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)

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)

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)

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)

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.

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.

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)

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)

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)

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)

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)

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)

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.

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.

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)

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.

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)

Name der Zeitschrift: Zeitschrift für Religionswissenschaft Jahrgang: 25 Heft: 1 Seiten: 6-29.

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.

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)

Summary The non-statement view of scientific theories contains a new conception of theoreticity: A function is „T-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.

Uvodno poglavje je pregled razprav o svobodi spod peresa določenih nevrofiziologov iz Nemčije. V tem okviru lahko pridemo do zaključka, da ni potrebna vrzel v vzročnosti narave, da bi lahko obstajalo nekaj takega kot svoboda. V tem oziru so Libetovi eksperimenti nekonsistentni. Svoboda je v bistvenem smislu prostost od določenosti volje po volji drugega. In svoboda ima enako kot človekova zavest bistveno družbeno formo. To pa še ne pomeni, da lahko podamo oris naravne zgodovine svobode, zgodovine, v kateri bi neizogiben (...) razvoj človeškega bitja in neomejena svoboda gibanja predstavljala bistveni razvojni fazi. Pričujoči članek je tako poskus razumevanja svobode v perspektivi zgodovine evolucije.In an introductory chapter I canvass a discussion concerning freedom which has been introduced, in Germany, by certain neurophysiologists. I conclude, with regard to this discussion, that no gap in the causality of nature is required in order for there to be freedom. In this respect, then, the Libet experiments prove inconclusive. Freedom is, essentially, freedom from the determination of one’s will by the will of others. And like human consciousness, freedom has an essentially social form. This, however, does not preclude that we may make a sketch of the natural history of freedom, a history in which the unfettered development of a living being and an uninhibited freedom of movement represent essential stages. This essay makes a case for placing the social and political understanding of freedom in the perspective of the history of evolution. (shrink)

Politicization of administration is generally held to be an innovative process : the administration seems to strip off its neutral phenotype. This false notion stems from a model of analysis that ignores the administration'senvironmental interrelations and the administrative function.A functional systems model is proposed which is capable of avoiding normative implications. This model helps to understand politicization of administration as an adaptive process of the capitalist state which is thus reacting to trends of economization and "socialization" of politics. The adaptation (...) is held to be partially successful only. Political and administrativeproblem-solving tends to come out more and more critical. The only solution to this - extended participation - cannot be conceded for system's reasons. (shrink)

„Substances capable of self-reproduction“ as cellular targets of chemical carcinogens.In the course of studies on chemical carcinogenesis, which included animal experiments with a carcinogenic azo dye and a mathematical analysis of the observed effects, Hermann Druckrey and Karl Küpfmüller showed in 1948 that carcinogens induce heritable changes by targeting cellular „substances capable of self-reproduction“. The authors did not discuss the chemical nature of these substances which remained unclear for a long time thereafter. It was not until 1964 that deoxyribonucleic acid (...) (DNA) was recognized, by Peter Brookes and Philip Lawley, as a target for the genotoxic action of chemical carcinogens. In retrospect, the results of Druckrey and Küpfmüller gave an early, indirect and until now not considered hint to an important role of DNA (the „substance“) malfunction in the development of cancer, since DNA is the only molecule capable of self-reproduction.The results are now appreciated in light of the scientific knowledge available at the time. (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.

Historically, blatantly untrue and defamatory conspiracy theories had disastrous consequences for those who were portrayed in them as evil-doers. At the same time, conspiratorial agreements at the expense of the common good between powerful groups in society do exist and have occasionally been uncovered. Against this background, the article describes different ways in which critical theory has looked at conspiracies. First, an attempt is made to show that Max Horkheimer's notes on `rackets' are an ambitious but flawed attempt to theorize (...) conspiracy. It is argued that Horkheimer's theory is imbued by the very conspiracy thinking that he proposed to criticize. Second, the author suggests recovering Franz Neumann's concept of `political alienation' as a more appropriate starting point to think critically about the ethical and epistemological questions raised by conspiracy theories. (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)

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.

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...

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)

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)

Using a contextual method the specific development of logic between c. 1830 and 1930 is explained. A characteristic mark of this period is the decomposition of the complex traditional philosophical omnibus discipline logic into new philosophical subdisciplines and separate disciplines such as psychology, epistemology, philosophy of science, and formal logic. In the 19th century a growing foundational need in mathematics provoked the emergence of a structural view on mathematics and the reformulation of logic for mathematical means. As a result formallogic (...) was taken over by mathematics in the beginning of the 20th century as is shown by sketching the German example. (shrink)

Entgegen rationalistisch verkürzten Handlungs- und Wissenstheorien wird mit der Philosophie des Empraktischen der der selbstbewussten Praxis immer je schon vorgängige leiblich gestimmte Handlungsvollzug thematisiert. Das Buch knüpft an aktuelle Debatten um unmittelbar körperliche, implizite Wissensformen und um eine Philosophie der Gefühle an.

In his new book on Pascal's Wager, Jeff Jordan argues that only the ‘Jamesian’ version of the wager argument, as he sees it presented in William James' essay The Will to Believe , constitutes a sound pragmatic argument in favour of theism, whereas Pascal's original wager argument is doomed to fail on various grounds. This article argues that Jordan's theory is untenable. The many-gods objection is used as an example: it is demonstrated that the Jamesian Wager argument too is powerless (...) to rebut this objection. (shrink)