This paper introduces the Theory of Spatial Materialization of Quantum Possibilities in an Infinite Space, proposing a novel perspective on the realization of quantum probabilities. Traditional interpretations of quantum mechanics, such as the Copenhagen interpretation and the Many-Worlds hypothesis, approach quantum probabilities as either collapsing into a single observable state or manifesting across parallel universes. This theory suggests an alternative: in an infinite space, quantum possibilities materialize simultaneously in distinct spatial regions, without requiring collapse or parallel universes. Building (...) on principles of infinite space and inevitable probabilities, the theory reinterprets phenomena such as superposition and cosmological configurations, offering a unified framework for understanding how quantum possibilities are distributed in space. The implications extend to questions of causality, time, and the nature of observable reality, while challenging traditional assumptions in quantum mechanics. Although speculative, this approach provides fertile ground for interdisciplinary exploration, bridging cosmology, philosophy of science, and quantum mechanics. (shrink)

In this paper, I aim to show that a certain form of immortality, without the need for any intervention from a supernatural being, is almost inevitable for human beings. I take a physicalist starting point: I am a certain configuration of physical particles. Thus, if these particles were reassembled in the same configuration, I would necessarily come back into existence. I address a number of objections raised against this prospect by Eric T. Olson, who argues that the reassembly of such (...) particles following their dispersal after death would be simply impossible, and that if it did occur, it would necessarily be a mere replica rather than the real ‘me’. I suggest that the random redistribution of particles can be thought of as the throw of cosmic ‘dice’. With any specific throw, the likelihood that it yields the particular configuration that constitutes ‘me’ is vanishingly small. But over infinite spans of time, this likelihood increases until it becomes a near certainty. I show that even if this reconfiguration lacks the same causal features as those that gave rise to the original me, this cannot imply that the reassembled me is a mere replica. I acknowledge that my conjectured form of immortality may be unappealing to theists and non-theists alike. I also note that it rests on a linear conception of time, which may not harmonise with current thinking in physics. However, these issues notwithstanding, my conjectured version of immortality is at least as inexorable as many other things we take for granted, which also rest on potentially flawed beliefs about the nature of time and space. (shrink)

The quantum measurement problem resolves according to the twofold nature of time. Whereas the continuous evolution of the wave function reflects the fundamental nature of time as continuous presence, the collapse of the wave function indicates the subsidiary aspect of time as the projection of instantaneity from the ongoing present. Each instant irreversibly emerges from the reversible temporal continuum implicit in the smoothly propagating wave function. The basis of this emergence is periodic conflict between quantum systems, the definitive resolution of (...) which requires the momentary reduction of each system from the potentially infinite dimensions of configuration space to the three dimensions of classical space at an instant. (shrink)

A natural extension of Heron's 2000 year old formula for the area of a triangle to the volume of a tetrahedron is presented. This gives the fourth power of the volume as a polynomial in six simple rational functions of the areas of its four faces and three medial parallelograms, which will be referred to herein as "interior faces." Geometrically, these rational functions are the areas of the triangles into which the exterior faces are divided by the points at which (...) the tetrahedron's in-sphere touches those faces. Part I presents an overview of these results and some necessary but little-known background in areal geometry. Part II derives the promised extension, and ends with a conjecture as to how the formula extends to n-dimensional simplices for all n>3. Part III explains how, for n=3, the zeros of the polynomial constitute a five-dimensional semi-algebraic variety consisting almost entirely of collinear tetrahedra with vertices separated by infinite distances, but with generically well-defined distance ratios; it further proves that these unconventional Euclidean configurations can be identified with a quotient of the Klein quadric by an action of a group of reflections isomorphic to ℤ42, wherein four-point configurations in the affine plane constitute a distinguished three-dimensional subvariety. Part IV consists of five appendices which show, among other things, that the algebraic structure of the zeros in the affine plane naturally defines the associated four-element, rank 3 chirotope, aka affine oriented matroid. (shrink)

Writers endorsing a general account of meaning as non-recuperable or non-coincidental from one instantiation to the next may nonetheless treat the heterogeneous contacts between instants of experience as transformations of fleeting forms, states, logics, structures, outlines, surfaces, presences, organizations, patterns, procedures, frames, standpoints. When thought as pattern, the structural- ranscendental moment of eventness upholds a certain logic of internal relation; the elements of the configuration mutually signify each other and the structure presents itself as a fleeting identity, a gathered field. (...) The particularity of eventness is not allowed to split the presumed (temporary) identity of the internal configuration that defines the structure as structure. History would be the endless reframing of a frame, the infinite shifting from paradigm to paradigm. Heidegger and Derrida argue instead that In their essence, Beings don’t HAVE structure or constitution. There is no such THING as a form, a structure, a state. There is no trans-formation but rather a trans-differentiation, (transformation without form, articulation as dislocation) What is being transcended is not form but difference. (shrink)

What is the form of that which can hold, size, and measure what is happening? Are there some gestures that can, in some sense, size what is occurring in absolute fragility? We trace forms that, suddenly, sometimes, can grasp in a vanishing present what cannot be grasped by any other means. Certain art practices can sustain and give shelter, for a while, to an echo of that multiple and unending past. These practices inexist. These inexistences compose artistic configurations, of (...) which the artworks referred to in this book are outstanding examples. The axiomatic declaration of the inexistence of art operates as an act of flight, a subtraction. Undomiciled artistic practices are multiple, infinite, and emancipatory. From these practices, we can find the sub-stance for an infrapolitical anarchitecture that works in constructing a future yet to be imagined. Another world is possible, of course. We must continue to whisper that other worlds are possible because we are already participants in that memory to come. On Gestural Apparatuses works as a mechanism of delay that aims to indicate an operative movement within artistic thinking. (shrink)

This paper discusses an infinite regress that looms behind a certain kind of historical explanation. The movement of one barbarian group is often explained by the movement of others, but those movements in turn call for an explanation. While their explanation can again be the movement of yet another group of barbarians, if this sort of explanation does not stop somewhere we are left with an infinite regress of barbarians. While that regress would be vicious, it cannot be (...) accommodated by several general views about what viciousness in infinite regresses amounts to. This example is additional evidence that we should prefer a pluralist approach to infinite regresses. (shrink)

For aggregative theories of moral value, it is a challenge to rank worlds that each contain infinitely many valuable events. And, although there are several existing proposals for doing so, few provide a cardinal measure of each world's value. This raises the even greater challenge of ranking lotteries over such worlds—without a cardinal value for each world, we cannot apply expected value theory. How then can we compare such lotteries? To date, we have just one method for doing so (proposed (...) separately by Arntzenius, Bostrom, and Meacham), which is to compare the prospects for value at each individual location, and to then represent and compare lotteries by their expected values at each of those locations. But, as I show here, this approach violates several key principles of decision theory and generates some implausible verdicts. I propose an alternative—one which delivers plausible rankings of lotteries, which is implied by a plausible collection of axioms, and which can be applied alongside almost any ranking of infinite worlds. (shrink)

People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call (...) *Countable Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

In western philosophy and beyond, a tension between pluralism and monism has sparked many developments and debates. Pluralism of norms, of forms of knowledge, of aesthetic and moral values, of interests etc. has often been pitted against monism. Monism usually implies a hierarchical order of such norms etc. After having traced the origin of this tension between pluralism and monism in ancient tragedy and philosophy, I’m asking in this article whether a rejection of monism and embrace of pluralism necessarily raises (...) the specter of inconsistency and contradiction. The threat of inconsistency need not be associated with pluralism as even with regard to logic an argument can be made for a ‘multiplicity of logics’, as van Lambalgen and Stenning argue in several places. They refer to the varieties in reasoning that can be observed in humans and which are partly due to there being ‘dual systems’ of reasoning: System 1 processes information fast, automatized, and emotional, while System 2 is rather slow, more deliberative, and more rational. In contrast to a widely held view, the authors argue that System 1 processing is not without logic, even though it is a different form of logic from System 2. In addition, the multiplicity of logics they discuss is related to the multiple semantics required for distinct domains of reasoning. This perspective raises the subsequent question how this pluralism can be available while maintaining consistency, how should the available options be configured or related to each other? In the remainer of this chapter I’m addressing several such options for configurating pluralism like: non-foundational pluralism and foundational pluralism, moderate or temporary pluralism, antagonistic pluralism, incompatible pluralism, incommensurable pluralism, ‘Anything goes’ pluralism, complementary pluralism, integrative pluralism, and interactive pluralism. The discussion and examples of these options show that irrespective of its domain, the encounter with different configurations of pluralism shows how some forms of pluralism are likely to be productive, whereas others are less so - which is an important lesson given the prominent pluralism of pluralisms in philosophy and beyond. (shrink)

Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian (...) “infinite book copies” objection, and that this provides an interesting way to defuse some cosmological arguments for the existence of God and to give a non-theistic but complete explanation of the Universe. In the course of my argumentation, I also show that circular explanations can be “self-explanatory” as well: explaining two items by each other can explain the couple of items tout court. (shrink)

In formal ontology, infinite regresses are generally considered a bad sign. One debate where such regresses come into play is the debate about fundamentality. Arguments in favour of some type of fundamentalism are many, but they generally share the idea that infinite chains of ontological dependence must be ruled out. Some motivations for this view are assessed in this article, with the conclusion that such infinite chains may not always be vicious. Indeed, there may even be room (...) for a type of fundamentalism combined with infinite descent as long as this descent is “boring,” that is, the same structure repeats ad infinitum. A start is made in the article towards a systematic account of this type of infinite descent. The philosophical prospects and scientific tenability of the account are briefly evaluated using an example from physics. (shrink)

Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue—the issue of grounding and infinite descent. I frame the discussion around two questions: (1) What is infinite descent of ground? and (2) Is infinite descent of ground possible? In addressing the (...) second question, I will consider a number of arguments that have been made for and against the possibility of infinite descent of ground. When relevant, I connect the discussion to two important views about the way reality can be structured by grounding: metaphysical foundationalism and metaphysical infinitism. (shrink)

A common argument for atheism runs as follows: God would not create a world worse than other worlds he could have created instead. However, if God exists, he could have created a better world than this one. Therefore, God does not exist. In this paper I challenge the second premise of this argument. I argue that if God exists, our world will continue without end, with God continuing to create value-bearers, and sustaining and perfecting the value-bearers he has already created. (...) Given this, if God exists, our world—considered on the whole—is infinitely valuable. I further contend that this theistic picture makes our world's value unsurpassable. In support of this contention, I consider proposals for how infinitely valuable worlds might be improved upon, focusing on two main ways—adding value-bearers and increasing the value in present value-bearers. I argue that neither of these can improve our world. Depending on how each method is understood, either it would not improve our world, or our world is unsurpassable with respect to it. I conclude by considering the implications of my argument for the problem of evil more generally conceived. (shrink)

We can have credences in an infinite number of propositions—that is, our opinion set can be infinite. Accuracy-first epistemologists have devoted themselves to evaluating credal states with the help of the concept of ‘accuracy’. Unfortunately, under several innocuous assumptions, infinite opinion sets yield several undesirable results, some of which are even fatal, to accuracy-first epistemology. Moreover, accuracy-first epistemologists cannot circumvent these difficulties in any standard way. In this regard, we will suggest a non-standard approach, called a relativistic (...) approach, to accuracy-first epistemology and show that such an approach can successfully circumvent undesirable results while having some advantages over the standard approach. (shrink)

Aggregative moral theories face a series of devastating problems when we apply them in a physically realistic setting. According to current physics, our universe is likely _infinitely large_, and will contain infinitely many morally valuable events. But standard aggregative theories are ill-equipped to compare outcomes containing infinite total value so, applied in a realistic setting, they cannot compare any outcomes a real-world agent must ever choose between. This problem has been discussed extensively, and non-standard aggregative theories proposed to overcome (...) it. This paper addresses a further problem of similar severity. Physics tells us that, in our universe, how remotely in time an event occurs is _relative_. But our most promising aggregative theories, designed to compare outcomes containing infinitely many valuable events, are sensitive to how remote in time those events are. As I show, the evaluations of those theories are then relative too. But this is absurd; evaluations of outcomes must be absolute. So we must reject such theories. Is this objection fatal for all aggregative theories, at least in a relativistic universe like ours? I demonstrate here that, by further modifying these theories to fit with the physics, we can overcome it. (shrink)

It is possible that the world contains infinitely many agents that have positive and negative levels of well-being. Theories have been developed to ethically rank such worlds based on the well-being levels of the agents in those worlds or other qualitative properties of the worlds in question, such as the distribution of agents across spacetime. In this thesis I argue that such ethical rankings ought to be consistent with the Pareto principle, which says that if two worlds contain the same (...) agents and some agents are better off in the first world than they are in the second and no agents are worse off than they are in the second, then the first world is better than the second. I show that if we accept four axioms – the Pareto principle, transitivity, an axiom stating that populations of worlds can be permuted, and the claim that if the ‘at least as good as’ relation holds between two worlds then it holds between qualitative duplicates of this world pair – then we must conclude that there is ubiquitous incomparability between infinite worlds. I show that this is true even if the populations of infinite worlds are disjoint or overlapping, and that we cannot use any qualitative properties of world pairs to rank these worlds. Finally, I argue that this incomparability result generates puzzles for both consequentialist and non-consequentialist theories of objective and subjective permissibility. (shrink)

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which (...) all reality can emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

Some environmental ethicists and economists argue that attributing infinite value to the environment is a good way to represent an absolute obligation to protect it. Others argue against modelling the value of the environment in this way: the assignment of infinite value leads to immense technical and philosophical difficulties that undermine the environmentalist project. First, there is a problem of discrimination: saving a large region of habitat is better than saving a small region; yet if both outcomes have (...) infinite value, then decision theory prescribes indifference. Second, there is a problem of swamping probabilities: an act with a small but positive probability of saving an endangered species appears to be on par with an act that has a high probability of achieving this outcome, since both have infinite expected value. Our paper shows that a relative concept of infinite value can be meaningfully defined, and provides a good model for securing the priority of the natural environment while avoiding the failures noted by sceptics about infinite value. Our claim is not that the relative infinity utility model gets every detail correct, but rather that it provides a rigorous philosophical framework for thinking about decisions affecting the environment. (shrink)

Supererogatory acts are those that lie “beyond the call of duty.” There are two standard ways to define this idea more precisely. Although the definitions are often seen as equivalent, I argue that they can diverge when options are infinite, or when there are cycles of better options; moreover, each definition is acceptable in only one case. I consider two ways out of this dilemma.

This book examines the philosophy of the nineteenth-century Indian mystic Sri Ramakrishna and brings him into dialogue with Western philosophers of religion, primarily in the recent analytic tradition. Sri Ramakrishna’s expansive conception of God as the impersonal-personal Infinite Reality, Maharaj argues, opens up an entirely new paradigm for addressing central topics in the philosophy of religion, including divine infinitude, religious diversity, the nature and epistemology of mystical experience, and the problem of evil.

The article presents a conceptual framework for distinguishing different sorts of heterogeneous digital materials. The hypothesis is that a wide range of heterogeneous data resources can be characterized and classified due to their particular configurations of hypertext features such as scripts, links, interactive processes, and time scalings, and that the hypertext configuration is a major but not sole source of the messiness of big data. The notion of hypertext will be revalidated, placed at the center of the interpretation of (...) networked digital media, and used in the analysis of the fast-growing amounts of heterogeneous digital collections, assemblages, and corpora. The introduction summarizes the wider background of a fast-changing data landscape. (shrink)

Drawing upon the practice of caregiving and the insights of feminist care ethics, I offer a phenomenology of caregiving through the work of Eva Feder Kittay and Emmanuel Lévinas. I argue that caregiving is a material dialectic of embodied response involving moments of leveling, attention, and interruption. In this light, the Levinasian opposition between responding to another's singularity and leveling it via parity-based principles is belied in the experience of care. Contra much of response ethics’ and care ethics’ respective literatures, (...) this dialectic suggests that they are complementary in ways that productively illuminate themes of each. I conclude by suggesting that when response and care ethics are thought together through the experience of caregiving, such labors produce finite responsibility with infinite hope. (shrink)

This paper uses a schema for infinite regress arguments to provide a solution to the problem of the infinite regress of justification. The solution turns on the falsity of two claims: that a belief is justified only if some belief is a reason for it, and that the reason relation is transitive.

My two principal aims in this essay are interconnected. One aim is to provide a new interpretation of the ‘infinite modes’ in Spinoza’s Ethics. I argue that for Spinoza, God, conceived as the one infinite and eternal substance, is not to be understood as causing two kinds of modes, some infinite and eternal and the rest finite and non-eternal. That there cannot be such a bifurcation of divine effects is what I take the ‘infinite mode’ propositions, (...) E1p21–23, to establish; E1p21–23 show that each and every one of the immanent effects of an infinite and eternal God is an infinite and eternal mode. The other aim is to show that these propositions can be understood as part of an extended critical response to Descartes’s infamous doctrine that God creates eternal truths and true and immutable natures. If we have the correct (Spinozan) conceptions of what God is and how God works, we see that an eternal and infinite God can only be understood to cause ‘eternal truths,’ and that these eternal truths are infinite and eternal modes of God. (shrink)

In this chapter I explain Spinoza's concept of "infinite modes". After some brief background on Spinoza's thoughts on infinity, I provide reasons to think that Immediate Infinite Modes are identical to the attributes, and that Mediate Infinite Modes are merely totalities of finite modes. I conclude with some considerations against the alternative view that infinite modes are laws of nature.

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Noether's Theorem produces the configuration (and symmetry) for everything in Nature.

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite (...) sums can be equipped with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

This article offers a reconstruction of an argument against infinite regress formulated by Aristotle in Posterior Analytics I 22. I argue against the traditional interpretation of the chapter, according to which singular terms and summa genera, in virtue of having restrict logical roles, provide limits for predicative chains, preventing them from proceeding ad infinitum. As I intend to show, this traditional reading is at odds with some important aspects of Aristotle’s theory of demonstration. More importantly, it fails to explain (...) how his proof is connected to a defence of the existence of ultimate explanations, a connection that must be the case if I 19-22 is advancing a foundationalist way-out to a sceptical challenge raised in I 3. (shrink)

We present a novel approach to defining the mathematical constant π through the infinite den- sification of a sweeping net, which approximates a circle as the net becomes infinitely dense. By developing and enhancing notation related to sweeping nets and saddle maps, we establish a rigor- ous framework for expressing π in terms of the densification process using reverse integration. This method, inspired by the concept that numbers ”come from infinity,” leverages a reverse integral approach to model the transition (...) from infinite densification to the finite circle. Our work not only offers a new perspective on the geometric interpretation of π but also provides insights into reverse integration techniques and their applications in mathematical analysis. (shrink)

Configurational Comparative Methods (CCMs) aim to learn causal structures from datasets by exploiting Boolean sufficiency and necessity relationships. One important challenge for these methods is that such Boolean relationships are often not satisfied in real-life datasets, as these datasets usually contain noise. Hence, CCMs infer models that only approximately fit the data, introducing a risk of inferring incorrect or incomplete models, especially when data are also fragmented (have limited empirical diversity). To minimize this risk, evaluation measures for sufficiency and necessity (...) should be sensitive to all relevant evidence. This article points out that the standard evaluation measures in CCMs, consistency and coverage, neglect certain evidence for these Boolean relationships. Correspondingly, two new measures, contrapositive consistency and contrapositive coverage, which are equivalent to the binary classification measures specificity and negative predictive value, respectively, are introduced to the CCM context as additions to consistency and coverage. A simulation experiment demonstrates that the introduced contrapositive measures indeed help to identify correct CCM models. (shrink)

Many have the intuition that human persons are both extremely and equally valuable. This seeming extremity and equality of vale is puzzling: if overall value is the sum of one’s final value and instrumental value, how could it be that persons share the same extreme value? One way that we can solve the Value Puzzle is by following Andrew Bailey and Josh Rasmussen. Philosophy and Phenomenological Research, 103, 264–277 (2020) and accepting that persons have infinite final value. But there (...) are some significant downsides to their way of thinking about values, which relies on the extended real numbers. We offer a different approach: if we model values using the hyperreal numbers, we can capture many of our intuitions about the extremity and relative equality of human value without incurring the substantial theoretical costs of using the extended real numbers. We also examine other ways of modeling the infinite value of persons and evaluate the strengths and weaknesses of these other accounts compared to ours. (shrink)

There is a long-standing debate in epistemology on the structure of justification. Some recent work in formal epistemology promises to shed some new light on that debate. I have in mind here some recent work by David Atkinson and Jeanne Peijnenburg, hereafter “A&P”, on infinite regresses of probabilistic support. A&P show that there are probability distributions defined over an infinite set of propositions {\ such that \ is probabilistically supported by \ for all i and \ has a (...) high probability. Let this result be “APR”. A&P oftentimes write as though they believe that APR runs counter to foundationalism. This makes sense, since there is some prima facie plausibility in the idea that APR runs counter to foundationalism, and since some prominent foundationalists argue for theses inconsistent with APR. I argue, though, that in fact APR does not run counter to foundationalism. I further argue that there is a place in foundationalism for infinite regresses of probabilistic support. (shrink)

There are infinitely many ways the world might be, and there may well be infinitely many people in it. These facts raise moral paradoxes. We explore a conflict between two highly attractive principles: a Pareto principle that says that what is better for everyone is better overall, and a statewise dominance principle that says that what is sure to turn out better is better on balance. We refine and generalize this paradox, showing that the problem is faced by many theories (...) of interpersonal aggregation besides utilitarianism, and by many decision theories besides expected value theory. Considering the range of consistent responses, we find all of them to be quite radical. (shrink)

I will explore the paradoxical nature of epistemic access. By critiquing the traditional conception of mental states that are labelled as ’knowledge’, I demonstrate the susceptibility of these states to an infinite regress, thus, challenging their existence and validity. I scrutinise the assumption that an epistemic agent can have complete epistemic access to all facts about a given object while simultaneously being ignorant of certain truths that impact the very knowledge claims about the object. I further analyse the implications (...) of this paradox when attempting to fine-grain the parameters of epistemic access, which happens to reveal the vacuity of such definitions and the inevitability of the regress. (shrink)

This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss (...) the issue of whether the hypercategorematic infinite is a “whole”, comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things. (shrink)

I analyze the role of infinite idealizations used in the renormalization group (RG hereafter) method in explaining universality across microscopically different physical systems in critical phenomena. I argue that despite the reference to infinite limit systems such as systems with infinite correlation lengths during the RG process, the key to explaining universality in critical phenomena need not involve infinite limit systems. I develop my argument by introducing what I regard as the explanatorily relevant property in RG (...) explanations: linearization* property; I then motivate and prove a proposition about the linearization* property in support of my view. As a result, infinite limit systems in RG explanations are dispensable. (shrink)

Infinity exists as a concept but has no existence in actuality. For infinity to have existence in actuality either time or space have to already be infinite. Unless something is already infinite, the only way to become infinite is by an 'infinity leap' in an infinitely small moment, and this is not possible. Neither does infinitely small have an existence since anything larger than zero is not infinitely small. Therefore infinity has no existence in actuality.

In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are too large to (...) be counted by any finite number, but too small to be counted by any infinite number – there is no number of natural numbers. (shrink)

Draft for presentation at the 14th International Kant-Congress, September 2024. -/- Abstract: Kant claims we intuit infinite space. There’s a problem: Kant thinks full awareness of infinite space requires synthesis—the act of putting representations together and comprehending them as one. But our ability to synthesize is finite. Tobias Rosefeldt has argued in a recent paper that Kant’s notion of decomposing synthesis offers a solution. This talk criticizes Rosefeldt’s approach. First, Rosefeldt is committed to nonconceptual yet determinate awareness of (...) (potentially) infinite space, but I argue that such awareness is (1) prima facie implausible, as well as contravened by textual evidence from Kant’s (2a) definitions of ‘infinity’ and (2b) account of geometrical construction. Second, scrutiny of how Kant thinks awareness of potential infinity is afforded by geometrical construction (e.g., extending a line segment ad indefinitum) indicates no essential role for decomposing synthesis. Familiar synthesis from parts to wholes is sufficient. (shrink)

Le passage spéculatif de la catégorie du mauvais infini dans le véritable infini reste l’un des plus importants dans la Science de la logique. Comme il est bien connu, ce passage est expliqué par Hegel à travers sa théorie de l’idéalité du fini. Pourtant, du fait de sa structure complexe, le surgissement du véritable infini au sein du fini par l’idéalisation peut être considéré comme un processus abstrait, consistant seulement à supprimer la dualité de l’infinité. Cet article se propose donc (...) d’examiner pourquoi l’idéalisation de la véritable infini ne signifie ni une simple neutralisation de la catégorie de la finité ni une infinitisation extérieure de celle-ci, mais un processus dynamique qui s’infinitise en supprimant l’opposition statique du fini et de l’infini. (shrink)

All cultures are infused by or even rooted in certain values. Although those values are generally recognised in all societies, they are diversely ranked or proritised in different human groups and different perceptions partly account for cultural diversity as not all values can be equally upheld in any community or by any individual. Though value universalism in a strict sense is unachievable, we can all agree on a pluralistic mutual understanding of and tolerance for diversity.

A comment on Paul Schoemaker's target article in Behavioral and Brain Sciences, 14 (1991), p. 205-215, "The Quest for Optimality: A Positive Heuristic of Science?" (https://doi.org/10.1017/S0140525X00066140). This comment argues that the optimizing model of decision leads to an infinite regress, once internal costs of decision (i.e., information and computation costs) are duly taken into account.

Suppose we wish to decide which of a pair of actions has better consequences in a case in which both actions result in infinite utility. Peter Vallentyne and others have proposed that one action has better consequences than a second if there is a time after which the cumulative utility of the first action always outstrips the cumulative utility of the second. I argue against this principle, in particular I show how cases may arise in which up to any (...) point of time action a1 produces more utility than action a2, yet for each individual involved a2 produces more utility. (shrink)

This paper responds to commentaries by Kaiserman and Magidor, and Hawthorne. The case of the infinite clowns can teach us several things.

Stable evolutionary strategy of Homo sapiens (SESH) is built in accordance with the modular and hierarchical principle and consists of the same type of self-replicating elements, i.e. is a system of systems. On the top level of the organization of SESH is the superposition of genetic, social, cultural and techno-rationalistic complexes. The components of this triad differ in the mechanism of cycles of generation - replication - transmission - fixing/elimination of adoptively relevant information. This mechanism is implemented either in accordance (...) with the Darwin-Weismann modus, or according to the Lamarck modus, the difference between them is clear from the title. The integral attribute of the system of systems including ESSH is the production of evolutionary risks. The sources of evolutionary risk for stable adaptive strategy of Homo sapiens are the imbalance of (1) the intra-genomic co-evolution (intragenomic conflicts); (2) the gene-cultural co- evolution; (3) the inter-cultural co-evolution; (4) techno-humanitarian balance; (5) inter- technological conflicts (technological traps). At least phenomenologically the components of the evolutionary risk are reversible, but in the aggregate they are in potentio irreversible destructive ones for bio-social, and cultural self-identity of Homo sapiens. When the actual evolution is the subject of a rationalist control and/or manipulation, the magnitude of the 4th and 5th components of the evolutionary risk reaches the level of existential significance. (shrink)

The study aims to investigate the effects of the spatial configuration of traditional Vietnamese houses on the design of apartment buildings in Ho Chi Minh (HCM) City, Vietnam. To achieve the objective, the following approaches were implemented. Firstly, the transformation of the socio-economic structure in HCM City, which is a primary factor affecting the development of apartment buildings was examined. Secondly, the well-known space syntax method for analyzing the spatial structure plan was outlined. Thirdly, a survey of traditional houses and (...) apartment buildings from 1960 to 2010 was conducted. Among the various traditional house styles, the Hue traditional garden house, which has primary effects on the modern housing design in HCM City, was selected as a representative sample to compare with apartment units. Lastly, the space syntax method was employed to analyze the spatial structure of the sample of traditional houses and apartment units. The effects of the Hue traditional house’s spatial configuration on apartment buildings were analyzed. The result shows that the spatial configuration of modern apartment buildings and traditional houses have similar characteristics, including having an adaptable natural environment, and they both reflect Vietnamese culture and society. The findings can be applied when predicting development trends for the unit plans of modern apartments in HCM City, Vietnam. (shrink)

本文对文化的价值多样性进行多元的理解，集中阐述和讨论“文化的价值组合配置”(cultural configurations of values)概念。主要包括以下几个要点：(1)在世界的各种文化中，人类的价值有不同的表现形式，但其基本价值是相似的，甚至相同的。(2)人类的各种基本价值之间不但有互相促进的关系，也有相互矛盾、相互竞 争、相互冲突的关系。(3)一种文化类型提供对相互冲突的价值的一种处理方式。不同的文化形成其各自的价值组合与配置。这种价值的配置与其社会环境相适应，是其文化的核心部分。文化差异性的一个重要方面就是，尽管 所有文化共有这些基本价值，但是他们会给予这些价值不同的权重，形成不同的价值配置形式。(4)有时在同一个社会里，会存在若干“亚文化”，会有不同的价值配置。随着时间的推移，文化和社会都会有改变。虽然它们在 价值组合配置普世化上可能永远无法达成一致，但是它们之间的共同价值为和平共处提供了基础。.

Infinite machines (IMs) can do supertasks. A supertask is an infinite series of operations done in some finite time. Whether or not our universe contains any IMs, they are worthy of study as upper bounds on finite machines. We introduce IMs and describe some of their physical and psychological aspects. An accelerating Turing machine (an ATM) is a Turing machine that performs every next operation twice as fast. It can carry out infinitely many operations in finite time. Many (...) ATMs can be connected together to form networks of infinitely powerful agents. A network of ATMs can also be thought of as the control system for an infinitely complex robot. We describe a robot with a dense network of ATMs for its retinas, its brain, and its motor controllers. Such a robot can perform psychological supertasks - it can perceive infinitely detailed objects in all their detail; it can formulate infinite plans; it can make infinitely precise movements. An endless hierarchy of IMs might realize a deep notion of intelligent computing everywhere. (shrink)