By contextualising the striking similarities in Feuerbach and Kierkegaard’s conceptions of sin as infinite qualitative difference, and the related question of the individual and the species as a shared response to the Hegelian Entzweiung, this article seeks to offer a new framework for understanding Feuerbach’s critique of Christian theology and of Kierkegaard’s famous articulation of the infinite qualitative difference as simultaneously ontological, hamartiological, and soteriological. It argues that Kierkegaard offers a modification of the Feuerbachian (...) account to argue against Feuerbach’s conclusion that the Christian doctrine of sin negates qualitative differences between individual humans, and to conversely affirm that sin differentiates not just God and humans, but each single individual too. Kierkegaard might be said to at once uphold Feuerbach’s critique of Hegelian theology, while inverting Feuerbach’s anti-theological programme by harnessing the ambiguities that appear in Feuerbach’s account of sin. It is thereby shown how both Feuerbach and Kierkegaard make use of Hegelian logic, both through their formal application of the concepts of quality and quantity, as well as their creative appropriation of the notion of Entzweiung. (shrink)

It is very natural to think that if two people, x and y, are qualitatively identical and have committed qualitatively identical actions, then it cannot be the case that one has committed something wrong whereas the other did not. That is to say, if x and y differ in their moral status, then it must be because x and y are qualitatively different, and not simply because x is identical to x and not identical to y. In this fictional dialogue (...) between Socrates and Cantor involving infinitely many qualitatively identical agents, this assumption is challenged. (shrink)

As an application of his Material Theory of Induction, Norton (2018; manuscript) argues that the correct inductive logic for a fair infinite lottery, and also for evaluating eternal inflation multiverse models, is radically different from standard probability theory. This is due to a requirement of label independence. It follows, Norton argues, that finite additivity fails, and any two sets of outcomes with the same cardinality and co-cardinality have the same chance. This makes the logic useless for evaluating multiverse models (...) based on self-locating chances, so Norton claims that we should despair of such attempts. However, his negative results depend on a certain reification of chance, consisting in the treatment of inductive support as the value of a function, a value not itself affected by relabeling. Here we define a purely comparative infinite lottery logic, where there are no primitive chances but only a relation of ‘at most as likely’ and its derivatives. This logic satisfies both label independence and a comparative version of additivity as well as several other desirable properties, and it draws finer distinctions between events than Norton's. Consequently, it yields better advice about choosing between sets of lottery tickets than Norton's, but it does not appear to be any more helpful for evaluating multiverse models. Hence, the limitations of Norton's logic are not entirely due to the failure of additivity, nor to the fact that all infinite, co-infinite sets of outcomes have the same chance, but to a more fundamental problem: We have no well-motivated way of comparing disjoint countably infinite sets. (shrink)

This paper presents an analysis of the sorites paradox for collective nouns and gradable adjectives within the framework of classical logic. The paradox is explained by distinguishing between qualitative and quantitative representations. This distinction is formally represented by the use of a different mathematical model for each type of representation. Quantitative representations induce Archimedean models, but qualitative representations induce non-Archimedean models. By using a non-standard model of \ called \, which contains infinite and infinitesimal numbers, the two (...) paradoxes are shown to have distinct structures. The sorites paradox for collective nouns arises from the use of infinite numbers, whereas the sorites paradox for gradable adjectives arises from the use of infinitesimal numbers. Each paradox can be traced to a different source of vagueness. The sorites paradox for collective nouns is caused by \, and the sorites paradox for gradable adjectives is caused by \ \. If correct, this analysis implies that infinite and infinitesimal numbers are cognitively real, and that they play a role in the semantic interpretation of natural language. (shrink)

In an article published in Prolegomena 2006, Christoph Schmidt-Petri has defended his interpretation and attacked mine of Mill’s idea that higher kinds of pleasure are superior in quality to lower kinds, regardless of quantity. Millian qualitative superiorities as I understand them are infinite superiorities. In this paper, I clarify my interpretation and show how Schmidt-Petri has misrepresented it and ignored the obvious textual support for it. As a result, he fails to understand how genuine Millian qualitative superiorities (...) determine the novel structure of Mill’s pluralistic utilitarianism, in which a social code of justice that distributes equal rights and duties takes absolute priority over competing considerations. Schmidt-Petri’s own interpretation is a non-starter, because it does noteven recognize that Mill is talking about different kinds of pleasant feelings, such that the higher kinds are intrinsically more valuable than the lower. I conclude by outlining why my interpretation is free of any metaphysical commitment to the “essence” of pleasure. (shrink)

In response to prevailing perceptions, I contend that Søren Kierkegaard (1813–55) conceives of the wholly otherness of God via his dialectical category of the ‘infinite qualitative difference’ between the human and the divine, initially through the self's consciousness of sin and ultimately through the self's acceptance of the gift of forgiveness. Therefore, I claim that while the common designation of Kierkegaard's God as ‘Wholly Other’ may initially evoke the alterity of sin; it is not ultimately sufficient to (...) describe the divine alterity which Kierkegaard regards as more faithfully manifest in the ‘impossible possibility’ of forgiveness. Through this reading, I finally suggest that the ‘Wholly Other’ is not ultimately representative of God in Kierkegaard's writings and might be more faithfully supplemented by the appellation of the Holy Other. (shrink)

There are possible worlds in which time is circular and finite in duration, forming a loop of, say, 12,000 years. There are also possible worlds in which time is linear and infinite in both directions and in which history is repetitive, consisting of infinitely many 12,000-year epochs, each two of which are exactly alike with respect to all intrinsic, purely qualitative properties. Could one ever have empirical evidence that one inhabits a world of the first kind rather than (...) a world of the second kind? We argue for the affirmative answer, contra Quine, Newton-Smith, and Bergström. Our argument for that conclusion differs from an argument for the same conclusion due to Weir. Weir’s argument is probabilistic and explicitly requires having evidence against determinism. Our argument is a direct appeal to the simplicity of laws, and it involves no probabilistic component. It is modeled on Shoemaker’s argument that one could have evidence of time without change. (shrink)

ABSTRACTThroughout his published work, Michel Henry expresses a deep appreciation for the writings of Kierkegaard, using them as an inspirational foundation for much of his own thought. However, Henry claims to be far more Kierkegaardian than he really is. Henry’s peers have identified several philosophical and theological deficiencies in Henry’s thought. These places of weakness also happen to be his most obvious points of departure from Kierkegaard. A Kierkegaardian confrontation with Henry demands a retrieval of the Infinite Qualitative (...) Difference between God and man as key to exploring the structure of the self. Kierkegaard’s texts correct Henry’s assumption that the ontological difference established in the act of creation would separate the self from God. They suggest instead that the IQD provides the necessary conditions for the truly theological self to emerge. (shrink)

Critical insights into Kierkegaard's influence on Barth's theology. Karl Barth was often critical of Søren Kierkegaard's ideas as he understood them. But close reading of the two corpora reveals that Barth owes a lot to the melancholy Dane. Both conceive of God as infinitely qualitatively different from humans, and both emphasize the shocking nearness of God in the incarnation. As public intellectuals, they used this theological vision to protect Christocentric faith from political manipulation and compromise. For Kierkegaard, this meant criticizing (...) the state church; for Barth, this entailed resisting Nazism. Meticulously crafted by a father-son team of renowned systematic theologians, Beyond Immanence demonstrates that Kierkegaard and Barth share a theological trajectory--one that resists cynical manipulation of Christianity for political purposes in favor of uncompromising devotion to a God who is radically transcendent yet established kinship with humanity in time. (shrink)

If a problem is the collision between a system and a fact, Spinozism and German idealism’s greatest problem is the corpse. Life’s end is problematic for the denial of death’s qualitative difference from life and the affirmation of nature’s infinite purposiveness. In particular, German idealism exemplifies immortalism – the view that life is the unconditioned condition of all experience, including death. If idealism cannot explain the corpse, death is not grounded on life, which invites mortalism – the (...) view that death is the unconditioned condition of experience. In “Philosophical Letters,” Schelling critiques idealism, arguing that death symbolizes the regulative ideal of a philosophical system’s derivation, our striving for which unifies our rational activity. I interpret Schelling’s critique as explaining how death puts philosophy into question, an idea he develops in the Freedom essay and Berlin lectures. Death is not a problem to be solved by a system, but represents philosophy’s highest yet unrealizable end. (shrink)

We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be (...) adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a ‘delay’ torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Christian Ethics and Commonsense Morality: An Intuitionist Account by Kevin JungAleksandar S. SantracChristian Ethics and Commonsense Morality: An Intuitionist Account Kevin Jung NEW YORK AND LONDON: ROUTLEDGE, 2014. 202 PP. $145.00In Christian Ethics and Commonsense Morality: An Intuitionist Account, Kevin Jung boldly constructs and defends a commonsense morality of intuition as a plausible ethical theory against both postmodern constructivist ethical systems and narrow objectivist theories. Following the antifoundationalist (...) ethical methods of postmodern approaches to reality and morality in chapter 1 and a moderate defense of realism in chapter 2, Jung attempts to save both objectivity and de-feasibility of moral realistic accounts, offering some modern reinterpretations of moral realism in chapters 3 and 4. All these forms of Wittgensteinian conceptions of realism unsatisfactorily lead to infinite regress in justifying claims because they are grounded only in the wishes, interests, and sentiments of the individual culture and society (60).After a brief introduction to the unique role of emotions in ethical theories, his investigation leads to reconciliation between objectivist naturalistic ethics [End Page 192] and theological forms of ethical theories. Theological ethicists can remain committed to intuitionism (objectivist and naturalistic forms of common morality) refined by particular religious expressions of morality (112). Intuitionism, broadly defined in chapter 7, is described as "initial appearances" (118); moral truths, according to Jung's intuitionist account, are "mediately self-evident" (128), not "immediately," because it still requires careful reflection and cognitive searching for objectivist grounds of morality. Jung's affirmation of the plausibility of intuitionism seems to be a final blow to all forms of postmodern and skeptical accounts of antifoundationalist forms of ethical theories; he successfully defends an intuitionist account of morality against its naturalist and religious critics.The last chapter offers three types of relationship between commonsense morality and Christian morality. The identity model reduces Christian morality to commonsense morality. The two-tier model considers Christian morality to be a superior form of morality with instrumental value of commonsense morality. And, finally, integration, Jung's favorite model, considers commonsense morality as neither identical nor subordinate but central to Christian morality (163). With this he affirms that Christian morality is unique not because of differences in moral beliefs but because "it is fully committed to recognizing the oneness of humanity and the universally accessible nature of basic moral truths for all human beings" (166). Jung's reflection is exceptionally insightful. Building the case as a good lawyer, he leads us to the defenseless nature of constructivist postmodern moral theories and their revisions as well as to a commitment of Christian morality to the objective commonsense morality. On this view, even heroic moral acts based on obedience to God (such as Christian sacrificial love) might be compatible with commonsense morality. It is surprising, however, that Jung never consulted or quoted Bernard Gert's account of the common morality, especially when discussing differences between moral duty and ideals (167). Additionally, Jung's argument that Christian morality is unexceptional since moral knowledge can be obtained through multiple sources in which God also reveals his will (178) does not sufficiently probe into the distinctiveness of God's sometimes radical demands of Jews/Christians (e.g., Abraham's sacrifice of Isaac), which come not from intuitionist accounts of objective natural reason or common sense but from faith. Christian saints are not heroes of general moral example but heroes of faith, a qualitatively different realm of human experience. Still, audiences interested in all aspects of ethics will greatly benefit from this superb engagement with recent discussions. [End Page 193]Aleksandar S. SantracWashington Adventist UniversityCopyright © 2017 Society of Christian Ethics... (shrink)

Stories about the divine are meant to help our imagination cope with what is ultimately not fully imaginable. In the process we make use of metaphors that rely on quantitative relationships to express the qualitative difference between the reality accessible to us and the transcendent reality of God. For example, because we have no notion of what it would mean to “be outside of time,” eternity tends to be explained in terms of infinite temporality. With the increasingly (...) bizarre and unimaginable worldview of contemporary physics, it is perhaps no longer clear what the difference is between the unknown and the unknowable, or even whether it is possible to articulate a meaningful difference. Science appears to have outrun theology in creating stories that engage our imagination. How to overcome the difficulties this raises, particularly with respect to a widening gulf between academic analysis and popular belief, is at present not clear. A “flight from metaphor” into formalized theory, although apparently valid in science, leads to a dead end in theology. A re‐thinking of many traditional concepts, such as immanence and transcendence, seems to be indicated. (shrink)

In the analysis of Anaxagoras’ physics in view of the relation between his teachings on multitude and heterogeneity, two central questions emerge: 1) How can the structure of the universe considered purely mereo-topologically help us explain that at the first cosmic stage no qualitative difference is manifest in spite of the fact that the entire qualitative heterogeneity is supposedly already present there? 2) How can heterogeneity become manifest at the second stage, resulting from the noûs intervention, if (...) according to fragment B 6 such a possibility requires the existence of “the smallest”, while according to the general principle stated in fragment B 3 there is not “the smallest” but always only “a smaller”? This paper showcases the perplexity of these two questions but deals only with the former. The answer follows from Anaxagoras’ being a thoroughgoing infinitist in the way in which no Greek physicist was: the principle of space isotropy operative in geometry is extended to physics as well. So any two parts of the original mixture are similar to each other not only in view of the smaller-larger relation but also because each contains everything that the other one contains. This in effect means that at the stage of maximal possible heterogeneity each part of any part contains infinitely many heterogeneous parts of any kind whatsoever. So, neither can there be homogeneous parts in view of any qualitative property, nor can there be predominance in quantity of parts of any kind that would make some property manifest. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Ad Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back InTony E. JacksonAd Infinitum: The Ghost in Turing’s Machine: Taking God Out of Mathematics and Putting the Body Back In, by Brian Rotman; xii & 203 pp. Stanford: Stanford University Press, 1993, $39.50 cloth, $12.95 paper.Brian Rotman’s book attempts to pull mathematics—the last, most solid home of metaphysical thought—off its absolutist (...) foundations and into the roiling current of postmodernism. His argument works in what has by now become a rather standard manner. He shows how the grounding ideas of mathematics rest upon the insupportable assumption of a realm of absolute truth, “truth perfect, truth outside time, outside space, outside the material world of matter, energy, and entropy, truth somehow able to be discovered or apprehended but never invented” (p. 19). Rotman questions this Platonic grounding in a number of ways.First, with the help of linguistics (de Saussure, Benveniste, Wittgenstein, and Peirce) he provides a semiotic analysis of mathematical arguments as real-world linguistic events. Proof he looks at “not as a form of inference engaged in preserving eternal truths, but as an historically conditioned species of rhetoric” (p. 35). Secondly, Rotman argues that one idea has most secured the fortress-like solidity of mathematical Platonism: the idea of ad infinitum or infinite iteration. Mathematics takes off from the givenness of the natural numbers, our everyday 1, 2, 3 and so on to infinity. It is the “so on to infinity” that frames up the house of arithmetic as it has stood since Euclid. (Euclidean in this context is equivalent to Platonic in the context of philosophy.) But what is the referent of these numbers? Ultimately they are said to be the symbolic representation of the action of counting, which is the “mathematical ur-cognition” (p. 51). And yet we cannot imagine any material human situation in which counting could actually go on to infinity. Therefore, some impossible, supernatural agent (the ghost of the title) must be projected in order for this conception to exist. Similarly, Rotman argues against the assumption of “perfect repeatability” because this notion depends upon some purely imaginary, ideal identity of object or action that could possibly be repeated. Ad infinitum requires and assumes both a disembodied, metaphysical counter and a disembodied, metaphysical counted.So Rotman sets about putting the body back into this symbolic system by rejecting the idea of ad infinitum. Instead of assuming the existence of counting activities that run, in principle, out to infinity without changing their nature, Rotman posits what he calls “realizable iteration,” that is, counting that admits the necessary dissolution or change of whatever repetitive function you begin with. Put simply, he includes the fact that quantitative accumulation or repetition always eventually brings about a qualitative change: at some point in everyday life a difference of degree of the “same” thing or action inevitably becomes a difference of kind. The natural numbers and the ad infinitum [End Page 390] remain blissfully sheltered from this inescapable real world truth, but Rotman reformulates mathematics so as to include this truth in the very idea of numbering.In fact (and he acknowledges this) he theorizes counting after the model of chaos or complexity theory in the physical sciences. Realizable iteration, he says, will bring in the “qualitative differences” forgotten or repressed (the language of Nietzsche, Heidegger, and Freud runs throughout) in the metaphysical version of number, and “display [the qualitative differences] as the emergent effects of repetition” (p. 131). Even numerical addition, for instance, which had been the most linearly continuous of activities, now will be linear beginning from some initial point, but will become increasingly nonlinear as quantitative increase tends towards some point of qualitative discontinuity with what had come before. The point of discontinuity, though certain to appear, is by its nature not specifiable beyond a horizon of probability, and in this, Rotman aligns his arithmetic not only with chaos theory, but also with quantum mechanics. In an appendix, Rotman elaborates at least to a degree the “pre-elements” of his non-Euclidean arithmetic.As chaos theory does not destroy everyday cause... (shrink)

Suppose, as biocentrists do, that even microorganisms have a good of their own – that is, some objective form of welfare. Still, human welfare is vastly greater and more valuable. If it were infinitely greater, individualistic bio-centrism would be pointless. But consideration of the facts of evolutionary history and of the conceptual relations between infinity and incommensurability reveals that there are no infinite welfare differences among living things. It follows, in particular, that there is some very large number of (...) bacteria whose aggregate overall welfare is not less than the welfare of a human being. (shrink)

The Principle of the Identity of Indiscernibles , according to which two objects are identical if they share all the same properties, has come in for much criticism. Michael Della Rocca has recently defended PII on the grounds that it is needed to forestall the possibility that where there appears to be only one object present, there is actually a multiplicity of exactly-overlapping such objects. Katherine Hawley has criticized this approach for violating a plausible “ground rule” in applying rules of (...) indiscernibility to questions of identity: where there is putative duplication, it must be qualitatively significant. Hawley further suggests that with this rule in hand, one can tell the difference between the presence of one and two indiscernible objects without recourse to either PII or brute, nonqualitative individuation. In this paper, I critically examine Hawley’s contention and find that her appeal to “qualitatively significant duplication” fails since its application to distinct indiscernibles involves a difference that is primarily quantitative anyway. The upshot is a different proposed set of “ground rules” for applying the criterion of qualitative difference when seeking a grounding or explanation for distinctness and identity. (shrink)

Throughout the long centuries of western metaphysics the problem of the infinite has kept surfacing in different but important ways. It had confronted Greek philosophical speculation from earliest times. It appeared in the definition of the divine attributed to Thales in Diogenes Laertius (I, 36) under the description "that which has neither beginning nor end. " It was presented on the scroll of Anaximander with enough precision to allow doxographers to transmit it in the technical terminology of the unlimited (...) (apeiron) and the indeterminate (aoriston). The respective quanti tative and qualitative implications of these terms could hardly avoid causing trouble. The formation of the words, moreover, was clearly negative or privative in bearing. Yet in the philosophical framework the notion in its earliest use meant something highly positive, signifying fruitful content for the first principle of all the things that have positive status in the universe. These tensions could not help but make themselves felt through the course of later Greek thought. In one extreme the notion of the infinite was refined in a way that left it appropriated to the Aristotelian category of quantity. In Aristotle (Phys. III 6-8) it came to appear as essentially re quiring imperfection and lack. It meant the capacity for never-ending increase. It was always potential, never completely actualized. (shrink)

In the chapter of Difference and Repetition entitled ‘Ideas and the synthesis of difference,’ Deleuze mobilizes mathematics to develop a ‘calculus of problems’ that is based on the mathematical philosophy of Albert Lautman. Deleuze explicates this process by referring to the operation of certain conceptual couples in the field of contemporary mathematics: most notably the continuous and the discontinuous, the infinite and the finite, and the global and the local. The two mathematical theories that Deleuze draws upon (...) for this purpose are the differential calculus and the theory of dynamical systems, and Galois’ theory of polynomial equations. For the purposes of this paper I will only treat the first of these, which is based on the idea that the singularities of vector fields determine the local trajectories of solution curves, or their ‘topological behaviour’. These singularities can be described in terms of the given mathematical problematic, that is for example, how to solve two divergent series in the same field, and in terms of the solutions, as the trajectories of the solution curves to the problem. What actually counts as a solution to a problem is determined by the specific characteristics of the problem itself, typically by the singularities of this problem and the way in which they are distributed in a system. Deleuze understands the differential calculus essentially as a ‘calculus of problems’, and the theory of dynamical systems as the qualitative and topological theory of problems, which, when connected together, are determinative of the complex logic of different/ciation. (DR 209). Deleuze develops the concept of a problematic idea from the differential calculus, and following Lautman considers the concept of genesis in mathematics to ‘play the role of model ... with respect to all other domains of incarnation’. While Lautman explicated the philosophical logic of the actualization of ideas within the framework of mathematics, Deleuze (along with Guattari) follows Lautman’s suggestion and explicates the operation of this logic within the framework of a multiplicity of domains, including for example philosophy, science and art in What is Philosophy?, and the variety of domains which characterise the plateaus in A Thousand Plateaus. While for Lautman, a mathematical problem is resolved by the development of a new mathematical theory, for Deleuze, it is the construction of a concept that offers a solution to a philosophical problem; even if this newly constructed concept is characteristic of, or modelled on the new mathematical theory. (shrink)

Pascal’s wager was sometimes viewed in the eighteenth-century as an argument conquering its whole demonstrative force not in the Pensées but in a passage of Locke’s Essay Concerning the Human Understanding (II, XXI, § 70) dealing with the preference to be given to a virtuous life when considering the possibility of another eternal life. In this paper, I intend to show that this interpretation is ill-founded. The argument of the wager highlights the discrepancy between the requirements of alethic reason on (...) the one side and of practical reason on the other side: the wager is to be seen not as a proposition, but as an act. When emphasizing the conditions on which this act can conform to rationality, the argument used of in the Pensées puts the comparison between a unity (my life ante mortem) and a multiplicity (other possible lives post mortem) on the front of the stage, in combination with a reckoning of the chances of winning or losing the bet on God’s existence. The reduction ad absurdum of the act of betting against God’s existence is deduced from a double infinitization, not only quantitative (an infinity of lives), but also qualitative (a reiterating infinity of happiness) of the second member in the comparison. Now, the case is different in Locke’s argumentation. Its reading is vitiated if we deem that the § 70 in the Essay II, XXI consists in a self-sufficient demonstration, understandable by itself. Through a close examination of the chapter XXI in its entire, it appears on the contrary that the thesis of an alleged improvement or even of a mere equivalent of Pascal’s wager in the Essay is defeated by the necessity to put back Locke’s own argument in its true place, actually as the result of a complex enquiry on the principle of the determination of the will. (shrink)

The authors reject a computationally powerful unconscious. Instead, they suggest that simple unconscious processes give rise to complex conscious representations. We discuss evidence showing contrastive effects of conscious and unconscious processes, suggesting a distinction between these types of processes. In our view, conscious processes often serve to correct or control negative consequences of relatively simple unconscious processes.

In a fair finite lottery with n tickets, the probability assigned to each ticket winning is 1/n and no other answer. That is, 1/n is unique. Now, consider a fair lottery over the natural numbers. What probability is assigned to each ticket winning in this lottery? Well, this probability value must be smaller than 1/n for all natural numbers n. If probabilities are real-valued, then there is only one answer: 0, as 0 is the only real and non-negative value that (...) is smaller than 1/n for all natural numbers n. However, this answer seems counter-intuitive, as it violates Regularity: for all possible events A that are assigned a probability, A is assigned a positive probability. It is possible for ticket i to win in the second lottery. So, the set {i} should be assigned a positive probability and not 0. Consequently, in order to satisfy Regularity, probabilities must be allowed to take on `non-real' values, e.g. a positive infinitesimal x that is smaller than 1/n for all natural numbers n. So, what regular probability is assigned to {i} in the second lottery? This probability value must be positive but smaller than 1/n for all natural numbers n. Given the definition of x, x is a correct answer. But x isn't unique, because every other positive infinitesimal is a correct answer as well and there are uncountably many positive infinitesimals. After all, every positive infinitesimal is strictly between 0 and 1/n for all natural numbers n. Nothing about a fair lottery over the natural numbers uniquely determines x as the correct answer and nothing about the lottery rules out other positive infinitesimals as a correct answer as well. What probability to assign to {i} is underdetermined. -/- In this thesis, I explore this difference between fair finite lotteries and fair infinite lotteries. The constraints governing the former uniquely determine the probabilities assigned to events in those lotteries, but this isn't true for the latter lotteries, when Regularity is a constraint on probabilities. Now, although there are uncountably many correct probability values that can be assigned to {i} in the second lottery, there are some applications of probability theory, for which at least one correct probability value must be chosen in order to accomplish that application, e.g. calculation of expected utilities. In this thesis, I spell out sufficient conditions for when a choice like that is problematic. These conditions apply to precise probabilities, imprecise probabilities, and qualitative probabilities. So, I will consider Benci et al. (2018)'s and Pruss (2021)'s suggestion of allowing probabilities to be imprecise, as well as resorting to qualitative probabilities, to overcome the choice problem. I will argue that both don't solve the problem. Furthermore, there's a hitherto unnoticed difficulty in deriving imprecise probabilities by supervaluating over precise `non-real' probability values. To avoid this difficulty, precise probability values should be real-valued. Thus, Regularity cannot be a constraint on probabilities. But as it turns out, dropping Regularity as a constraint and requiring precise probabilities to be real-valued solve the choice problem. (shrink)

The iltifāt (reference switching) is one of the arts of high literary value, widely practiced in the Qurʾān. This art takes place in the form of switching to another person, verb mode, number, preposition or sentence type contrary to the necessity of the situation, while continuing the word as a certain person, verb mode, number, preposition or sentence type. The art of iltifāt adds certain meanings to words such as certainty, continuity and movement. It keeps the curiosity, desire, excitement and (...) shiver alive. Similar to those who read the Qurʾān, those who read the translation of the Qurʾān are expected to be able to notice these meanings as much as possible and feel the literary pleasure of this art. There are important structural differences between Arabic and Turkish. In addition, the text that needs to be translated into Turkish is Holy Qurʾān, which has a divine infinite dimension, and it is a limited human mind attempts to translate it. This situation requires an advanced level of caution and diligence in transferring the art of iltifāt to the translations of Qurʾān. The issue of the art of iltifāt and the transfer of this art to the translations of the Qurʾān has also been studied in scientific research in different world languages such as Arabic, English and Indonesian. As far as we can determine, the only study in Turkish that examines the reflection of the iltifāt in the Qurʾān is the article titled "The Translation Problem of the Art of iltifāt in the Translation of the Qurʾān" by Haşim Özdaş. In the mentioned article, five different Qurʾān translations of eight verses from different types of the art of iltifāt were examined. It has been claimed that there is no art of iltifāt in Turkish language and literature, and that the translation of the art of iltifāt in the verses into Turkish is an obstacle to understanding the verses and leads to a wrong or incomplete understanding. As a solution, while the verses are being given and translated, it is suggested that the art of iltifāt in the verses be ignored. In this research article, the cases of the translations of the Qurʾān reflecting the art of iltifāt, as an example of iltifāt between māzī (past tense) and muzāriʻ (present tense) verbs modes in the verses are discussed. In addition, it discusses the opinions that say there is no art of iltifāt in the Turkish language, that the exact transfer of the art of iltifāt found in the Qurʾān to the translations of the Qurʾān causes wrong or incomplete understanding, therefore, the art of iltifāt should be ignored when the verses are being translated. As a result, the present study argues that the art of iltifāt is also a subject of Turkish rhetoric, which should be reflected in the translations of the Qurʾān as much as possible, and the transfer of the art of iltifāt in the translations of the Qurʾān does not constitute an obstacle to understanding the verses, on the contrary, the reference to this art in the verses will contribute to the realization of the divine purpose and wisdom. The data sources of the research were created from 6 verses and their 22 different translations, using various sampling methods. The data collected from these were analysed using the comparative text analysis method on the basis of the inductive approach. Qualitative data was converted into quantitative data, processed in the SPSS application, and the findings were presented as numerical figures in tables. At the end of the research, it was determined that iltifāt between māzī and muzāriʻ verbs modes studied in the science of rhetoric was also a subject of grammar as the phenomenon of time shifts in verbs. It was seen that the art of iltifāt was applied in an average of 800 places in the Qurʾān, and the iltifāt between māzī and muzāriʻ verbs modes accounted for 6.9% (55 pieces) of this amount. Most of these fifty-five iltifāts were iltifāt from the māzī verb mode to the muzāriʻ verb mode (63.6%), while the amount of iltifāt the muzāriʻ verb mode to the māzī verb mode was less (36.4%). In the analysed translations of the Qurʾān, it was determined that the iltifāt between māzī and muzāriʻ verbs modes was not reflected at a rate of 90.9%, and the art of iltifāt was completely abandoned in 14 of the 22 translations. It was concluded that the reason why the art of iltifāt in the verses was not reflected in the translations of the Qurʾān was the belief that this art was not found in Turkish and that the transfer of this art leads to wrong and incomplete understanding. In the research, it was proposed to increase the number of scientific studies in which various translation strategies and techniques were tested in the transfer of the art of iltifāt in the verses in the translations of the Qurʾān. In this respect, this research article is expected to pave the way for more research on the issue of transferring the arts used in the Qurʾān and to be useful for future translations of the Qurʾān. (shrink)

A number of philosophers have thought that fair lotteries over countably infinite sets of outcomes are conceptually incoherent by virtue of violating countable additivity. In this article, I show that a qualitative analogue of this argument generalizes to an argument against the conceptual coherence of a much wider class of fair infinite lotteries—including continuous uniform distributions. I argue that this result suggests that fair lotteries over countably infinite sets of outcomes are no more conceptually problematic than (...) continuous uniform distributions. Along the way, I provide a novel argument for a weak qualitative, epistemic version of regularity. (shrink)

§1. Iterated Gödelian extensions of theories. The idea of iterating ad infinitum the operation of extending a theory T by adding as a new axiom a Gödel sentence for T, or equivalently a formalization of “T is consistent”, thus obtaining an infinite sequence of theories, arose naturally when Godel's incompleteness theorem first appeared, and occurs today to many non-specialists when they ponder the theorem. In the logical literature this idea has been thoroughly explored through two main approaches. One is (...) that initiated by Turing in his “ordinal logics” and taken very much further in Feferman's work on transfinite progressions, which also introduced the more general study of extensions by reflection principles, of which consistency statements are a special case. This approach starts from an assignment of theories to ordinal notations, and extracts sequences of theories through a suitable choice of a path in the set of ordinal notations. The second approach, illustrated in particular by the work of Schmerl and Beklemishev, starts instead from a suitably well-behaved primitive recursive well-ordering, which is used to define a sequence of theories. This second approach has led to precise results about the relative proof-theoretical strength of sequences of theories obtained by iterating different reflection principles. The Turing-Feferman approach, on the other hand, lends itself well to an investigation in qualitative and philosophical terms of the relevance of such iterated reflection extensions to mathematical knowledge, in particular because of two developments associated with this approach. (shrink)

The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's (...) solution is to distinguish between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved. (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)

The article analyses two first Schelling's works devoted to philosophy of identity: "Darstellung meines Systems der Philosophie" from 1801 and dialogue "Bruno oder über das göttliche und natürliche Prinzip der Dinge" from 1820. In the first one the absolute mind is presented as absolute qualitative identity of object and subject, as absolutely simple and not diverse substance. The form of being of absolute identity is cognition, which realises as infinite constitution of object. Particular things as potencies are quantitative (...) difference between that which is subjective and that which is objective. According to dialogue Bruno, idea as true and eternal reality is unity of what is real and ideal, finite and unfinite. On the other hand, finite things contain their opposite (lack of unity) of their components. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

From the earliest moments in human history, the relationship between God, the universe, and humanity has been a subject of discussion, not only among followers of divine religions but also among representatives of positive sciences. Various theories have been put forth, and numerous evaluations have been made regarding the details of this relationship. The discussions around this topic continue to be relevant today From the perspective of divine religions, one of the most notable and fundamental aspects of the Quran-centered revelation (...) system in Islam is the clear distinction between the Creator and the created. According to this understanding, all entities outside of Allah are categorized as created beings, and they owe their existence and continuity to Allah, who is incomparable to anything else. Additionally, the Quran frequently emphasizes that the universe was created with precise measures, balance, and order. Indeed, these criteria form the starting point of the teleological argument, which extensively utilizes them to demonstrate the existence of Allah, especially His unity. All of this suggests that nothing in the universe is the result of random chance; rather, it implies that the universe embodies a sense of regularity or lawfulness. In our view, “Sunnatullah” is a term used in the Quran to express this regularity or lawfulness. The issue of the unchangeability of the “Sunnatullah” has brought forth discussions on determinism first through causality and then, within the context of determinism, debates on deism. Indeed, interpreting the concept of “Sunnatullah” through a rigid deterministic understanding may open the door to deism, while attributing events in the universe to chance rather than standard laws brings about a process leading to atheism by excluding the Creator. Therefore, it is crucial to approach the phenomenon of “Sunnatullah” in the context of the relationship between God, the universe, and humans in a way that eliminates these risks. For this reason, we have chosen to focus on the relationship between “Sunnatullah” and legality within the context of “immutability.” In addressing this topic, we have attempted to consider not only the data of revelation but also the factual domain. In doing so, our fundamental approach has been not to view the Quran as a purely scientific book and not to operate under the assumption that “everything happening in nature is detailed in the Quran.” However, we have endeavored not to overlook the fact that there is harmony between nature/physics, created by the same entity, and the Quran. In our opinion, this harmony has the potential to create an objective foundation for reaching belief in Allah based on the movement from nature/physics. While composing our text, we emphasized concept analysis and highlighted historical and empirical realities. Document analysis was chosen as the method for this qualitative research. We explored the framework of the concept of “Sunnatullah” and attempted to elucidate its relationship with causality. In our research, the term “Sunnatullah” has been used in a sense encompassing all laws pertaining to society and nature within the context of the relationship between God, humans, and the universe. Additionally, it has been argued that the introduction of different laws into the nature and operation of anything in various areas and conditions of life does not imply that the law is susceptible to change. In our view, the unchangeability of the law refers to the detail that the same law will come into effect under the same conditions. Conditions may change, but the law that comes into effect according to those specific/appropriate conditions remains unchanged. Indeed, in line with His infinite knowledge and power, Allah has not overlooked any detail and has established a law for every possible situation in the universe with its causes and effects. The relationship between “Sunnatullah” and causality occurs in this context. (shrink)

In his 1676 text De Quadratura Arithmetica, Leibniz distinguished infinita terminata from infinita interminata. The text also deals with the notion, originating with Desargues, of the point of intersection at infinite distance for parallel lines. We examine contrasting interpretations of these notions in the context of Leibniz’s analysis of asymptotes for logarithmic curves and hyperbolas. We point out difficulties that arise due to conflating these notions of infinity. As noted by Rodríguez Hurtado et al., a significant difference exists (...) between the Cartesian model of magnitudes and Leibniz’s search for a qualitative model for studying perspective, including ideal points at infinity. We show how respecting the distinction between these notions enables a consistent interpretation thereof. (shrink)