We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.

We provide a list of open problems in the research area of generalised Baire spaces, compiled with the help of the participants of two workshops held in Amsterdam (2014) and Hamburg (2015).

In this introduction we discuss the motivation behind the workshop “Towards a New Epistemology of Mathematics” of which this special issue constitutes the proceedings. We elaborate on historical and empirical aspects of the desired new epistemology, connect it to the public image of mathematics, and give a summary and an introduction to the contributions to this issue.

We give characterizations for the sentences "Every $\Sigma^1_2$-set is measurable" and "Every $\Delta^1_2$-set is measurable" for various notions of measurability derived from well-known forcing partial orderings.

We investigate the possibility of arguing for or against the philosophical position that mathematics is an _epistemic exception_ on the basis of agreement data from the mathematical peer review process and argue that Cohen’s \(\kappa \), the standard agreement measure used for inter-rater agreement, is unable to detect epistemic exceptionality from peer review data.

Maddy gave a semi-formal account of restrictiveness by defining a formal notion based on a class of interpretations and explaining how to handle false positives and false negatives. Recently, Hamkins pointed out some structural issues with Maddy's definition. We look at Maddy's formal definitions from the point of view of an abstract interpretation relation. We consider various candidates for this interpretation relation, including one that is close to Maddy's original notion, but fixes the issues raised by Hamkins. Our work brings (...) to light additional structural issues that we also discuss. (shrink)

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

This review essay looks at Andrew Brei’s edited volume, Ecology, ethics and hope, Candis Callison’s How climate change comes to matter: The communal life of facts, Randall Curren and Ellen Metzger’s Living well now and in the future: Why sustainability matters, Willis Jenkins’ The future of ethics: Sustainability, social justice, and religious creativity, and Byron Williston’s The Anthropocene project: Virtue in the age of climate change. These recent works highlight various normative approaches for engaging with what is often referred to (...) as the Anthropocene. Drawing on virtue ethics, pragmatism, and concepts such as intergenerational justice, they seek to address some of the defining moral challenges of our time: how we should respond to this unprecedented era of anthropogenic climate and environmental change, and what ethical resources we can draw on to guide our response. On a larger level, they reveal how the climate crisis is testing the limits of our current moral systems and helping to drive greater ethical innovation and adaptation in the process. (shrink)

We show that the theories ZF and ZFU are synonymous, answering a question of Visser.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

We argue that mathematical knowledge is context dependent. Our main argument is that on pain of distorting mathematical practice, one must analyse the notion of having available a proof, which supplies justification in mathematics, in a context dependent way.

The distinction between data and phenomena introduced by Bogen and Woodward (Philosophical Review 97(3):303–352, 1988) was meant to help accounting for scientific practice, especially in relation with scientific theory testing. Their article and the subsequent discussion is primarily viewed as internal to philosophy of science. We shall argue that the data/phenomena distinction can be used much more broadly in modelling processes in philosophy.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

We look at bimodal logics interpreted by cartesian products of topological spaces and discuss the validity of certain bimodal formulae in products of so-called cardinal spaces. This solves an open problem of van Benthem et al.

We give an example of a theory that strongly maximizes over ZFC and discuss possible consequences of this finding.

The “right to belong” is a human right in two ways. First, there is the right to belong in a limited sense, i.e., to the extent necessary for individuals to secure all other human rights, such as those recognized by the United Nations Universal Declaration of Human Rights. Second, there is a deeper aspect of the right to belong, that which is necessary to flourish as a human being. To establish, first, that the right to belong in a limited sense (...) should be a human right, I draw upon Hannah Arendt’s claim that stateless persons are without rights, as only communities can grant them. I argue that this limited level of belonging is a necessary but insufficient condition for human flourishing. Full human flourishing requires belonging on a deeper level. To articulate the nature of this deeper level of belonging I draw on Simone Weil’s definition of the “need for roots” and John Dewey and Jane Addams’ constructions of the self as social. I then show how “belonging” in a deeper sense necessarily connects with how a person is perceived and received by individuals and institutions in a community and argue that full perception by and participation in a community is necessary for humans to flourish. Thus, the right to belong imposes an ethical obligation on other members of the community to perceive undocumented immigrants as full human persons with the potential to lead flourishing lives. (shrink)

We consider all combinatorially possible systems corresponding to subsets of finite set theory (i.e., Zermelo-Fraenkel set theory without the axiom of infinity) and for each of them either provide a well-founded locally finite graph that is a model of that theory or show that this is impossible. To that end, we develop the technique of axiom closure of graphs.

Hamkins and Löwe proved that the modal logic of forcing is S4.2 . In this paper, we consider its modal companion, the intermediate logic KC and relate it to the fatal Heyting algebra H ZFC of forcing persistent sentences. This Heyting algebra is equationally generic for the class of fatal Heyting algebras. Motivated by these results, we further analyse the class of fatal Heyting algebras.

Maddy's notion of restrictiveness has many problematic aspects, one of them being that it is almost impossible to show that a theory is not restrictive. In this note the author addresses a crucial question of Martin Goldstern (Vienna) and points to some directions of future research.

Maddy's notion of restrictiveness has many problematic aspects, one of them being that it is almost impossible to show that a theory is not restrictive. In this note the author addresses a crucial question of Martin Goldstern (Vienna) and points to some directions of future research.

IntroductionLittle is known about risk factors for both Long COVID and somatic symptoms that develop in individuals without a history of COVID-19 in response to the pandemic. There is reason to assume an interplay between pathophysiological mechanisms and psychosocial factors in the etiology of symptom persistence.ObjectiveTherefore, this study investigates specific risk factors for somatic symptom deterioration in a cohort of German adults with and without prior SARS-CoV-2 infection.MethodsGerman healthcare professionals underwent SARS-CoV-2 IgG antibody testing and completed self-rating questionnaires at baseline (...) and 21 months later between April 2020 and February 2022. Differences in variables between the time points were analyzed and a regression analysis was performed to predict somatic symptom deterioration at follow-up.ResultsSeven hundred fifty-one adults completed both assessments. Until follow-up, n = 58 had contracted SARS-CoV-2 confirmed by serology. Between baseline and follow-up, signs of mental and physical strain increased significantly in the sample. Symptom expectations associated with COVID-19 and a self-reported history of COVID-19, but not serologically confirmed SARS-CoV-2 infection, significantly predicted somatic symptom deterioration at follow-up. A further predictor was baseline psychological symptom burden.ConclusionsThis study supports a disease-overarching biopsychosocial model for the development of burdensome somatic symptoms during the COVID-19 pandemic and supports research findings that symptom burden may be more related to the psychosocial effects of the pandemic than to infection itself. Future studies on Long COVID should include SARS-CoV-2 negative control groups and consider symptom burden prior to infection in order to avoid an overestimation of prevalence rates. (shrink)

We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”. This answers a question of Tony Martin.

This volume contains papers based on invited lectures from the 16th International Congress of Logic, Methodology and Philosophy of Science and Technology, descriptions of congress symposia, and other materials relating to the congress and DLMPST.

a few months into the covid-19 pandemic, Marilyn Fischer and Judy Whipps were commiserating about an isolated future that seemed to stretch out with no end in sight. They came up with the idea of starting their own Scholars Circle, inspired by the November 2019 Feminist Pragmatist Colloquium in Rochester, New York. At that conference, participants could submit abstracts of work at any stage of development. Participants were grouped in small circles of three or four, with each person sharing their (...) work and giving feedback and suggestions to the others. Participants at that conference were uniformly enthusiastic about how this format enriched their thinking and gave them a sense of support and camaraderie. As one of... (shrink)

The complete characterisation of order types of non-standard models of Peano arithmetic and its extensions is a famous open problem. In this paper, we consider subtheories of Peano arithmetic (both with and without induction), in particular, theories formulated in proper fragments of the full language of arithmetic. We study the order types of their non-standard models and separate all considered theories via their possible order types. We compare the theories with and without induction and observe that the theories without induction (...) tend to have an algebraic character that allows model constructions by closing a model under the relevant algebraic operations. (shrink)

The complete characterisation of order types of non-standard models of Peano arithmetic and its extensions is a famous open problem. In this paper, we consider subtheories of Peano arithmetic (both with and without induction), in particular, theories formulated in proper fragments of the full language of arithmetic. We study the order types of their non-standard models and separate all considered theories via their possible order types. We compare the theories with and without induction and observe that the theories without induction (...) tend to have an algebraic character that allows model constructions by closing a model under the relevant algebraic operations. (shrink)

The theory of infinite games with slightly imperfect information has been developed for games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{Bl-AD}_\mathbb{R}}$$\end{document} (as an analogue of the axiom of real determinacy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{AD}_\mathbb{R}}$$\end{document}). We prove that the consistency strength of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{Bl-AD}_\mathbb{R}}$$\end{document} is strictly greater than that of AD. (shrink)

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).

We do not believe that logic is the sole answer to deep and intriguing questions about human behaviour, but we think that it might be a useful tool in simulating and understanding it to a certain degree and in specifically restricted areas of application. We do not aim to resolve the question of what rational behaviour in games with mistaken and changing beliefs is. Rather, we develop a formal and abstract framework that allows us to reason about behaviour in games (...) with mistaken and changing beliefs leaving aside normative questions concerning whether the agents are behaving “rationally”; we focus on what agents do in a game. In this paper, we are not concerned with the reasoning process of the (ideal) economic agent; rather, our intended application is artificial agents, e.g., autonomous agents interacting with a human user or with each other as part of a computer game or in a virtual world. We give a story of mistaken beliefs that is a typical example of the situation in which we should want our formal setting to be applied. Then we give the definitions for our formal system and how to use this setting to get a backward induction solution. We then apply our semantics to the story related earlier and give an analysis of it. Our final section contains a discussion of related work and future projects. We discuss the advantages of our approach over existing approaches and indicate how it can be connected to the existing literature. (shrink)

Emerging Moral Vocabularies challenges the broad assertion that Western post-industrial societies are inevitably becoming more individualistic and self-centered, and instead encourages scholars to examine emerging forms for moral and ethical meaning, which form new moral boundaries.

"Foundations of the Formal Sciences" is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our (...) philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic. (shrink)

my comments focus on jane addams's methode of ethical deliberation, as understood through Dr. Fischer's detailed explication, especially as offered in chapter 2, "An Evolutionary Method of Ethical Deliberation." As Fischer points out, this explication is of one iteration of Jane Addams's method, a particularized response to how Jane Addams believed the settlement residents should respond to the many labor strikes in Chicago during the 1890s. I offer my comments from the perspective of both a scholar, seeking to better apply (...) Addams's insights to my own work, and an educator, seeking to better integrate Addams's work into my teaching. My hope is to flesh out more clearly my own understanding and, in so doing... (shrink)