We prove that all finitely axiomatizable tense logics with temporal operators for ‘always in the future’ and ‘always in the past’ and determined by linear fows time are coNP-complete. It follows, for example, that all tense logics containing a density axiom of the form ■n+1F p → nF p, for some n ≥ 0, are coNP-complete. Additionally, we prove coNP-completeness of all ∩-irreducible tense logics. As these classes of tense logics contain many Kripke incomplete bimodal logics, we obtain many (...) natural examples of Kripke incomplete normal bimodal logics which are nevertheless coNP-complete. (shrink)

A finitely alternative normal tense logic \ is a normal tense logic characterized by frames in which every point has at most n future alternatives and m past alternatives. The structure of the lattice \\) is described. There are \ logics in \\) without the finite model property, and only one pretabular logic in \\). There are \ logics in \\) which are not finitely axiomatizable. For \, there are \ logics in \\) without the FMP, and infinitely (...) many pretabular extensions of \. (shrink)

Suppose one accepts the argument that past infinity is not acceptable. This does not eliminate the possibility that the beginning of time is not equivalent across objects. Along with breakdown of absolute simultaneity of events in relativity, there may even be no agreement on whether an event existed. There may be no consistent way to totally order events. In such a case, despite every object, conscious or not, having finite lifetime, there may be no single point called “the (...) beginning,” and the universe stays as it is without requiring a cause of existence. (shrink)

The view that chances are relative frequencies of occurrence within actual, finite reference classes has long been written off. I argue that it ought to be reconsidered. Focusing on non-deterministic chance, I defend a version of finite frequentism in which reference classmates are required to have qualitatively identical pasts. While my analysis can evade or resist several standard objections, it has a counterintuitive consequence: non-trivial chances entail the existence of past light cones that are perfect intrinsic duplicates. (...) In mitigation, I argue that our scientific knowledge is consistent with the hypothesis that there are many such duplicates in the actual world. Moreover, my analysis has some striking advantages: it is simple, it is metaphysically undemanding, and it makes possible a satisfying explanation of the chance–credence connection. 1 Introduction2 Target3 Sketch and Skirmish4 Articulation5 Standard Worries5.1 Frequency tolerance5.2 Leibniz’s dictum5.3 Single case chance5.4 Missing values5.5 Explanation5.6 Counterfactual chances6 Chance and Credence6.1 An indefeasible indifference intuition6.2 Articulating the credence principle6.3 Appraising the credence principle7 Confirmation8 Laws9 Summing Up. (shrink)

What are the assumptions and tasks hidden in contemporary calls to "overcome" the metaphysical tradition? Reflecting upon the internal contradictions of the notions of "tradition" and "finiteness," Dennis J. Schmidt offers novel insights into how philosophy must relate to its traditions if it is to retain a vital sense of the plurality of "edges" that constitute its finiteness. He does this through a close examination of issues found in the work of Hegel and Heidegger, two philosophers who made the ideas (...) of both tradition and finiteness the center of their concern.Schmidt begins by asking how Heidegger can claim to have destroyed metaphysics despite Hegel's claim to have perfected its possibilities. Systematically following the development of Heidegger's critique of Hegel, Schmidt generates a dialogue between them. The topic of that dialogue is the nature of finiteness as it is articulated in time, nothing, the dialectical and hermeneutical circles, and in the notions of experience, work, technology, history, and preSocratic thought.Beginning with Heidegger's critique of Hegel in Being and Time, Schmidt's strategy is to disclose the complexities of philosophical discourse about the finite by drawing out the proximities between Hegel and Heidegger. The dialogue that results presents novel portraits of both philosophers. It also reveals that Heidegger's early, unacknowledged failure to separate himself from the Hegelian dialectic is the motive behind many of the turns and decisions of his later career.In concluding, Schmidt offers an interpretation of the wider significance of the results of that dialogue, and connects his study to other contemporary discussions of postmodernism. He expands upon the idea of the plurality of edges opened by finiteness, arguing that philosophy only understands its own past and future once it recognizes the meaning of its own finiteness.Dennis J. Schmidt is Associate Professor of Philosophy at the State University of New York at Binghamton. The Ubiquity of the Finite is included in the series Studies in Contemporary German Social Thought, edited by Thomas McCarthy. (shrink)

We continue the study of adequate sets which we began in (Krueger in Forcing with adequate sets of models as side conditions) by introducing the idea of a strongly adequate set, which has an additional requirement on the overlap of two models past their comparison point. We present a forcing poset for adding a club to a fat stationary subset of ω 2 with finite conditions, thereby showing that a version of the forcing posets of Friedman (Set theory: (...) Centre de Recerca Matemàtica, Barcelona, 2003–2004, Trends in Mathematics. Birkhäuser Verlag, 2006) and Mitchell (Trans Am Math Soc 361(2):561601, 2009) for adding a club on ω 2 can be developed in the context of adequate sets. (shrink)

We define a new type of two player game occurring on a tree. The tree may have no root and may have arbitrary degrees of nodes. These games extend the class of games considered by Gurevich-Harrington in [5]. We prove that in the game one of the players has a winning strategy which depends on finite bounded information about the past part of a play and on future of each play that is isomorphism types of tree nodes. This (...) result extends further the Gurevich-Harrington determinacy theorem from [5]. (shrink)

Discussions on indeterminism in physics focus on the possibility of an open future, i.e. the possibility of having potential alternative future events, the realisation of one of which is not fully determined by the present state of affairs. Yet, can indeterminism affect also the past, making it open as well? We show that by upholding principles of finiteness of information one can entail such a possibility. We provide a toy model that shows how the past could be fundamentally (...) indeterminate, while also explaining the intuitive (and observed) asymmetry between the past—which can be remembered, at least partially—and the future—which is impossible to fully predict. (shrink)

We start by considering the Alternate Strike (AS) scheme, a real-life arbitration scheme where two parties select an arbitrator by alternately crossing off at each round one name from a given panel of arbitrators. We find out that the AS scheme is not invariant to “bad” alternatives. We then consider another alternating-move scheme, the Voting by Alternating Offers and Vetoes (VAOV) scheme, which is invariant to bad alternatives. We fully characterize the subgame perfect equilibrium outcome sets of these above two (...) schemes in terms of the rankings of the parties over the alternatives only. We also identify some of the typical equilibria of these above two schemes. We then analyze two additional alternating-move schemes in which players’ current proposals have to either honor or enhance their previous proposals. We show that the first scheme’s equilibrium outcome set coincides with that of the AS scheme, and the equilibrium outcome set of the second scheme coincides with that of the VAOV scheme. Finally, it turns out that all schemes’ equilibrium outcome sets converge to the Equal Area solution’s outcome of cooperative bargaining problem, if the alternatives are distributed uniformly over the comprehensive utility possibility set and as the number of alternatives tends to infinity. Journal of Economic Literature Classification Number: C72. (shrink)

On the rise over the past 20 years has been ‘moderate supernaturalism’, the view that while a meaningful life is possible in a world without God or a soul, a much greater meaning would be possible only in a world with them. William Lane Craig can be read as providing an important argument for a version of this view, according to which only with God and a soul could our lives have an eternal, as opposed to temporally limited, significance, (...) by virtue of our moral choices then making an ultimate difference. I present two major objections to this position. On the one hand, I contend that if God existed and we had souls that lived forever, then, in fact, all our lives would turn out the same. On the other hand, I maintain that, if this objection is wrong, so that our moral choices would indeed make an ultimate difference and thereby confer an eternal significance on our lives (only) in a supernatural realm, then Craig could not capture the view, aptly held by moderate supernaturalists, that a meaningful life is possible in a purely natural world. An eternal significance would be ‘too big’, reducing any meaning possible during an earthly life to nothing by comparison. I conclude that moderate supernaturalists would be wise to avoid appealing to eternal (or infinite) meaning when spelling out the way God and a soul could alone impart a great meaning to our lives; some other notion of greatness should be considered, perhaps one involving a temporary afterlife. (shrink)

The aim of this article is to reveal with an overall approach, how the psycho-social background, starting from woman image in first periods and reach modern day, is embraced by outstanding theorists of modern psychology, and also how these collected works are reflected in their definitions of woman. If it is considered that woman has been discussed with reflections against and not from primary sources throughout history, it can be seen that the most essential roots of woman narrations can be (...) found in oral culture and the parts of written texts are made over symbol, metaphor, proposition and story. However myths (stories) that take place in oral and partly written culture about primitive man, are sacred tales, they will also present data regarding human image. Therefore with a limited effort of human being to understand the infinite, it can be understood what human being think, feel and how they interpret rather than gods/goddesses ontology. From this point of view, this article that consists of two parts, first of all will mention especially about perception of Goddess in those reflected to image of God, maintaining its efficiency in conscious or unconscious as a system of symbols intrinsic to human nature and cultural code background and then the woman image will be roughly discussed with a descriptive style over the world of mythology, psychology and faith. In the second part, it will be examined in detail how all the written and oral information about understanding woman by modern anthropologists are interpreted with the perspective of modern psychology specific to theorists such as Freud, Jung and Fromm. Eventually, it will be emphasized that past and future are integrated with information, experience and feelings with an active relationship; perception and approach of woman have stayed up to date in time continually; mythology, psychology and religion are important factors within this matter.Summary: Human being has also used historical, temporal and spatial attributions for God. Infinite human being has expressed their thoughts about the finite God by analogy. Despite the dominance of male gender in the images of God in these analogies which are the products of human experience, female Gods that is to say Goddesses are not few. The matter of how the image of goddess come to the fore in a distinctly male-dominant society is a noteworthy matter. The narration of Earth Mother over female symbol in myths in which the harmony is constantly secured within the inner and exterior world and mention about living in harmony with the universe is an important data in order to understand female characteristics attributed to God. Human being has also used historical, temporal and spatial attributions for God. Infinite human being has expressed their thoughts about the finite God by analogy.The woman subject is influenced by transferred life experience within the historical process, and it is an undeniable fact that ancient “woman perception” has reflections to the present day. Within the history of humanity, striking definitions about woman can be seen in sacred statements in symbol language. Therefore, it is proper to examine primarily the image of sacred and then examine female meaning that is charged on that image. The aim of this study can be summed up with two themes: a) try to understand the general framework of reflections of the present image of woman, style of narration and comprehension in psychological, sociological, and religious terms by getting help from myths which mention about ancient image of God, although there is centuries old difference between those stories and us, b) reveal the image of woman in Freud, Jung, and Fromm’s approach which establishes a bond between mythology that is a system of symbols special to human nature and human psychology and discuss this subject by using psychology of religion.When reviewed ancient Far East and Middle East myths and also Ancient Greek mythology, it can be seen that gods are not cloistered supernatural beings who do not have abstract personalities and also do not lead a wholly metaphysic life. The crucial issue here is; the reality that Gods and Goddesses are shown as a model to both man and woman. Psychologists who examine religion in terms of psychology state that first outcomes about the image of God come up not with behavior but with emotion. The attributions of gender, related to the emotion in question are cited during the transfer of those emotions as well. Therefore; philosophers, culture and religion historians, theologians, anthropologists, archaeologists, psychologists, and sociologists have contributed to this transfer when they discuss the cult of God or Goddess throughout the history. It is interesting that the usage of the term of God maintains while the usage of the term of Goddess decreases. Civilization historians claim that the appearance of divine religions particularly quickens the course of transition from goddess to god. According to them, during this period in which there is a transfer from polytheist image of God to monotheist image of God, the quantitative change in the perception of God comes with a qualitative change. According to Fromm, during this power gathering period, there has been a transfer from mother and feminine (woman) centered religion to father and masculine (man) centered religious experience/ God image. According to him, in the second stage of humanity development, “the children of Earth Mother turn into the children of divine father”, there is a transition from unconditional love of mother to authoritarian sympathy of father, from an image of supplemental and surrounding Goddess to authoritarian image of God who makes requests by his nature, lays down principles and laws, and supports the power and search for a successor to deliver the power.The perception of women who led to Prophet Adam deviated from the truth and expelled from heaven is spread around especially the regions of one-God religions. This has strengthened the idea that divine religions have a negative view towards women. Including Islam, the reason of all divine religions’ encountering with claims that they have a negative approach against woman stem from applying to that religions’ human resources rather than essential religious sources which are existing or lost earliest forms.Oedipus complex is an important thesis of Freud which explains the development of religion and morals; establish the base of his psychology, and in fact, important in terms of his making connection with difference of kinds and flow or non-flow of request and needs while explaining human behaviors. According to Freud who points to sexuality and aggression which are the most powerful two instinct in the biology of male or female; the first three or five years of a newly born human- this is the period in which the basic part of personality is formed- the definition of self is extremely influenced by his/her gender (in both biological and sociocultural terms). Freud who put forward father-son conflict in the struggle to survive between Zeus and his sons in Moses and Monotheism (1998c) and Totem and Taboo (1998a), makes an explanation about the origin of religion and humanity over two male characters. Jung pays attention to goddess image as much as the image of god and do not approach this situation only as a polytheism or sociocultural explanation or childish appearances of a primitive mind. He accepts goddesses as a reflection of archetypes in human. Male has a feminine side, female has a masculine side, and a unity occurs when both complete each other. According to Fromm, a taxonomy referring to woman and man is primarily a sociology-based approach rather than a biology-based one. Fromm (1995) thinks that the whole depiction shows individuals’ own desire and needs, that is to say, their psychology rather than a theology. Transition from mother (woman) centered religion to father (man) centered religious experience and God image is essentially one of the most important breaking/inversion points of human being, not humanity. As a result, it can be said that it is an important point to clearly understand the story of mankind to examine that intense freshness at hand and centeredness of quantitative and qualitative changes of divine or God image of ancient societies come down after psychological, sociological, religious, economic, political, and cultural changes. (shrink)

This paper offers a critical assessment of the Successive Addition Argument (SAA) in support of past finitism, i.e., the thesis that the past of the universe is finite in duration. This old philosophical argument, re-popularized by William Lane Craig in modern times, contends that the universe’s past cannot be infinite because an infinite series cannot be formed by successive addition. I first address a recently popular objection to the argument, namely the Zeno Objection, showing that it (...) can be easily dismissed once each addition is taken to have the same duration. Nevertheless, I contend that the _onus_ of the proof lies on those who propose the SAA, and that their main argumentative strategies fail. Indeed, many of their arguments are based on the supposedly uncontroversial claim that one cannot traverse the infinite by starting somewhere. I argue that a complete traversal of the infinite, with a beginning infinitely far from its end, is logically and metaphysically possible. Other popular arguments against traversed infinities are based on thought experiments such as the backward counter or the Tristram Shandy thought experiments. I argue that, once infinitely far beginnings are granted, none of the arguments based on such thought experiments prove effective, so that the SAA must be rejected. (shrink)

When "Finite and Infinite Goods" was published in 1999, it took its place as one of the few major statements of a broadly Augustinian ethical philosophy of the past century. By "broadly Augustinian" I refer to the disposition to combine a Platonic emphasis on a transcendent source of value with a traditionally theistic emphasis on the value-creating capacities of absolute will. In the form that this disposition takes with Robert Merrihew Adams, it is the resemblance between divine and (...) a finite excellence that makes the finite excellence objectively of value, and it is the correspondence of an obligation to a divine command that makes the obligation objectively obligatory. I look closely at the complexity of this ethical division of labor--between the good and the right--mainly as it appears in the context of "Finite and Infinite Goods", but also with attention to the broader corpus of Adams's writings, particularly his work on Leibniz and the essays of his that have been gathered together in "The Virtue of Faith". I argue that there is a creative tension in his work between his desire to secure an objective basis for ethics and his affirmation of the value of grace, a love that is not proportioned to the excellence of its object. This tension, I further argue, ought to be resolved in the direction of grace. (shrink)

Starting with the emphasis that Levinas puts on the role of otherness in the constitution of subjective dimension, this paper discusses how the articulation of this process and the consequences that derive from it recall specifically Fichtean themes. Although the relation between Levinas and Fichte has not been thoroughly examined in the literature yet, it can nevertheless be shown that themes such as the “call” of the subject from the outside, from the unattainable dimension of an otherness irreducible to any (...) immanence and the factual and finite character of its correlative freedom can be understood by reference to the categories that Fichte develops in his texts on law and morals. The reference to Fichte, who already in his considerations on the Wissenschaftslehre recognizes an external Anstoß as determining the reality of the subject, will allows to elucidate the fundamental structure of Levinas’ thought. Particular attention is paid in Levinas to the belonging of otherness to an immemorial past, which in the impossibility of being traced back to the presence of consciousness finds the guarantee of its radical transcendence. Thus, another temporal dimension is configured which also in Fichte refers to an “exteriority” that cannot be assumed by the subject, but only ascertained a posteriori, hence its factual character. Through an interpretation of the fundamental meaning that the primacy of otherness over sameness has in Levinas and the attempt to reflect this relationship through the reference to similar Fichtean motifs, it becomes clearer that the basic meaning of a radical thought of otherness does not cancel the sameness of subject, but on the contrary allows to found it by referring it to its constitutive, unavoidable heteronomy. (shrink)

This essay explores a simple argument for a Ground of Being, objections to it, and limitations on it. It is nonsensical to refer to Nothing in the sense of utter absence, hence nothing can be claimed to come from Nothing. If, as it seems, the universe, or any physical ensemble containing it, is past-finite, it must be caused by an uncaused Ground. Speculative many-worlds, pocket universes and multiverses do not affect this argument, but the quantum cosmologies of Alex (...) Vilenkin, and J. B. Hartle and Stephen Hawking, which claim that the universe came from literally nothing, would. I argue that their novel project cannot work for reasons both physical (their "nothing" is actually a vacuum state governed by eternal physical laws) and methodological (physical theory cannot explain the emergence of the physical per se). Thus my argument stands. However, as David Hume showed, a posteriori arguments like mine infer a creation, and Creator, of a certain character, namely, a stochastic concept of creation and a panentheistic, partly physical Creator lacking omniscience and omnipotence. Rather than undermining the cosmological argument, as Hume intended, these limitations liberate the concept of the Ground from unnecessary problems, as Hartshorne suggested. (shrink)

William Lane Craig modified Bertrand Russell’s Tristram Shandy example in order to derive an absurdity that would demonstrate the finitude of the past. Although his initial attempt at such an argument faltered, further developments in the literature suggested that such an absurdity was indeed in the offing provided that a couple extra statements were also shown to be true. This article traces the development of a particular line of argument that arose from Craig’s Tristram Shandy example before advancing an (...) argument of its own that attempts to fill in the relevant gaps so as to yield a new argument for the finitude of the past. (shrink)

A covariant quantum mechanics for systems of finite-mass particles at finite energy follows from interpreting as Wick-Yukawa fluctuations in particle number the quantum fluctuations which are needed by Phipps to understand measurement theory and by Gyftopoulos to understand the second law of thermodynamics. The dynamical one-variable equations require as input the (N − 1)-particle transition matrices and an N-N vertex or coupling constants at three-particle vertices.

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove (...) its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included. (shrink)

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as (...) N4-lattices which correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

Over the past two decades, several consistent procedures have been designed to infer causal conclusions from observational data. We prove that if the true causal network might be an arbitrary, linear Gaussian network or a discrete Bayes network, then every unambiguous causal conclusion produced by a consistent method from non-experimental data is subject to reversal as the sample size increases any finite number of times. That result, called the causal flipping theorem, extends prior results to the effect that (...) causal discovery cannot be reliable on a given sample size. We argue that since repeated flipping of causal conclusions is unavoidable in principle for consistent methods, the best possible discovery methods are consistent methods that retract their earlier conclusions no more than necessary. A series of simulations of various methods across a wide range of sample sizes illustrates concretely both the theorem and the principle of comparing methods in terms of retractions. (shrink)

Over the past decade, sequence learning has gradually become a central paradigm through which to study implicit learning. In this chapter, we start by briefly summarizing the results obtained with different variants of the sequence learning paradigm. We distinguish three subparadigms in terms of whether the stimulus material is generated either by following a fixed and repeating sequence (e.g., Nissen & Bullemer, 1987), by relying on a complex set of rules from which one can produce several alternative deterministic sequences (...) (e.g., Lewicki, Hill & Bizot, 1988; Stadler, 1989), or by following the output of a probabilistic set of rules such as instantiated by noisy finite-state grammars (Cleeremans & McClelland, 1991; Jiménez, Mendéz & Cleeremans, 1996). Next, we focus on the processes involved in sequence representation and acquisition. We suggest that the sensitivity to the sequential structure observed in the probabilistic subparadigm can only be a result of the acquisition of a representation of the statistical constraints of the material, and that this sensitivity emerges through the operation of mechanisms that are well instantiated by connectionist models such as the Simple Recurrent Network (Elman, 1990; Cleeremans, 1993b). We present new simulation work meant to explore to what extent the model can also account for specific data obtained in a paradigmatic instance of deterministic, rule-based sequence learning task: Lewicki et al. (1988)'s situation. Finally, we report on the results of an experiment that compares learning on otherwise similar deterministic and probabilistic structures, and we show that learning of both types of structures is equivalent only under conditions that maximally hinder explicit acquisition. Taken together, these simulation and experimental data lend support to the claim that implicit learning in all three sequence learning subparadigms can amount to a form of statistical sequence learning. They also suggest that distinguishing among several theories of sequence representation and acquisition may require us to analize the data in great detail. Hopefully, however, some truth can be found in such details.. (shrink)

Introduction. During the past two decades philosophers of psychology have considered a large variety of computational models for philosophy of mind and more recently for cognitive science. Among the suggested models are computer programs, Turing machines, pushdown automata, linear bounded automata, finite state automata and sequential machines. Many philosophers have found finite state automata models to be the most appealing, for various reasons, although there has been no shortage of defenders of programs and Turing machines. A paper (...) by Arthur Burks convinced me long ago that “all natural human functions” are, or can be fruitfully modeled to be, finite state automata with output. Further work in the field has reinforced this conviction. There is room, however, for the use of any of the above models in philosophy of mind and in the ongoing development of cognitive science. (shrink)

Human consciousness is a finite entity; therefore, memory must be selective: remembering must also mean being able to forget. In 2006, James McGaugh documented the first known case of hyperthymesia—a syndrome that affects a very limited percentage of the world population. The main symptoms of this mental disorder involve the concept of memory stuck in the past, where the individual is imprisoned by his or her own memories, and any projection towards the future is precluded. The inevitable change (...) produced by the flowing of time naturally helps people to find reasons to live and to search for a sense of being in the world. The present study puts forward a phenomenological approach to hyperthymesia in the quest for a natural, healthy form of oblivion, or the ability to forget. Through existential analysis, it could be possible for the individual to recover the natural and necessary structure of Dasein. (shrink)

In the past four decades, the notion of quantum polynomial-time computability has been mathematically modeled by quantum Turing machines as well as quantum circuits. This paper seeks the third model, which is a quantum analogue of the schematic definition of recursive functions. For quantum functions mapping finite-dimensional Hilbert spaces to themselves, we present such a schematic definition, composed of a small set of initial quantum functions and a few construction rules that dictate how to build a new quantum (...) function from the existing ones. We prove that our schematic definition precisely characterizes all functions that can be computable with high success probabilities on well-formed quantum Turing machines in polynomial time, or equivalently uniform families of polynomial-size quantum circuits. Our new, schematic definition is quite simple and intuitive and, more importantly, it avoids the cumbersome introduction of the well-formedness condition imposed on a quantum Turing machine model as well as of the uniformity condition necessary for a quantum circuit model. Our new approach can further open a door to the descriptional complexity of quantum functions, to the theory of higher-type quantum functionals, to the development of new first-order theories for quantum computing, and to the designing of programming languages for real-life quantum computer. (shrink)

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as (...) N4-lattices which correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth (...) Infinitesimal Analysis, as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

Locality is a key concept not only in linguistic theorizing, but in explaining pattern of acquisition and patterns of recovery in garden path sentences, as well. If syntax relates sound and meaning over an infinite domain, syntactic dependencies and operations must be restricted in such a way to apply over limited, finite domains in order to be detectable at all. The theory of what these finite domains are and how they relate to the fundamentally unbounded nature of syntax (...) is the theory of locality. The papers in this collection all deal with the concept of locality in syntactic theory, and, more specifically, describe and analyze the various contributions Luigi Rizzi has made to this area over the past three and a half decades. The authors are all eminent linguists in generative syntax who have collaborated with Rizzi closely, and in eleven chapters, they explore locality in both pure syntax and psycholinguistics. This collection is essential reading for students and scholars of linguistic theory, generative syntax, and comparative syntax. (shrink)

Early Vedic possesses a chameleon-like verb form called the injunctive, whose uses partly overlap with, and alternate with, those of the subjunctive, optative and imperative moods, and with the past and present tenses. Being morphologically tenseless and moodless, the injunctive has attracted interest from a comparative Indo-European perspective because it appears to be an archaic layer of the finite verb morphology. Its place and function in the verb system, however, remains disputed. In Kiparsky 1968 I argued that it (...) is tenseless and moodless not only morphologically but also functionally, and that injunctive forms acquire modal and temporal interpretations only contextually. The injunctive’s only intrinsic grammatical features are aspect, voice and person/number. This paper provides new evidence for that view (section 1), and goes on to argue that such underspecified forms in paradigms support morpheme-based theories of morphology over realizational theories such as Paradigm Function Morphology (section 2), and that the rise and loss of the injunctive is connected to other changes in the pre- and post-Vedic aspect, tense, and mood system (section 3). (shrink)

In this paper, I attempt to consider Jewish philosophy in opposition to the anti-ocularcentrism that defined the German Jewish philosophical tradition after Kant, namely the idea that Judaism—or at least its philosophical expression in Maimonidean philosophy—is aniconic and cognitively abstract. I do so by attempting to rethink the epistemic-veridical place of the imagination and visual experience in the Guide of the Perplexed . Once the imagination has been disciplined by reason, is there any cognitive status to an image or sound (...) that the eye or the ear perceives, and to that mental faculty that combines and recombines such impressions? Is the sight or sound of revelation a hallucination or just a mere figure of speech? Does it bear any relation to a spiritual reality external to the human mind and finite physical existence? To address these questions I explore the visual images, both iconic and aniconic-abstract, that distinguish the Guide . There is no getting past the visual imagination, although I am not sure Maimonides would have recognized it as such. Even when he leaves behind figurative visual cues such as the false image-work of the undisciplined imagination or the appearance of angels and images of God found in lower grades of prophecy, he turns to another visual register, namely the “abstract art“ of pure, dazzling light. In regard to these questions, Maimonides was more Greek than German, ascribing, cautiously, penultimate cognitive status to the visual imagination. (shrink)

continent. 1.2 (2011): 70-75. cartography of ghosts . . . And as a way to talk . . . of temporality the topography of imagination, this body whose dirty entry into the articulation of history as rapturous becoming & unbecoming, greeted with violence, i take permission to extend this grace —Akilah Oliver from “An Arriving Guard of Angels Thusly Coming To Greet” Our disappearance is already here. —Jacques Derrida, 117 I wrestled with death as a threshold, an aporia, a bandit, (...) a part of life. —Akilah Oliver Moraine in geological lingo is that which is left behind. Moraine- a euphemism for the de-stabilizing referent of the writer-ly body as a “troubled and troubling landscape marked by cultural and historical signifiers, the body as flesh memory [...] the body as transitory” (Oliver, Author Statement). Moraine— a geological metaphor of the poet as a holder of memory, as an accumulation of rocks and debris carried along the edge, terminal, dropped at the foot of language (in language). “Flesh Memory” according to Akilah Oliver is "that which my body recalls [...] everything has to do with the task of remembrance and its narrative reinvention [...] I was always translating an idea of the world as it presented itself at any given time. To write was a choice about how to be seen, how to enter the world as translator, actor, participant, in the dialogues that apparently made the real 'real'" (Levitsky). Flesh. Memory. The stuff some poems are made from. The stuff that gets abandoned, gleaned, and picked up by more flesh and memory. "My body, my life has always felt like a kaleidoscopic rip in the dominant fabric [...] has always been a dialogue with the impossible and the apparent” (Levitsky). The impossible-body or poet's body anticipates and performs (through language) an irretrievable death. IN APORIA I realized everything I must have been doing must have been Death. It was Christmas or Labor Day—a holiday—and every time you turned on the radio they said something like ‘four million’ or ‘going to die’.” — Andy Warhol I’m trying on egos, [a justification for the planet’s continuance]. Oh hello transgressor, you’ve come to collect utilitarian debts, humbling narrative space. Give me condition and wheatgrass, I his body disintegrating. I his body is ossification. Death my habit radius, yeah yeah. I his body can’t refuse this summons. I can’t get out this fucking room. Tell me something different about torture dear Trickster. Tell me about the lightness my mother told me to pick the one i love the best how it signals everything I ever wish to believe true just holy on my ship. I jump all over this house. this is it [what I thought is thought only, nothing more deceptive than]: I his body keeps thinking someone will come along, touch me. As like human or lima bean. I’m cradling you to my breast, you are looking out. A little wooden lion you & Peter carve on Bluff Street is quieting across your cheekbone. Not at all like the kind of terror found in sleep, on trembling grounds. It is yesterday now. I have not had a chance to dance in this century. Tonight I shall kill someone, a condition to remember Sunday morning. To think of lives as repetitions [rather than singular serial incarnations]. To understand your death is as exacerbating as trying to figure out why as schoolchildren in mid-nineteen-sixties Southern California we performed reflexive motions: cutting out lace snowflakes, reading Dick and Jane search for their missing mittens, imagining snow. Disintegrat ing . The -ing gerund catapults from the non-finite verb into past, present, future. The -ing as a tail pinned to death, a dog spinning to bite and never fully reaching itself, always shy of the end, circumreferential; a double copulative: deathing. Possessively AO calls it “habit radius” (a virtual fetish attribute) or an inescapable death presence that “confronts us with the paradox of an unattainable object [...] through it’s being unattainable” (Agamben, 27). A flirtation or dialogue with an unknowable thing and aporia utilized as investigative instrument to engage (death) while (in Southern California) we “perform reflexive motions,” cut lace snowflakes, imagine snow, and pay rent like “yeah, yeah” what else is new. And this too, fiction. The book I wish to right. The restored fallen, heroic. Did you expect a different grace from the world? Or upon exit? I’m working on “tough.” They think I am already. All ready. Who is the dead person? Is "I'm sorry" real to a dead person? Browning grass. My hands on this table. A contentious century. A place to pay rent. Redemptive moments. Am I now the dead person? Dead person, dead person, will you partake in my persimmon feast? The body inside the body astounds, confesses sins of the funhouse. I too have admired the people of this planet. Their frilly, orderly intellects. The use they’ve made of cardamom, radiation as well. How they’ve pasteurized milk, loaned surnames to stars, captured tribes, diseases, streets, and ideas too. The living-body as archive: is it possible to experience the living-body as archive without a (kind of) death? Sifting the rubble, rummaging through hoarded debris, skin sheds, memory-napping, and re-awoken (in flesh and) on terrain. “An investigative poetics seeks to unravel staid communities of thought and grasp at what might always be just beyond reach; a poetics of inquiry that lies between language as meaning, and language as rapturous entry into the world of posited ideas and idealism”( Levitsky). Something snaps. Lights blow out prior to embarking upon an investigative poetics. It begins with a question (often a sexy aporia) that leads to openings. "Every politics of memory [...] implies an intervention of the state. It's a state that legislates and acts with regard to the nonfinite mass of materials to be stored, materials which must be collected, preserved” (Derrida & Stiegler, 62). It seems poetic investigation already contains the potentiality of an (invisible) archive if the writer is “always writing” especially when not. Here’s my stupid digital romantic inclination: the living-body (of a poet) is a self-sustaining archive of non-finite memories. But not even I really believe that. AO innovated and sculpted an investigative poetic praxis. In a conversation with poet Rachel Levitsky, poetic-voice is viewed not as a precious identifier, but as a means to think through/about form, concluding that form is linked to framing. While poetic-voice may have tendency to precede form, it also erupts as a result of framing techniques. “They are frames that hold the shape of thinking (which is also to say of imagining) [...].”7 This reminds me of my rabbit who symmetrically chewed the corners of his hutch, which makes me wonder if it’s an expression of the shape of some animal anxiety tick I won’t ever have access to. Beyond the form/frame, death is an unoriginal yet unique limit; death is a damn deathless thing. It functions as a source of poetic investigation; that thing always “just beyond reach.” And how is death not a fetish (in this case an obsessive reverence for something non-material)? “Insofar as it [death] is a presence, a fetish [...] it is in fact something concrete and tangible; but insofar as it is the presence of an absence, it is, at the same time, immaterial and intangible, because it alludes continuously beyond itself to something that can never really be possessed [...] The fetish is [...] a sign of an absence, it is not an unrepeatable unique object; on the contrary, it is something infinitely capable of substitution, without any successive incarnations ever succeeding in exhausting the nullity of which it is the symbol” (Agamben, 33). AO utilized absence (the absent body [catapulted by the death of a beloved]) as an apparatus to investigate. In the process of conversing with absence or that which is absent, the absent body is affectionately objectified, incessantly summonsed back to a place of recognition, of objects, a desire for the absent body to remain intact while exiting the structural limits of grammar and syntax by moving into chant forms “to say what cannot be said” (Levitsky). from AN ARRIVING GUARD OF ANGELS THUSLY COMING TO GREET dear oluchi- the light is blinking rapidly on the black boxy machine. your room seems bigger than before and i am still planning to read some of those robert jordan books of yours. yesterday at the used bookstore where i was browsing the mysteries to “stall reality” (they are really not mysteries at all, they just employ death as the plot mistress but are unable to grasp its mystery at all)—well the point is, things were calm down here for a while and the world was little. i want to be big like you. or i want you not vast, not dead, not gone, but human small and here. i am so selfish. that is what i really want. to see you again. to oil your scalp. to hear you walk in the door, say ma i’m home . give me a chance to say welcome home son. or when leaving, don’t forget your hat . what do you wear out there? i wish you could have taken your new shoes with you. i’m so proud of you. i’m sorry for the way you died. i miss you all the time. even before, i missed you. out there, one time, some different men said: “shake for me girl, i wanna be your backdoor man.” who dat you love. 5/18/03 A letter-poem in sixteen lines “dear oluchi-” is safe-housed in epistolary form. Poetic voice is rendered as internal thought meanderings, a not-so-much confession, private/(pillow?) talk in the desire to be heard/witnessed by the referent and reader with an intent to absolve. The diminutive “i” bears a relation to poet Fanny Howe’s “little g God” in that “One of the (many) things I like about little g God is that you can have a vodka tonic while you talk to little g God, sing along to Bowie’s “I’m Afraid Of Americans,” and hum Coltrane’s “A Love Supreme,” though maybe not all at the same time” (Oliver, 2009). Towards the middle of the poem AO is at a used bookstore and remarks on the funny employment of death as a ‘plot mistress’ that ‘they’ (the dubious employed mystery authors) are ‘unable to grasp’, thereby giving death a mouthpiece, a modeling job, something to do to pass the time. from THE VISIBLE UNSEEN When I first saw graffiti, I recognized in it an ugly aesthetic, a dialectics of violence, a distortion of limbs, a hieroglyph. It was only later when I read the names of the dead that I then saw the path of ghosts charted there; its narrative of loss for the visible unseen whose place in history has been fictionalized and rendered unseen under the totalizing glare of history. Inscriptions, traces, specters. Graffiti begs a public face just as ghosts require non-ghosts (humans) to sense them. The “visible unseen” is a game of hide-and-seek between public viewer and graffiti-inscriber, an ephemeral-violent aesthetic on an ephemeral-policed canvas. Graffiti-inscribers already submit to being forgotten, expect to be washed away; perhaps it’s a holy urban mandala created by gangster-type monks without Buddhism. [...] in its refusal to disappear it forces a discourse in the public imagination we are forced to see what we would rather not, to make sense of an encoded language that we cannot read on the level of meaning. it irritates, forces its agency on us, speaks outside and beyond semiotic reach. An epic font-size pervading the public’s imagination, illegible, I could just close my eyes, remain passive, drive past, abandon it beyond reach, push it further away beyond death walls. In Barcelona I watched a clean up crew wash walls with an awesome water hose but I was more intrigued by their bodies; not a distortion of limbs, not hieroglyph but also not entirely legible; the laboring body permanently erasing specters of the city, and of course they knew it was also an invitation for the ghosts to return. Graffiti is death’s little sister, is also an aporia. [...] Graffiti (fr GK -graph(os), something drawn or written, to diagram or chart) attempts to stage the impossible: to erase the essence of its own subjectivity. Graffiti is a cartography of ghosts, a mapping of elegiac rapture (the transporting of a person from one place to another, as in heaven) and rupture (the state of being broken open.) Dwelling is a fiction stasis. [...] The notion of the past as being something done with, a look-back event, inhibits the possibility of reading graffiti as rapture, as rupture. If graffiti posits history as always in the process of becoming undone. [...] Because what is the body, if not also a complex temple, an unstable site through which to negotiate subjects, materiality, economies, gods, and modes of representations? The site where we are all already belated. Graphein meaning “to write.” “Derrida says every archive makes a law, and the law of genre is its own rupture” (Bloch, 39). However, graffiti is an (non/anti)-archive of erasure due to (the politics of) washing out its subjectivity, which only adds onto (or is symptomatic of) its character. The inhibition of “reading graffiti as rapture, as rupture” is partly due to it being a “look-back” event in that it’s process involves scratching through layers to reveal previous specters underneath. Graffiti (as an ancient genre) has always been a thing of ‘becoming undone’, and therefore ‘belated and always in arrival’ (Levitsky). It’s a Dionysian activity done at night with it’s back turned toward us. "The specter [...] is of the visible, but of the invisible visible, it is the visibility of a body which is not present in flesh and blood [...] appearing for vision, to the brightness of day [...] something becomes almost visible which is visible only insofar as it is not visible in flesh and blood. It is a night visibility. As soon as there is a technology of the image, visibility brings night. It incarnates in a night body, it radiates in a night light" (Derrida & Stiegler, 115). (shrink)

ignate remote or historical past, the perfect being furthermore restricted to events not witnessed by the speaker.3 In the intervening stage of Vedic Sanskrit, the past tenses show a complex mix of temporal, aspectual, and discourse functions. On top of that, Rigvedic retains the injunctive, a chameleon-like category of underspecified finite verbs whose many uses partly overlap with those of the past tenses. The present study of the Rigvedic system is offered as a preliminary step towards (...) the reconstruction and theoretical interpretation of this aspect-to-tense trajectory. (shrink)

In _The History of the Race Idea: From Ray to Carus,_ Eric Voegelin places the rise of the race idea in the context of the development of modern philosophy. The history of the race idea, according to Voegelin, begins with the postChristian orientation toward a natural system of living forms. In the late seventeenth century, philosophy set about a new task--to oppose the devaluation of man's physical nature. By the middle of the eighteenth century the effort of philosophy was to (...) place man, with his variety of physical manifestations throughout the world, within a systemic order of nature. Voegelin perceives the problem of race as the epitome of the difficulties presented by this new theoretical approach. Part I covers the development of race theories from the English naturalist John Ray to Blumenbach and Kant. Voegelin, anticipating fairly recent genetic insights, explains that human beings must be seen as one speciesdifferent races must not be interpreted as emerging from separate species. In Part II, Voegelin discusses the evolution of the concepts of the body, the organism, and the person. The finite image of the person as a body-mind unit in which body is equal to mind in value provides the basis for Carl Gustav Carus' theory of race, the first significant racial ideology, in Voegelin's estimation. Voegelin's complex analysis levels a scathing critique at Nazi pretensions. He writes: "Compared to its classical form, the current condition of race theory is one of decay.... [T]hese men, with no eyes for the brilliance of the German spirit, want to interfere in human relations and ultimately presume to explicate the German nation to us and to the world--an undertaking with evil consequences.... [The] great thinkers of the past would have been orrified at somebody finding in himself all the traits of the Nordic race with the help of a book on anthropology and then imagining himself to be somebody special who does not have to do anything else. "Let us now take a look at contemporary race theory--we will see an image of destruction.... It is a nightmare to think that we should recognize the people whom we follow and whom we allow to come near us not by their looks, their words, and their gestures, but by their cranial index." Ultimately, Voegelin dismisses any attempt to reduce the human being--his existence, appearance, or actionsto a lower level: "Man as mind-body and historical substance cannot be 1explained' by an element that is less than man himself.". (shrink)

On the other side of the ledger there seem to be equally powerful reasons for countenancing negative events and states. The first and foremost reason is that since every true proposition about the world supposedly corresponds with some event, there must be a negative event corresponding to every true negative proposition about the world. Second, there can be no determinate reality without negative facts, since something can be a definite individual only if it has finite boundaries, which require that (...) it is not the same as everything else. Third, change requires temporal passage consisting in the shift of the present to ever later times; however, this requires that there be a past and future, which are the no-longer and the not-yet. Fourth, we seem to perceive negative things such as lacks and absences, but whatever we perceive must exist. Fifth, for those who believe in real essences or substantial natures, there are objective teleological negations consisting in a certain kind of object not realizing all of its natural functions. And, finally, it seems to be inconsistent to say that there are no negative facts, for supposedly there will be at least one negative fact consisting in there not being any negative facts. (shrink)

The cosmic singularity provides negligible evidence for creation in the finite past, and hence theism. A physical theory might have no metric or multiple metrics, so a ‘beginning’ must involve a first moment, not just finite age. Whether one dismisses singularities or takes them seriously, physics licenses no first moment. The analogy between the Big Bang and stellar gravitational collapse indicates that a Creator is required in the first case only if a Destroyer is needed in the (...) second. The need for and progress in quantum gravity and the underdetermination of theories by data make it difficult to take singularities seriously. The singularity exemplifies the sort of gap that is likely to be closed by scientific progress, obviating special divine action. The apparent irrelevance of cardinality to practices of counting infinite sets in classical field theory and Fourier analysis is noted. Introduction The Doctrine of Creation and Its Warrant Cardinality and Sizes of Infinity Modern Cosmology and Creation Tolerance or Intolerance toward Singularities? Leibniz against Incompetent Watchmaker? Induction from Earlier Theories' Breakdown? Stellar Collapse Implies Theistic Destroyer Stacking the Deck for GTR Quantum Gravity Tends to Resolve Singularities Vicious God-of-the-Gaps Character Fluctuating or Inaccessible Warrant Big Bang Cosmology Not Especially Congenial to Faith CiteULike Connotea Del.icio.us What's this? (shrink)

This paper contributes to the debate about ‘tenseless languages’ by defending a tensed analysis of a superficially tenseless language. The language investigated is St’át’imcets (Lillooet Salish). I argue that although St’át’imcets lacks overt tense morphology, every finite clause in the language possesses a phonologically covert tense morpheme; this tense morpheme restricts the reference time to being non-future. Future interpretations, as well as ‘past future’ would-readings, are obtained by the combination of covert tense with an operator analogous to Abusch’s (...) (1985) WOLL. I offer St’át’imcets-internal evidence (of a kind not previously adduced) that the WOLL-like operator is modal in nature. It follows from the analysis presented here that there are only two (probably related) differences between St’át’imcets and English in the area of tense. The first is that St’át’imcets lacks tense morphemes which are pronounced. The second is that the St’át’imcets tense morpheme is semantically underspecified compared to English ones. In each of these respects, the St’át’imcets tense morpheme displays similar properties to pronouns, which may be covert and which may fail to distinguish person, number or gender. Along the way, I point out several striking and subtle similarities in the interpretive possibilities of St’át’imcets and English. I suggest that these similarities may reveal non-accidental properties of tense systems in natural language. I conclude with discussion of the implications of the analysis for cross-linguistic variation, learnability and the possible existence of tenseless languages. (shrink)

A practical hermeneutics of time. The Possible Present unfolds from within a freely reinterpreted hermeneutic perspective and provides an original theoretical proposal on the topic of time. In dialogue especially with the philosophies of Husserl and Heidegger, but resorting also to suggestions coming from a theological background (Barth and Bonhoeffer), the work proposes a personal and original theory of time centered on a conception of the present that does not reduce temporality to a succession of mere instants. When one claims (...) that time is ungraspable, one refers neither to the past (which is rather irretrievable) nor to the future (which is rather uncertain) but to the present. The present in which we are is in fact what fades from our hands without break. The present is a decisive threshold for finite existence. It is the threshold where past and future meet and can give birth to a livable horizon of meaning. Dilating the present and giving it a meaningful chance to be is a task for philosophy. It is the attempt of giving time to time and also giving it shape, place, and space. To succeed at this task while rediscovering the sources of a narrative way of thinking that in truth it has never abandoned, philosophy must go back and turn time into the primary object of discourse, like in stories, which are precisely the attempt at disposing the temporal flow of events according to a meaning. Perone argues that in time, however, what passes is not simply decline, but rather something irreducible, an exteriority that must be said. (shrink)

Building on Alfred Schütz’s work, this essay conceptually scrutinizes virtual worlds with an aim to clarify what is at stake with the virtualization of the late modern society. The diffusion of technological artifacts, devices of communication and the Internet in particular, have transformed the life-world of essentially everyone. In the past few years our everyday life, including its livelihoods, has seen a proliferation of activities within virtual worlds, such as games and virtual social networks. We can now live and (...) experience actively in different virtual realms, as compared to being mere passive receivers in the era of television and radio. This has direct implications for what is inherently relevant for people and, in consequence, we have to take such transformation into account also in conceptual terms. This article makes a major contribution to the conceptual understanding of phenomenological sociology that due to the virtualization, we can no more equate the paramount reality as the zone of primary relevance. The paramount reality as conceived as the sensorily perceivable, physical world of concrete objects is increasingly far from being equated to that part of the world within our reach which we can immediately observe and also at least partially dominate, that is, the zone of primary relevance. It is furthermore argued that the ongoing virtualization of societies urges us to conceive of virtual worlds as transforming the chief finite province of meaning, that of the world of working, instead of seeing virtual worlds merely as other sub-universes of reality. (shrink)

In English, the present perfect, unlike future, past, and non-finite perfects, cannot be modified by so-called ‘positional’ adverbials (Comrie 1976, McCoard 1978, a.o.). This phenomenon is known as the present perfect puzzle (Klein 1992).

Summarizes Virilio's speculations about the impact that accidents will have on the planet now that we operate on one-world time. Based upon a 1996 conversation Paul Virilio had with French journalist Phillipe Petit, The Politics of the Very Worst summarizes Virilio's speculations about the impact that accidents will have on the planet now that we operate on one-world time. Virilio argues that accidents have now lost all particularity. Accidents and events can no longer be confined to markers in history like (...) Auschwitz or Hiroshima. Trajectories once had three dimensions: past, present, and future. But now, the hyper-concentration of time into "real time" reduces all trajectories to nothing. Consequently, an accident of time is bound to affect our entire being as well as the entire planet. And this is the hidden face of technical and scientific progress that Virilio is attempting to reveal, shrugging off any illusion we may have left about its alleged benefits.Globalization doesn't make the planet bigger, it signals the beginning of "the great confinement." Speed pollutes the distances of the world. After the "green ecology", we are now experiencing another, more invisible and mental, kind of pollution: the "gray ecology." Soon, Virilio suggests, we are going to experience the end of the world--not the apocalyptic end, but the world as finite. The communication revolution, the attainment of absolute speed, is the reduction of the world to a virtual city in which democracy is no longer possible. This extermination of world-space is a cataclysmic event. For the first time, history has hit a cosmological limit. (shrink)

A popular critique of the kalām cosmological argument is that one argument for its second premise illicitly assumes a finite starting point for the series of past temporal events, thereby begging the question against opponents. Rejecting this assumption, opponents say, eliminates any objections to the possibility that the past is infinitely old and undermines the IFA’s ability to support premise 2. I contend that the plausibility of this objection depends on ambiguities in extant formulations of the IFA (...) and that we may resolve these ambiguities in a way that does not presuppose a finite staring point. I also argue that this disambiguation allows us to construct an argument demonstrating that the concept of an infinite past entails a contradiction. (shrink)

This article explores the affinities between film and philosophy by returning to a shared meditation on death and the nature of time. Death has been considered the muse of philosophy and can also be considered the muse of film-philosophy. But what does it mean to say that to film-philosophise is to learn to die, or a kind of training for dying? Film is an artistic object that reminds us of death’s inevitability; it is a meditation on the transient and (...) class='Hi'>finite nature of time. Films as diverse as Mizoguchi’s Tales of Ugetsu, Resnais’s Hiroshima mon Amour, and Guzmán’s Nostalgia for the Light take an uncanny approach to the subject, expressing the paradoxical coexistence of life and death and of different temporal dimensions. This article explores the philosophical concept of the death-image and time through a Deleuzian approach to cinema, meditating on the flashback, the coexistence of the present and the past, and the emergence of a new type of Lazarean character – one who returns from the dead. The article aims to clarify not simply death’s unquestionable omnipresence in film but also cinema’s role as a contemporary version of the trope of memento mori. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Nonplaces:An Anecdoted Topography of Contemporary French TheoryBruno Bosteels (bio)In its juridical sense, a non-lieu is a judgment that suspends, annuls, or withdraws a case without bringing it to trial. It is thus a judgment that announces or enunciates that there will be no judgment as to guilt or innocence, a finding that there is no place to judge. It therefore renders justice by refusing to render it under the (...) law, which it does when it pronounces or enunciates the non-lieu.—Peggy Kamuf, "Béance"1Inside the Spatial TurnIf modernity will always be remembered as an era dominated by questions of time and history, then perhaps the steady waning of modern ideals invites us to think of the entry into something called the postmodern as a passage dominated by questions of space and geography. As Michel Foucault once famously observed in a 1967 conference paper, first published two decades ago: "Perhaps we might say that some of the ideological conflicts that animate today's polemics oppose the pious descendants of time and the willful inhabitants of space" ["Of Other Spaces" 22]. This conflict over time and space presupposes a much larger argument that is not only historical but also methodological in nature. What is at stake is both a question of the passage, or transition, from modernity to postmodernity, if that is indeed what we decide to name modernity's aftermath, and a question of the theoretical consequences that follow from giving precedence to space over time in treating this very transition. With regard to this second question, too, Foucault's work stands as exemplary insofar as he was able to show the degree to which a vital emphasis on space, geography, and territoriality [End Page 117] forces us to take leave of the modern paradigm of consciousness—typically associated with the category of time and its unfolding in the mind or spirit—in favor of a situated understanding of knowledge, subjectivity, and power. "Metaphorizing the transformations of discourse in a vocabulary of time necessarily leads to the utilisation of the model of individual consciousness with its intrinsic temporality," Foucault observes in an interview with the editors of the French journal of geography Hérodote, and he continues: "Endeavouring on the other hand to decipher discourse through the use of spatial, strategic metaphors enables one to grasp precisely the points at which discourses are transformed in, through and on the basis of relations of power" ["Questions on Geography" 69–70]. Whether real or metaphorical, a willful displacement of our categorial apparatus from time to space thus might enable one to avoid the idealist temptation inherent in a strictly discursive or textual model, by inscribing all discourses and practices in the geopolitics of power relations.My aim in the following pages is not to go over the much-discussed shift from time to space once more, even as I take advantage of several of its methodological principles along the way. Instead, I want to map out a momentous change of perspective that has been taking place over the past few decades within the parameters of the so-called spatial turn itself. In fact, if and when modernity is coming to an end, both in the sense of completing itself and of revealing its character as a finite historical entity, not only does whatever shape critical thought takes in the face of this turnabout need to be securely fastened onto specific places and spaces but, if we are to believe a growing number of authors, particularly but by no means exclusively in France, the study of art, literature, politics, philosophy, and even anthropology would also require a thorough consideration of so-called "nonplaces" as a rigorous category for critical thinking today [for a brief discussion of the use of "nonplace" in Anglo-American anthropology, including Melvin M. Webber's notion of "nonplace urban realm" from the mid-1960s, see Weiner]. In the end, these proponents of the nonplace confront us with one disarmingly simple question: how can critical thinking in the present time respond to the task of having to work through whatever lies outside of the order that is actually in place?The Exhaustion of... (shrink)

Thomas Sebeok and Noam Chomsky are the acknowledged founding fathers of two research fields which are known respectively as Biosemiotics and Biolinguistics and which have been developed in parallel during the past 50 years. Both fields claim that language has biological roots and must be studied as a natural phenomenon, thus bringing to an end the old divide between nature and culture. In addition to this common goal, there are many other important similarities between them. Their definitions of language, (...) for example, have much in common, despite the use of different terminologies. They both regard language as a faculty, or a modelling system, that appeared rapidly in the history of life and probably evolved as an exaptation from previous animal systems. Both accept that the fundamental characteristic of language is recursion, the ability to generate an unlimited number of structures from a finite set of elements (the property of ‘discrete infinity’). Both accept that human beings are born with a predisposition to acquire language in a few years and without apparent efforts (the innate component of language). In addition to similarities, however, there are also substantial differences between the two fields, and it is an historical fact that Sebeok and Chomsky made no attempt at resolving them. Biosemiotics and Biolinguistics have become two separate disciplines, and yet in the case of language they are studying the same phenomenon, so it should be possible to bring them together. Here it is shown that this is indeed the case. A convergence of the two fields does require a few basic readjustments in each of them, but leads to a unified framework that keeps the best of both disciplines and is in agreement with the experimental evidence. What is particularly important is that such a framework suggests immediately a new approach to the origin of language. More precisely, it suggests that the brain wiring processes that take place in all phases of human ontogenesis (embryonic, foetal, infant and child development) are based on organic codes, and it is the step-by-step appearance of these brain-wiring codes, in a condition that is referred to as cerebra bifida, that holds the key to the origin of language. (shrink)

Definition of the problem In light of the ubiquitous role of time in human life, the importance of time for medical practices and for the ethical reflections of these practices seems all too obvious. However, the growing number of ethical reflections on temporal implications of medical practices all too often lack a systematic understanding of time. Aim of the article This article therefore aims to provide a map of temporal distinctions which should be both of theoretical interest and of practical (...) and ethical relevance. Procedure Starting with the fundamental distinction between time and temporality, four temporal dimensions will be discussed: linear time as chronological order of events, intersubjective time of social interactions, the cyclical temporal structure of biological rhythms and social routines, and the biographical time of the past, present and future of a single life, its finiteness and irreversibility. The article elucidates these distinctions from the perspective of different philosophical approaches and outlines how temporal distinctions may help to better understand the ethical importance of time in the realm of medicine. (shrink)

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combining arbitrary logical systems L i , i ∈ I, to form a new system L I . The methodology `fibres' the semantics K i of L i into a semantics for L I , and `weaves' the proof theory (axiomatics) of L i into a proof system of L I . There are various ways of doing this, we (...) distinguish by different names such as `fibring', `dovetailing' etc, yielding different systems, denoted by L F I , L D I etc. Once the logics are `weaved', further `interaction' axioms can be geometrically motivated and added, and then systematically studied. The methodology is general and is applied to modal and intuitionistic logics as well as to general algebraic logics. We obtain general results on bulk, in the sense that we develop standard combining techniques and refinements which can be applied to any family of initial logics to obtain further combined logics. The main results of this paper is a construction for combining arbitrary, (possibly not normal) modal or intermediate logics, each complete for a class of (not necessarily frame) Kripke models. We show transfer of recursive axiomatisability, decidability and finite model property. Some results on combining logics (normal modal extensions of K) have recently been introduced by Kracht and Wolter, Goranko and Passy and by Fine and Schurz as well as a multitude of special combined systems existing in the literature of the past 20-30 years. We hope our methodology will help organise the field systematically. (shrink)

This paper draws attention to the tendency of a range of technologies to reduce pedagogical interactions to a series of datafied transactions of information. This is problematic because such transactions are always by definition reducible to finite possibilities. As the ability to gather and analyse data becomes increasingly fine-grained, the threat that these datafied approaches over-determine the pedagogical space increases. Drawing on the work of Hegel, as interpreted by twentieth century French radical philosopher Alexandre Kojève, this paper develops a (...) model of relational pedagogy which highlights three points of incompatibility with a datafied learning environment reduced to finite measures. Firstly: Kojève’s accont of authority in Hegel posits two aspects to the mimetic relation between teacher and student: recognition and realisation, which belong to the ipseity or about-self-ness of the subject, and are incompatible with a general definition of data. Secondly, the Hegelian approach to human historical time, in particular the assertion that time and desire are begun in the future, not the past, renders it incompatible with mathematical time as used in data processing. Finally, from these it is possible to derive a distinctive notion of the work of pedagogy, grounded in Kojève’s realist reading of Hegel, irreducible to information processing. In consequence of this threefold irreducibility, the paper draws attention to a need for relations of human pedagogical work to be inherent in the design of educational technologies and highlights the dangers of presuming a machine intelligence model in the design of learning environments. (shrink)

Time may be infinite in both directions. If it is, then, if persons could live at most once in all of time, the probability that you would be alive now would be zero. But if persons can live more than once, the probability that you would be alive now would be nonzero. Since you are alive now, with certainty, either the past is finite, or persons can live more than once.

In this article I concentrate on three issues. First, Graham Oppy’s treatment of the relationship between the concept of infinity and Zeno’s paradoxes lay bare several porblems that must be dealt with if the concept of infinity is to do any intellectual work in philosophy of religion. Here I will expand on some insightful remarks by Oppy in an effort ot adequately respond to these problems. Second, I will do the same regarding Oppy’s treatment of Kant’s first antinomy in the (...) first critique, which deals in part with the question of whether the world had a beginning in time or if time extends infinitely into the past. And third, my examination of these two issues will inform what I have to say regarding a key topic in philosophy of religion: the question regarding the proper relationship between the infinite and the finite in the concept of God. (shrink)