of biology have been solved or are very nearly solved by an analytic technique that is now loosely called “molecular biology.” But it is not specifically the “molecular” aspect of biology of the last twenty years that has led to its success. It is, rather, the analytic aspect, the belief that by breaking systems down into their component parts, by simplifying them or using simpler organisms, one can learn about more complex systems. As it happens, the problems that were attacked and are being attacked by this method lead to answers in terms of molecules and cell organelles.... There is a host of problems in biology, however, that has been much neglected in these twenty exciting years, because the answers to them cannot be meaningfully framed in molecular and cellular terms.37Lewontin is referring, of course, to problems in evolution. The remainder of his remarks is devoted to an argument for the applicability of the method, if not the content, of molecular biology to these problems. He writes, “It is not the case that molecular biology is Cartesian and analytic while population biology is holistic. Population biology is properly analytic and operates, within the framework of its own problems, by the process of simplification, analysis, and resynthesis.”38 With these remarks, he leads into the criticism of the “holists” who have “held up progress.”This new ethic of simplicity, clarity, and mechanism — embodying the very virtues lauded by Williams — was explicitly carried into evolutionary biology in the name of scientific progress. As it happened, the values implied also fit conveniently well with other values — each set of values providing crucial support for the other.However substantive the scientific gains may have been in some respects, the net effect of this ethic has also been a systematic “perceptual bias” — a bias with profound practical consequences for the entire program of methodological individualism in evolutionary biology, if not elsewhere as well. It may well be that the whole is equivalent to the reconstituted aggregate of its parts, if, in the process of aggregation or summation, all possible interactions among the parts are included. But if certain kinds of interactions are systematically excluded, our confidence in that program necessarily founders. My claim here is that such systematic exclusion does occur, and that it occurs on a number of different levels. To briefly review the interlocking kinds of “bias” that I see occurring in practice, I suggest the following schematic listing:On the most general level: The ethic of simplicity — the privileging of certain values, even certain methodologies, as having an a priori superior claim to scientific credibility.Only slightly less general, and crucially related, is the equation of “scientific” with “tractible”: Given the techniques of analysis available, the equation of science with what we can do inevitably leads to a systematic technical bias favoring simplicity. That is, because we don't know how to model complex dynamics, nonlinear interactions are systematically biased against because of the limitations of our technical know-how. The consequences of this equation of the scientific with the tractible are greatly compounded by the additional equation between what we can do and what is — that is, by our temptation to confuse tractibility with reality.Finally, and also closely related, a further kind of elision occurs even within the confines of tractibility. This kind of elision — taking the form almost of inferring tractibility from one's prior assumptions of what is real — is exemplified by the history of a mathematical ecology of mutualism. Even when mutualism can be introduced into the same technical machinery, it is still not pursued. The basic assumption is that competition is what is real, not because it is easier to model, but because it is what we expect. When the actual difficulties of modeling competition are then in turn suppressed, as in the Robert May story, what we have, given the temptation to equate the tractible with the real, is the possibility of a truly self-fulfilling prophecy. (shrink)

Although far from unanimous, there seems to be a general consensus that neither mind nor brain can be reduced without remainder to the other. This essay argues that indeed both mind and brain need to be included in a nonreductionistic way in any genuinely integral theory of consciousness. In order to facilitate such integration, this essay presents the results of an extensive cross-cultural literature search on the ‘mind’ side of the equation, suggesting that the mental phenomena that need (...) to be considered in any integral theory include developmental levels or waves of consciousness, developmental lines or streams of consciousness, states of consciousness, and the self . A ‘master template’ of these various phenomena, culled from over one-hundred psychological systems East and West, is presented. It is suggested that this master template represents a general summary of the ‘mind’ side of the brain-mind integration. The essay concludes with reflections on the ‘hard problem', or how the mind-side can be integrated with the brain-side to result a more integral theory of consciousness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 35.2 (2002) 153-174 [Access article in PDF] LSDNA: Rhetoric, Consciousness Expansion, and the Emergence of Biotechnology Richard Doyle I had to struggle to speak intelligibly. —Albert Hofmann on his self-experiment with LSD-25 Finding a place to start is of utmost importance. Natural DNA is a tractless coil, like an unwound and tangled audio tape on the floor of the car in the dark. —Kary Mullis on (...) the invention of Polymerase Chain Reaction 1. Undoing life What happened is this: Once upon a time there was a narrative of vitality. Ok, not a narrative, but an apprehension, a fear, a vision. It didn't have a beginning, middle, or end. It was. Its contours were no more determinable than those of consciousness. Indeed, our consciousness, as humans, was our sole alleged difference from it. From something called "life." We were more than life, but were also, tragically, confined to it. You know the story all too well. Some of its major authors were Cuvier, Lamarck, Darwin, Bichat. Even Shelley.Just because this sudden transformation happened on paper doesn't mean it was easy to endure. Enormous numbers of humans went on tranquilizers just to deal with the effects. Others, elsewhere, knew nothing but rumors. Nonetheless, they became increasingly implicated in its effects, the effects of understanding and experiencing both "life" and "consciousness" as informatic events. Suddenly—and it is sudden, a real surprise—both our vitality and our thought were distributed, scattered across a network and nowhere in particular. Timothy Leary and Francis Crick were speaking the same language, the language of information where the organic and the machinic enfold each other helically and, sometimes, the capacity for replication goes through the ceiling. This new language of information would [End Page 153] introduce a novel response and abyss: the pleasures and hells of eternal replication. The distribution of both life and consciousness enabled a dream of immortality from which we have not yet awakened, as the mere specter of infinite clonal replicants provokes entropies of identity even as it preserves the self from onslaughts of decay. 1In at least one of its characteristics this shift toward an informatic understanding of life is perhaps not really so novel. The seductions of control are hardly, historians of science tell us, foreign to the practices and effects of technoscience. Evelyn Fox Keller makes this point concisely and precisely in her not-quite eponymous essay, "From Secrets of Life to Secrets of Death," itself a self-professed sequel to her 1986 "Making Gender Visible." Here the scientific "impulse" is underwritten by a perennial motif that underlies much of scientific creativity, namely, the urge to fathom the secrets of nature and the collateral hope that, in fathoming the secrets of nature, we will fathom (and hence gain control of) our own mortality (Secrets, 29).Surely Keller is correct that the nascent practices of molecular biology were cryptographic in character, an espionage project unknowingly launched by Erwin Schrodinger during the Second World War. Surely it is crucial to this moment that while Schrodinger's 1943 Dublin lectures were introducing audiences to the concept of the code-script, Alan Turing again brilliantly decrypted a modified U-boat code, giving the Allies code superiority for the remainder of the war. 2 But in this segment on that strange growth called "biotechnology," I want to focus on what Keller has called the "collateral" of hope in this cryptographic impulse, namely the collateral equation between inquiry and control, specifically the control of mortality.For is "fathoming" a secret identical to the exercise of control? The very cadence and rhetorical encryption of Keller's formulation here, a general parenthetical syllogistic conclusion within and alongside a hyphenated invocation of particularity, suggest that concepts and practices of secrecy are more unstable than Keller implies with her invocation of Feynman's "disease" of lock picking: "One of my diseases, one of my things in life, is that anything that is secret, I try to undo" (40).For Keller, Feynman's confession is emblematic of a desire to control life and death... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:205 TIME AND THE IDEA OF TIME Hume entitled Part II of Book I of the Treatise "Of the Ideas of Space and Time." Students of this most obscure Part of the Book are aware, however, that he spends little time in it on time. The main reason for his concentration on space. is polemical. In Part II his primary object is to exhibit the contradictions and absurdities implicit (...) in the science of his day with its postulation of empty space and of the mathematics with its notion of infinite divisibility, and then to show how these difficulties can be overcome by the adoption and implementation of the theory of ideas he had developed in Part I. As a result, with the exception of a discussion that occupies approximately three pages in Section III, most of his references to time in Part II are little more than brief appendages tacked on to his arguments concerning space. Hume commentators have generally taken their cue from him. Although the literature contains substantial analyses of his views about space, very little can be found on the subject of time. In this paper, I shall attempt to add something to that slim literature. As its title indicates, this paper will be concerned with two subjects, time and the idea of time. Hume accepts the ordinary distinction between thé two. Time and our idea of time are separate realities, the former being a part of the world independent of us and the latter being a part of the content of our consciousness. I shall observe this distinction, beginning with an account of what Hume means by time and following that with an explanation of his theory of the origin and nature of the idea of time. After finishing these two expository sections I shall devote 206 the remainder of the paper to a critical examination of Hume's views on both subjects, ending with a suggestion about a possible alternative route he might have followed in his argument about time and the idea of time in Part II. A final preliminary point: Although Hume devotes most of his attention to space in Part II, he makes it clear that, because space and time (as well as our ideas of them) are analogous to each other in certain vital respects, his views concerning the former can easily be transferred and applied to the latter. 1. Time Hume states or implies several things about the nature of time in Part II. (1)He equates time with duration, treating the two terms as equivalent throughout his discussion. (2)Time is an objective reality, or aspect of the external world. This interpretation may be questioned because Hume never asserts an objectivistic view of time unequivocally and in certain passages writes in a way that could be interpreted as implying that time is a characteristic of our conscious experience. "As 'tis from the disposition of visible and tangible objects we receive the idea of space, so from the succession of ideas and impressions we form the idea of time..." (T 35). But later he writes: "...time is nothing but the manner, in which some real objects exist..." (T 64). Also, in the titles of his first two sections he makes a clear distinction, labelling Section I "Of the infinite divisibility of our ideas of space and time" and Section II "Of the infinite divisibility of space and time." Since, in Section II, it is apparent that he is talking about space as a part 207 of the external world, the natural inference is that he is talking about time in the same way, as, for example, when he writes, "The infinite divisibility of space implies that of time, as is evident from the nature of motion" (T 31). (3)Time is not infinitely divisible but is made up of parts Hume calls 'moments' (T 31). These moments are the 'building blocks' of time and are ultimate and indivisible. They are analogous to the ultimate, indivisible parts of space, which Hume labels 'mathematical points' (T 40). (4)The moments of time are not co-existent but successive. In this respect time differs from space. "'Tis also evident, that these parts [of... (shrink)

Although far from unanimous, there seems to be a general consensus that neither mind nor brain can be reduced without remainder to the other. This essay argues that indeed both mind and brain need to be included in a nonreductionistic way in any genuinely integral theory of consciousness. In order to facilitate such integration, this essay presents the results of an extensive cross-cultural literature search on the "mind" side of the equation, suggesting that the mental phenomena that need (...) to be considered in any integral theory include developmental levels or waves of consciousness, developmental lines or streams of consciousness, states of consciousness, and the self . A "master template" of these various phenomena, culled from over one-hundred psychological systems East and West, is presented. It is suggested that this master template represents a general summary of the "mind" side of the brain-mind integration. The essay concludes with reflections on the "hard problem," or how the mind-side can be integrated with the brain-side to generate a more integral theory of consciousness. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Motherhood According to KristevaOn Time and Matter in Plato and KristevaFanny SöderbäckThe state of the maternal has been disputed among feminists for quite some time. Julia Kristeva, whose work will be my focus of attention here, has been criticized for her emphasis on the maternal, particularly with regards to her alleged equation of maternity with femininity. Critics have suggested that such equation risks reducing woman to the (...) biological function of motherhood. Judith Butler, to give an example to which I will return at length, speaks of a “compulsory obligation on women’s bodies to reproduce” (Butler 1999, 115; I will refer to this text as GT for the remainder of this essay). Kristeva herself has noted that “it seems... difficult to speak today of maternity without being accused of normativism, read: of regression” (Kristeva 2003, 207).I will argue that Kristeva by no means reduces woman to the function of motherhood. Rather, she returns to the maternal body at least in part to free woman from this very reduction. By bringing the mother out of the shadows, she provides women with a past (a genealogy of their own, a community of women, a history hitherto repressed) and, simultaneously, with a future (in the sense of liberating them from predefined roles and positions—from motherhood as the only form of subjectivity available to them). It is exactly the future that is at stake when Kristeva speaks of the maternal, and more specifically, it is the possibility of temporal change that depends on it. The maternal body to which she urges us to return must, as I see it, be understood qua temporalization : that to which we return is temporal, moving, displacing, renewing. The return is neither nostalgic nor aimed at preserving some essential notion of motherhood—it makes possible [End Page 65] new beginnings, allowing for a future pregnant with change and transformation. Butler ends her critique of Kristeva with the following remark—one that is meant to describe what would happen if we stopped focusing on the mother in the way Kristeva has done hitherto: “The culturally constructed body will then be liberated, neither to its ‘natural’ past, nor to its original pleasures, but to an open future of cultural possibilities” (GT, 119). I will attempt to show that these words in fact capture Kristeva’s own project, that such “open future” is exactly what she is aiming at through her continuous return to the maternal body.The implication of this retrieval of the maternal is twofold: First, it situates Kristeva within a materialist tradition and allows her to articulate and inscribe a morphological-phenomenological legacy of embodiment contra merely constructionist or discursive narratives.1 Second, it gives her ground to rearticulate time as inseparable from space and thus to challenge and overcome the deep-rooted tradition that divides time and space alongside a mind-body dualism. Surprisingly, perhaps, she establishes this ground by returning to a thinker who for many feminist scholars is the example par excellence of the very dualism that is put into question: Plato. This essay aims at carefully tracing Kristeva’s engagement with Plato, and I will argue that the breakdown of the distinction between time and space is to be found at the core of his writing. If, as I will argue here, the maternal body to which Kristeva returns must be understood not only as corporeal but also as a temporal principle, then we are forced to think through the intimate relation between temporality and materiality in ways that will come to challenge and renew the very materialist tradition that Kristeva herself most often is understood to represent.Kristeva’s earliest thematization of the maternal appears in her doctoral dissertation, Revolution in Poetic Language. It is here that she first articulates her notion of the semiotic chora, associating it with the maternal body and early heterogeneous drives.2 Kristeva herself picks up the Greek term chora from Plato’s Timaeus; a dialogue that more than anything deals with the question of beginnings, as it narrates the story of how the cosmos and its living creatures were created. I will turn both to the Platonic text and to... (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)

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)

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

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)

This paper provides a philosophical analysis of the Price equation and its role in evolutionary theory. Traditional models in population genetics postulate simplifying assumptions in order to make the models mathematically tractable. On the contrary, the Price equation implies a very specific way of theorizing, starting with assumptions that we think are true and then deriving from them the mathematical rules of the system. I argue that the Price equation is a generalization-sketch, whose main purpose is to (...) provide a unifying framework for researchers, helping them to develop specific models. The Price equation plays this role because, like other scientific principles, shows features as abstractness, unification and invariance. By underwriting this special role for the Price equation some recent disputes about it could be diverted. (shrink)

Recent accounts of actual causation are stated in terms of extended causal models. These extended causal models contain two elements representing two seemingly distinct modalities. The first element are structural equations which represent the or mechanisms of the model, just as ordinary causal models do. The second element are ranking functions which represent normality or typicality. The aim of this paper is to show that these two modalities can be unified. I do so by formulating two constraints under which extended (...) causal models with their two modalities can be subsumed under so called which contain just one modality. These two constraints will be formally precise versions of Lewissystem of weights or priorities” governing overall similarity between possible worlds. (shrink)

We introduce and study (weakly) semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.

Hall [(2007), Philosophical Studies, 132, 109–136] offers a critique of structural equations accounts of actual causation, and then offers a new theory of his own. In this paper, I respond to Hall’s critique, and present some counterexamples to his new theory. These counterexamples are then diagnosed.

We study the relative strength of the two axioms Every Pell equation has a nontrivial solution Exponentiation is total over weak fragments, and we show they are equivalent over IE1. We then define the graph of the exponential function using only existentially bounded quantifiers in the language of arithmetic expanded with the symbol #, where # = x[log2y]. We prove the recursion laws of exponentiation in the corresponding fragment.

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.

A logic is said to admit an equational completeness theorem when it can be interpreted into the equational consequence relative to some class of algebras. We characterize logics admitting an equational completeness theorem that are either locally tabular or have some tautology. In particular, it is shown that a protoalgebraic logic admits an equational completeness theorem precisely when it has two distinct logically equivalent formulas. While the problem of determining whether a logic admits an equational completeness theorem is shown to (...) be decidable both for logics presented by a finite set of finite matrices and for locally tabular logics presented by a finite Hilbert calculus, it becomes undecidable for arbitrary logics presented by finite Hilbert calculi. (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 ...

We consider the Dirac equation in 3+1 dimensions with spherical symmetry and coupling to 1/r singular vector potential. An approximate analytic solution for all angular momenta is obtained. The approximation is made for the 1/r orbital term in the Dirac equation itself not for the traditional and more singular 1/r 2 term in the resulting second order differential equation. Consequently, the validity of the solution is for a wider energy spectrum. As examples, we consider the Hulthén and (...) Eckart potentials. (shrink)

Locus equations contain an economical set of hidden (i.e., not directly observable in the data) parameters of speech that provide an elegant way of characterizing the ubiquitous context-dependent behaviors exhibited in speech acoustics. These hidden parameters can be effectively exploited to constrain the huge set of context-dependent speech model parameters currently in use in modern, mainstream speech recognition technology.

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.

It has been known for long time that most of the existing cosmology models have singularity problem. Cosmological singularity has been a consequence of excessive symmetry of flow, such as “Hubble’s law”. More realistic one is suggested, based on Newtonian cosmology model but here we include the vertical-rotational effect of the whole Universe. We review a Riccati-type equation obtained by Nurgaliev, and solve the equation numerically with Mathematica. It is our hope that the new proposed method can be (...) verified with observation data. (shrink)

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...) century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.

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)

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)

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 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)

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)

There exist two conjectures for constraint satisfaction problems of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities satisfied by its polymorphisms clone, together with the natural uniformity on (...) it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core. (shrink)

We consider algebras on binary relations with two main operators: relational composition and dynamic negation. Relational composition has its standard interpretation, while dynamic negation is an operator familiar to students of Dynamic Predicate Logic (DPL) (Groenendijk and Stokhof, 1991): given a relation R its dynamic negation R is a test that contains precisely those pairs (s,s) for which s is not in the domain of R. These two operators comprise precisely the propositional part of DPL.This paper contains a finite equational (...) axiomatization for these dynamic relation algebras. The completenessresult uses techniques from modal logic. We also lookat the variety generated by the class of dynamic relation algebras and note that there exist nonrepresentable algebras in this variety, ones which cannot be construedas spaces of relations. These results are also proved for an extension to a signature containing atomic tests and union. (shrink)

Given a positive universal formula in the language of residuated lattices, we construct a recursive basis of equations for a variety, such that a subdirectly irreducible residuated lattice is in the variety exactly when it satisfies the positive universal formula. We use this correspondence to prove, among other things, that the join of two finitely based varieties of commutative residuated lattices is also finitely based. This implies that the intersection of two finitely axiomatized substructural logics over FL + is also (...) finitely axiomatized. Finally, we give examples of cases where the join of two varieties is their Cartesian product. (shrink)

The Einstein equations can be written as Fierz-Pauli equations with self-interaction, $W\gamma _{ik} = - G_{ik} + \tfrac{1}{2}g_{ik} g^{mn} G_{mn} - k(T_{ik} - \tfrac{1}{2}g_{ik} g^{mn} T_{mn} )$ together with the covariant Hilbert-gauge condition, $(\gamma _i^h - \tfrac{1}{2}\delta _i^k g^{mn} \gamma _{mn} )_{;k} = 0$ where W denotes the covariant wave operator and G ik the Einstein tensor of the metric g ik collecting all nonlinear terms of Einstein's equations. As is known, there do not, however, exist plane-wave solutions γ ik(z)with (...) g ik Z,i Z,k=0of these equations such that what is essential to the introduction of gravitons is not satisfied in general relativity. This nonexistence corresponds with the uncertainty relation,Δp(Δg*)2(Δx)3≥h hG/ c 3 concerning the total nonlinear gravitational field g *ik =g k +γ k. (shrink)