This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.

In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.

This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{<\alpha};$ the exact proof-theoretic ordinals of these systems are presented.

This paper deals with: (i) the theory ID # 1 which results from $\widehat{\mathrm{ID}}_1$ by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω 0.

In this article we introduce systems for metapredicative Mahlo in explicit mathematics and admissible set theory. The exact upper proof-theoretic bounds of these systems are established.

This paper deals with: (i) the theory $\mathrm{ID}^{\tt\#}_1$ which results from $\widehat{\mathrm{ID}}_1$ by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory $\mathrm{BON}(\mu)$ plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are $\Sigma$ in the ordinals. We show that these systems have proof-theoretic strength $\varphi\omega 0$.

In this paper we study applicative theories of operations and numbers with the non-constructive minimum operator in the context of a total application operation. We determine the proof-theoretic strength of such theories by relating them to well-known systems like Peano Arithmetic PA and the system <0 of second order arithmetic. Essential use will be made of so-called fixed-point theories with ordinals, certain infinitary term models and Church-Rosser properties.

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.

This paper deals with universes in explicit mathematics. After introducing some basic definitions, the limit axiom and possible ordering principles for universes are discussed. Later, we turn to least universes, strictness and name induction. Special emphasis is put on theories for explicit mathematics with universes which are proof-theoretically equivalent to Feferman's.

In this paper we establish the proof-theoretic equivalence of (i) $\hbox {\sf ATR}$ and $\widehat{\hbox{\sf ID}}_{\omega}$ , (ii) $\hbox{\sf ATR}_0+ (\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\omega^\omega} , and (iii) $\hbox {\sf ATR}+(\Sigma^1_1-\hbox{\sf DC})$ and $\widehat{\hbox {\sf ID}}_{<\varepsilon_0} $.

We study elementary second order extensions of the theoryID 1 of non-iterated inductive definitions and the theoryPA Ω of Peano arithmetic with ordinals. We determine the exact proof-theoretic strength of those extensions and their natural subsystems, and we relate them to subsystems of analysis with arithmetic comprehension plusΠ 1 1 comprehension and bar induction without set parameters.

We show that the principle of ω model reflection for Π1n − 1 formulas is equivalent over ACA0 to the scheme of Π1n bar induction. This extends and refines previous results of Friedman and Simpson.

We give a broad discussion of reflection principles in explicit mathematics, thereby addressing various kinds of universe existence principles. The proof-theoretic strength of the relevant systems of explicit mathematics is couched in terms of suitable extensions of Kripke–Platek set theory.

Buchholz’s Ω μ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz (Iterated (...) inductive definitions and subsystems of analysis: recent proof theoretic studies. Lecture notes in mathematics, vol. 897, pp. 189–233, Springer, Berlin, 1981). (shrink)

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)

In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm 0 of admissible set theory, transfinite induction along initial segments of the ordinal φω00, for φ being a ternary Veblen function, is derivable. This reveals that the upper bounds given for these two systems in the (...) paper Jager and Strahm [11] are indeed sharp. (shrink)

For some modal fixed point logics, there are deductive systems that enjoy syntactic cut-elimination. An early example is the system in Pliuskevicius [15] for LTL. More recent examples are the systems by the authors of this paper for the logic of common knowledge [5] and by Hill and Poggiolesi for PDL[8], which are based on a form of deep inference. These logics can be seen as fragments of the modal mu-calculus. Here we are interested in how far this approach can (...) be pushed in general. To this end, we introduce a nested sequent system with syntactic cut-elimination which is incomplete for the modal mu-calculus, but complete with respect to a restricted language that allows only fixed points of a certain form. This restricted language includes the logic of common knowledge and PDL. There is also a traditional sequent system for the modal mu-calculus by Jäger et al. [9], without a syntactic cut-elimination procedure. We embed that system into ours and vice versa, thus establishing cut-elimination also for the shallow system, when only the restricted language is considered. (shrink)

This paper is a companion to work of Feferman, Jäger, Glaß, and Strahm on the proof theory of the type two functionals μ and E1 in the context of Feferman-style applicative theories. In contrast to the previous work, we analyze these two functionals in the context of Schlüter's weakened applicative basis PRON which allows for an interpretation in the primitive recursive indices. The proof-theoretic strength of PRON augmented by μ and E1 is measured in terms of the two subsystems of (...) second order arithmetic, Π10-CA and Π11-CA, respectively. (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)

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.

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.

v. 1. Editorial introduction -- v. 2. The English and Latin texts (i) -- v. 3. The English and Latin texts (ii).

We conducted two eye-tracking experiments investigating the processing of the Mandarin reflexive ziji in order to tease apart structurally constrained accounts from standard cue-based accounts of memory retrieval. In both experiments, we tested whether structurally inaccessible distractors that fulfill the animacy requirement of ziji influence processing times at the reflexive. In Experiment 1, we manipulated animacy of the antecedent and a structurally inaccessible distractor intervening between the antecedent and the reflexive. In conditions where the accessible antecedent mismatched the animacy cue, (...) we found inhibitory interference whereas in antecedent-match conditions, no effect of the distractor was observed. In Experiment 2, we tested only antecedent-match configurations and manipulated locality of the reflexive-antecedent binding (Mandarin allows non-local binding). Participants were asked to hold three distractors (animate vs. inanimate nouns) in memory while reading the target sentence. We found slower reading times when animate distractors were held in memory (inhibitory interference). Moreover, we replicated the locality effect reported in previous studies. These results are incompatible with structure-based accounts. However, the cue-based ACT-R model of Lewis and Vasishth ( 2005 ) cannot explain the observed pattern either. We therefore extend the original ACT-R model and show how this model not only explains the data presented in this article, but is also able to account for previously unexplained patterns in the literature on reflexive processing. (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.

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)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

When making decisions, humans can observe many kinds of information about others' activities, but their effects on performance are not well understood. We investigated social learning strategies using a simple problem-solving task in which participants search a complex space, and each can view and imitate others' solutions. Results showed that participants combined multiple sources of information to guide learning, including payoffs of peers' solutions, popularity of solution elements among peers, similarity of peers' solutions to their own, and relative payoffs from (...) individual exploration. Furthermore, performance was positively associated with imitation rates at both the individual and group levels. When peers' payoffs were hidden, popularity and similarity biases reversed, participants searched more broadly and randomly, and both quality and equity of exploration suffered. We conclude that when peers' solutions can be effectively compared, imitation does not simply permit scrounging, but it can also facilitate propagation of good solutions for further cumulative exploration. (shrink)

The article presents proofs of the context freeness of a family of typelogical grammars, namely all grammars that are based on a uni- ormultimodal logic of pure residuation, possibly enriched with thestructural rules of Permutation and Expansion for binary modes.

In this note it is shown that in explicit mathematics the strong power type axiom is inconsistent with (uniform) elementary comprehension and discuss some general aspects of power types in explicit mathematics.

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)

In this book Thomas Wren uncovers and assesses the largely hidden philosophical assumptions about human motivation that have shaped contemporary psychological ...

INTRODUCTION Although the writings of Thomas Reid are very fertile and interesting, his life is biographically barren in comparison to such seventeenth - and ...

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)