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.

Bewusstsein, Außenwelt und Sprache bilden eine untrennbare Einheit in der Frage nach dem Sinn und der Bedeutung sprachlicher Ausdrücke. Zeichen und ihre Verwendung lassen sich daher weder durch rein internalistische Bewusstseinsanalysen noch durch rein externalistische Gegenstandsbezüge angemessen rekonstruieren. Daher befinden sich Bedeutungen weder „innerhalb" noch „außerhalb" des Kopfes. Unterschiedliche Gebrauchsweisen und somit Bedeutungen spiegeln sich vielmehr in der Fähigkeit wieder, sprachliche Zeichen zu verstehen und auf unsere subjektiven Erlebnisse sowie die uns umgebende Welt anzuwenden. Volker Munz zeigt, inwieweit sowohl (...) rein phänomenale als auch rein physikalistische Interpretationsansätze zu kurz greifen, die Bedeutung sprachlicher Ausdrücke zu bestimmen. Beide Positionen stehen nicht in Widerstreit zueinander, sondern ergänzen einander vielmehr in der Bestimmung des Sinnes und der Bedeutung sprachlicher Zeichen. Sowohl externalistische Semantiken (Putnams Zwillingserde, Kripkes Marsianer, Davidsons Sumpfmann etc.) als auch internalistische Positionen (Locke, Thomas Nagel, Jackson etc.) werden anhand spezifischer Gedankenexperiment kritisch auf ihre Rolle und Schlüssigkeit hin überprüft und mit alternativen Gedankenszenarios konfrontiert. Neben den genannten Autoren werden auch Russell, Frege und insbesondere Wittgenstein ausführlich diskutiert. (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)

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)

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.

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)

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)

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)

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)

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)

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.

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)

A substitutional account of logical validity for formal first‐order languages is developed and defended against competing accounts such as the model‐theoretic definition of validity. Roughly, a substitution instance of a sentence is defined as the result of uniformly substituting nonlogical expressions in the sentence with expressions of the same grammatical category and possibly relativizing quantifiers. In particular, predicate symbols can be replaced with formulae possibly containing additional free variables. A sentence is defined to be logically true iff all its substitution (...) instances are satisfied by all variable assignments. Logical consequence is defined analogously. Satisfaction is taken to be a primitive notion and axiomatized.For every set‐theoretic model in the sense of model theory there exists a corresponding substitutional interpretation in a sense to be specified. Conversely, however, there are substitutional interpretations – in particular the ‘intended’ interpretation – that lack a model‐theoretic counterpart. The substitutional definition of logical validity overcomes the weaknesses of more restrictive accounts of substitutional validity; unlike model‐theoretic logical consequence, the substitutional notion is trivially and provably truth preserving. In Kreisel's squeezing argument the formal notion of substitutional validity naturally slots into the place of intuitive validity. (shrink)

The Qing dynasty scholar Liu Yuan (1768-1856) developed a unique system of thought, merging Confucian learning with ideas and practices from Daoism and Buddhism, and was eventually venerated as the founding patriarch of an influential movement combining the characteristics of a scholarly circle and a religious society. Liu Yuan, a native of Sichuan, was an outstanding Confucian scholar whose teachings were commonly referred to as Liumen (Liu School). Assisted by his close disciples, Liu edited a Daoist ritual canon titled Fayan (...) huizuan (Compendium of Ritual Words). Daoist priests affiliated with the Liumen community and using the Fayan huizuan canon in their rituals constituted an independent liturgical branch of Daoism, which is still extant and known under the name of "Fayan tan" (Altar of Ritual Words). Following a comprehensive description of the Liumen tradition, the volume by Volker Olles discusses the compilation history of the Fayan huizuan canon, the lineage of the Fayan tan priests, as well as the temporal framework of their liturgy. The main part of the volume consists of a detailed study of the ritual canon, identifying its textual sources and describing its pantheon, the influence of the Liumen ideology on its texts, as well as the function and performance of its rituals in contemporary religious practice. Furthermore concluding thoughts about the Fayan tan tradition's role in present-day Sichuan constitute the epilogue. By showing how members of the Confucian elite were involved in the evolution of modern Daoism, this study sheds light on hitherto obscure or poorly understood aspects of the intellectual and spiritual culture of Southwest China. (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)

Inhalt: I. Satze der Form A glaubt, dass P. - II. Elementarsatz und phanomenologische Sprache. - III. Die wandelnde Bedeutung der Elementarsatze im Rahmen des Farbeninkompatibilitatsproblems. - IV. Regel und notwendiger Satz. G.E. Moore uber Wittgensteins Auffassung von Necessary Propositions. - V. Wittgensteins Single Lecture on Necessary Propositions. - VI. Eine behaviouristische Fehlinterpretation.".

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.

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 (which he had developed earlier in his De trinitate) 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 (not least because they can directly promote knowledge of the fundamentals of the faith), even if the heresy being opposed is of no immediate relevance or importance to the North Africa of Augustine’s day (e.g., that of the “Sabellians” or the “Apollinarians”). Surprisingly, the second half of the work (consisting as it does of shorter homilies or, better, drafts of homilies) 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)

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 European Union’s history has an unique character: it has achieved the creation of unity without cancelling the singularities that uphold it; it has the capability of action without depriving its member states of their functions. Carl Schmitt is hereby confuted: sovereignty can be divided. Europe thus appears as a laboratory for international political history. In more than two millennia Europeans have carried out experiments with themselves developing a self-understanding as representatives of humanity. Now they can again understand themselves as (...) an example that they show to themselves, such as each one should be, in his own person, an example for humanity. He who becomes a model for others cannot obtain pretences from it. He can only be satisfied in establishing that he is understood. (shrink)

Nowadays the question of toleration is less related to an international clash of civilizations than to the clashes that take place within the states and polities themselves. The article addresses the sources of toleration in this new global scenario, starting from the following set of questions: Do the sources of toleration differ across time and space? Does toleration have different roots in different civilizational contexts, such as China, India or Islam? Or, is toleration the result of particular institutional frameworks and (...) designs? In this case, does the concept of toleration vary from one institutional setting to the other? Do empires, republics and democracies give rise to different forms of toleration? And last but not least, isn’t toleration rather a matter of individual morality, as many liberal theories sustain? The article distinguishes between three different sources of toleration: individuals, cultures and institutions. Kant and contemporary liberals, as John Rawls who follows him, situate t... (shrink)

This compilation refers to the springs, prehistory, foundation and effectiveness of the oldest surgical school in Saxony. This institute for second-rate physicians, surgeons and barbers was necessary because especially the military medicine and the medical practice turned out to be a weak spot. The „Collegium medico-chirurgicum (1748–1813) in Dresden had disposed of the first clinical hospital with lessons at the sickbed, the first maternity ward and the first dental-surgery lectureship in Saxony. it was an exemplary and guiding educational establishment which (...) did not belong to the university but connected theory and practice sometimes better than the universities. (shrink)

In groupware tools, the activation of a function may affect other users who might have conflicting interests. We developed technical mechanisms to support users in resolving them. Contrary to current implementations of groupware tools, these mechanisms strengthen the position of the users who are affected by the activation of said functions. Supporting the visibility of a function's activation, and providing a channel for communication or means to intervene against the function's activation are approaches which constitute a framework to implement these (...) mechanisms. We conclude with showing implementation examples of the framework and their evaluation in the POLITeam project. (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)

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)

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)

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...

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)