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

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

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

In this paper we discuss extensions of Feferman's theory T 0 for explicit mathematics by the so-called limit and Mahlo axioms and present a novel approach to constructing natural recursion-theoretic models for systems of explicit mathematics which is based on nonmonotone inductive definitions.

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

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

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

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

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

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

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

Der Download enthält die penultimative Fassung (noch unter dem vorläufigen Titel "Molina über Vorsehung und Freiheit"). Diese ausführliche Einleitung zu dem Band "Luis de Molina: Göttlicher Plan und menschliche Freiheit", hg. und übersetzt von C. Jäger, H. Kraml und G. Leibold, Hamburg: Meiner 2018, rekonstruiert auf 165 S. Molinas berühmte Theorie der Willensfreiheit und die Frage ihrer Vereinbarkeit mit göttlichem Vorherwissen und göttlicher Vorsehung. Sie zeichnet wesentliche Stationen der Debatte um den theologischen Determinismus nach, wie sie sich von Augustinus und (...) Boethius über Anselm, Thomas von Aquin, Scotus, Ockham und andere bis zu Molina und von dort bis in die jüngste, vor allem analytische Religionsphilosophie hinein entwickelt. (shrink)

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

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

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

This handbook article gives a critical overview of recent discussions of epistemic authority. It favors an account that brings into balance the dictates of rational deference with the ideals of intellectual self-governance. A plausible starting point is the conjecture that neither should rational deference to authorities collapse into total epistemic submission, nor the ideal of mature intellectual self-governance be conflated with (illusions of) epistemic autarky.

One of the key tenets of Linda Zagzebski’s book " Epistemic Authority" is the Preemption Thesis. It says that, when an agent learns that an epistemic authority believes that p, the rational response for her is to adopt that belief and to replace all of her previous reasons relevant to whether p by the reason that the authority believes that p. I argue that such a “Hobbesian approach” to epistemic authority yields problematic results. This becomes especially virulent when we apply (...) Preemption to cases in which the agent and the authority share their belief, maybe even for the same reasons, or in which both have either a positive or a negative graded doxastic attitude toward a given proposition. As an alternative I propose a “Socratic account”, according to which the authority will not only motivate us to adopt her belief, but also provide us with higher-order reasons for re-assigning our own considerations their proper place in the web of reasons for and against the view in question. (shrink)

Jäger, G., Fixed points in Peano arithmetic with ordinals, Annals of Pure and Applied Logic 60 119-132. This paper deals with some proof-theoretic aspects of fixed point theories over Peano arithmetic with ordinals. It studies three such theories which differ in the principles which are available for induction on the natural numbers and ordinals. The main result states that there is a natural theory in this framework which is a conservative extension of Peano arithmeti.

An epistemic agent A is a false epistemic authority for others iff they falsely believe A to be in a position to help them accomplish their epistemic ends. A major divide exists between what I call "epistemic quacks", who falsely believe themselves to be relevantly competent, and "epistemic charlatans", i.e., false authorities who believe or even know that they are incompetent. Both types of false authority do not cover what Lackey (2021) calls "predatory experts": experts who systematically misuse their social-epistemic (...) status as a cover for predatory behavior. Qua experts, predatory experts are competent and thus could (and maybe sometimes do) help their clients. But should we count them as genuine epistemic authorities? No, I argue, they are false epistemic authorities because, in addition to their practical and moral misconduct, such experts systematically deceive their clients, thereby thwarting the clients’ epistemic ends. (shrink)

We discuss the social-epistemic aspects of Catherine Elgin’s theory of reflective equilibrium and understanding and argue that it yields an argument for the view that a crucial social-epistemic function of epistemic authorities is to foster understanding in their communities. We explore the competences that enable epistemic authorities to fulfil this role and argue that among them is an epistemic virtue we call “epistemic empathy”.

Suppose your evil sibling travels back in time, intending to lethally poison your grandfather during his infancy. Determined to save grandpa, you grab two antidotes and follow your sibling through the wormhole. Under normal circumstances, each antidote has a 50% chance of curing a poisoning. Upon finding young grandpa, poisoned, you administer the first antidote. Alas, it has no effect. The second antidote is your last hope. You administer it---and success: the paleness vanishes from grandpa's face, he is healed. As (...) you administered the first antidote, what was the chance that it would be effective? -/- This essay offers a systematic account of this case, and others like it. The central question is this: Given a certain time travel structure, what are the chances? In particular, I'll develop a theory about the connection between these chances and the chances in ordinary, time-travel-free contexts. Central to the account is a Markov condition involving the boundaries of spacetime regions. (shrink)

According to Fred Dretske's externalist theory of knowledge a subject knows that p if and only if she believes that p and this belief is caused or causally sustained by the information that p. Another famous feature of Dretske's epistemology is his denial that knowledge is closed under known entailment. I argue that, given Dretske's construal of information, he is in fact committed to the view that both information and knowledge are closed under known entailment. Hence, if it is true (...) that, as Dretske also believes, accepting closure leads to skepticism, he must either embrace skepticism or abandon his information theory of knowledge. (shrink)

This paper explores the phenomenon of meta-emotions. Meta-emotions are emotions people have about their own emotions. We analyze the intentional structure of meta-emotions and show how psychological findings support our account. Acknowledgement of meta-emotions can elucidate a number of important issues in the philosophy of mind and, more specifically, the philosophy and psychology of emotions. Among them are (allegedly) ambivalent or paradoxical emotions, emotional communication, emotional self-regulation, privileged access failure for repressed emotions, and survivor guilt.

Gärdenfors (Conceptual spaces, 2000) argues that the semantic domains that natural language deals with have a geometrical structure. He gives evidence that simple natural language adjectives usually denote natural properties, where a natural property is a convex region of such a “conceptual space.” In this paper I will show that this feature of natural categories need not be stipulated as basic. In fact, it can be shown to be the result of evolutionary dynamics of communicative strategies under very general assumptions.

I raise two objections against Christian List and Peter Menzies' influential account of high-level causation. Improving upon some of Stephen Yablo's earlier work, I develop an alternative theory which evades both objections. The discussion calls into question List and Menzies' main contention, namely, that the exclusion principle, applied to difference-making, is false.

Is speaker knowledge necessary or sufficient for enabling hearers to know from testimony? Here, we offer a novel argument for the answer no, based on the systematic effects of partial belief and the hearer’s view prior to hearing testimony. Modelling partial belief by credence, we show that a requirement entailed by the principles of necessity and sufficiency apparent in the literature is inconsistent with Bayesian updating. Consequently, even when the other grounds of knowledge are in place, the audience correctly updating (...) their partial belief can block the transmission of speaker knowledge, so it need not be sufficient. Nor need speaker knowledge be necessary, because the hearer correctly updating their partial belief can put them in the position to know even though no one in the speaker’s chain knows. We articulate the correct principles of testimonial knowledge transmission. The first supports a shared-credit view of transmission. The second gives a novel and systematic argument for testimony sometimes being a generative (not transmissive) source of knowledge, an argument that makes Lackey’s statement account of testimony otiose. Finally, on at least one account of causation, the two amended principles together show how speaker knowledge can be a cause whose effect is hearer’s knowledge. (shrink)

There are many psychic mechanisms by which people engage with their selves. We argue that an important yet hitherto neglected one is self-appraisal via meta-emotions. We discuss the intentional structure of meta-emotions and explore the phenomenology of a variety of examples. We then present a pilot study providing preliminary evidence that some facial displays may indicate the presence of meta-emotions. We conclude by arguing that meta-emotions have an important role to play in higher-order theories of psychic harmony.

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

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Der Band versammelt Beiträge renommierter Vertreter unterschiedlicher Disziplinen zu der Frage, ob wir tatsächlich einen Zugang zur Wirklichkeit haben oder lediglich von unseren eigenen Konstruktionen der Wirklichkeit umgeben sind. In der Debatte kommt der Sprache eine zentrale Rolle zu. Konstruktivistische Positionen gehen davon aus, dass unsere Wörter und Sätze nie die Dinge an sich bezeichnen, sondern dies immer aus einer bestimmten Perspektive tun. Einer ‚Wirklichkeit an sich‘ nachzujagen, ist zwecklos, als wichtig gilt das Aufzeigen der Perspektiven. Nicht selten geschieht das (...) in aufklärerischer Absicht, wenn etwa Formulierungen wie die von der „Größe eines Volkes“, der „historischen Bestimmung einer Nation“ oder der „Natur des Geschlechts“ kritisch hinterfragt werden. Diesen Versuchen, die Wirklichkeit als interessengeleitet konstruierte auszuweisen, wird mit dem Argument begegnet, der Akt der Aufklärung diene letztlich nur dazu, die jeweils eigene Position als die ‚eigentlich richtige‘ durchzusetzen. Außerdem widerspreche die Annahme eines umfassenden Konstruiertseins unserer Wirklichkeitsbilder jeder Alltagserfahrung von der Präsenz und Widerständigkeit der Welt. An diesem Punkt der Kontroverse setzt der vorliegende Band an. Andreas Gardt : Wort und Welt. Konstruktivismus und Realismus in der Sprachtheorie Markus Gabriel : Der Neue Realismus zwischen Konstruktion und Wirklichkeit John R. Searle : The Philosophy of Perception and the Bad Argument Bernhard Pörksen : Der Blick des Kritikers. Die Debatte über den Konstruktivismus in der deutschsprachigen Kommunikationswissenschaft – ein Beispiel für die Auseinandersetzung zwischen realistischen und relativistischen Wissenschaftlern Siegfried J. Schmidt : Wie wirklich ist die Wirklichkeit? Heinz Bude : Realitäten in der Wirklichkeit Paul Kirchhof : Rechtssprache zwischen Ideal und Wirklichkeit Paul-Gerhard Klumbies : Gott – bewusst gemacht oder bewusstgemacht? Eine theologische Rückmeldung zu Konstruktivismus und Neuem Realismus Wolf-Andreas Liebert : Können wir mit Engeln sprechen? Über die eigenartige Wirklichkeit der Verständigung im Religiösen Gerhard Roth : Wahrnehmung und Erkenntnis: Grundzüge einer neurobiologisch fundierten Erkenntnistheorie Thomas Fuchs : Die gemeinsame Wahrnehmung der Wirklichkeit. Skizze eines enaktiven Realismus Alexander Ziem/Björn Fritsche : Von der Sprache zur Wirklichkeit: Die konstruktivistische Perspektive der Kognitiven Linguistik Max Düsterhöft/Robert Jacob/Marco Lehmann-Waffenschmidt : Konstruiert oder real? Die konstruierte Alltagswirklichkeit des Geldes Ludwig Jäger : „Outthereness". Über das Problem des Wirklichkeitsbezugs von Zeichen Matthias Attig : Begriffsrealismus als sprachwissenschaftliches Problem. Überlegungen zur kategorialen Eigenart von Termini Josef Klein : ‚Betrachten der Wirklichkeit‘ und politisches Framing. Am Beispiel der CDU-Wahlkampagne 2013 Ekkehard Felder : Wahrheit und Wissen zwischen Wirklichkeit und Konstruktion: Freiheiten und Zwänge beim sprachlichen Handeln. (shrink)

In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf's Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of (...) psychologically and psychologically motivated assumptions about the working of horizontal language transmission. (shrink)

Two classes of account have been proposed to explain the memory processes subserving the processing of reflexive-antecedent dependencies. Structure-based accounts assume that the retrieval of the antecedent is guided by syntactic tree-configurational information without considering other kinds of information such as gender marking in the case of English reflexives. By contrast, unconstrained cue-based retrieval assumes that all available information is used for retrieving the antecedent. Similarity-based interference effects from structurally illicit distractors which match a non-structural retrieval cue have been interpreted (...) as evidence favoring the unconstrained cue-based retrieval account since cue-based retrieval interference from structurally illicit distractors is incompatible with the structure-based account. However, it has been argued that the observed effects do not necessarily reflect interference occurring at the moment of retrieval but might equally well be accounted for by interference occurring already at the stage of encoding or maintaining the antecedent in memory, in which case they cannot be taken as evidence against the structure-based account. We present three experiments (self-paced reading and eye-tracking) on German reflexives and Swedish reflexive and pronominal possessives in which we pit the predictions of encoding interference and cue-based retrieval interference against each other. We could not find any indication that encoding interference affects the processing ease of the reflexive-antecedent dependency formation. Thus, there is no evidence that encoding interference might be the explanation for the interference effects observed in previous work. We therefore conclude that invoking encoding interference may not be a plausible way to reconcile interference effects with a structure-based account of reflexive processing. (shrink)

Keith DeRose has argued that ‘the knowledge account of assertion – according to which what one is in a position to assert is what one knows – ... provides a ... powerful positive argument in favor of contextualism’ (2009: 80). The truth is that it yields a powerful argument against contextualism, at least against its most popular, anti-sceptical versions. The following argument shows that, if we conjoin (such versions of) epistemic contextualism with an appropriate meta-linguistic formulation of the knowledge account (...) of assertion, contextualism cannot coherently be stated. (shrink)

In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf’s Law and universal properties of color terms, respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of (...) psychologically and psychologically motivated assumptions about the working of horizontal language transmission. (shrink)

We study and some of its most important extensions primarily from a proof-theoretic perspective, determine their consistency strengths by exhibiting equivalent systems in the realm of traditional set theory and introduce a new and interesting extension of which is conservative over.