I show the inadequacy of whitrow's recent argument ("british journal for the philosophy of science", Volume 29, Pages 39-45) against the possibility of an infinite past. I argue that it is impossible to prove "a priori" the non-Existence of an infinite past or future.

Benardete paradoxes involve a beginningless set each member of which satisfies some predicate just in case no earlier member satisfies it. Such paradoxes have been wielded on behalf of arguments for the impossibility of an infinite past. These arguments often deploy patchwork principles in support of their key linking premise. Here I argue that patchwork principles fail to justify this key premise.

Philosophers have long discussed whether time really passes. Simultaneously, they have also discussed whether time could have begun from an infinite past. This paper clarifies the relationship between the reality of time’s passage and an infinite past. I assert that time cannot have an infinite past if time really passes. This argument is based on a proposition that an infinite series of events cannot be completed if time really passes. A seemingly strong objection (...) to this proposition is that no movement is possible if an infinite series cannot be completed. However, movement is clearly possible; thus, an infinite series can be completed. I argue that although it is sure that an infinite series can be completed in the static view, an infinite series cannot be completed (and thus, time could not have begun from an infinite past) in the dynamic view. (shrink)

Based on a recently published essay by Jeremy Gwiazda, I argue that the possibility that the present state of the universe is the product of an actually infinite series of causally-ordered prior events is impossible in principle, and thus that a major criticism of the Secunda Via of St. Thomas is baseless after all.

I show the inadequacy of whitrow's recent argument ("british journal for the philosophy of science", Volume 29, Pages 39-45) against the possibility of an infinite past. I argue that it is impossible to prove "a priori" the non-Existence of an infinite past or future.

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must (...) have a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

One of the principal lines of argument deployed by the friends of the kalām cosmological argument against the possibility of a beginningless series of events is a quite general argument against the possibility of an actual infinite. The principal thesis of the present paper is that if this argument worked as advertised, parallel considerations would force us to conclude, not merely that a series of discrete, successive events must have a first member, but also that such a series must (...) have a final member. Anyone who thinks that an endless series of events is possible must therefore reject this popular line of argument against the possibility of an actual infinite. (shrink)

ABSTRACT W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude of (...) the past, Puryear claims, because there can be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

W.L. Craig has argued that the universe has a beginning because (1) the infinitude of the past entails the existence of actual infinite multitudes of past intervals of time, and (2) the existence of actual infinite multitudes is impossible. Puryear has rejected (1) and argued that what the infinitude of the past entails is only the existence of an actual infinite magnitude of past time. But this does not preclude the infinitude of the (...) past, Puryear claims, because there can be no justification for the claim that actual infinite magnitudes are impossible. I argue, against Puryear, that there can be such a justification. I claim, nevertheless, that, for reasons entirely different from Puryear’s, the finitude of the past cannot be established based either on the impossibility of actual infinite multitudes or on the impossibility of actual infinite magnitudes. My arguments in this paper draw on insights from al-Kindī and Avicenna. (shrink)

The creation-of-matter hypothesis of the Bondi-Gold-Hoyle steady-state cosmology requires that in an infinite time to which the first transfinite number may be assigned the number of atoms of matter produced would be equal to the cardinal number of the set of mathematical points in the continuum. The existence of a set of finite atoms with that cardinal number is physically unacceptable. The argument for the production of a non-denumerable set of atoms, in infinite time, is given in terms (...) of a model which is shown to be isomorphic with the original Cantor "diagonal" proof for the existence of a non-denumerable infinity. An alternative model which meets the requirements of the steady-state theory is presented; in this model, the number of atoms is explicitly no greater than countably infinite, and remains countably infinite as long as the past time of the universe is restricted to the unlimited set of finite unit-time intervals. If the origin of the steady-state universe is taken as being within that infinite set, expressed by the negative natural numbers, the contradiction of an atom at every mathematical point does not arise. The contradiction does arise if the origin is not within the set of finite numbers, and accordingly there is a restriction as to which concept of infinite past may properly be maintained in the steady-state theory. (shrink)

In this paper I show that the existence of an infinite temporal regress does not undermine the soundness of Craigs version of the Kalam Cosmological Argument. To this end I shall focus on a particular complication that Craig raises against one of his arguments in support of a finite temporal regress. I will show that this complication can be made innocuous by extending the notion of A-theoretic time, which is presupposed by Craigs argument, to include a notion of temporal (...) becoming that is compatible with the existence of an infinite regress of temporal events. All this shows that God could have created an infinite temporal regress a finite time in the past without this entailing a contradiction. (shrink)

It is often said that time must have a beginning because otherwise the series of past events would have the paradoxical features of an actual infinite. In the present paper, we show that, even given a dynamic theory of time, the cardinality of an endless series of events, each of which will occur, is the same as that of a beginningless series of events, each of which has occurred. Both are denumerably infinite. So if an endless series (...) of events is possible, then the possibility of a beginningless series of past events should not be rejected merely on the ground that it would be an actual infinite. What would be required to rebut our argument is a symmetry breaker – something that motivates treating the past relevantly differently to the future. We consider several attempts to provide a symmetry breaker and show that none of them is successful. (shrink)

Is it possible to venture beyond daily living and experience heightened states of awareness? Deepak Chopra says that higher consciousness is available here and now. “Metahuman helps us harvest peak experiences so we can see our truth and mold the universe’s chaos into a form that brings light to the world.”—Dr. Mehmet Oz, attending physician, New York–Presbyterian, Columbia University New York Times bestselling author Deepak Chopra unlocks the secrets to moving beyond our present limitations to access a field of (...) class='Hi'>infinite possibilities. How does one do this? By becoming metahuman. To be metahuman, however, isn’t science fiction and is certainly not about being a superhero. To be metahuman means to move past the limitation constructed by the mind and enter a new state of awareness where we have deliberate and concrete access to peak experiences that can transform people’s lives from the inside out. Humans do this naturally—to a point. For centuries the great artists, scientists, writers, and many so-called ordinary people have gone beyond the everyday physical world. But if we could channel these often bewildering experiences, what would happen? Chopra argues we would wake up to experiences that would blow open your body, mind, and soul. Metahuman invites the reader to walk the path here and now. Waking up, we learn, isn’t just about mindfulness or meditation. Waking up, to become metahuman, is to expand our consciousness in all that we think, say, and do. By going beyond, we liberate ourselves from old conditioning and all the mental constructs that underlie anxiety, tension, and ego-driven demands. Waking up allows life to make sense as never before. To make this as practical as possible, Chopra ends the book with a 31-day guide to becoming metahuman. Once you wake up, he writes, life becomes transformed, because pure consciousness—which is the field of all possibilities—dawns in your life. Only then does your infinite potential become your personal reality. (shrink)

Modernity in the late eighteenth century transformed all domains of European life -intellectual, industrial, and social. Not least affected was the experience of time itself: ever-accelerating change left people with briefer intervals of time in which to gather new experiences and adapt. In this provocative and erudite book Reinhart Koselleck, a distinguished philosopher of history, explores the concept of historical time by posing the question: what kind of experience is opened up by the emergence of modernity? Relying on an extraordinary (...) array of witnesses and texts from politicians, philosophers, theologians, and poets to Renaissance paintings and the dreams of German citizens during the Third Reich, Koselleck shows that, with the advent of modernity, the past and the future became 'relocated' in relation to each other.The promises of modernity -freedom, progress, infinite human improvement -produced a world accelerating toward an unknown and unknowable future within which awaited the possibility of achieving utopian fulfillment. History, Koselleck asserts, emerged in this crucial moment as a new temporality providing distinctly new ways of assimilating experience. In the present context of globalization and its resulting crises, the modern world once again faces a crisis in aligning the experience of past and present. To realize that each present was once an imagined future may help us once again place ourselves within a temporality organized by human thought and humane ends as much as by the contingencies of uncontrolled events. (shrink)

The aim of this paper is to present a proof to the conclusion that is impossible to traverse an infinite series (in particular, an infinite series of past moments). This may also show (given additional assumptions) that the series of past moments cannot be infinite. In the first section I formulate five theses concerning traversing, successive addition and successive subtraction and I present the idea of the argument: if it were possible to traverse an (...) class='Hi'>infinite past, it should be in principle possible to go back, which is, however, impossible. The main body of the paper is concerned with working out a simple mathematical representation of some structural features of processes like traversing and successive addition. I also make a crucial distinction between completion of a process at a particular time and its timeless "completion" in infinite time. In section V, I present the formal proof and defend it against a possible objection of question-begging. Finally, I suggest that my argume. (shrink)

In defense of his claim that the universe must have been created, William Lane Craig gives two distinct philosophical arguments against the possibility of an infinite past. The first appeals to various paradoxes allegedly generated by the idea of an actual infinite. The second appeals to a dynamic theory of the nature of time, and tries to show on that basis that an infinite series of events could not have been “formed by successive addition.” The present (...) paper is concerned with the second of these two arguments. I try to show that it cannot stand on its own independently of the first argument, that Craig does not succeed in defending it against standard objections, and that even those who are inclined to accept a dynamic theory of time should not be convinced by what Craig says in its defense. (shrink)

In a series of much discussed articles and books, William Lane Craig defends the view that the past could not consist in a beginningless series of events. In the present paper, I cast a critical eye on just one part of Craig's case for the finitude of the past – viz. his philosophical argument against the possibility of actually infinite sets of objects in the ‘real world’. I shall try to show that this argument is unsuccessful. I (...) shall also take a close look at several considerations that are often thought to favour the possibility of an actual infinite, arguing in each case that Craig's response is inadequate. (shrink)

What one can say about the past, present and future of set theory depends on what one expects or at least hopes set theory will accomplish. In order to gauge the early expectations, I begin with a quote from the inaugural lecture in 1903 of my mathematical grandfather, the internationally known Finnish mathematician Ernst Lindelöf. The subject of his lecture was – guess what – Cantor’s set theory. In his conclusion, Lindelöf says of Cantor’s results: For mathematics they have (...) lent new tools and opened up new fields of research, they have thrown entirely new light on the foundations of analysis and brought clarity and order where there was only disorder and contradictions. Thus they have greatly contributed to the harmony that is the essence of mathematics, a harmony a grasp of which is the reward of mathematical research. (Quoted in Olli Lehto, Tieteen aatelia, Otava, Helsinki, 2008, p. 263) We can all agree with the compliments Lindelöf pays to set theory as an impressive specimen of mathematical research, including the theory of infinite cardinals and ordinals. But as far as the foundational role of set theory is concerned, in the perspective of the subsequent century his words read as an example of supreme historical irony. Far from bringing harmony into the foundations of mathematics, problems arising from set theory led to a schism between different schools of thought. Few mathematicians think of set theory as a tool for reaching new results outside set theory.. On the contrary, an interesting rich tradition called reverse mathematics takes significant mathematical results and asks what set-theoretical assumptions are needed to prove them. Set-theoretical paradoxes have greatly increased mathematicians’ concerns about contradictions instead of assuaging them. Many foundationalists would blandly deny that we have even now, more than a hundred years later, reached “clarity and order” about the foundations of analysis. What Lindelöf took to be the results of set theory thus were in reality so many hopes that set theory was expected to fulfill.. (shrink)

infinite, and offer several arguments in sup port of this thesis. I believe their arguments are unsuccessful and aim to refute six of them in the six sections of the paper. One of my main criticisms concerns their supposition that an infinite series of past events must contain some events separated from the present event by an infinite number of intermediate events, and consequently that from one of these infinitely distant past events the present could (...) never have been reached. I introduce.. (shrink)

In a recent paper, I claimed that if a familiar line of argument against the possibility of a beginningless series of events worked as advertised, it would work just as well against the possibility of an endless series of pre-determined events. The present paper is my response to objections by William Lane Craig. It argues that neither Craig’s claim that an endless series of events is a merely potential infinite nor his claim that future events don’t exist is successful (...) in blocking my original conclusion. (shrink)

In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the "Mindscape," where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Here Rucker acquaints us with Gödel's rotating universe, in which it is theoretically possible to travel into the past, and explains an interpretation of quantum mechanics in which billions of parallel worlds are produced every microsecond. It is in the realm of infinity, (...) he maintains, that mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise from this merging, we can learn a great deal about the human mind, its powers, and its limitations. Using cartoons, puzzles, and quotations to enliven his text, Rucker guides us through such topics as the paradoxes of set theory, the possibilities of physical infinities, and the results of Gödel's incompleteness theorems. His personal encounters with Gödel the mathematician and philosopher provide a rare glimpse at genius and reveal what very few mathematicians have dared to admit: the transcendent implications of Platonic realism. (shrink)

Emmanuel Levinas asks, “In what meaning can community dress itself without reducing Difference?” (OB 154 / AE 197). Can there be a community that does not create its unity by erasing the differences between those whom it joins, a community that does not establish itself by imposing the Same? His answer is yes. Contrary to the thinkers of community in the philosophical tradition, thinkers like Hobbes, Rousseau, and Kant, Levinas states, “between the one I am and theother for whom I (...) am responsible there gapes a difference, without a basis in community. The unity of the human race is in fact posterior to fraternity” (OB 166 / AE 211 ). “Community with him begins in my obligation to him” (OB 87 / AE 109–10) rather than in something that we share. It begins in hospitality, in which the Infinite is consummated (TI 27 / TeI xv) because obligation is infinite, because the third is revealed in the face of the Other. Hospitality is a welcome of not only the one who faces me, but the third implicated in that face, a face that “compels me to goodness, which is better than goods received... a he in the depth of the Thou.”1 This original relation of difference between oneself and the other person, an asymmetric relation that opens the possibility of equality, is the nonfoundational foundation, the original being-together in being-apart, on which the social and political community of law and equal rights can be built — and continually rebuiltin light of the goodness toward which I am compelled, in light of the eschatology of peace. (shrink)

Emmanuel Levinas asks, “In what meaning can community dress itself without reducing Difference?” (OB 154 / AE 197). Can there be a community that does not create its unity by erasing the differences between those whom it joins, a community that does not establish itself by imposing the Same? His answer is yes. Contrary to the thinkers of community in the philosophical tradition, thinkers like Hobbes, Rousseau, and Kant, Levinas states, “between the one I am and theother for whom I (...) am responsible there gapes a difference, without a basis in community. The unity of the human race is in fact posterior to fraternity” (OB 166 / AE 211 ). “Community with him begins in my obligation to him” (OB 87 / AE 109–10) rather than in something that we share. It begins in hospitality, in which the Infinite is consummated (TI 27 / TeI xv) because obligation is infinite, because the third is revealed in the face of the Other. Hospitality is a welcome of not only the one who faces me, but the third implicated in that face, a face that “compels me to goodness, which is better than goods received... a he in the depth of the Thou.”1 This original relation of difference between oneself and the other person, an asymmetric relation that opens the possibility of equality, is the nonfoundational foundation, the original being-together in being-apart, on which the social and political community of law and equal rights can be built — and continually rebuiltin light of the goodness toward which I am compelled, in light of the eschatology of peace. (shrink)

"This article presents an analysis of William Lane Craig’s argument of the finitude of the past based on the impossibility of the formation of an actual infinite. To achieve the aim of this academic work we use, as a primary base, a book written by Craig called Reasonable Faith: Christian Truth and Apologetics and a chapter written by the same author along with James Sinclair called The Kalam Cosmological Argument in The Blackwell Companion to Natural Theology. These works, (...) in our opinion, provide sufficient primary material to study the topic. However, other articles and books by Craig are also referenced, and the commentaries of some other authors, who deal with this problem, are also used. Throughout this work, we consider the historical context and Craig’s incorporation of the kalam cosmological argument. We go on to analyse the presuppositions given by this author and consequently we study, progressively, the formulations that Craig himself made to reach his conclusion. /// Este artigo apresenta uma análise do argumento de William Lane Craig sobre a finitude do passado baseado na impossibilidade da formação de um infinito atual. Para atingir o objetivo deste trabalho acadêmico, utilizamos como fonte primária uma obra escrita pelo próprio Craig, intitulada Fé racional: verdade cristã e apologética, e um capítulo escrito pelo mesmo autor em colaboração com James Sinclair chamado O argumento cosmológico kalam, em The Blackwell Companion to Natural Theology. Estes trabalhos, em nossa opinião, oferecem suficientes elementos para o estudo do tópico. Entretanto, outros artigos e livros de Craig também foram citados, bem como os comentários de vários autores que tratam do problema. No decorrer deste trabalho consideramos o contexto histórico e a incorporação de Craig ao argumento cosmológico kalam. Mais adiante, analisamos primeiramente os pressupostos dados pelo mencionado autor e, em consequência, estudamos progressivamente as formulações feitas pelo próprio Craig para obter suas conclusões. ". (shrink)

The Successive Addition Argument (SAA) is one of the arguments proposed by the defenders of the Kalām Cosmological Argument to support the claim that the universe has a beginning. The main premise of SAA states that a collection formed by successive addition cannot be an actual infinite. This premise is challenged by an argument originally proposed by Fred Dretske. According to Dretske’s Argument (DA), the scenario of a counter who starts counting numbers and never stops can provide a counterexample (...) to the main premise of SAA. I argue that neither DA nor its past-oriented counterpart—which discusses the scenario of a counter who has always been counting negative integers from the infinite past—can play a decisive role in our evaluation of the strength of the arguments that are intended to establish the finitude of the past based on the impossibility of an actually infinite number of successive additions. (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)

I develop a new argument to the effect that past causal chains cannot extend back infinitely, but must instead terminate in a first uncaused cause. It has the advantage of sidestepping a historically prominent objection to cosmological arguments of this general type, one leveled by Aquinas and various other Scholastics.

I develop a new argument to the effect that past causal chains cannot extend back infinitely, but must instead terminate in a first uncaused cause. It has the advantage of sidestepping a historically prominent objection to cosmological arguments of this general type, one leveled by Aquinas and various other Scholastics.

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 key premise of the kalam cosmological argument is that the universe began to exist. However, while a number of philosophers have offered powerful criticisms of William Lane Craig’s defense of the premise, J.P. Moreland has also offered a number of unique arguments in support of it, and to date, little attention has been paid to these in the literature. In this paper, I attempt to go some way toward redressing this matter. In particular, I shall argue that Moreland’s philosophical (...) arguments against the possibility of traversing a beginningless past are unsuccessful. (shrink)

Wes Morriston argues that even if we take an endless series of events to be merely potentially, rather than actually, infinite, still no distinction between a beginningless and an endless series of events has been established which is relevant to arguments against the metaphysical possibility of an actually infinite number of things: if a beginningless series is impossible, so is an endless series. The success of Morriston’s argument, however, comes to depend on rejecting the characterization of an endless (...) series of events as a potential infinite. It turns out that according to his own analysis it is vitally relevant whether the series of events is potentially, as opposed to actually, infinite. If it is reasonable to maintain that an endless series of events is potentially infinite while a beginningless series is actually infinite, then a relevant distinction has been established for any person who thinks that an actual infinite cannot exist. (shrink)

In a recent commendable article, Quentin Smith (1987) exposes fatal flaws in several recent attempts to demonstrate that it is logically impossible for the past to be infinite. However, his analysis of one of these flawed arguments--involving an interesting version of Russell's "Tristram Shandy paradox"--is off the mark, as I show in this paper.

Several difficulties that accompany Plato's theory of Forms have received considerable attention in the philosophical literature in the past half century. A great deal of discussion and controversy surrounds the dialogue Parmenides and the group of considerations commonly called the “Third Man Argument”. Our purpose here is to strike out in one direction suggested by this passage, but it can in no way be thought of as an exegesis nor a logical elucidation of the “Third Man Argument” itself. While (...) what we shall say here has an obvious affinity and connection with the Parmenides passage, the two principal questions that concern us here are of a more general nature than the specific points in the Parmenides. The first is whether Plato's theory of Forms involves a regress which is ruinous to the theory. The second is, if a self-destructive regress is a necessary consequence of the theory, what elements of Plato's theory make the regress inescapable. (shrink)

There is an infinity of figures and of movements, present and past, which enter into the efficient cause of my present writing, and in its final cause, there are an infinity of slight tendencies and dispositions of my soul, present and past.1.

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)

Drawing from the critical phenomenology of Alia Al-Saji, Christina Sharpe’s notion of “the wake,” and Jan Slaby’s work on affect, this paper offers a critique of George Ciccariello-Maher’s (2017) formulation of Frantz Fanon’s decolonized dialectic. I argue that Ciccariello-Maher’s formulation, while excellent in most respects, nevertheless contains a significant lacuna. While he is correct to point out that Fanon’s critique of universal reconciliation forces his dialectical activity to remain firmly rooted in the present, by failing to fully draw out how (...) the past always already weighs on the present, Ciccariello-Maher runs the risk of obscuring the affective weight of Fanon’s historical critique. This is problematic for the way it obscures the full range of ethical possibilities that stem from this particular affective experience—possibilities that Jan Slaby (2020: 189–95) makes clear via Christina Sharpe’s notion of “the wake.” In other words, while Ciccariello-Maher seems to frame Fanon’s recourse to infinitely deferred reconciliation as a reflection of the “ethical nihilism” (2017: 62) that characterizes the system of oppression he is responding to, a reformulation of Ciccariello-Maher’s observations with respect to affectivity re-frames this infinite deferral as an “embodied ethics of being and knowing” (Slaby 2020: 189). I will ultimately argue that this reformulation helps us understand Fanon’s parting words in Black Skin White Masks—“Oh my body, always make me a man who questions!” (Fanon 2008b: 206; 1952: 188)—as a call for the type of ethics suggested by Sharpe’s notion of “the wake” (2016). (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)

Ex ante predicted outcomes should be interpreted as counterfactuals (potential histories), with errors as the spread between outcomes. But error rates have error rates. We reapply measurements of uncertainty about the estimation errors of the estimation errors of an estimation treated as branching counterfactuals. Such recursions of epistemic uncertainty have markedly different distributial properties from conventional sampling error, and lead to fatter tails in the projections than in past realizations. Counterfactuals of error rates always lead to fat tails, regardless (...) of the probability distribution used. A mere .01% branching error rate about the STD (itself an error rate), and .01% branching error rate about that error rate, etc. (recursing all the way) results in explosive (and infinite) moments higher than 1. Missing any degree of regress leads to the underestimation of small probabilities and concave payoffs (a standard example of which is Fukushima). The paper states the conditions under which higher order rates of uncertainty (expressed in spreads of counterfactuals) alters the shapes the of final distribution and shows which a priori beliefs about conterfactuals are needed to accept the reliability of conventional probabilistic methods (thin tails or mildly fat tails). (shrink)

Aggregative consequentialism and several other popular moral theories are threatened with paralysis: when coupled with some plausible assumptions, they seem to imply that it is always ethically indifferent what you do. Modern cosmology teaches that the world might well contain an infinite number of happy and sad people and other candidate value-bearing locations. Aggregative ethics implies that such a world contains an infinite amount of positive value and an infinite amount of negative value. You can affect only (...) a finite amount of good or bad. In standard cardinal arithmetic, an infinite quantity is unchanged by the addition or subtraction of any finite quantity. So it appears you cannot change the value of the world. Modifications of aggregationism aimed at resolving the paralysis are only partially effective and cause severe side effects, including problems of “fanaticism”, “distortion”, and erosion of the intuitions that originally motivated the theory. Is the infinitarian challenge fatal? (shrink)

Wes Morriston argues that even if we take an endless series of events to be merely potentially, rather than actually, infinite, still no distinction between a beginningless and an endless series of events has been established which is relevant to arguments against the metaphysical possibility of an actually infinite number of things: if a beginningless series is impossible, so is an endless series. The success of Morriston’s argument, however, comes to depend on rejecting the characterization of an endless (...) series of events as a potential infinite. It turns out that according to his own analysis it is vitally relevant whether the series of events is potentially, as opposed to actually, infinite. If it is reasonable to maintain that an endless series of events is potentially infinite while a beginningless series is actually infinite, then a relevant distinction has been established for any person who thinks that an actual infinite cannot exist. (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 compact volume, belonging to the Cambridge Elements series, is a useful introduction to some of the most fundamental questions of philosophy and foundations of mathematics. What really distinguishes realist and platonist views of mathematics from anti-platonist views, including fictionalist and nominalist and modal-structuralist views?1 They seem to confront similar problems of justification, presenting tradeoffs between which it is difficult to adjudicate. For example, how do we gain access to the abstract posits of platonist accounts of arithmetic, analysis, geometry, etc., (...) including numbers, functions, sets, points, lines, spaces, etc., whether it be such objects themselves or the possibilities of such, as postulated by modal and modal structural accounts?2 What real difference does it make, whether it be the existence of such things or the mathematical possibility of such things? Even fictionalist views seem to confront analogous problems. After all, we rely on mathematics for myriad scientific applications; so such mathematics had better at least be coherent, even if not true. But coherence requires at least formal consistency; so we seem implicitly to be committed to things like formal derivations, viz. the absence of any such having contradictory consequences, framed within the appropriate system of axioms and rules. But derivations are themselves akin to mathematical objects, as derivations are strings of strings of symbols. Moreover, derivations provided by axioms and rules form an infinite class, such that, at any future time, infinitely many will not have been written down. Moreover, such strings, as Gödel famously showed, can be coded as natural numbers. Thus, even fictionalist accounts (such as that of Field in his Science without Numbers [2016]) seem to confront problems very much like those plaguing platonist accounts. (shrink)

This book explores the nature and importance of sound in virtual reality. Approaching the subject from a holistic perspective, the book delivers an emergent framework of VR sound. This framework brings together numerous elements that collectively determine the nature of sound in VR; from various aspects of VR technology, to the physiological and psychological complexities of the user, to the wider technological, historical and sociocultural issues. Garner asks, amongst other things: what is the meaning of sound? How have fictional visions (...) of VR shaped our expectations for present technology? How can VR sound hope to evoke the desired responses for such an infinitely heterogeneous user base? This book if for those with an interest in sound and VR, who wish to learn more about the great complexities of the subject and discover the contemporary issues from which future VR will surely advance. (shrink)