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)

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)

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)

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)

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)

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)

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)

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)

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)

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.

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)

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)

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)

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)

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)

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)

"AGM members lunch." Ethos: Official Publication of the Law Society of the Australian Capital Territory, (198), pp. 13.

James A. Diefenbeck, Wayward Reflections on the History ofPhilosophyThomas R. Flynn Sartre, Foucault and Historical Reason. Volume 1:Toward an Existential Theory of HistoryMark Golden and Peter Toohey Inventing Ancient Culture:Historicism, Periodization and the Ancient WorldZenonas Norkus Istorika: Istorinis IvadasEverett Zimmerman The Boundaries of Fiction: History and theEighteenth‐Century British Novel.

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 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)

Spinoza ’s letter of June 2, 1674 to his friend Jarig Jelles addresses several distinct and important issues in Spinoza ’s philosophy. It explains briefly the core of Spinoza ’s disagreement with Hobbes’ political theory, develops his innovative understanding of numbers, and elaborates on Spinoza ’s refusal to describe God as one or single. Then, toward the end of the letter, Spinoza writes: With regard to the statement that figure is a negation and not anything positive, it is obvious that (...) matter in its totality, considered without limitation [indefinitè consideratam], can have no figure, and that figure applies only to finite and determinate bodies. For he who says that he apprehends a figure, thereby means to indicate simply this, that he apprehends a determinate thing and the manner of its determination. This determination therefore does not pertain to the thing in regard to its being [esse]; on the contrary, it is its non-being [non-esse]. So since figure is nothing but determination, and determination is negation [Quia ergo figura non aliud, quam determinatio, et determinatio negatio est], figure can be nothing other than negation, as has been said. Arguably, what is most notable about this letter is the fate of a single subordinate clause which appears in the last sentence of this passage: et determinatio negatio est. That clause was to be adopted by Hegel and transformed into the slogan of his own dialectical method: Omnis determinatio est negatio. Of further significance is the fact that, while Hegel does credit Spinoza with the discovery of this most fundamental insight, he believes Spinoza failed to appreciate the importance of his discovery. The issue of negation and the possibility of self-negation stand at the very center of the philosophical dialogue between the systems of Spinoza and Hegel, and in this paper I will attempt to provide a preliminary explication of this foundational debate between the two systems. In the first part of the paper I will argue that the “determination is negation” formula has been understood in at least three distinct senses among the German Idealists, and as a result many of the participants in the discussion of this formula were actually talking past each other. The clarification of the three distinct senses of the formula will lead, in the second part of the paper, to a more precise evaluation of the fundamental debate between Spinoza and Hegel regarding the possibility of self-negation. In this part I will evaluate the validity of each interpretation of the determination formula, and motivate the positions of the various participants in the debate. (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)

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)

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 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)

Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates (...) choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis. (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)

Thomas Hofweber takes the semantic paradoxes to motivate a radical reconceptualization of logical validity, rejecting the idea that an inference rule is valid just in case every instance thereof is necessarily truth-preserving. Rather than this “strict validity”, we should identify validity with “generic validity”, where a rule is generically valid just in case its instances are truth preserving, and where this last sentence is a generic, like “Bears are dangerous”. While sympathetic to Hofweber’s view that strict validity should be replaced (...) by something allowing for exceptions, I argue that this should instead be truth-conduciveness, a matter of a large majority of instances being truth-preserving. The fact that inference rules have uncountably many instances, I argue, can be handled by defining truth-conduciveness as relative to finite sets of instances. Moreover, I argue that Hofweber’s position, while seemingly radical, may be less so under closer scrutiny. For the mere claim that classical rules and unrestricted truth rules are generically valid (or truth-conducive) is not in itself controversial. Also, if there is an answer to the question of which of these are also strictly valid, then the claim that generic validity is the central notion in logic is at most an interest-relative matter, since there is then also a fact of the matter as to which inference rules are (not) strictly valid. If no solution operating with strict validity to the paradoxes can be had, however, then the claim that validity should be identified with a weaker notion is better motivated. I argue that it is reasonable, in view of past failures, to conjecture that no ordinary solution will score high enough relative to standard (uncontroversial) desiderata to merit justified belief. Hence, it is unknowable which solution is correct. I further argue that this is best explained by its being metaphysically indeterminate which solution is correct. If this conjecture is true, then we ought instead to think of validity as allowing exceptions, and then take the “true logic” to be one that takes both the classical rules and the truth rules to be valid, i.e., truth-conducive. This logic scores very high on the desiderata on logics, and is therefore preferable to any logic operating with strict validity. (shrink)

In this chapter what I call the “backside” of habit is explored. I am interested in the philosophical implications of the physical and physiological processes that mediate, and which allow for what comes to appear as almost magic; namely the various sensorimotor associations and integrations that allows us to replay our past experiences, and to in a certain sense perceive potential futures, and to act and bring about anticipated outcomes – without quite knowing how. Thus, the term “backside” is (...) meant to refer both the actual mediation and the epistemic opacity of these backstage intermediaries that allow for the front stage magic. The question is if the epistemic complexities around sensorimotor mediation gives us valuable insights into the nature of human agency and further how it might begin to show us new ways to think of the mind as truly embodied yet not reducible to any finite body-as-object. (shrink)

Many philosophers have argued that the past must be finite in duration because otherwise reaching the present moment would have involved something impossible, namely, the sequential occurrence of an actual infinity of events. In reply, some philosophers have objected that there can be nothing amiss in such an occurrence, since actually infinite sequences are ‘traversed’ all the time in nature, for example, whenever an object moves from one location in space to another. This essay focuses on one of (...) the two available replies to this objection, namely, the claim that actual infinities are not traversed in nature because space, time, and other continuous wholes divide into parts only in so far as we divide them in thought, and thus divide into only a finite number of parts. I grant that this reply succeeds in blunting the anti-finitist objection, but I argue that it also subverts the very argument against an eternal past that it was intended to save. (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.

Quantum mechanics involves a generalized form of information, that of quantum information. It is the transfinite generalization of information and re-presentable by transfinite ordinals. The physical world being in the current of time shares the quality of “choice”. Thus quantum information can be seen as the universal substance of the world serving to describe uniformly future, past, and thus the present as the frontier of time. Future is represented as a coherent whole, present as a choice among infinitely many (...) alternatives, and past as a well-ordering obtained as a result of a series of choices. The concept of quantum information describes the frontier of time, that “now”, which transforms future into past. Quantum information generalizes information from finite to infinite series or collections. The concept of quantum information allows of any physical entity to be interpreted as some nonzero quantity of quantum information. The fundament of quantum information is the concept of ‘quantum bit’, “qubit”. A qubit is a choice among an infinite set of alternatives. It generalizes the unit of classical information, a bit, which refer to a finite set of alternatives. The qubit is also isomorphic to a ball in Euclidean space, in which two points are chosen. (shrink)

Some philosophers contend that the past must be finite in duration, because otherwise reaching the present would have involved the sequential occurrence of an actual infinity of events, which they regard as impossible. I recently developed a new objection to this finitist argument, to which Andrew Ter Ern Loke and Travis Dumsday have replied. Here I respond to the three main points raised in their replies.

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)

We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and faithful (...) translation of${\sf MIPC}$into${\sf TS4}$. We compare this new translation of${\sf MIPC}$with the Gödel translation by showing that both${\sf TS4}$and${\sf MS4}$can be translated fully and faithfully into a tense extension of${\sf MS4}$, which we denote by${\sf MS4.t}$. This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for${\sf MS4.t}$using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. (shrink)

In the perspective of the philosophical archaeology proposed, here, the arkhé towards which archaeology regresses must not be understood in any way as an element that can be situated in chronology ; it is, rather, a force that operates in history—much in the same way in which Indoeuropean words express a system of connections among historically accessible languages, in which the child in psychoanalysis expresses an active force in the psychic life of the adult, in which the big bang, which (...) is supposed to have originated the universe, continues to send towards us its fossil radiation. But the arkhé is not a datum or a substance. It is much rather a field of bipolar historical currents within the tension of anthropogenesis and history, between point of emergence and becoming, between arch-past and present. And as such—that is to say, to the extent to which it is something that it is necessarily supposed to have factually happened, and which yet cannot be hypostatized in any chronologically identifiable event—it is solely capable of guaranteeing the intelligibility of historical phenomena, of ‘saving’ them archaeologically within a future perfect, yet not grasping its origin, but rather its history, at once finite and untotalizable. (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)