Classical Arguments Research Articles

Sharp propagation of chaos for the ensemble Langevin sampler

AbstractThe aim of this paper is to revisit propagation of chaos for a Langevin‐type interacting particle system recently proposed as a method to sample probability measures. The interacting particle system we consider coincides, in the setting of a log‐quadratic target distribution, with the ensemble Kalman sampler [SIAM J. Appl. Dyn. Syst. 19 (2020), no. 1, 412–441], for which propagation of chaos was first proved by Ding and Li in [SIAM J. Math. Anal. 53 (2021), no. 2, 1546–1578]. Like these authors, we prove propagation of chaos with an approach based on a synchronous coupling, as in Sznitman's classical argument. Instead of relying on a boostrapping argument, however, we use a technique based on stopping times in order to handle the presence of the empirical covariance in the coefficients of the dynamics. The use of stopping times to handle the lack of global Lipschitz continuity in the coefficients of stochastic dynamics originates from numerical analysis [SIAM J. Numer. Anal. 40 (2002), no. 3, 1041–1063] and was recently employed to prove mean‐field limits for consensus‐based optimization and related interacting particle systems [arXiv:2312.07373, 2023; Math. Models Methods Appl. Sci. 33 (2023), no. 2, 289–339]. In the context of ensemble Langevin sampling, this technique enables proving pathwise propagation of chaos with optimal rate, whereas previous results were optimal only up to a positive .

Editorial: Memory from Below

The editorial provides an overview of this issue of the Journal of Early Modern Studies. First it lays out the research questions that were at the origin of the project. Then it sketches out its conceptual and historiographical armature, pointing to some classical and recent arguments about memory, the history of literacy, and popular writing. Finally, this essay surveys the structure of the special issue and summarizes the object and argument of each one of the fifteen contributions.

The many faces of the Liar Paradox

The Liar Paradox is a classic argument that creates a contradiction by reflection on a sentence that attributes falsity to itself: ‘this sentence is false’. In our paper we will discuss the ways in which the Liar sentence (and its paradoxical argument) can be represented in first-order logic. The key to the representation is to use first-order logic to model a self-referential language. We will also discuss several related sentences, like the Liar cycles, the empirical versions of the Liar and the Truth teller sentences.

Aristotle’s Sea Battle, Excluded Middle and Bivalence

In this paper, I present a formal reconstruction of the classical argument for fatalism set forth by Aristotle in On Interpretation 9. From there, I expose two different formal solutions for avoiding the unwanted conclusion based on the traditional interpretation of Aristotle’s rejection of the Principle of Bivalence: On the one hand, Łukasiewicz's three-valued logic and, on the other hand, supervaluation semantics. I also address some criticisms made against these two proposals. To finish, I remark on some alternative interpretations of Aristotle’s intentions maintaining that the Stagirite philosopher rejected fatalism without abandoning the Principle of Bivalence.

Quantum Mechanics, Fields, Black Holes, and Ontological Plurality

The ontology behind quantum mechanics has been the subject of endless debate since the theory was formulated some 100 years ago. It has been suggested, at one time or another, that the objects described by the theory may be individual particles, waves, fields, ensembles of particles, observers, and minds, among many other possibilities. I maintain that these disagreements are due in part to a lack of precision in the use of the theory’s various semantic designators. In particular, there is some confusion about the role of representation, reference, and denotation in the theory. In this article, I first analyze the role of the semantic apparatus in physical theories in general and then discuss the corresponding ontological implications for quantum mechanics. Subsequently, I consider the extension of the theory to quantum fields and then analyze the semantic changes of the designators with their ontological consequences. In addition to the classical arguments to rule out a particle ontology in the case of non-relativistic quantum field theory, I show how the existence of black holes makes the proposal of a particle ontology in general spacetimes unfeasible. I conclude by proposing a provisional pluralistic ontology of fields and spacetime and discussing some prospects for possible future ontological economies.

Revisiting the evidence on thermostatic response to democratic change: degrees of democratic support or researcher degrees of freedom?

Abstract Prominent recent work argues that support for democracy behaves thermostatically—that democratic erosion boosts democratic support while deepening democracy yields public backlash—and further contends that there is no evidence for the classic argument that democracy itself increases democratic support over time. Here, we document how these conclusions depend on subtle choices in measurement coding that constitute “researcher degrees of freedom”: analyses employing alternative reasonable choices provide little or no support for the original conclusions. The fragility of the statistical results demonstrates that researcher degrees of freedom in measurement must be taken seriously and that the question of the relationship between democratic institutions and democratic support remains unsettled.

Spectrum of the Laplacian with mixed boundary conditions in a chamfered quarter of layer

We investigate the spectrum of a Laplace operator with mixed boundary conditions in an unbounded chamfered quarter of layer. This problem arises in the study of the spectrum of the Dirichlet Laplacian in thick polyhedral domains having some symmetries such as the so-called Fichera layer. The geometry we consider depends on two parameters gathered in some vector \kappa=(\kappa_{1},\kappa_{2}) which characterises the domain at the edges. By exchanging the axes and/or modifying their orientations if necessary, it is sufficient to restrict the analysis to the cases \kappa_{1}\ge0 and \kappa_{2}\in[-\kappa_{1},\kappa_{1}] . We identify the essential spectrum and establish different results concerning the discrete spectrum with respect to \kappa . In particular, we show that for a given \kappa_{1}>0 , there is some h(\kappa_{1})>0 such that discrete spectrum exists for \kappa_{2}\in[-\kappa_{1},0)\cup(h(\kappa_{1}),\kappa_{1}] whereas it is empty for \kappa_{2}\in[0,h(\kappa_{1})] . The proofs rely on classical arguments of spectral theory such as the max-min principle. The main originality lies rather in the delicate use of the features of the geometry.

Upper Bound of Barrow Entropy Index from Black Hole Fragmentation

Both classical and quantum arguments suggest that if Barrow entropy is correct, its index δ must be energy-dependent, which would affect the very early universe. Based on thermodynamic stability that sufficiently large black holes should not fragment, we argue that Barrow entropy correction must be small, except possibly at the Planckian regime. Furthermore, the fact that a solar mass black hole does not fragment implies an upper bound δ≲O(10−3), which surprisingly lies in the same range as the bound obtained from some cosmological considerations assuming fixed δ. This indicates that allowing δ to run does not raise its allowed value. We briefly comment on the case of Kaniadakis entropy.

Does Artificial Intelligence Speak Our Language?: A Gadamerian Assessment of Generative Language Models

The language argument is a classic argument for human distinctiveness that, for millenia, has been used to distinguish humans from non-human animals. Generative language models (GLMs) pose a challenge to traditional language-based models of human distinctiveness precisely because they can communicate and respond in a manner resembling humanity’s linguistic capabilities. This article asks: have GLMs acquired natural language? Employing Gadamer’s theory of language, I argue that they have not. While GLMs can reliably generate linguistic content that can be interpreted as “texts,” they lack the linguistically mediated reality that language provides. Missing from these models are four key features of a linguistic construction of reality: groundedness to the world, understanding, community, and tradition. I conclude with skepticism that GLMs can ever achieve natural language because they lack these characteristics in their linguistic development.

New estimates for a class of non-local approximations of the total variation

We consider a class of non-local functionals recently introduced by H. Brezis, A. Seeger, J. Van Schaftingen, and P.-L. Yung, which offers a novel way to characterize functions with bounded variation.We give a positive answer to an open question related to these functionals in the case of functions with bounded variation. Specifically, we prove that in this case the liminf of these functionals can be estimated from below by a linear combination in which the three terms that sum up to the total variation (namely the total variation of the absolutely continuous part, of the jump part and of the Cantor part) appear with different coefficients. We prove also that this estimate is optimal in the case where the Cantor part vanishes, and we compute the precise value of the limit in this specific scenario.In the proof we start by showing the results in dimension one by relying on some measure theoretic arguments in order to identify sufficiently many disjoint rectangles in which the difference quotient can be estimated, and then we extend them to higher dimension by a classical sectioning argument.

On the obstacle problem associated to the Kolmogorov–Fokker–Planck operator with rough coefficients

This work is devoted to the study of the obstacle problem associated to the Kolmogorov–Fokker–Planck operator with rough coefficients through a variational approach. In particular, after the introduction of a proper anisotropic Sobolev space and related properties, we prove the existence and uniqueness of a weak solution for the obstacle problem by adapting a classical perturbation argument to the convex functional associated to the case of our interest. Finally, we conclude this work by providing a one-sided associated variational inequality, alongside with an overview on related open problems.

Numerical discretization for Fisher-Kolmogorov problem with nonlocal diffusion based on mixed Galerkin BDF2 scheme

Nonlocal problems involving fourth-order terms pose several difficulties such as numerical discretization and its related convergences analysis. In this paper, the well-posedness of the extended Fisher-Kolmogorov equation with nonlocal diffusion is first analyzed using the Faedo-Galerkin technique and the classical compactness arguments. Moreover, we adopt a BDF2 scheme for time discretization and a mixed Galerkin scheme for spatial discretization. Then, we derive the optimal order convergence rates of the fully discrete system. Finally, some numerical simulations and convergence results are provided to confirm the theoretical results and the accuracy of the proposed scheme.

Biased Knowers, Biased Reasons, and Biased Philosophers

Abstract In Bias: A Philosophical Study, Thomas Kelly offers a response to epistemological skepticism grounded in his account of bias. According to Kelly, the classic argument for skepticism is best understood as an attempt to show that our commonsense beliefs are biased against the skeptic. Kelly grants that this is true but argues that biased beliefs can still be knowledge. I offer two objections. First, if we are applying Kelly’s theory of bias to skepticism, it is best to think of the skeptic’s challenge to be that our anti-skeptical beliefs are based on what we know to be biased reasons. Kelly has not shown that this sort of bias is compatible with knowledge. Second, Kelly’s approach to the problem of skepticism is an example of what I have called “unambitious epistemology.” And, for that reason, it is not a satisfactory answer to skepticism.

Beyond the Business Case for Responsible Artificial Intelligence: Strategic CSR in Light of Digital Washing and the Moral Human Argument

This paper, normative in nature and scope, addresses the perks and limits of the strategic CSR approach when confronted with current debates on the ethics of artificial intelligence, responsible artificial intelligence, and sustainable technology in business organizations. The paper summarizes the classic arguments underpinning the “business case” for the social responsibility of businesses and the main moral arguments for responsible and sustainable behavior in light of recent technological ethical challenges. Both streams are confronted with organizational ethical dilemmas arising in designing and deploying artificial intelligence, yielding tensions between social and economic goals. While recognizing the effectiveness of the business argument for responsible behavior in artificial intelligence, the paper addresses some of its main limits, particularly in light of the “digital washing” phenomenon. Exemplary cases of digital washing and corporate inconsistencies here discussed are taken from the literature on the topic and re-assessed in light of the proposed normative approach. Hence, the paper proposes to overcome some limits of the business case for CSR applied to AI, which mainly focuses on compliance and reputational risks and seeks returns in digital washing, by highlighting the normative arguments supporting a moral case for strategic CSR in AI. This work contributes to the literature on business ethics and strategic CSR at its intertwining with the ethics of AI by proposing a normative point of view on how to deploy the moral case in organizations when dealing with AI-related ethical dilemmas. It does so by critically reviewing the state-of-the-art studies on the debate, which, so far, contain different streams of research, and adding to such a body of literature what is here identified and labeled as the “human argument”.

On the convolution equivalence of tempered stable distributions on the real line

We show the convolution equivalence property of univariate tempered stable distributions in the sense of Rosiński (2007). This makes rigorous various classic heuristic arguments on the asymptotic similarity between the probability and Lévy densities of such distributions. Some specific examples from the literature are discussed.

Insensitizing control problems for the stabilized Kuramoto–Sivashinsky system

In this work, we address the existence of insensitizing controls for a nonlinear coupled system of fourth- and second-order parabolic equations known as the stabilized Kuramoto–Sivashinsky model. The main idea is to look for controls such that some functional of the states (the so-called sentinel) is locally insensitive to the perturbations of the initial data. Since the underlying model is coupled, we shall consider a sentinel in which we may observe one or two components of the system in a localized observation set. By some classical arguments, the insensitizing problem can be reduced to a null-controllability one for a cascade system where the number of equations is doubled. Upon linearization, the null-controllability for this new system is studied by means of Carleman estimates but unlike other insensitizing problems for scalar models, the election of the Carleman tools and the overall control strategy depends on the initial choice of the sentinel due to the (lack of) couplings arising in the extended system. Finally, the local null-controllability of the extended (nonlinear) system (and thus the insensitizing property) is obtained by applying the inverse mapping theorem.

The Sanjaya Myth: Sanjaya Belatthiputta and the Catuskoti

Respected modern scholars regard the pre-Buddhist philosopher Sañjaya Belaṭṭhiputta—a significant figure in the Buddhist canon—as the originator of the important classical argument- forms known as the catuṣkoṭi and catuṣkoṭi vinirmukta. We argue that the early Buddhist texts do not in fact support this view of the origin of these argument-forms; the question of their origin is open. While it is certainly true that the Pāli Sāmaññaphala Sutta and some of its parallels portray Sañjaya as deploying the catuṣkoṭi, there is nothing in these passages to suggest that he was its originator. The situation concerning the catuṣkoṭi vinirmukta is perhaps even more surprising: There is nothing in the early Pāli texts and their parallels—nor in Buddhagosa’s famous Pāli commentary on the early texts—to show that Sañjaya even deployed the catuṣkoṭi vinirmukta let alone originated it. Further, our investigations also call into question the standard portrayal of Sañjaya as an obfuscator and prevaricator. It appears he may have been a more interesting and able philosopher than the Sāmaññaphala Sutta—and modern accounts based on it—maintain.

Эволюция и научный прогресс. Осмысление взглядов А. Берда

In this paper, Alexander Bird’s argument against semantic and functional-internalist description of the development of science in favor of a cumulative description in the article “What is scientific progress?” is critically comprehended. Bird distorts and limits the ideas of his opponents by transferring the specific properties of one type of scientific knowledge to another, in particular practical knowledge to theoretical knowledge and vice versa. After that, Bird reduces his opponents’ positions to his own. He also cites quite traditional arguments about the failure of “pessimistic induction”, not noticing that he himself uses it in the core of his argument. Furthermore, he fails to see the problematic nature of his approach, teleologically describing the history of science, and gives no answer to the obvious traditional objections to his position. The same applies to his statment that a critical position does not make a positive contribution to science, while he forgets about the argument about the positivity of knowledge gained as a result of criticism. Bird’s reduction of his opponents’ positions to his own, does not follow logically from his arguments either, and moreover, in its further development, it turns against him. The novelty of the research lies in the originality of the responses to both classical and innovative arguments put forward by Byrd.

Meromorphic solutions of linear q-difference equations

In this article, we construct explicit meromorphic solutions of first order linear q-difference equations in the complex domain and we describe the location of all their zeros and poles. The homogeneous case leans on the study of four fundamental equations, providing the previous informations in the framework of entire or meromorphic coefficients. The inhomogeneous situation, which stems from the homogeneous one and two fundamental equations, is also described in detail. We also address the case of higher-order linear q-difference equations, using a classical factorization argument. All these results are illustrated by several examples.

Lacunary maximal functions on homogeneous groups

We observe that classical arguments of Ricci–Stein can be used to prove Lp bounds for maximal functions associated to lacunary dilates of a fixed measure in the setting of homogeneous groups. This recovers some recent results on averages over Korányi spheres and horizontal spherical averages of a type introduced by Nevo–Thangavelu. Moreover, the main theorem applies much more broadly and we explore its consequences through a variety of explicit examples.