ZusammenfassungLuther bemühte sich intensiv, den Sinn der Zusage Jesu an Petrus, ihm die Schlüssel des Himmelreichs zu geben , zu erfassen und damit ihre Metaphorik zu entschlüsseln. Sein Horizont fokussierte sich dabei immer mehr auf seine Auseinandersetzung mit dem Papsttum, die ihn auch tief existentiell traf. Luther entwickelte die Konzeption eines Schlüsselamtes, das als Alternative zum Papstamt seine eigene reformatorische Position beschrieb: Die Verkündigung der Sündenvergebung als Inbegriff des Evangelium in strenger Konzentration auf Wort und Glauben. Allerdings gelang es ihm (...) nicht, diesen seinen Entwurf exegetisch und praktisch-kirchlich zureichend zu plausibilisieren. Das zeigt sich schon daran, dass die lutherische Tradition Luthers Verständnis dieser Schriftstelle nicht rezipierte, sondern eigene Wege suchte, ohne selbst zu einer eindeutigen Auffassung zu gelangen. Exegetische Beobachtungen am matthäischen Basistext erlauben einen Ansatz, der nicht an der konfessionellen Konfrontation orientiert ist, sondern den Text vor dem Hintergrund der Situation, in der sich die judenchristliche Gemeinde zur Zeit des Evangelisten befand, zu verstehen sucht.SummaryLuther took great trouble to comprehend the sense of Jesus' promise to Peter, that he would give him the keys of the kingdom of heaven , and through this to unravel the imagery. His horizon focussed increasingly in this question on his clash with the papacy which was indeed existential for him. Luther developed the concept of an Office of the Keys, which described his own reformatory position as an alternative to the papacy: the proclamation of the forgiveness of sins as epitome of the gospel in strict concentration on Word and faith. However, he was not successful in backing up his outline sufficiently in exegetical and practical or ecclesiastical terms. This becomes evident, for example, in that the Lutheran tradition did not adopt Luther's understanding of this text, but instead went other ways, without achieving a clear conception. Exegetical observations on the basic text in Matthew allow a starting point which is not orientated on a confessional confrontation, but attempts to understand the text in the light of the situation in which the Jewish-Christian congregation found itself in the lifetime of the evangelist. (shrink)
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 Partly drawing on still unpublished transcripts of lectures, public talks and radio broadcasts from the 1950s and ’60s, the article offers an account of Adorno’s concept and practice of a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)
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)
Companies that contribute to charitable organizations rightly hope that their philanthropic work will also be good for the bottom line. Marketers of good corporate conduct must be especially careful, however, to market such conduct in a morally acceptable fashion. Although marketers typically engage in mild deception or take artistic license when marketing goods and services, these sorts of practices are far more morally troublesome when used to market good corporate conduct. I argue that although mild deception is not substantially worrisome (...) with respect to the marketing of most goods and services, it is a far greater moral blunder to use such methods in the marketing of good corporate character. These erode trust and demonstrate alack of adequate respect for the moral good. In light of these concerns, I suggest that such practices must be re-examined when applied to the marketing of corporate character and good conduct. Finally, I develop a revised set of ethical guidelines that are needed in order to address the problems peculiar to the marketing of morally praiseworthy behavior. (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.
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)
If □ is conceived as an operator, i.e., an expression that gives applied to a formula another formula, the expressive power of the language is severely restricted when compared to a language where □ is conceived as a predicate, i.e., an expression that yields a formula if it is applied to a term. This consideration favours the predicate approach. The predicate view, however, is threatened mainly by two problems: Some obvious predicate systems are inconsistent, and possible-worlds semantics for predicates of (...) sentences has not been developed very far. By introducing possible-worlds semantics for the language of arithmetic plus the unary predicate □, we tackle both problems. Given a frame (W, R) consisting of a set W of worlds and a binary relation R on W, we investigate whether we can interpret □ at every world in such a way that □ $\ulcorner A \ulcorner$ holds at a world ᵆ ∊ W if and only if A holds at every world $\upsilon$ ∊ W such that ᵆR $\upsilon$ . The arithmetical vocabulary is interpreted by the standard model at every world. Several 'paradoxes' (like Montague's Theorem, Gödel's Second Incompleteness Theorem, McGee's Theorem on the ω-inconsistency of certain truth theories, etc.) show that many frames, e.g., reflexive frames, do not allow for such an interpretation. We present sufficient and necessary conditions for the existence of a suitable interpretation of □ at any world. Sound and complete semi-formal systems, corresponding to the modal systems K and K4, for the class of all possible-worlds models for predicates and all transitive possible-worlds models are presented. We apply our account also to nonstandard models of arithmetic and other languages than the language of arithmetic. (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)
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)
The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.
Summary The non-statement view of scientific theories contains a new conception of theoreticity: A function is âT-theoretical if T must be presupposed for its calculation. On the basis of this conception some philosophers came to the conclusion that scientific theories are not empirically testable because they contain T-theoretical functions. It is claimed that the attempt to test them ends in a circularity: The test of T presupposes T itself.
A theory of the transfinite Tarskian hierarchy of languages is outlined and compared to a notion of partial truth by Kripke. It is shown that the hierarchy can be embedded into Kripke's minimal fixed point model. From this results on the expressive power of both approaches are obtained.
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)
Race and Gender in the Classroom explores the paradoxes of education, race, and gender, as Laurie Cooper Stoll follows eighteen teachers carrying out their roles as educators in an era of “post-racial” and “post-gendered” politics.
Race and Gender in the Classroom explores the paradoxes of education, race, and gender, as Laurie Cooper Stoll follows eighteen teachers carrying out their roles as educators in an era of “post-racial” and “post-gendered” politics.
This paper gives a survey of David Hilbert's (1862â1943) changing attitudes towards logic. The logical theory of the GÃ¶ttingen 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 GÃ¶ttingen 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 Îµ-axiom which should serve for avoiding infinite operations in logic. (shrink)
The general notions of object- and metalanguage are discussed and as a special case of this relation an arbitrary first order language with an infinite model is expanded by a predicate symbol T0 which is interpreted as truth predicate for . Then the expanded language is again augmented by a new truth predicate T1 for the whole language plus T0. This process is iterated into the transfinite to obtain the Tarskian hierarchy of languages. It is shown that there are natural (...) points for stopping this process. The sets which become definable in suitable hierarchies are investigated, so that the relevance of the Tarskian hierarchy to some subjects of philosophy of mathematics are clarified. (shrink)
Nietzsche consistently valorizes artistic falsehoods. On standard interpretations, this is because art provides deceptive yet salutary fictions that help us affirm life. This reading conflicts, however, with Nietzsche’s insistence that life-affirmation requires untrammeled honesty. I present an alternative interpretation which navigates the interpretive impasse. With special attention to the influence of Friedrich Schiller, the paper argues for three claims: (1) Nietzsche does not hold that art is false because it “beautifies,” but because it produces mere semblances of, its objects; (2) (...) these semblances are essentially non-deceptive; (3) he values artistic illusions because they dispose us positively to illusion more generally. Such ‘evaluative reorientation,’ I argue, is not merely consistent with, but integral to, achieving Nietzsche’s ideal of honesty. (shrink)
The article addresses the following question: if an extensive period of globalization and also democratization after the fall of the Berlin Wall has been followed by populism, does this mean that there is something wrong with liberalism itself? Must liberalism be substituted by alternative economic and political concepts? The article presents three alternatives to liberalism that are supposed to counter populism: a new communitarianism, a renewal of the democratic project as much as novel conceptions of social justice. However, it takes (...) also into account positions that address the current crisis from within the liberal framework itself. (shrink)
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)
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.
It is shown that David Hilbert's formalistic approach to axiomaticis accompanied by a certain pragmatism that is compatible with aphilosophical, or, so to say, external foundation of mathematics.Hilbert's foundational programme can thus be seen as areconciliation of Pragmatism and Apriorism. This interpretation iselaborated by discussing two recent positions in the philosophy ofmathematics which are or can be related to Hilbert's axiomaticalprogramme and his formalism. In a first step it is argued that thepragmatism of Hilbert's axiomatic contradicts the opinion thatHilbert style (...) axiomatical systems are closed systems, a reproachposed by Carlo Cellucci. In the second section the question isdiscussed whether Hilbert's pragmatism in foundational issuescomes close to an a-philosophical ``naturalism in mathematics'' assuggested by Penelope Maddy. The answer is ``no'', because forHilbert philosophy had its specific tasks in the general projectto found mathematics. This is illuminated in the concludingsection giving further evidence for Hilbert's foundationalapriorism by discussing his ``axiom of the existence of mind'' andrelating it to the ``one and only axiom'' of the German algebraistof logic, Ernst Schröder, postulating the inherence of signs onthe paper. (shrink)
Scholars agree that Christology is at the center of the In Iohannis euangelium tractatus. In his exegesis of the Gospel of John, Augustine particularly highlights the human nature of the Incarnated, even as he integrates Trinitarian arguments as a cornerstone of his homiletic teaching. This may have been important for the later reception of Augustine’s Trinitarian thought. Christology is clearly present throughout the various parts of the work. The differences between the parts can be traced to the various contexts in (...) which they were composed and/or delivered: e.g., the Anti-Donatist controversy that is behind the first sermons, and the Anti-Pelagian and Anti-Homean controversies that often fueled the later ones. Sometimes anti-heretical strategies are used as a crucial step for advancing the teaching of the preacher, even if the heresy being opposed is of no immediate relevance or importance to the North Africa of Augustine’s day. Surprisingly, the second half of the work contains various passages in which anti-heretical strategies were clearly pursued. It is particularly Augustine’s Anti-Pelagian strategy that provides us with clues regarding the historical context of this part of the work. (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.
We prove Yablo’s paradox without the diagonal lemma or the recursion theorem. Only a disquotation schema and axioms for a serial and transitive ordering are used in the proof. The consequences for the discussion on whether Yablo’s paradox is circular or involves self-reference are evaluated.
According to structuralism in philosophy of mathematics, arithmetic is about a single structure. First-order theories are satisfied by models that do not instantiate this structure. Proponents of structuralism have put forward various accounts of how we succeed in fixing one single structure as the intended interpretation of our arithmetical language. We shall look at a proposal that involves Tennenbaum's theorem, which says that any model with addition and multiplication as recursive operations is isomorphic to the standard model of arithmetic. On (...) this account, the intended models of arithmetic are the notation systems with recursive operations on them satisfying the Peano axioms. [A]m Anfang […] ist das Zeichen. (shrink)
This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical context will be dealt with only in passing. The main object of study will be the algebra of logic in its British and German versions. Special emphasis will be laid on the systems of George Boole and above all of his German follower Ernst Schröder.
. Although the courts have ruled that companies are legal persons, they have not yet made clear the extent to which political free speech for corporations is limited by the strictures legitimately placed upon corporate commercial speech. I explore the question of whether or not companies can properly be said to have the right to civil free speech or whether corporate speech is always de facto commercial speech not subject to the same sorts of legal protections as is the right (...) to civil free speech. In the absence of clearly defined legal precedent, I emphasize moral reasons for determining the appropriate limits of corporate civil free speech. Appealing to arguments typically used to justify individual rights to civil free speech, I examine the extent to which this sort of justification may or may not be legitimately extended to corporations. I conclude that corporate rights to civil free speech must be restricted because granting rights of free speech to institutions may, in practice, undermine the moral rationale and practical feasibility of guaranteeing rights of civil free speech to individuals. Furthermore, I argue that granting corporations full rights to civil free speech will undercut attempts to develop good moral character in corporate institutions by undermining the efforts of watchdog organizations. (shrink)
To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation φ/Tφ and conecessitation T φ/φ and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is w-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)
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