In this paper, we examine the locality condition for non‐splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove the following. Suppose that K$\mathcal {K}$ is an abstract elementary class satisfying (1)the joint embedding and amalgamation properties with no maximal model of cardinality μ$\mu$, (2)stability in μ$\mu$, (3)κμ∗(K)<μ+$\kappa ^*_\mu (\mathcal {K})<\mu ^+$, (4)continuity for non-μ-splitting${\rm non}\text{-}\mu\text{-}{\rm splitting}$ (i.e., if p∈ga-S(M)$p\in \operatorname{ga-S}(M)$ and M$M$ (...) is a limit model witnessed by ⟨Mi|i<α⟩$\langle M_i| i<\alpha \rangle$ for some limit ordinal α<μ+$\alpha <\mu ^+$ and there exists N≺M0$N \prec M_0$ so that p↾Mi$p\mathord {\upharpoonright }M_i$ does not μ$\mu$‐split over N$N$ for all i<α$i<\alpha$, then p$p$ does not μ$\mu$‐split over N$N$). Then for ϑ$\vartheta$ and δ$\delta$ limit ordinals <μ+$<\mu ^+$ both with cofinality ≥κμ∗(K)$\ge \kappa ^*_\mu (\mathcal {K})$, if K$\mathcal {K}$ satisfies symmetry for non-μ-splitting${\rm non}\text{-}\mu\text{-}{\rm splitting}$ (or just (μ,δ)$(\mu,\delta)$‐symmetry), then, for any M1$M_1$ and M2$M_2$ that are (μ,ϑ)$(\mu,\vartheta)$ and (μ,δ)$(\mu,\delta)$‐limit models over M0$M_0$, respectively, we have that M1$M_1$ and M2$M_2$ are isomorphic over M0$M_0$. Note that no tameness is assumed. (shrink)

We claim that the Universe’s fundamental structure is not discoverable through rationalism. The various frameworks studied are logic, mathematics, their application through theories in physics, and finally, the pivotally separate application of logic to historical evidence in formal religious belief. The basis of the prohibition is that rational structure has a limit for consistency that falls short of completeness in absolute terms. The limit of observability reaches only a framework in which correlated elements are formed paradoxically within a (...) parent structure. Apart from our advanced ability in human reasoning, we have the same fundamental sentience possessed by other living creatures. Beyond that limit of awareness, the Universe in its native form is immaculately nonordered. We examine the dimensional relationship between quantum and classical frameworks to justify the theory. Mathematics requires operational consistency across its elements. In contrast, the Universe incorporates a feature of inconsistency in its native form. The companion paper to this document examines in detail how complexity develops from a null condition across dimensional levels. The argument’s foundation applies a general framework of stationary action and self-organization principles to the theory and experimental data on Hardy’s paradox. The complementary format to the dichotomy of paradoxical elements is its sliding scale of uncertainty between their extremes. The argument extends that the root source of societal biases, conflicts, and bigotries is the fundamental and systemic mechanism of paradox. (shrink)

This article revisits a principle of distributive justice accepted by most, if not all, scholars of climate justice. The principle at stake, the limit, protects those who are very badly off from bearing the costs of climate change mitigation. The persistent noncompliance of developed states with their obligations toward burden sharing, however, means that this principle is increasingly in tension with successful climate change mitigation, given it seems to require that those in poverty have continued access to emissions in (...) cases where alternative forms of energy are not provided. In the first half of the paper I outline this tension and show how the dominant expression of the limit in the literature, advanced by Henry Shue, must be abandoned. I argue that any attempt to articulate the limit in current circumstance, where the carbon budget is very scarce, must consider the climate harm associated with continued subsistence emissions. The second half of the article defends a principle, the exemption, which is best able to maintain the strong commitment to shielding those below the minimal threshold from the costs of mitigation, even in light of the potential harm that will result if they require emissions to fuel their energy needs. (shrink)

This work introduces the concept of the Fundamental Limit of Quantum Computation (FLQC) - a precision limit of any quantum computing device arising from the discrete structure of spacetime at the Planck scale. The limit cannot be overcome by any technological progress. Consequences for Shor's algorithm, error correction, and an experimental programme on QPUs at T_c are discussed. FLQC-Protocol uploaded to GitHub.

The proper way in which limit-problems [Grenzprobleme]—birth, death, dreamless sleep, the “prior to birth” [das vor der Geburt], the “after death” [das nach dem Tod], etc.—can be accessed according to Husserl is by means of so-called “construction” [Konstruktion] or “reconstruction” [Rekonstruktion]. Contrary to what is usually claimed with respect to this method, and therefore the acts it is composed of, this paper will attempt to prove that they do not consist in non-intuitive acts, but rather in intuitive, but non-sensible (...) acts. In other words, the aforementioned acts of construction consist in categorial acts. More specifically, they represent acts akin to the ones involved in the constitution of exact material essences of a qualitative (the “pure” red, the “pure” blue …) or of a geometrical kind (a triangle, a chiliagon …): both the acts involved in the constitution of elementary exact essences, or acts of idealization, and the acts involved in the constitution of derived exact essences, or acts of deriving. However, the acceptance of such acts of construction suggests a serious reconsideration of some of the basic tenets of Husserlian phenomenology. Indeed, it challenges the idea that phenomenology is an eidetic science of inexact—morphological, descriptive …—material essences, namely the essence of a subjective sphere (the essence of consciousness, the essence of ego …); in fact, it turns phenomenology, at least partially, into something Husserl explicitly repudiates on multiple occasions: a “geometry” of lived experience. It is thus important to determine whether these acts of construction should be integrated into Husserlian phenomenology, and, if yes, how they should be integrated into it. Providing an indication of this will be the ultimate goal of this paper. (shrink)

Judith Butler’s theory of performativity emphasizes the idea that gender is constructed through a series of repeated acts. Within this framework, labels such as ‘masc’ and ‘femme’ can play a role in shaping gender identity and expression, especially in womenloving- women (WLW) relationships. Even though queerness is famously understood as a space for challenging gender norms, and WLW relationships to that extension should be a site for gender fluidity, the use of these labels in WLW relationships can reinforce patriarchal structures (...) by replicating binary gender expressions. The act of labeling oneself or one’s partner as ‘masc’ or ‘femme’ is evidence of binary gender expression persisting even in queer spaces. More importantly, in the context of WLW relationships, it goes to show that even though labels like ‘masc’ and ‘femme’ can provide a sense of belonging, they can also limit gender expression and replicate gender binaries. Situating within Judith Butler’s theory of performativity, this article analyzes the use of labels such as ‘masc’ and ‘femme’ and doing performative acts of these labels, especially within the WLW relationship dynamics. The article contends that in using labels such as ‘masc’ and femme’ which are fixed categories, we run the risk of becoming complicit in reinforcing patriarchal structures and power structures. (shrink)

This major new work by Anthony J. Steinbock, a leading authority in Phenomenology and Husserl Studies, explores an interrelated set of problems in Husserl's phenomenology and provides an excellent example of phenomenology in practice, demonstrating how its methods and resources shed light on philosophical problems.

At what point can we concede that the realities of world politics require that moral principles be compromised, and how do we know when a real ethical limit has been reached? This volume gathers leading constructivist scholars to explore the issue of moral limit and possibility in global political dilemmas. The contributors examine pressing ethical challenges such as sanctions, humanitarian intervention, torture, the self-determination of indigenous peoples, immigration, and the debate about international criminal tribunals and amnesties in cases (...) of atrocity. Their analyses entail theoretical and empirical claims about the conditions of possibility and limits of moral change in world politics, therefore providing insightful leverage on the ethical question of 'what ought we to do?' This is a valuable contribution to the growing field of normative theory in International Relations and will appeal to scholars and advanced students of international ethics and political theory. (shrink)

Speech‐on‐speech listening involves selectively attending to a target talker while ignoring a simultaneous competing talker. Spatially separating the talkers improves performance, a phenomenon known as spatial release from masking (spatial RM). The same is true of spectral separation, that is, filtering the talkers into non‐overlapping frequency bands (spectral RM). The relative benefit of spatial versus spectral RM is currently unknown. Furthermore, it is unclear how listeners’ ability to exploit spatial versus spectral cues is related to individual differences in cognition. The (...) resource‐limit account suggests that cognitive resources are required to support the processing of degraded speech, implying the strongest cognition/performance relationship when RM is limited or absent. However, an alternative claim, referred to as the data‐limit account, suggests that cognitive resources cease to be useful when the target is severely degraded. In this study, participants (N = 240) completed a selective listening task in which they transcribed the speech of one of two simultaneously presented talkers. The speech was filtered into interleaved or overlapping frequency bands (spectral RM vs. no spectral RM) and presented dichotically or collocated (a proxy for spatial RM vs. no spatial RM). A battery of cognitive tasks was administered to assess working memory/attention. Spectral RM provided at least as much benefit as spatial RM, with the best performance when both RM types were present. Cognitive scores were significantly positively correlated with RM benefits. However, the weakest correlation between cognitive scores and performance was observed in the no‐RM condition. The results therefore support an account of speech‐on‐speech listening that lies on a continuum from data‐limited to resource‐limited processing as a function of the quality of the target speech signal. (shrink)

Deconstruction both by its friends and enemies has come to be associated with a set of cliches that completely misunderstands its ethical aspiration. It is particularly within the field of law that we can see the ethical force of deconstruction, and also illuminate its concrete and practical importance. In The Philosophy of the Limit Drucilla Cornell examines the relationship of deconstruction to questions of ethics, justice and legal interpretation. She argues that renaming deconstruction "the philosophy of the limit" (...) will allow us to be more precise about what deconstruction actually is philosophically and hence to articulate more clearly its significance for law. Cornell explores the ethical and juridical significance of the so-called postmodern rebellion against metaphysics. A shared ethical rebellion links philosophers as different as Theodor Adorno, Jacques Derrida, Jacques Lacan, and Emmanuel Levinas. Together they present a new ethical configuration, new in its difference from both the critical social theory of J$u$urgen Habermas and the analytic jurisprudence of Nagel and Rawls. A key aspect of this newness is the centrality given to the relationship between questions of ethics and sexual difference. Cornell argues that the appeal of Lacan's analysis to feminists is that it helps to explain the profound hold the gender hierarchy has over Western culture, including its theories of political transformation. Under a Lacanian analysis the law of gender identity will be replicated in the laws of an existing legal system. This means that we cannot hope to sustain legal reforms unless the gender hierarchy is challenged. Cornell examines Derrida's position on the significance of the gender hierarchy in philosophy and explores its ethical and political importance. Derrida's intervention against legal positivism has important implications for the legal reforms necessary to protect marginalized groups. His emphasis on the limit, she argues, is crucial to thosewhose well-being and very lives may depend on legal transformation, women and homosexuals, for example. In an important contribution to legal philosophy, Cornell explores the affinities of Derrida's writings with recent liberal analytic jurisprudence. She also explores the differences. Comparing Rawls's and Derrida's accounts of justice, she argues that Derrida gives greater attention to the necessary utopian moment in his insistence on maintaining the divide between law, established norms, and justice. Cornell's focus on the importance of the limit and the centrality of the gender hierarchy allows her to offer a view of jurisprudence different from both critical social theory and analytic jurisprudence. As we watch the long-fought-for civil rights of women systematically overturned, we have reason to think about how the connections she makes shed light on an underlying truth of our social, political, and legal reality. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Limit Formations:Violence, Philosophy, RhetoricOmedi Ochieng For Megha Sharma SehdevNow days are dragon-ridden, the nightmareRides upon sleep: a drunken soldieryCan leave the mother, murdered at her door,To crawl in her own blood, and go scot-free;The night can sweat with terror as beforeWe pieced our thoughts into philosophy,And planned to bring the world under a rule,Who are but weasels fighting in a hole.—W. B. Yeats, "Nineteen Hundred and Nineteen"Violence is (...) a limit formation. It is neither reducible to a brute fact nor is it ineffably ethereal. To write about violence, then, is to confront—if only as disavowed remainder—critical limits, no less of the writer than of the writing itself. Fewer subjects have proven as confounding for philosophy and rhetoric, this journal's primary charge. In both its general particulars and its specific manifolds, violence nonpluses philosophical commonplaces, upends rhetorical tropologies.Philosophy imagines itself mediator to reality's arche, the bedrock of being. Ancient Greek philosophy sought to distinguish necessity from contingency, essence from accident, dialectic from rhetoric, logic from fallacy. Those who took up this intellectual tradition came to conceptualize violence as first and foremost a question of "nature"—more specifically, those marked out by nature to rule (propertied male citizens) and those marked [End Page 330] out by nature for subjection (the enslaved, women, nonhuman animals). In the early modern context of European philosophy, still, despite its pretensions, deeply indebted to this Mediterranean legacy, the canonical lexicon of sensemaking centered on legitimacy and its conceptual appurtenances of sovereignty, will, and rights.Strikingly, it is in the opposed registers of analytic and continental philosophy that violence's cataphilosophic figuration appears most salient. Consider, for example, one such famous symposium convened in the analytic journal Philosophy and Public Affairs, as narrated by political philosopher Michael Walzer:In an earlier issue of Philosophy & Public Affairs there appeared a symposium on the rules of war which was actually (or at least more importantly) a symposium on another topic. The actual topic was whether or not a man can ever face, or ever has to face, a moral dilemma, a situation where he must choose between two courses of action both of which it would be wrong for him to undertake. Thomas Nagel worriedly suggested that this could happen and that it did happen whenever someone was forced to choose between upholding an important moral principle and avoiding some looming disaster. R. B. Brandt argued that it could not possibly happen, for there were guidelines we might follow and calculations we might go through which would necessarily yield the conclusion that one or the other course of action was the right one to undertake in the circumstances (or that it did not matter which we undertook). R. M. Hare explained how it was that someone might wrongly suppose that he was faced with a moral dilemma: sometimes, he suggested, the precepts and principles of an ordinary man, the products of his moral education, come into conflict with injunctions developed at a higher level of moral discourse. But this conflict is, or ought to be, resolved at the higher level; there is no real dilemma.(1973, 160–61)Analytic political philosophy's resolute disavowals could not be here better splayed. Morality is construed as all-encompassing. The political is not so much effaced as it is rendered derivative to a foundational drama of will, obligation, choice. Analytic philosophy's oft-preened claim to clear, transparent, terse style proves constitutive of its desire to contain, if it cannot altogether moralize away violence. [End Page 331]Where analytic philosophy conceives of violence as an object, its limits defined by morality's handmaiden, the "well-ordered society" (Rawls 2001, 8), continental philosophy conjures a sublime violence that shatters and transfigures normative violence. Walter Benjamin posits a binary opposition between mythical and divine violence: "If mythical violence is lawmaking, divine violence is law-destroying; if the former sets boundaries, the latter boundlessly destroys them; if mythical violence brings at once guilt and retribution, divine power only expiates, if the former threatens, the latter strikes, if the former is bloody, the latter is lethal without spilling... (shrink)

There are basically four options to which state the limiting instant in a change from one state to its opposite belongs – only the first, only the second, both or none. This situation is usually referred to as the limit decision problem since all of these options seem troublesome: The first two alleged solutions are asymmetric and thus need something to ground this asymmetry in ; while the last two options leave the realm of classical logic. I argue that (...) including the debate about dispositions enables new options for solutions to the temporal limit decision problem. Metaphysical considerations function as a symmetry-breaker and thus remove the need for a non-classical solution. Dispositions bring about the changes in the world, so they constitute the metaphysical background for the instant of change. In particular, I argue that according to the triadic process account of dispositions, the limiting instant belongs to the second interval and only the second interval. (shrink)

By means of the averaging method of the first order, we introduce the maximum number of limit cycles which can be bifurcated from the periodic orbits of a Hamiltonian system. Besides, the perturbation has been used for a particular class of the polynomial differential systems.

Bohmian mechanics is a realistic interpretation of quantum theory. It shares the same ontology of classical mechanics: particles following continuous trajectories in space through time. For this ontological continuity, it seems to be a good candidate for recovering the classical limit of quantum theory. Indeed, in a Bohmian framework, the issue of the classical limit reduces to showing how classical trajectories can emerge from Bohmian ones, under specific classicality assumptions. In this paper, we shall focus on a technical (...) problem that arises from the dynamics of a Bohmian system in bounded regions; and we suggest that a possible solution is supplied by the action of environmental decoherence. However, we shall show that, in order to implement decoherence in a Bohmian framework, a stronger condition is required rather than the usual one. (shrink)

The paper studies political consequences of the establishment of neoliberal democ-racy, which means the onset of a post-political state of the world. It is demonstrated that at the “end of politics,” the democratic principle of equal rights turns into its opposite—a radical inequality between transnational elites, personifying the power of “pure” capital, and the local population, representing the idea of “pure” life. Neoliberal democracy is studied as a limit concept, which shows the exhaustion of the democratic principle of equality. (...) The paper shows that the return to democracy as the principle of equality becomes the driving ambition of modern politics of activism as a subjective process, unfolding in places where a situation of radical inequality arises. (shrink)

In the first part, a first exploration is made on the issue of sayability and unsayability using conceptual and investigative resources taken from the phenomenological descriptions made by Husserl in Ideas I. A first and still broad result is reached, namely, that any Erlebnis, taken in its fullness and plenitude, is ineffable, and therefore, life itself, because it is only a stream of lived experiences, as it is lived at each and every mo-ment, is unsayable, ineffable. The limit of (...) linguistic expression referred to in the title is, thus, its impossibility to express a full Erlebnis. Then, linguistic expression is examined against the background of the plenitude of this life that it cannot express but from which and in which it emerges, and this inspection brings to light in a preliminary way the several horizons that encircle it.En la primera parte, se hace una primera exploración del tema de la decibilidad y la indecibilidad empleando recursos metodológicos y conceptuales tomados de las descripciones fenomenológicas hechas por Husserl en Ideas I. Con ello se alcanza un primer resultado todavía muy amplio, a saber, que toda vivencia, tomada en su integridad y plenitud, es inefable, y por tanto, la vida misma, puesto que consiste en una corriente de vivencias, tal como es vivida en todos y cada uno de sus instantes, es precisamente inefable, indecible. El límite de la expresión lingüística a que el título se refiere es, pues, su imposibilidad para expresar una vivencia plena. Luego, se examina la expresión lingüística contra el fondo de la plenitud de la vida que no puede expresar pero de la cual y en la cual emerge, y esta inspección trae a luz de manera preliminar los diversos horizontes que la circundan. (shrink)

We begin with standard material regarding the basic asymptotic limit theorems of information and Control theories, supplemented by some related formalities. Information theory formalisms are restricted here to the stationary ergodic domain in which Shannon uncertainties can be expressed in terms of entropy-like expressions in probability distributions. Later developments extend matters to more interesting and comprehensive nonergodic realms in which cross sectional means are not the same as longitudinal means, resulting in path-by-path expressions for information source uncertainties. This will (...) lead to a much richer theory. (shrink)

In a time when controlling the spread of the virus in the United States requires drastic measures to limit the number of people coming in and out of intensive care units (ICU), the presence of prison guards is not justified. Transfers from American prisons to hospitals have increased dramatically during the pandemic and with each prison patient comes a cohort of prison guards. The theoretical benefits of having prison guards–such as preventing escape, protecting staff, and stopping unwanted visitation–are minimal: (...) critically ill prisoners are chained to their bed and pose minimal threat to the staff or flight risk. Unwanted visitation is already heavily regulated by the hospital. The risks of having more people in the ICU are significant during the pandemic: more potential exposures for staff, other patients, and the guards themselves. In order to limit the spread of the virus, the number of prison guards in the ICU should be limited. (shrink)

Wittgenstein’s pre-occupation with the notion of limit (of thought, sense, and language), was described by Alain Badiou as an aesthetic one. The limit is aesthetic because it is not an object to be theorized nor a concept, but rather, what has to be demonstrated, made to be seen, clearly displayed. In this paper, the conjunction between limits, as highlighted in Wittgenstein’s Tractatus, and the act of aesthetic demonstration is explored, both in the aesthetic tradition and in contemporary thought (...) about art, in order to explain why the limit which is aesthetically set, cannot be crossed. (shrink)

The ontological abyss that separates real objects from sensual objects is one of the central principles of Object-Oriented Ontology (OOO), which has its most explicit and profuse modulation in Timothy Morton’s notion of rift. This article argues that, despite succeeding in explaining the radical difference that inhabits every object, Morton’s rift fails to explain the object’s unification, rendering the overall theory inconsistent. An alternative approach that accounts simultaneously for disjunction and conjunction between essences and appearances can be found in Eugenio (...) Trías’s philosophy of the limit, a term widely ignored in OOO despite its deeply non-relational conception of the reality of things. The article further argues that the reinterpretation of Trías’s twofold liminal approach in light of OOO successfully addresses the inconsistencies found in Morton’s rift, paving the way for a theory of limits within Harman’s ontological framework. (shrink)

The standard means of seeking the classical limit in Bohmian mechanics is through the imposition of vanishing quantum force and quantum potential for pure states. We argue that this approach fails, and that the Bohmian classical limit can be realized only by combining narrow wave packets, mixed states, and environmental decoherence.

We give a new characterization of the hyperarithmetic sets: a set X of integers is recursive in e α if and only if there is a Turing machine which computes X and "halts" in less than or equal to the ordinal number ω α of steps. This result represents a generalization of the well-known "limit lemma" due to J. R. Shoenfield [Sho-1] and later independently by H. Putnam [Pu] and independently by E. M. Gold [Go]. As an application of (...) this result, we give a recursion theoretic analysis of clopen determinacy: there is a correlation given between the height α of a well-founded tree corresponding to a clopen game $A \subseteq \omega^\omega$ and the Turing degree of a winning strategy f for one of the players--roughly, f can be chosen to be recursive in 0 α and this is the best possible (see § 4 for precise results). (shrink)

Let K denote prefix-free Kolmogorov complexity, and let $K^A$ denote it relative to an oracle A. We show that for any n, $K^{\emptyset ^{(n)}}$ is definable purely in terms of the unrelativized notion K. It was already known that 2-randomness is definable in terms of K (and plain complexity C) as those reals which infinitely often have maximal complexity. We can use our characterization to show that n-randomness is definable purely in terms of K. To do this we extend a (...) certain “limsup” formula from the literature, and apply Symmetry of Information. This extension entails a novel use of semilow sets, and a more precise analysis of the complexity of $\Delta _2^0$ sets of minimal descriptions. (shrink)

This entry explores Charles Peirce's account of truth in terms of the end or ‘limit’ of inquiry. This account is distinct from – and arguably more objectivist than – views of truth found in other pragmatists such as James and Rorty. The roots of the account in mathematical concepts is explored, and it is defended from objections that it is (i) incoherent, (ii) in its faith in convergence, too realist and (iii) in its ‘internal realism’, not realist enough.

The first English translation of key texts by Georges Bataille pertaining to The Accursed Share that also map out his transition from "dissident surrealist" to systematic thinker.

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)

It is proved that for any k, the class of classical categorial grammars that assign at most k types to each symbol in the alphabet is learnable, in the Gold (1967) sense of identification in the limit from positive data. The proof crucially relies on the fact that the concept known as finite elasticity in the inductive inference literature is preserved under the inverse image of a finite-valued relation. The learning algorithm presented here incorporates Buszkowski and Penn's (1990) algorithm (...) for determining categorial grammars from input consisting of functor-argument structures. (shrink)

Among scholars of ancient economic thought, it is widely recognized that Aristotle established an upper limit to money-making. This “natural limit” has been variously construed, with some claiming that it might be settled independently of Aristotle’s ethical theory. This paper defends the opposite thesis: Aristotle’s natural limit is inextricably tied to his account of human flourishing. It also argues that Aristotle precludes the wealth-seeking path as coincident with a flourishing life. Why? For Aristotle, money-making as an end (...) in itself is endemic to the life of pleasure, not the good life. Moreover, the unchecked pursuit of ever more money is likely to crowd out other intrinsically valuable goods, such as friendship, agency, and autonomy. Finally, from the standpoint of Aristotle’s virtue ethics, wealth acquisition beyond the natural limit is considered to be a vice, not a virtue. (shrink)

There may be a limit on our capacity to suppress anthropocentric tendencies toward non-human others. Normally, we do not reach this limit in our dealings with animals, the environment, etc. Thus, continued striving to overcome anthropocentrism when confronted with these non-human others may be justified. Anticipation of super artificial intelligence may force us to face this limit, denying us the ability to free ourselves completely of anthropocentrism. This could be for our own good.

This article develops the hypothesis that the performing arts—unlike visual, musical, or pictorial arts—constitute an essential limit to digitalization. Their irreducible requirement of embodied co‑presence (Phelan 1993; Fischer‑Lichte 2008), their ephemeral temporality (Phelan 1993; Schneider 2011), and their intersubjective structure of meaning‑making position them as a privileged site of resistance to algorithmic rationality. Drawing on classical Greek theater, philosophical anthropology, and contemporary analyses of digital temporality (Stiegler 1998; Crary 2013; Chun 2016), the article argues that theatrical action reactivates the (...) political, existential, and communal dimensions of human coexistence. In an era of pervasive digital communication and surveillance (Zuboff 2019; Crawford 2021), the performing arts re‑emerge as forms of subversive rupture that recreate free public time and reassert the primacy of lived experience. (shrink)

BackgroundThis article explores the reasons in favour of revising and extending the current 14-day statutory limit to maintaining human embryos in culture. This limit is enshrined in law in over a dozen countries, including the United Kingdom. In two recently published studies, scientists have shown that embryos can be sustained in vitro for about 13 days after fertilisation. Positive reactions to these results have gone hand in hand with calls for revising the 14-day rule, which only allows embryo (...) research until the 14th day after fertilisation.Main textThe article explores the most prominent arguments in favour of and against the extension of the 14-day limit for conducting research on human embryos. It situates these arguments within the history of the 14-day limit. I start by discussing the history of the 14-day limit in the United Kingdom and the reasons behind the decision to opt for a compromise between competing moral views. I then analyse the arguments that those who are generally in favour of embryo research put forward in support of extending the 14-day rule, namely the argument of the beneficence of research and the argument of technical feasibility. I then show how these two arguments played a role in the recent approval of two novel techniques for the replacement of faulty mitochondrial DNA in the United Kingdom. Despite the popularity and widespread use of these arguments, I argue that they are ultimately problematic and should not be straightforwardly accepted. I end by making a case for respecting value pluralism in the context of embryo research, and I present two reasons in favour of respecting value pluralism: the argument of public trust and the argument of democracy.ConclusionI argue that 14-day limit for embryo research is not a valuable tool despite being a solution of compromise, but rather because of it. The importance of respecting value pluralism needs to be considered in any evaluation concerning a potential change to the 14-day rule. (shrink)

Context: Contemporary consciousness science remains in a state of methodological crisis, perpetually reproducing the "hard problem" and traditional dichotomies. This work proposes an alternative approach by analyzing the limits of cognition and mapping the structure of the cognizable. Approach: The work argues that the "hard problem" arises from a categorical error—an attempt to locate consciousness among objects, when consciousness is in fact logically bound to the immanent limit of the act of cognition itself. A conceptual apparatus is introduced that (...) distinguishes structural information (I₊) from negative information (I₋), where I₋ operates as the active aspect of indeterminacy. A minimal ontological model is proposed: the Question–Answer cognitive cycle. Findings: The "hard problem" is reinterpreted as a particular manifestation of universal gnoseological constraints. Consciousness is defined both structurally — as the limit mode of cognition, wherein a system operates with maximal I₋/I₊ ratio — and procedurally — as the outcome of cognitive cycle intensification that engenders proactive self-reference. The model provides solutions to classical paradoxes (Mary's room, the Chinese room, philosophical zombies), derives the irreducible properties of consciousness as logically necessary, and engages in productive dialogue with several contemporary theories. Conclusion: This approach furnishes a conceptual framework that redirects focus from static neural correlates to the dynamics of indeterminacy generation and resolution, thereby opening new perspectives for interdisciplinary consciousness research. (shrink)

I argue that it is possible to give an interpretation of the classical ℏ→0 limit of quantum mechanics that results in a partial explanation of the success of classical mechanics. The interpretation...

Karl Jaspers describes limit situations as experiences that fundamen­tally challenge our existing worldview and self-image, bringing us to the brink of existence. In this sense, trauma can also be subsumed under this term: as an event that shatters all previous assumptions about the world and cannot be appropriated and integrated into the context of existing life. The intrusion of something foreign into one’s own body, the experience of powerlessness and helplessness, can irreversibly shake one’s fundamental trust in the world. (...) Those affected remain scarred by the physical limit experience to which they were exposed. How this limit situation can nevertheless be reintegrated into life in the long term is the central question for trauma therapy. (shrink)

In this paper, we examine the limit of applicability of Gödel’s first incompleteness theorem. We first define the notion “G1 holds for the theory T”. This paper is motivated by the following question: can we find a theory with a minimal degree of interpretation for which G1 holds. To approach this question, we first examine the following question: is there a theory T such that Robinson’s R interprets T but T does not interpret R and G1 holds for T? (...) In this paper, we show that there are many such theories based on Jeřábek’s work using some model theory. We prove that for each recursively inseparable pair (A,B), we can construct a r.e. theory $U_{(A,B)}$ such that $U_{(A,B)}$ is weaker than R w.r.t. interpretation and G1 holds for $U_{(A,B)}$. As a corollary, we answer a question from Albert Visser. Moreover, we prove that for any Turing degree $0< d<0^{\prime }$, there is a theory T with Turing degree d such that G1 holds for T and T is weaker than R w.r.t. Turing reducibility. As a corollary, based on Shoenfield’s work using some recursion theory, we show that there is no theory with a minimal degree of Turing reducibility for which G1 holds. (shrink)

In a series of presentations at Sainte-Anne Hospital, published in English under the title _Talking to Brick Walls_, Lacan offers one of the few explicit references to Bataille in his _œuvre_. He interposes a stark disagreement between himself and Bataille on the status of possible knowledge regarding ontological questions. Lacan reads Bataille as a mystic who proposes that the pursuit of knowledge is a futile task and that knowledge of being is _only _possible _per viam negativam_. In order to advance (...) this reading, Lacan emphasises Bataille’s fixation with “nonknowledge.” At first glance, one can understand why Lacan identifies him as a mystic, and many commentators on Bataille’s writings offer similar reading; however, this ignores subtle nuances of Bataille’s arguments regarding what he calls “inner experience.” More crucially, it ignores his explicit rejection of mysticism on the very basis of the knowledge that results from nonknowledge. This comparison frames a problem for fundamental ontology, of which I hope to elaborate only one aspect: The incompleteness of thought implies a non-relation between thought and being, and we can have a knowledge about this non-relation through an analysis of the limit as phantasmatic and structural rather than as real. (shrink)

We argue against claims that the classical ℏ → 0 limit is “singular” in a way that frustrates an eliminative reduction of classical to quantum physics. We show one precise sense in which quantum mechanics and scaling behavior can be used to recover classical mechanics exactly, without making prior reference to the classical theory. To do so, we use the tools of strict deformation quantization, which provides a rigorous way to capture the ℏ → 0 limit. We then (...) use the tools of category theory to demonstrate one way that this reduction is explanatory: it illustrates a sense in which the structure of quantum mechanics determines that of classical mechanics. (shrink)

It is well known that the Penrose–Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight distribution. Here we provide parametric examples that give necessary conditions for the existence of limit results for the Penrose–Banzhaf index.

We study the relationship between common knowledge and the sequence of iterated mutual knowledge from a topological point of view. It is shown that common knowledge is not equivalent to the limit of the sequence of iterated mutual knowledge. On that account the new epistemic operator limit knowledge is introduced and analyzed in the context of games. Indeed, an example is constructed where the behavioral implications of limit knowledge of rationality strictly refine those of common knowledge of (...) rationality. More generally, it is then shown that limit knowledge of rationality is capable of characterizing any solution concept for some appropriate epistemic-topological conditions. Finally, some perspectives of a topologically enriched epistemic framework for games are discussed. (shrink)

Chris Fraser’s interpretation of the Zhuangzi’s 莊子 ethics emphasizes the importance of skill stories. He argues that eudaimonism in the Zhuangzi centers around the exercise of de 德 rather than moral virtue and presents a conception of personal flourishing as “wandering.” A person living a flourishing life is one who can use their de to skillfully respond to changing circumstances and follow the dao道. Fraser’s interpretation suggests that interpersonal conduct is a “field of skill” and that the question of how (...) to treat others is not fundamentally different from questions about how to undertake any course of activity. (shrink)

We use the path integral form of quantum electrodynamics to show that a causal classical limit to QED can be derived by functionally integrating over the photon coordinates, starting from an initial photon vacuum and ending in a final coherent radiation state driven by the anticipated classical charged particle trajectories. The resulting charged particle transition amplitude depends only on particle coordinates. When the \ limit is taken, only those particle paths that are not constrained by the final radiation (...) state are varied. These results demonstrate that the collapse from an infinity of charged particle paths, a path integral description, to causally interacting classical trajectories, a stationary-action description, is critically dependent on including final coherent state radiation and maintaining the distinction between particle paths that are free to vary and those trajectories that can be monitored by the final state radiation. (shrink)

The structure and style of philosophy has evolved in response to philosophy's confrontation with its own limits. Are these limits real or are they just phantoms haunting the philosophical project? How do philosophy and philosophers attempt to overcome these limits, or at least come to terms with them? In "Philosophy at the Limit" David Wood pursues this theme in modern philosophers from Hegel to Derrida including Nietzsche, Wittgenstein, Heidegger and Gadamer. He focuses on questions of philosophical style, problems with (...) dialogue and in direct communication, the structural closure of philosophical texts, and performative strategy in philosophy. "Philosophy at the Limit" is an accessible discussion of some of the complex issues that empower continental philosophy. It may appeal to students of philosophy and contemporary thought at every level, and to the general reader interested in the heart of the current debates in European thought. (shrink)

In exploring the nature of excess relative to a phenomenology of the limit, Testing the Limit claims that phenomenology itself is an exploration of excess. What does it mean that "the self" is "given"? Should we see it as originary; or rather, in what way is the self engendered from textual practices that transgress—or hover around and therefore within—the threshold of phenomenologial discourse? This is the first book to include Michel Henry in a triangulation with Derrida and Levinas (...) and the first to critique Levinas on the basis of his interpolation of philosophy and religion. Sebbah claims that the textual origins of phenomenology determine, in their temporal rhythms, the nature of the subjectivation on which they focus. He situates these considerations within the broader picture of the state of contemporary French phenomenology (chiefly the legacy of Merleau-Ponty), in order to show that these three thinkers share a certain "family resemblance," the identification of which reveals something about the traces of other phenomenological families. It is by testing the limit within the context of traditional phenomenological concerns about the appearance of subjectivity and ipseity that Derrida, Henry, and Levinas radically reconsider phenomenology and that French phenomenology assumes its present form. (shrink)

This text is an extended abstract of the full text: Kolomytsev D. Consciousness as the Limit Mode of Cognition (Reframing the Hard Problem). The "hard problem" is treated as a specific manifestation of universal gnoseological constraints. Consciousness is defined structurally—as a limit mode of cognition in which a system operates under maximized indeterminacy—and procedurally—as the outcome of an intensified cognitive cycle that gives rise to proactive self‑reference. The model offers unified treatments of classical thought experiments (Mary’s room, the (...) Chinese room, philosophical zombies), derives the irreducible properties of consciousness as logically necessary, and situates them within a structured dialogue with several leading contemporary theories. (shrink)

The maximum entropy principle is widely used to determine non-committal probabilities on a finite domain, subject to a set of constraints, but its application to continuous domains is notoriously problematic. This paper concerns an intermediate case, where the domain is a first-order predicate language. Two strategies have been put forward for applying the maximum entropy principle on such a domain: applying it to finite sublanguages and taking the pointwise limit of the resulting probabilities as the size n of the (...) sublanguage increases; selecting a probability function on the language as a whole whose entropy on finite sublanguages of size n is not dominated by that of any other probability function for sufficiently large n. The entropy-limit conjecture says that, where these two approaches yield determinate probabilities, the two methods yield the same probabilities. If this conjecture is found to be true, it would provide a boost to the project of seeking a single canonical inductive logic—a project which faltered when Carnap's attempts in this direction succeeded only in determining a continuum of inductive methods. The truth of the conjecture would also boost the project of providing a canonical characterisation of normal or default models of first-order theories. Hitherto, the entropy-limit conjecture has been verified for languages which contain only unary predicate symbols and also for the case in which the constraints can be captured by a categorical statement of quantifier complexity. This paper shows that the entropy-limit conjecture also holds for categorical statements of complexity, for various non-categorical constraints, and in certain other general situations. (shrink)

This volume frames the question of responsibility as a problem of agency in relation to the systems and structures of globalization. According to Ricoeur responsibility is a “shattered concept” when considered too narrowly as a problem of act, agency and individual freedom. To examine this Esther Reed develops a short genealogy of modern liberal and post-liberal concepts of responsibility in order to understand better the relationship dominant modern framings of the meanings of responsibility. Reed engages with writings by major modern (...) (Schleiermacher, Hegel, Marx, Weber) and post-liberal (Buber, Levinas, Derrida, Badiou, Butler, Young, Critchley) theorists to illustrate the shift from an ethnic responsibility built on notions of accountability and attributions to an ethic responsibility that starts variously from the 'other'. Reed sees Dietrich Bonhoeffer as the most promising partner of this theological dialogue, as his learning of responsibility from the risen Christ present now in the (global) church is a welcome provocation to new thinking about the meaning of responsibility learned from land, distant neighbour, (global) church and the bible. Bonhoeffer's reflections on the centre, boundaries and limits of responsibility remain helpful to Christian people struggling with an increasingly exhausted concept of accountability. (shrink)

This article asks how can we articulate the limit of artificial intelligence, which virtually has no limit? Or maybe the definition of AI already implies its limit, how Marvin Minsky once declared that there is no generally accepted theory of intelligence, and that AI is only one particular way of modelling it. This article revisits the debate between Minsky and Hubert Dreyfus and repositions them in terms of an opposition between mechanism and organism, in order to expose (...) the limit of Dreyfus’s Heideggerian critique. It suggests reflecting on the relation between noodiversity and technodiversity to methodologically broaden the concept of intelligence, and on how different concepts of intelligence could be thought by introducing the Chinese philosopher Mou Zongsan’s interpretation of Kant’s intellectual intuition. (shrink)