The notions of common knowledge or common belief play an important role in several areas of computer science , in philosophy, game theory, artificial intelligence, psychology and many other fields which deal with the interaction within a group of “agents”, agreement or coordinated actions. In the following we will present several deductive systems for common knowledge above epistemic logics –such as K, T, S4 and S5 –with a fixed number of agents. We focus on structural and proof-theoretic properties of these (...) calculi. (shrink)

Let ≺ be a primitive recursive well-ordering on the natural numbers and assume that its order-type is greater than or equal to the proof-theoretic ordinal of the theory T. We show that the proof-theoretic strength of T is not increased if we add the negation of the statement which formalizes transfinite induction along ≺.

In this paper we discuss extensions of Feferman's theory T 0 for explicit mathematics by the so-called limit and Mahlo axioms and present a novel approach to constructing natural recursion-theoretic models for systems of explicit mathematics which is based on nonmonotone inductive definitions.

In ‘A reductio of coherentism’ (Analysis 67, 2007) Tom Stoneham offers a novel argument against epistemological coherentism. ‘On the face of it’, he writes, ‘the argument gives a conclusive reductio ad absurdum of any coherence theory of justification. But that cannot be right, can it?’ (p. 254). It could be right, but it isn’t. I argue that coherentists need not accept the central premises of Stoneham’s argument and that, even if these premises were acceptable and true, Stoneham’s reductio would not (...) follow. (shrink)

In a series of influential papers and in his groundbreaking book Knowledge in a Social World Alvin Goldman argues that sometimes “know” just means “believe truly” (Goldman 1999; 2001; 2002b; Goldman & Olsson 2009). I argue that Goldman's (and Olsson's) case for “weak knowledge”, as well as a similar argument put forth by John Hawthorne, are unsuccessful. However, I also believe that Goldman does put his finger on an interesting and important phenomenon. He alerts us to the fact that sometimes (...) we ascribe knowledge to people even though we are not interested in whether their credal attitude is based on adequate grounds. I argue that when in such contexts we say, or concede, that S knows that p , we speak loosely. What we mean is that S would give the correct answer when asked whether p . But this doesn't entail that S knows that her answer is right or that S knows that p . My alternative analysis of the Hawthorne-Goldman-Olsson examples preserves the view that knowledge requires, even in the contexts in question, true (firm) belief that is based on adequate grounds. (shrink)

I discuss Alston's theory of religious experience and maintain that his argument to the effect that it is rational to suppose that the 'mystical doxastic practice' is epistemically reliable does not stand up to scrutiny. While Alston's transitions from practical to epistemic rationality don't work here, his arguments may be taken to show that, under certain conditions, it is not epistemically irresponsible to trust one's religious experiences.

Let T be Kripke–Platek set theory with infinity extended by the axiom (Beta) plus the schema that claims that every set-bounded Σ-definable monotone operator from the collection of all sets to Pow(a) for some set a has a fixed point. Then T proves that every such operator has a least fixed point. This result is obtained by following the proof of an analogous result for von Neumann–Bernays–Gödel set theory in an earlier work by Sato, with some minor modifications.

This handbook article gives a critical overview of recent discussions of epistemic authority. It favors an account that brings into balance the dictates of rational deference with the ideals of intellectual self-governance. A plausible starting point is the conjecture that neither should rational deference to authorities collapse into total epistemic submission, nor the ideal of mature intellectual self-governance be conflated with (illusions of) epistemic autarky.

Der Download enthält die penultimative Fassung (noch unter dem vorläufigen Titel "Molina über Vorsehung und Freiheit"). Diese ausführliche Einleitung zu dem Band "Luis de Molina: Göttlicher Plan und menschliche Freiheit", hg. und übersetzt von C. Jäger, H. Kraml und G. Leibold, Hamburg: Meiner 2018, rekonstruiert auf 165 S. Molinas berühmte Theorie der Willensfreiheit und die Frage ihrer Vereinbarkeit mit göttlichem Vorherwissen und göttlicher Vorsehung. Sie zeichnet wesentliche Stationen der Debatte um den theologischen Determinismus nach, wie sie sich von Augustinus und (...) Boethius über Anselm, Thomas von Aquin, Scotus, Ockham und andere bis zu Molina und von dort bis in die jüngste, vor allem analytische Religionsphilosophie hinein entwickelt. (shrink)

Semantic noise, the effect ensuing from the denotative and thus functional variability exhibited by different terms in different contexts, is a common concern in natural language processing (NLP). While unarguably problematic in specific applications (e.g., certain translation tasks), the main argument of this paper is that failing to observe this linguistic matter of fact as a generative effect rather than as an obstacle, leads to actual obstacles in instances where language model outputs are presented as neutral. Given that a common (...) and long-standing challenge in NLP is the interpretation of ambiguous – i.e., semantically noisy – cases, this article focuses on an exemplar ambiguity-resolution task in NLP: the problem of anaphora in Winograd schemas. The main question considered is: to what extent is the standard approach to disambiguation in NLP subject to a stagnant “image of language”? And, can a transdisciplinary, dynamic approach combining linguistics and philosophy elucidate new perspectives on these possible conceptual shortcomings? In order to answer these questions we explore the term and concept of noise, particularly in its presentation as semantic noise. Owing to its definitional plurality, and sometimes even desirable unspecificity, the term noise is thus used as proof of concept for semantic generativity being an inherent characteristic in linguistic representation, and its concept is used to interrogate assumptions admitted in the resolution of Winograd schemas. The argument is speculative and theoretical in method, and the result is an analysis which provides an account of the fundamentally dialogical and necessarily open-ended effects of semantic noise in natural language. (shrink)

An important finding of the game theoretic research on signaling games is the insight that under many circumstances, a signal obtains credibility by incurring costs to the sender. Therefore it seems questionable whether or not cheap talk—signals that are not payoff relevant—can serve to transmit information among rational agents. This issue is non-trivial in strategic interactions where the preferences of the players are not aligned. Researchers like Crawford & Sobel, Rabin, and Farrell demonstrated, however, that even in the case of (...) partially divergent interests, cheap talk may be informative. They assume that signals have an exogenously given meaning that is common knowledge between the players, and they explore the conditions under which such a signal is credible. This discussion has obvious relevance to the program of Gricean pragmatics in linguistics. According to Grice’s "Cooperative Principle”, this research tradition only considers scenarios where the interests of the players are aligned. Nevertheless, the assumption of differential signaling costs introduces an element of non-aligned interests. The present paper proposes a framework that combines these two research strands. Using an inference protocol of iterated best response, it gives a recipe for how the interlocutors derive rationalizable strategies from exogeneously given "literal” meanings of signals. No special assumptions about the alignment of interests or signaling costs are made. After introducing the formal model, the paper sketches several applications of this model to problems in linguistic pragmatics, like scalar implicatures, the division of pragmatic labor, and the interpretation of measure terms. (shrink)

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

I discuss two accounts of rational religious faith that have recently been proposed by Peter Rohs and Volker Gerhardt, respectively, and critically explore the relations between (i) faith and knowledge and (ii) faith and hope. I argue that, if faith essentially involves some form of eschatological hope, then a theory of rational faith will have to include an analysis of rational hope.

The comments focus on a presumed circular reasoning in the operator hierarchy and the necessity of understanding life’s origin for defining life. Below it is shown that its layered structure prevents the operator hierarchy from circular definitions. It is argued that the origin of life is an insufficient basis for a definition of life that includes multicellular and neural network organisms.

This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic, but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to (...) methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic. (shrink)

Logoi : the history and definition of art and aesthetics -- The broader context -- An ontological foundation -- Doxa : the nature of art -- Inspired by the spirit -- Universal beauty -- Aesthetics of hope -- Praxis : the purpose of art -- Art and creation as play -- Serious art qo -- Church art.

Goldman and Olsson ( 2009 ) have responded to the common charge that reliabilist theories of knowledge are incapable of accounting for the value knowledge has beyond mere true belief. We examine their “conditional probability solution” in detail, and show that it does not succeed. The conditional probability relation is too weak to support instrumental value, and the specific relation they describe is inessential to the value of knowledge. At best, they have described conditions in which knowledge indicates that additional (...) epistemic value is likely to be forthcoming in the future. We also argue that their motive analogy breaks down. The problem, we conclude, is that being produced by a reliable process is not sufficient for a belief to be justified. (shrink)

Gaston Bachelard's thought remains a continual source of inspiration for a phenomenological psychology that takes human habitation as a fundamental given and as an abiding mystery of the human condition. the following essay explores the ideas Bachelard developed in the course of his study of poetry. It examines in particular his vision of imagination as a unique passage way by means of which we reach an inhabitable, intersubjective and fully human world. Within that perspective, our lives are constantly renewed by (...) the appearance of a revealing image or a telling metaphor. Each time that we are awakened by this appeal we commemorate the birth and rebirth of a human world. (shrink)

In this article we study several reduction principles in the context of Simpson’s set theory ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} and Kripke-Platek set theory KP (with infinity). Since ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} is the set-theoretic version of ATR0 there is a direct link to second order arithmetic and the results for reductions over ATR0S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ATR_{0}^{S}$$\end{document} are as expected and more or less (...) straightforward. However, over KP we obtain several interesting new results and are lead to some open questions. (shrink)

The diverse things that surround us in our daily life become virtual extensions of our corporeal life. As such, they provide an important mediating role in our relationship to our social and natural environment. This careful descriptive study of household objects attempts to widen our psychological horizons. It also contributes significantly to our understanding of art and architecture.

This book extends a theory of art that addresses the present era’s shift towards global pluralism. By focusing on extrinsic rather than intrinsic qualities of art, this book helps viewers evaluate art across cultural boundaries. Art can be universally classified by an evaluation of its guiding narrative, and can be understood and judged through hermeneutical methods. Since artists engage culture through various local, transnational, and emerging global narratives, it is difficult to decipher what standards are used for evaluation, and which (...) authoritative body evaluates the work. This book implements a narrative-hermeneutical approach to properly classify an artwork and establish its meaning and value. (shrink)

Many church fathers have been identified as having held a xenolalic view on the gift of tongues. Scholars who have shown evidence of this have, however, omitted to give sufficient attention to the scope of the tongues the church fathers detailed. Many of these church fathers, referenced, identify the gift of tongues as the ability to speak all languages. This supernatural ability to speak all languages has been appropriately designated as pan-xenolalia. This article aimed to highlight the existence and prevalence (...) of the pan-xenolalic view among the church fathers and examined the works of the relevant church fathers to determine how they gave expression to their view, which passages of Scripture they applied their view to and how they motivated their view. The pan-xenolalic sentiments of many church fathers could be confirmed though they used various phrases to express it. These references to pan-xenolalia were used in the context of both Acts and 1 Corinthians. Their possible motivations for holding this view seemed to have come from sources outside of the text itself, with tradition, expectation and purpose of tongues from their perspective being the most likely influences. Contribution: The patristic perspective on tongues were not merely xenolalic but pan-xenolalic. Pan-xenolalia as interpretive key to 1 Corinthians 12–14 provides a fresh perspective to reading the text, which may pose some significant challenges to how the text is interpreted. Establishing the veracity of the pan-xenolalic view lays the foundation for scholars to evaluate a reading of 1 Corinthians 14 from this perspective. (shrink)

This article discusses textually problematic passages in Catullus 63, a particularly corrupt poem from a particularly corrupt manuscript tradition. It proposes new conjectures and revives several old ones. Throughout there are notes on punctuation, conjecture attribution and an analysis of the structure of Attis’ lament.

Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction (...) is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system <0 of second-order arithmetic. (shrink)

This paper is mainly concerned with proof-theoretic analysis of some second-order systems of explicit mathematics with a non-constructive minimum operator. By introducing axioms for variable types we extend our first-order theory BON to the elementary explicit type theory EET and add several forms of induction as well as axioms for μ. The principal results then state: EET plus set induction is proof-theoretically equivalent to Peano arithmetic PA <0).

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning (...) the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)

We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998 , J Semant 17(3):189–216, 2000 ) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000 ), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional (...) optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition. (shrink)

We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning (...) the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule Grice (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game. (shrink)