At the centre of the traditional discussion of truth is the question of how truth is defined. Recent research, especially with the development of deflationist accounts of truth, has tended to take truth as an undefined primitive notion governed by axioms, while the liar paradox and cognate paradoxes pose problems for certain seemingly natural axioms for truth. In this book, Volker Halbach examines the most important axiomatizations of truth, explores their properties and shows how the logical results impinge on (...) the philosophical topics related to truth. In particular, he shows that the discussion on topics such as deflationism about truth depends on the solution of the paradoxes. His book is an invaluable survey of the logical background to the philosophical discussion of truth, and will be indispensable reading for any graduate or professional philosopher in theories of truth. (shrink)

Logical consequence in first-order predicate logic is defined substitutionally in set theory augmented with a primitive satisfaction predicate: an argument is defined to be logically valid if and only if there is no substitution instance with true premises and a false conclusion. Substitution instances are permitted to contain parameters. Variants of this definition of logical consequence are given: logical validity can be defined with or without identity as a logical constant, and quantifiers can be relativized in substitution instances or not. (...) It is shown that the resulting notions of logical consequence are extensionally equivalent to versions of first-order provability and model-theoretic consequence. Every model-theoretic interpretation has a substitutional counterpart, but not vice versa. In particular, in contrast to the model-theoretic account, there is a trivial intended interpretation on the substitutional account, namely, the homophonic interpretation that does not substitute anything. Applications to free logic, and theories and languages other than set theory are sketched. (shrink)

Wittgenstein’s Whewell’s Court Lectures contains previously unpublished notes from lectures given by Ludwig Wittgenstein between 1938 and 1941. The volume offers new insight into the development of Wittgenstein’s thought and includes some of the finest examples of Wittgenstein’s lectures in regard to both content and reliability.

This article—mainly referring to the situation in Germany—consists of three parts. In a first section the current presence of neurosciences in the public discourse will be described in order to illuminate the background which is relevant for contemporary educational thinking. The prefix ‘neuro-’ is ubiquitous today and therefore concepts like ‘neuropedagogy’ or ‘neurodidactics’ seem to be in the mainstream of modern thinking. In the second part of the article the perspective changes from the public discourse to the disciplinary discourse; a (...) brief excursus into developmental psychiatry, neuropsychology and modern psychoanalysis will be made in order to demonstrate how the results of neuroscientific research are integrated in their theoretical frameworks. These three disciplines have no difficulty in integrating neuroscientific findings because each of them possesses a systematic core composed of ‘native concepts’. In contrast to them, educational theory has much more difficulty with such integration, as will be shown in the third part of the essay. On the one hand, neuroscientific thinking seems to be able to dominate education rather easily and without great resistance, especially in the fields of early childhood education, instruction and learning—mainly by simplifying educational processes and by reducing the complexity of the educational task to a mere ‘relationship problem’. On the other hand, this attraction of neuroscience in education might be understood as the reflection of a theoretical deficit in educational theory itself, with the significance of affect and emotion not receiving proper attention. (shrink)

The attempts to mitigate the unprecedented health, economic, and social disruptions caused by the COVID-19 pandemic are largely dependent on establishing compliance to behavioral guidelines and rules that reduce the risk of infection. Here, by conducting an online survey that tested participants’ knowledge about the disease and measured demographic, attitudinal, and cognitive variables, we identify predictors of self-reported social distancing and hygiene behavior. To investigate the cognitive processes underlying health-prevention behavior in the pandemic, we co-opted the dual-process model of thinking (...) to measure participants’ propensities for automatic and intuitive thinking vs. controlled and reflective thinking. Self-reports of 17 precautionary behaviors, including regular hand washing, social distancing, and wearing a face mask, served as a dependent measure. The results of hierarchical regressions showed that age, risk-taking propensity, and concern about the pandemic predicted adoption of precautionary behavior. Variance in cognitive processes also predicted precautionary behavior: participants with higher scores for controlled thinking (measured with the Cognitive Reflection Test) reported less adherence to specific guidelines, as did respondents with a poor understanding of the infection and transmission mechanism of the COVID-19 virus. The predictive power of this model was comparable to an approach (Theory of Planned Behavior) based on attitudes to health behavior. Given these results, we propose the inclusion of measures of cognitive reflection and mental model variables in predictive models of compliance, and future studies of precautionary behavior to establish how cognitive variables are linked with people’s information processing and social norms. (shrink)

Definitional and axiomatic theories of truth -- Objects of truth -- Tarski -- Truth and set theory -- Technical preliminaries -- Comparing axiomatic theories of truth -- Disquotation -- Classical compositional truth -- Hierarchies -- Typed and type-free theories of truth -- Reasons against typing -- Axioms and rules -- Axioms for type-free truth -- Classical symmetric truth -- Kripke-Feferman -- Axiomatizing Kripke's theory in partial logic -- Grounded truth -- Alternative evaluation schemata -- Disquotation -- Classical logic -- Deflationism (...) -- Reflection -- Ontological reduction -- Applying theories of truth. (shrink)

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...) KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

According to the disquotationalist theory of truth, the Tarskian equivalences, conceived as axioms, yield all there is to say about truth. Several authors have claimed that the expression of infinite conjunctions and disjunctions is the only purpose of the disquotationalist truth predicate. The way in which infinite conjunctions can be expressed by an axiomatized truth predicate is explored and it is considered whether the disquotationalist truth predicate is adequate for this purpose.

To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation and conecessitation T and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is -inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give an analysis (...) of its proof theory. (shrink)

We study operator equations within the Turing machine based framework for computability in analysis. Is there an algorithm that maps pairs to solutions of Tx = u ? Here we consider the case when T is a bounded linear mapping between Hilbert spaces. We are in particular interested in computing the generalized inverse T†u, which is the standard concept of solution in the theory of inverse problems. Typically, T† is discontinuous and hence no computable mapping. However, we will use effective (...) versions of theorems from the theory of regularization to show that the mapping ↦ T†u is computable. We then go on to study the computability of average-case solutions with respect to Gaussian measures which have been considered in information based complexity. Here, T† is considered as an element of an L2-space. We define suitable representations for such spaces and use the results from the first part of the paper to show that ↦ T† is computable. (shrink)

The purpose of this article is to explore the potential contribution of Axel Honneth's critical theory of recognition to empirical and normative debates on global justice. I first present, very briefly, an overview of recent theories of global distributive justice. I argue that theorists of distributive justice do not pay enough attention to sources of self-respect and conditions for identity formation, and that they are blind toward the danger of harming people's sense of self even by well-intentioned redistributive policies. Honneth's (...) theory suffers from complementary shortcomings; it is anti-technocratic but largely oblivious to the global nature of many contemporary justice claims. Given this situation, I seek to broaden the theory's scope by outlining transnational extensions of the recognition principles of love, rights and solidarity identified by Honneth. In conclusion, I show how utilizing a broadened conceptualization of the struggle for recognition allows us to better understand the changing logic of justice-oriented foreign policies. (shrink)

When Benno Kerry died at the age of 30 he was already well‐known for his competent and thoroughgoing philosophical criticism of Cantor’s set theory and Frege’s early philosophy of mathematics.Before his death he was working on a theory of limits which was an elaboration of his Habilitationsschrift of 1884 and of which only a first part was published posthumously.This paper gives a survey of Kerry’s basic biographical data, and a first description of his Habilitationsschrift which had been missing for a (...) long time but was found by chance in the Nachlass of the German philosopher Leonard Nelson. (shrink)

On the one hand, the concept of truth is a major research subject in analytic philosophy. On the other hand, mathematical logicians have developed sophisticated logical theories of truth and the paradoxes. Recent developments in logical theories of the semantical paradoxes are highly relevant for philosophical research on the notion of truth. And conversely, philosophical guidance is necessary for the development of logical theories of truth and the paradoxes. From this perspective, this volume intends to reflect and promote deeper interaction (...) and collaboration between philosophers and logicians investigating the concept of truth than has existed so far.Aside from an extended introductory overview of recent work in the theory of truth, the volume consists of articles by leading philosophers and logicians on subjects and debates that are situated on the interface between logical and philosophical theories of truth. The volume is intended for graduate students in philosophy and in logic who want an introduction to contemporary research in this area, as well as for professional philosophers and logicians. (shrink)

Disquotational theories of truth, that is, theories of truth based on the T-sentences or similar equivalences as axioms are often thought to be deductively weak. This view is correct if the truth predicate is allowed to apply only to sentences not containing the truth predicate. By taking a slightly more liberal approach toward the paradoxes, I obtain a disquotational theory of truth that is proof theoretically as strong as compositional theories such as the Kripket probe the compositional axioms.

The uniform reflection principle for the theory of uniform T-sentences is added to PA. The resulting system is justified on the basis of a disquotationalist theory of truth where the provability predicate is conceived as a special kind of analyticity. The system is equivalent to the system ACA of arithmetical comprehension. If the truth predicate is also allowed to occur in the sentences that are inserted in the T-sentences, yet not in the scope of negation, the system with the reflection (...) schema for these T-sentences assumes the strength of the Kripke-Feferman theory KF, and thus of ramified analysis up to go. (shrink)

Der Phänomenologe Oskar Becker beschäftigte sich zeit seines Lebens mit der Philosophie der Mathematik, insbesondere mit dem Unendlichkeitsproblem und seinen Implikationen für die Ontologie mathematischer Gegenstände. Durch Anwendung der phänomenologischen Methode versuchte er einen intuitiven Zugang zum Unendlichen zu ermöglichen. Während er im mathematischen Grundlagenstreit Position bezog für den Intuitionismus L.E.J. Brouwers und H. Weyls, kritisierte er den Formalismus D. Hilberts heftig. Sein besonderes Interesse galt darüber hinaus der Geschichte insbesondere der antiken Mathematik. Die Beiträge des Bandes behandeln die mathematikphilosophischen (...) und -historischen Interessen Beckers in ihrer ganzen Breite und stellen seine Ansichten in den mathematikphilosophischen, aber auch hermeneutisch-phänomenologischen Kontext ihrer Zeit. In diesem Zusammenhang relevante, bisher ungedruckte Briefwechsel und Einzelbriefe werden hier erstmals veröffentlicht. (shrink)

The purpose of Key Approaches to Biblical Ethics is to address fundamental as well as practical questions of methodology in examining the ethical material of the Bible. Sixteen scholars of international reputation, most of them leaders in the field of biblical ethics, discuss questions of biblical interpretation from the perspectives of the Hebrew Bible and New Testament ethics in close dialogue with one another. In the present volume both established and new approaches to biblical ethics are presented and discussed. The (...) result is a volume of unprecedented scholarly interaction that provides key insights into issues of biblical ethics that play a significant role both for biblical interpretation as well as for methodological questions in Jewish and Christian ethics today. (shrink)

Zermelos Zeit in Göttingen (1897?1910) kann als wissenschaftlich fruchtbarste Periode in seiner Karriere angesehen werden. Gleichwohl stehen bisher Untersuchungen aus. die eine Einbettung von Zermelos Werk in den biographischen und sozialen Kontext ermöglichen Die vorliegende Studie will diese Lücke unter Konzentration auf zwei Gegenstandsbereiche teileweise ausfüllen: (1) den historischen Entstehungskontext von Zermelos ersten Arbeiten über die Grundlagen der Mengenlehre; (2) die Vorgeschichte und näheren Umstände des 1907 an Zermelo verliehenen Lehrauftrages für mathematische Logik und verwandte Gegenstände. mit dem ein erster (...) Schritt zur Institutionalisierung dieses Faches als mathematischer Teildisziplin gemacht wurde. Beides wird in enger Verbindung zur ersten Phase des Hilbertschen Programms zur Grundlegung der Mathematik gesehen. Es wird aber auch gezeigt, daß für die Erteilung des Lehrauftrages neben diesen systematischen und forschungspolitischen Motiven auch persönliche und institutspolitische Rücksichten ausschlaggebend waren. Im Anhang werden Teile eines Briefwechsels zwischen Ernst Zermelo und dem Göttinger Philosophen Leonard Nelson ediert sowie die Anträge der Direktoren des Göttinger mathematisch-physikalischen Seminars auf Erteilung des Lehrauftrags und auf Ernennung Zermelos zum außerordentlichen Professor. Zermelo's Göttingen period (1897?1910) can be regarded as the most fruitful period in his scientific career. Nevertheless, up till now there have been no investigations which enable us to embed his work in its biographical and social contexts. This study tries to partially fill the gap, concentrating on two major themes: (I) the historical context of the development of Zermelo's early work on the foundations of set theory; (2) the prehistory and particulars of his lectureship for mathematical logic and related topics, this lectureship, which he was awarded in 1907, being the first step taken in Germany towards the establishment of this subject as a separate mathematical discipline. Both will be seen in close connection with the first phase of Hilbert's programme of founding mathematics. It is shown, however, that this lectureship was not only created to further the aims of Hilbert's research programme but that personal and institutional motives also played a role. In the appendices, parts of a correspondence between Ernst Zermelo and the Göttingen Philosopher Leonard Nelson are edited, as well as the applications of the directors of the Göttingen Mathematisch-physikalisches Seminar for awarding the lectureship to Zermelo in 1907, and for appointing Zermelo to an extraordinary professorship in 1910. (shrink)

It is a commonplace that in the development of modern logic towards its actual shape at least two directions or traditions have to be distinguished. These traditions may be called, following the mo...

Against competing political theories of the integration of immigrants, we propose to reframe the relationship between the populations of host countries and arriving refugees in terms of a neo-Maussian theory of gift exchange. Using the example of the European refugee crisis of 2015 and the welcoming attitude of significant parts of German civil society, we argue that this particular situation should be understood as epitomizing the trend toward internal transnationalism. Increasingly, the “international” is becoming part and parcel of the “domestic” (...) sphere. Since Marcel Mauss was concerned with the question of how separate, culturally different communities can establish ties of solidarity and cooperation between each other, we use his work to answer key questions about the relations between international refugees and native citizens in their home countries: What are the expectations underlying gift-giving in the context of welcoming refugees? Should refugees feel obliged to repay the arrival gifts? How sh... (shrink)

In this sequel toSelf-reference in arithmetic Iwe continue our discussion of the question: What does it mean for a sentence of arithmetic to ascribe to itself a property? We investigate how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed point for the expressing formulae are obtained. In this second part we look at some further examples. In particular, we study sentences apparently expressing their Rosser-provability, their own${\rm{\Sigma (...) }}_n^0$-truth or their own${\rm{\Pi }}_n^0$-truth. Finally we offer an assessment of the results of both papers. (shrink)

Over the past decades, we have witnessed calls for greater transdisciplinary engagement between scientific and societal actors to develop more robust answers to complex societal challenges. Although there seems to be agreement that these approaches might nurture innovations of a new kind, we know little regarding the research practices, their potential, and the limitations. To fill this gap, this article investigates a funding scheme in the area of transdisciplinary sustainability research. It offers a detailed analysis of the imaginaries and expectations (...) on which the funding scheme rests and how researchers actually practice transdisciplinarity within the respective projects. Identifying three ideal typical models of science–society relations at work, attention is paid to how, where, and when societal and scientific arenas get entangled. This article discusses the tensions between classical academic values and efforts to open research to society, the prevailing power structures that make societal participation challenging, the importance of place and technopolitical cultures, and how temporal project structures impede more radical openings to new ways of knowledge production. We finally emphasize that transdisciplinary knowledge production can only become a serious option for addressing societal challenges if broader changes are made to the knowledge regimes in place. (shrink)

Im Rahmen einer Fallstudie ('Okonomische Theorie der Demokratie' von Anthony Downs) wird gezeigt, dass realwissenschaftliche Theorien, unabhangig davon, ob sie sozial- oder naturwissenschaftlicher Provenienz, in bezug auf ihre logische Struktur identisch sind. Mit der stringenten Anwendung des metatheoretischen Rekonstruktionskonzeptes des Strukturalismus auf eine politikwissenschaftliche Theorie wird ein Rahmen entwickelt, der es erlaubt, politikwissenschaftliche Theorien nicht nur praziser zu erfassen, sondern auch eine fundierte Klarung dessen zu erbringen, was eine politikwissenschaftliche Theorie sein kann.".

Every educational system requires some kind of management and control. This is particularly true in the case of occupational education and dual apprenticeship. Nevertheless, the didactical value and the overall success of such kind of educational systems can vary considerably. Any educational system, any system of apprenticeship requires either some kind of coordination or some kind of co-operation. In Germany, despite the fact that there is a lot of rumors about the importance of cooperation for over a decade by now, (...) the well-known dual system of vocational education is firmly grounded on the management principle of co-ordination. The control of the system ‘by plans’ apparently has proved to be the most adequate approach to its organization and management structures. Starting from the idea of a duality which is characterized by its didactical dimension, the set of qualities needed for this purpose can be illustrated by following the logic of different didactical approaches in vocational education. (shrink)

400 years after Bruno's death by fire in Rome the question arises whether Bruno did in fact die as martyr of truth. If we consider his philosophical arguments we can understand his cosmological concept of the infinite universe as essentially contradictory to some of Aristotle's ideas of philosophy of nature. Alongside his belief in the omnipresence of divinity in nature he takes the view of the universe as a living organism, an area where he was influenced by the hermetic tradition. (...) Above all Bruno's cosmology also includes ethical elements. So if we ask for the actual reason of Bruno's conviction, some theological consequences of his cosmological ideas did presumably influence the judgement of the inquisition. In contrast to Galileo Bruno's condemnation has not so far been withdrawn. However such reconsideration is possible and counting on the church's spirit of reconciliation should come to pass. (shrink)

Das neueHandbuch bietet demGynäkologen in Praxis und Klinik Handlungsanleitungen für die Schwangerenberatung und -behandlung im Falle einer mütterlichen Erkrankung. Von A-Z gegliedert werden über 100 Diagnosen hinsichtlich Definition, Klinik und geburtshilflichem Management beschrieben. Ein Merksatz fasst das Wichtigste für die Behandlung zusammen. Durch die alphabetische Auflistung der Diagnosen und die praxisnahen und kurzgefassten einzelnen Einträge ist das Buch ein wertvolles Nachschlagewerk für jeden Gynäkologen. Literaturangaben zu jedem Eintrag verweisen auf relevante weiterführende Quellen.

Die Frage nach dem aWozuo der Geschichte(n) eroffnet ein weites Feld von eng miteinander verschlungenen Problemkomplexen, das durch die Begriffe Geschichtsbewusstsein und Identitat, Geschichtsphilosophie und Historik in seinen Grenzen ...

This article suggests reading Theodor Adorno not as a notoriously pessimistic sociologist but as a committed public educator. Partly drawing on still unpublished transcripts of lectures, public talks and radio broadcasts from the 1950s and ’60s, the article offers an account of Adorno’s concept and practice of a ‘democratic pedagogy’. The key question is how we should understand the difference between Adorno the social philosopher, on the one hand, and Adorno the educator, on the other. It is argued that Adorno’s (...) pedagogical interventions are not a footnote to his social theory, but a key to understanding his entire oeuvre. (shrink)

This paper gives a survey of David Hilbert's (1862–1943) changing attitudes towards logic. The logical theory of the Göttingen mathematician is presented as intimately linked to his studies on the foundation of mathematics. Hilbert developed his logical theory in three stages: (1) in his early axiomatic programme until 1903 Hilbert proposed to use the traditional theory of logical inferences to prove the consistency of his set of axioms for arithmetic. (2) After the publication of the logical and set-theoretical paradoxes by (...) Gottlob Frege and Bertrand Russell it was due to Hilbert and his closest collaborator Ernst Zermelo that mathematical logic became one of the topics taught in courses for Göttingen mathematics students. The axiomatization of logic and set-theory became part of the axiomatic programme, and they tried to create their own consistent logical calculi as tools for proving consistency of axiomatic systems. (3) In his struggle with intuitionism, represented by L. E. J. Brouwer and his advocate Hermann Weyl, Hilbert, assisted by Paul Bemays, created the distinction between proper mathematics and meta-mathematics, the latter using only finite means. He considerably revised the logical calculus of thePrincipia Mathematica of Alfred North Whitehead and Bertrand Russell by introducing the ε-axiom which should serve for avoiding infinite operations in logic. (shrink)

The book provides a thematic account of the changing political thought of critical theorists from Adorno to Habermas and Honneth. Its purpose is to establish the relevance of this tradition for contemporary political theory and philosophy.

Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.

Solutions to semantic paradoxes often involve restrictions of classical logic for semantic vocabulary. In the paper we investigate the costs of these restrictions in a model case. In particular, we fix two systems of truth capturing the same conception of truth: of the system KF of Feferman formulated in classical logic, and the system PKF of Halbach and Horsten, formulated in basic De Morgan logic. The classical system is known to be much stronger than the nonclassical one. We assess the (...) reasons for this asymmetry by showing that the truth theoretic principles of PKF cannot be blamed: PKF with induction restricted to non-semantic vocabulary coincides in fact with what the restricted version of KF proves true. (shrink)