We prove that the property "P doesn't make the old reals Lebesgue null" is preserved under countable support iterations of proper forcings, under the additional assumption that the forcings are nep (a generalization of Suslin proper) in an absolute way. We also give some results for general Suslin ccc ideals.

Let S be the set of those α ∈ ω₂ that have cofinality ω₁. It is consistent relative to a measurable that the nonempty player wins the pressing down game of length ω₁, but not the Banach-Mazur game of length ω + 1 (both games starting with S).

We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.

For f, g $ \in \omega ^\omega $ let $c_{f,g}^\forall $ be the minimal number of uniform g-splitting trees (or: Slaloms) to cover the uniform f-splitting tree, i.e., for every branch v of the f-tree, one of the g-trees contains v. $c_{f,g}^\exists $ is the dual notion: For every branch v, one of the g-trees guesses v(m) infinitely often. It is consistent that $c_{f \in ,g \in }^\exists = c_{f \in ,g \in }^\forall = k_ \in $ for N₁ many (...) pairwise different cardinals $k_ \in $ and suitable pairs $(f_{ \in ,g \in } ).$ For the proof we use creatures with sufficient bigness and halving. We show that the lim-inf creature forcing satisfies fusion and pure decision. We introduce decisiveness and use it to construct a variant of the countable support iteration of such forcings, which still satisfies fusion and pure decision. (shrink)

For \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f,g\in\omega^\omega}$$\end{document} let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\forall_{f,g}}$$\end{document} be the minimal number of uniform g-splitting trees needed to cover the uniform f-splitting tree, i.e., for every branch ν of the f-tree, one of the g-trees contains ν. Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f,g}}$$\end{document} be the dual notion: For every branch ν, one of the g-trees guesses ν(m) infinitely often. We show that (...) it is consistent that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${c^\exists_{f_\epsilon,g_\epsilon}{=}c^\forall_{f_\epsilon,g_\epsilon}{=}\kappa_\e psilon}$$\end{document} for continuum many pairwise different cardinals \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa_\epsilon}$$\end{document} and suitable pairs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(f_\epsilon,g_\epsilon)}$$\end{document}. For the proof we introduce a new mixed-limit creature forcing construction. (shrink)

Using GCH, we force the following: There are continuum many simple cardinal characteristics with pairwise different values.

We give a self-contained proof of the preservation theorem for proper countable support iterations known as “tools-preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals.

In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin- functions” and later “Kolmogorovian models”, which employs a nonstandard notion of probability. We describe Pitowsky’s analysis and argue that his notion of hidden variables is in fact just super-determinism. Pitowsky’s first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue (...) that it supports the opposing view, i.e., the widespread intuition “if you need a non-measurable function, it is physically irrelevant”. (shrink)

We introduce the notion of effective Axiom A and use it to show that some popular tree forcings are Suslin+. We introduce transitive nep and present a simplified version of Shelah’s “preserving a little implies preserving much”: If I is a Suslin ccc ideal (e.g. Lebesgue-null or meager) and P is a transitive nep forcing (e.g. P is Suslin+) and P does not make any I-positive Borel set small, then P does not make any I-positive set small.

There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.

We investigate the pressing down game and its relation to the Banach Mazur game. In particular we show: consistently, there is a nowhere precipitous normal ideal I on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_2}$$\end{document} such that player nonempty wins the pressing down game of length \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\aleph_1}$$\end{document} on I even if player empty starts.

We present a method to iterate finitely splitting lim-sup tree forcings along non-wellfounded linear orders. As an application, we introduce a new method to force (weak) measurability of all definable sets with respect to a certain (non-ccc) ideal.

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences (for some regular [Formula: see text]). As an application, we show that consistently the following cardinal characteristics can be different: The (“independent”) characteristics in Cichoń’s diagram, plus [Formula: see text]. (So we get thirteen different values, including [Formula: see text] and continuum). We also give constructions to alternatively separate other MA-numbers (instead of [Formula: see text]), namely: MA for [Formula: see (...) text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber. (shrink)

We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new <κ-sequences. As an application, we show that consistently the followi...

Climate change mitigation has become a paradigm case both for externalities in general and for the game-theoretic model of the Tragedy of the Commons (ToC) in particular. This situation is worrying, as we have reasons to suspect that some models in the social sciences are apt to be performative to the extent that they can become self-fulfilling prophecies. Framing climate change mitigation as a hardly solvable coordination problem may force us into a worse situation, by changing real-world behaviour to fit (...) our model, rather than the other way around. But while this problem of the performativity of the ToC has been noted in a recent paper in this journal by Matthew Kopec, his proposed strategies for dealing with their self-fulfilling nature fall short of providing an adequate solution. Instead of relying on the idea that modelling assumptions are always strictly speaking false, this paper shows that the problem may be better framed as a problem of underdetermination between competing explanations. Our goal here is to provide a framework for choosing between this set of competing models that allows us to avoid a ‘Russian Roulette’-like situation in which we gamble with existential risk. (shrink)

Knowledge: to know is to love -- Love: Abraham, Moses, and the meaning of circumcision -- Seasons: Hanukah and Purim reconfigured -- Women: marital and universal peace -- Holiness: commandments as intruments -- Asseverations: socila responsibility and sanctifying God's name -- Agriculture: sanctifying all human beings -- Temple service: the divinity of the comandments -- Offerings: the morality of the commandments -- Reitual purity: intellectual and moral purity -- Damages: who is a Jew? -- Acquision: slavery versus universal humkanity -- (...) Civil laws: God of Aristotle in the God of Abraham -- Judges: Messianic universalism -- Appendix: Maimonides' cosmic paradigm. (shrink)

Maimonides' Guide of the Perplexed addressed Jews of his day who felt challenged by apparent contradictions between Torah and science. We Are Not Alone: A Maimonidean Theology of the Other uses Maimonides' writings to address Jews of today who are perplexed by apparent contradictions between the morality of the Torah and their conviction that all human beings are created in the image of God and are the object of divine concern, that other religions have value, that genocide is never justified, (...) and that slavery is evil. Individuals who choose to emphasize the moral and universalist elements of Jewish tradition can often find support in positions explicitly held by Maimonides or implied by his teachings. We Are Not Alone offers an ethical and universalist vision of traditionalist Judaism. (shrink)

The period from Plato's birth to Aristotle's death (427-322 BC) is one of the most influential and formative in the history of Western philosophy. The developments of logic, metaphysics, epistemology, ethics and science in this period have been investigated, controversies have arisen and many new theories have been produced. But this is the first book to give detailed scholarly attention to the development of dialectic during this decisive period. It includes chapters on topics such as: dialectic as interpersonal debate between (...) a questioner and a respondent; dialectic and the dialogue form; dialectical methodology; the dialectical context of certain forms of arguments; the role of the respondent in guaranteeing good argument; dialectic and presentation of knowledge; the interrelations between written dialogues and spoken dialectic; and definition, induction and refutation from Plato to Aristotle. The book contributes to the history of philosophy and also to the contemporary debate about what philosophy is. (shrink)

There is surprising evidence that introspection of our phenomenal states varies greatly between individuals and within the same individual over time. This puts pressure on the notion that introspection gives reliable access to our own phenomenology: introspective unreliability would explain the variability, while assuming that the underlying phenomenology is stable. I appeal to a body of neurocomputational, Bayesian theory and neuroimaging findings to provide an alternative explanation of the evidence: though some limited testing conditions can cause introspection to be unreliable, (...) mostly it is our phenomenology itself that is variable. With this account of phenomenal variability, the occurrence of the surprising evidence can be explained while generally retaining introspective reliability. (shrink)

A series of recent developments points towards auditing as a promising mechanism to bridge the gap between principles and practice in AI ethics. Building on ongoing discussions concerning ethics-based auditing, we offer three contributions. First, we argue that ethics-based auditing can improve the quality of decision making, increase user satisfaction, unlock growth potential, enable law-making, and relieve human suffering. Second, we highlight current best practices to support the design and implementation of ethics-based auditing: To be feasible and effective, ethics-based auditing (...) should take the form of a continuous and constructive process, approach ethical alignment from a system perspective, and be aligned with public policies and incentives for ethically desirable behaviour. Third, we identify and discuss the constraints associated with ethics-based auditing. Only by understanding and accounting for these constraints can ethics-based auditing facilitate ethical alignment of AI, while enabling society to reap the full economic and social benefits of automation. (shrink)

A series of recent developments points towards auditing as a promising mechanism to bridge the gap between principles and practice in AI ethics. Building on ongoing discussions concerning ethics-based auditing, we offer three contributions. First, we argue that ethics-based auditing can improve the quality of decision making, increase user satisfaction, unlock growth potential, enable law-making, and relieve human suffering. Second, we highlight current best practices to support the design and implementation of ethics-based auditing: To be feasible and effective, ethics-based auditing (...) should take the form of a continuous and constructive process, approach ethical alignment from a system perspective, and be aligned with public policies and incentives for ethically desirable behaviour. Third, we identify and discuss the constraints associated with ethics-based auditing. Only by understanding and accounting for these constraints can ethics-based auditing facilitate ethical alignment of AI, while enabling society to reap the full economic and social benefits of automation. (shrink)

A new theory is taking hold in neuroscience. It is the theory that the brain is essentially a hypothesis-testing mechanism, one that attempts to minimise the error of its predictions about the sensory input it receives from the world. It is an attractive theory because powerful theoretical arguments support it, and yet it is at heart stunningly simple. Jakob Hohwy explains and explores this theory from the perspective of cognitive science and philosophy. The key argument throughout The Predictive Mind (...) is that the mechanism explains the rich, deep, and multifaceted character of our conscious perception. It also gives a unified account of how perception is sculpted by attention, and how it depends on action. The mind is revealed as having a fragile and indirect relation to the world. Though we are deeply in tune with the world we are also strangely distanced from it. (shrink)

Important decisions that impact humans lives, livelihoods, and the natural environment are increasingly being automated. Delegating tasks to so-called automated decision-making systems can improve efficiency and enable new solutions. However, these benefits are coupled with ethical challenges. For example, ADMS may produce discriminatory outcomes, violate individual privacy, and undermine human self-determination. New governance mechanisms are thus needed that help organisations design and deploy ADMS in ways that are ethical, while enabling society to reap the full economic and social benefits of (...) automation. In this article, we consider the feasibility and efficacy of ethics-based auditing as a governance mechanism that allows organisations to validate claims made about their ADMS. Building on previous work, we define EBA as a structured process whereby an entity’s present or past behaviour is assessed for consistency with relevant principles or norms. We then offer three contributions to the existing literature. First, we provide a theoretical explanation of how EBA can contribute to good governance by promoting procedural regularity and transparency. Second, we propose seven criteria for how to design and implement EBA procedures successfully. Third, we identify and discuss the conceptual, technical, social, economic, organisational, and institutional constraints associated with EBA. We conclude that EBA should be considered an integral component of multifaced approaches to managing the ethical risks posed by ADMS. (shrink)

The proposed European Artificial Intelligence Act (AIA) is the first attempt to elaborate a general legal framework for AI carried out by any major global economy. As such, the AIA is likely to become a point of reference in the larger discourse on how AI systems can (and should) be regulated. In this article, we describe and discuss the two primary enforcement mechanisms proposed in the AIA: the _conformity assessments_ that providers of high-risk AI systems are expected to conduct, and (...) the _post-market monitoring plans_ that providers must establish to document the performance of high-risk AI systems throughout their lifetimes. We argue that the AIA can be interpreted as a proposal to establish a Europe-wide ecosystem for conducting AI auditing, albeit in other words. Our analysis offers two main contributions. First, by describing the enforcement mechanisms included in the AIA in terminology borrowed from existing literature on AI auditing, we help providers of AI systems understand how they can prove adherence to the requirements set out in the AIA in practice. Second, by examining the AIA from an auditing perspective, we seek to provide transferable lessons from previous research about how to refine further the regulatory approach outlined in the AIA. We conclude by highlighting seven aspects of the AIA where amendments (or simply clarifications) would be helpful. These include, above all, the need to translate vague concepts into verifiable criteria and to strengthen the institutional safeguards concerning conformity assessments based on internal checks. (shrink)

Lauritz Munch and Björn Lundgren have recently replied to a paper published by us in this journal. In our original paper, we defended a novel version of the so-called ‘control theory’ of the moral right to privacy. We argued that control theorists should define ‘control’ as what we coined ‘Negative Control’. Munch and Lundgren have recently provided a range of interesting and challenging objections to our view. Independently of each other, they give almost identical counterexamples to our definition of Negative (...) Control. In this comment, we show that while the counterexamples are genuine counterexamples, they do not force us to abandon the idea of Negative Control. Furthermore, we reply to two additional objections raised by Lundgren. One of these replies involves giving a new account of what the relation is between the concept of privacy and the right to privacy. (shrink)

Sociability and Its Enemies contributes both to contemporary studies of political theory and to discourse on postwar Germany by reconstructing the arguments concerning the nature and value of sociability as a form of interaction and interconnection particular to modern bourgeois society. Jakob Norberg argues that the writings of Hannah Arendt, Jürgen Habermas, Carl Schmitt, and the historian Reinhart Koselleck present conflicting responses to a hitherto neglected question or point of contention: whether bourgeois sociability should serve as a therapeutic practice (...) and politically relevant ideal for postwar Germany. The book sheds light on previously neglected historical and conceptual connections among political theorists, and it enriches established narratives of postwar intellectual history. (shrink)

Departing from popular imaginations around artificial intelligence (AI), this article engages in the I in the AI acronym but from perspectives outside of mathematics, computer science and machine learning. When intelligence is attended to here, it most often refers to narrow calculating tasks. This connotation to calculation provides AI an image of scientificity and objectivity, particularly attractive in societies with a pervasive desire for numbers. However, as is increasingly apparent today, when employed in more general areas of our messy socio-cultural (...) realities, AI- powered automated systems often fail or have unintended consequences. This article will contribute to this critique of AI by attending to Nicholas of Cusa and his treatment of intelligence. According to him, intelligence is equally dependent on an ability to handle the unknown as it unfolds in the present moment. This suggests that intelligence is organic which ties Cusa to more contemporary discussions in tech philosophy, neurology, evolutionary biology, and cognitive sciences in which it is argued that intelligence is dependent on having—and acting through—an organic body. Understanding intelligence as organic thus suggests an oxymoronic relationship to artificial. (shrink)

An exciting theory in neuroscience is that the brain is an organ for prediction error minimization. This theory is rapidly gaining influence and is set to dominate the science of mind and brain in the years to come. PEM has extreme explanatory ambition, and profound philosophical implications. Here, I assume the theory, briefly explain it, and then I argue that PEM implies that the brain is essentially self-evidencing. This means it is imperative to identify an evidentiary boundary between the brain (...) and its environment. This boundary defines the mind-world relation, opens the door to skepticism, and makes the mind transpire as more inferentially secluded and neurocentrically skull-bound than many would nowadays think. Therefore, PEM somewhat deflates contemporary hypotheses that cognition is extended, embodied and enactive; however, it can nevertheless accommodate the kinds of cases that fuel these hypotheses. (shrink)

Die irreführende technologische Metapher der Informationsübertragung impliziert paradoxerweise uninformative Information. Dem steht jener Informationsbegriff gegenüber, der mit Wissen und Verstehen assoziiert ist. Informativ wird etwas nicht wegen etwas Übertragenem, sondern in Relation zu Interessen und Befähigungen verstehender Wesen. Jakob Krebs zeigt, dass ein aufgeklärtes Selbstverständnis der Informationsgesellschaft somit einer genaueren Bestimmung von Informativität bedarf. Die ist nicht nur philosophisch aufschlussreich, sondern auch für alle Praktiken des Kommunizierens, Lernens und Lehrens. Denn Information lässt sich genauso wenig übertragen wie sich eine (...) Grippe ausschwitzen lässt. (shrink)

Recently, Jardas _et al_ have convincingly defended the patient preference predictor (PPP) against a range of autonomy-based objections. In this response, I propose a new autonomy-based objection to the PPP that is not explicitly discussed by Jardas _et al_. I call it the ‘objection from higher-order preferences’. Even if this objection is not sufficient reason to reject the PPP, the objection constitutes a pro tanto reason that is at least as powerful as the ones discussed by Jardas _et al._.

Berichte zur Wissenschaftsgeschichte, Volume 45, Issue 1-2, Page 87-111, June 2022.

Overzicht van de westerse wijsgerige visies op het lichaam gevolgd door een eigen visie.