Michael A PetersBeijing Normal UniversityChatGPT is an AI chatbot released by OpenAI on November 30, 2022 and a ‘stable release’ on February 13, 2023. It belongs to OpenAI’s GPT-3 family (generativ...

A Cantor series expansion for a real number x with respect to a basic sequence $Q=(q_1,q_2,\dots )$, where $q_i \geq 2$, is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $\boldsymbol {\Pi }^0_3$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio (...) normality, and distribution normality. These notions are equivalent for base b expansions, but not for more general Cantor series expansions. We show that for any basic sequence the set of distribution normal numbers is $\boldsymbol {\Pi }^0_3$ -complete, and if Q is $1$ -divergent then the sets of normal and ratio normal numbers are $\boldsymbol {\Pi }^0_3$ -complete. We further show that all five non-trivial differences of these sets are $D_2(\boldsymbol {\Pi }^0_3)$ -complete if $\lim _i q_i=\infty $ and Q is $1$ -divergent. This shows that except for the trivial containment that every normal number is ratio normal, these three notions are as independent as possible. (shrink)

We show that all the projective ordinals $\delta^1_n$ are supercompact through their supremum $\aleph_{\varepsilon 0}$, and a ways beyond.

We formulate and prove a combinatorial property assuming AD + V = L(R). As a consequence, we show that every regular κ which is either a Suslin cardinal or the successor of a Suslin cardinal is δ 2 1 -supercompact. In particular, all the projective ordinals δ 1 n are δ 2 1 -supercompact.

Assuming AD + (V = L(R)), it is shown that for κ an admissible Suslin cardinal, o(κ) (= the order type of the stationary subsets of κ) is "essentially" regular and closed under ultrapowers in a manner to be made precise. In particular, o(κ) ≫ κ +, κ ++ , etc. It is conjectured that this characterizes admissibility for L(R).

We work under the assumption of the Axiom of Determinacy and associate a measure to each cardinal $\kappa < \aleph_{\varepsilon_0}$ in a recursive definition of a canonical measure assignment. We give algorithmic applications of the existence of such a canonical measure assignment (computation of cofinalities, computation of the Kleinberg sequences associated to the normal ultrafilters on all projective ordinals).

Let X and Y be uncountable Polish spaces. We show in ZF that there is a coanalytic subset P of X × Y with countable sections which cannot be expressed as the union of countably many partial coanalytic, or even PCA = Σ 1 2 , graphs. If X = Y = ω ω , P may be taken to be Π 1 1 . Assuming stronger set theoretic axioms, we identify the least pointclass such that any such coanalytic P (...) can be expressed as the union of countably many graphs in this pointclass. This last result is extended (under suitable hypotheses) to all levels of the projective hierarchy. (shrink)

We survey some results and problems arising from a classic problem of Steinhaus: Is there a subset S of R 2 such that each isometric copy of mathbbZ 2 (the lattice points in the plane) meets S in exactly one point.

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply the nonexistence of Borel complete sections with certain features.

Let E be a coanalytic equivalence relation on a Polish space X and (A n ) n∈ω a sequence of analytic subsets of X. We prove that if lim sup n∈K A n meets uncountably many E-equivalence classes for every K ∈ [ω] ω , then there exists a K ∈ [ω] ω such that ⋂ n∈K A n contains a perfect set of pairwise E-inequivalent elements.

Corporate sustainability can be defined as organizations’ commitment to profitability, environment, and social well-being. This study uses a transactional culture analysis of CS reporting practices to explain why some Indian organizations conform to voluntary CS reporting guidelines and others do not. The literature contains two different perspectives on culture, defined broadly as a set of values that guide people’s behavior at a given time. Most past studies typically use national culture to explain differences in CS practices across nations. This concept (...) embeds corporate cultures within the larger national culture, neglecting intranation diversity. Conversely, according to the transactional culture approach used in this study, cultures are plural and independent of geoethnic boundaries, and emerge through social transactions. TCA encourages multilevel explorations of complex social phenomena. Since CS reporting preferences are the outcome of ongoing transactions among organizational stakeholders across different levels, TCA is more appropriate for this study. Since this application requires an understanding of social accountability, the authors use Mary Douglas’s Cultural Framework, a transactional framework of social accountability. A qualitative exploration of six Indian organizations using DCF reveals different dominant forms of social accountability in these organizations: either alone or as paired hybrids. Consequently, each organization prioritizes different stakeholders and reacts differently to voluntary CS reporting guidelines. Identifying the dominant form or forms of social accountability in their organizations and understanding their underlying reasons for resisting voluntary CS guidelines enables managers to secure better collaboration for their CS initiatives. (shrink)

How, in a secular world, should we resolve ethically controversial and troubling issues relating to health care? Should we, as some argue, make a clean sweep, getting rid of the Hippocratic ethic, such vestiges of it as remain? Jennifer Jackson seeks to answer these significant questions, establishing new foundations for a traditional and secular ethic which would not require a radical and problematic overhaul of the old. These new foundations rest on familiar observations of human nature and human needs. (...) Jackson presents morality as a loose anatomy of constituent virtues that are related in different ways to how we fare in life, and suggests that in order to address problems in medical ethics, a virtues-based approach is needed. Throughout, attention is paid to the role of philosophy in medical ethics, and how it can be used to clarify key notions and distinctions that underlie current debates and controversial issues. By reinstating such concepts as justice, cardinal virtue, and moral duty, Jackson lays the groundwork for an ethics of health care that makes headway toward resolving seeming dilemmas in medical ethics today. This penetrating and accessible book will be invaluable to students of sociology and health care, as well as those who are interested in the ethical uncertainties faced by the medical world. (shrink)

An affirmative answer is given to the question quoted in the title.

This essay concerns the question of how we make genuine epistemic progress through conceptual analysis. Our way into this issue will be through consideration of the paradox of analysis. The paradox challenges us to explain how a given statement can make a substantive contribution to our knowledge, even while it purports merely to make explicit what one’s grasp of the concept under scrutiny consists in. The paradox is often treated primarily as a semantic puzzle. However, in “Sect. 1” I argue (...) that the paradox raises a more fundamental epistemic problem, and in “Sects.1 and 2” I argue that semantic proposals—even ones designed to capture the Fregean link between meaning and epistemic significance—fail to resolve that problem. Seeing our way towards a real solution to the paradox requires more than semantics; we also need to understand how the process of analysis can yield justification for accepting a candidate conceptual analysis. I present an account of this process, and explain how it resolves the paradox, in “Sect. 3”. I conclude in “Sect. 4” by considering the implications for the present account concerning the goal of conceptual analysis, and by arguing that the apparent scarcity of short and finite illuminating analyses in philosophically interesting cases provides no grounds for pessimism concerning the possibility of philosophical progress through conceptual analysis. (shrink)

Steve Awodey and Erich H. Reck. Completeness and Categoricity: 19th Century Axiomatics to 21st Century Senatics.

This paper explores the implications of libertarianism for welfare policy. There are two central arguments. First, the paper argues that if one adopts a libertarian framework, it makes most sense to be a Lockean right-libertarian. Second, the paper argues that this form of libertarianism leads to the endorsement of a fairly extensive set of redistributive welfare programs. Specifically, the paper argues that Lockean right-libertarians are committed to endorsing welfare programs under which the receipt of benefits is conditional on meeting a (...) work requirement, and also endorsing some form of publicly funded jobs of last resort for potential welfare recipients. (shrink)

This brief article is intended to introduce the reader to the field of algebraic set theory, in which models of set theory of a new and fascinating kind are determined algebraically. The method is quite robust, applying to various classical, intuitionistic, and constructive set theories. Under this scheme some familiar set theoretic properties are related to algebraic ones, while others result from logical constraints. Conventional elementary set theories are complete with respect to algebraic models, which arise in a variety of (...) ways, including topologically, type-theoretically, and through variation. Many previous results from topos theory involving realizability, permutation, and sheaf models of set theory are subsumed, and the prospects for further such unification seem bright. (shrink)

Standard epistemology takes it for granted that there is a special kind of value: epistemic value. This claim does not seem to sit well with act utilitarianism, however, since it holds that only welfare is of real value. I first develop a particularly utilitarian sense of “epistemic value”, according to which it is closely analogous to the nature of financial value. I then demonstrate the promise this approach has for two current puzzles in the intersection of epistemology and value theory: (...) first, the problem of why knowledge is better than mere true belief, and second, the relation between epistemic justification and responsibility. (shrink)

Felicity Haynes earned Honours degrees in English and French literature from The University of Western Australia and completed her doctorate on reason and understanding at the University of Illinoi...

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy (...) type theory. It also gives the new system of foundations a distinctly structural character. (shrink)

Coutinho respects the multiplicity of Daoist philosophies while also revealing a distinctive philosophical sensibility, and he provides clear explanations of these complex texts without resorting to oversimplification.

Following Schelling (1960), coordination problems have mainly been considered in a context where agents can achieve a common goal (e.g., rendezvous) only by taking common actions. Dynamic versions of this problem have been studied by Crawford and Haller (1990), Ponssard (1994), and Kramarz (1996). This paper considers an alternative dynamic formulation in which the common goal (dispersion) can only be achieved by agents taking distinct actions. The goal of spatial dispersion has been studied in static models of habitat selection, location (...) or congestion games, and network analysis. Our results show how this goal can be achieved gradually, by indistinguishable non-communicating agents, in a dynamic setting. (shrink)

How should we treat animals? The long-held belief that other animals exist solely for human use has undergone radical challenge in the past half century. How much further do we need to go to minimize, and even eliminate, animal suffering? The field of animal rights raises big questions about how humans treat the other animals with which we share the planet. These questions are becoming more pressing as livestock farming exerts an ever-greater toll on the planet and the animals themselves, (...) and we learn more about their capacity to think and experience pain. This book shows why animals ought to have greater rights and what the world might look like if they did. (shrink)

When the policies and activities of one country or generation harm both other nations and later generations, they constitute serious injustices. Recognizing the broad threat posed by anthropogenic climate change, advocates for an international climate policy development process have expressly aimed to mitigate this pressing contemporary environmental threat in a manner that promotes justice. Yet, while making justice a primary objective of global climate policy has been the movement's noblest aspiration, it remains an onerous challenge for policymakers. -/- Atmospheric Justice (...) is the first single-authored work of political theory that addresses this pressing challenge via the conceptual frameworks of justice, equality, and responsibility. Throughout this incisive study, Steve Vanderheiden points toward ways to achieve environmental justice by exploring how climate change raises issues of both international and intergenerational justice. In addition, he considers how the design of a global climate regime might take these aims into account. Engaging with the principles of renowned political philosopher John Rawls, he expands on them by factoring in the needs of future generations. Vanderheiden also demonstrates how political theory can contribute to reaching a better understanding of the proper human response to climate change. By showing how climate policy offers insights into resolving contemporary controversies within political theory, he illustrates the ways in which applying normative theory to policy allows us to better understand both. -/- Thoroughly researched and persuasively argued, Atmospheric Justice makes an important step toward providing us with a set of carefully elaborated first principles for achieving environmental justice. (shrink)

In this riveting collection, which he has been working on for twenty-five years, Pyke presents 100 black-and-white portraits of contemporary philosophers, ...

There is a growing perception among economists that their field is becoming increasingly irrelevant due to its disregard for reality. Critical realism addresses the failure of mainstream economics to explain economic reality and proposes an alternative approach. This book debates the relative strengths and weaknesses of critical realism, in the hopes of developing a more fruitful and relevant socio-economic ontology and methodology. With contributions from some of the leading authorities in economic philosophy, it includes the work of theorists critical of (...) this approach. In the first part, contributors develop and deepen economics as a realist social theory by considering the work of individuals, various schools of thought, socio- economic phenomena and methodology. In the second part, contributors weigh the strengths and weaknesses of critical realism. (shrink)

Drawing on several issues and methods in Western philosophy, from analytical philosophy to semiotics and hermeneutics, the author throws new light on the ancient Zhuangzi text. Engaging Daoism and contemporary Western philosophical logic, and drawing on new developments in our understanding of early Chinese culture, Coutinho challenges the interpretation of Zhuangzi as either a skeptic or a relativist, and instead seeks to explore his philosophy as emphasizing the ineradicable vagueness of language, thought and reality. This new interpretation of the Zhuangzi (...) offers an important development in the understanding of Daoist philosophy, describing a world in flux in which things themselves are vague and inconsistent, and tries to show us a Way (a Dao) to negotiate through the shadows of a "chaotic" world. (shrink)

This new volume addresses the central questions which surround the process of reasoning. This emerging topic of analytic philosophy intersects with numerous other areas of philosophy, such as epistemology, philosophy of mind, philosophy of language, and metaethics, and also psychological work on reasoning.

A comprehensive reference to category theory for students and researchers in mathematics, computer science, logic, cognitive science, linguistics, and philosophy. Useful for self-study and as a course text, the book includes all basic definitions and theorems, as well as numerous examples and exercises.