This article is concerned with reflection principles in the context of Cantor’s conception of the set-theoretic universe. We argue that within such a conception reflection principles can be formulated that confer intrinsic plausibility to strong axioms of infinity.

We show that assuming modest large cardinals, there is a definable class of ordinals, closed and unbounded beneath every uncountable cardinal, so that for any closed and unbounded subclasses $P, Q, {\langle L[P],\in,P \rangle }$ and ${\langle L[Q],\in,Q \rangle }$ possess the same reals, satisfy the Generalised Continuum Hypothesis, and moreover are elementarily equivalent. Examples of such P are Card, the class of uncountable cardinals, I the uniform indiscernibles, or for any n the class $C^{n}{=_{{\operatorname {df}}}}\{ \lambda \, | \, (...) V_{\lambda } \prec _{{\Sigma }_{n}}V\}$ ; moreover the theory of such models is invariant under ZFC-preserving extensions. They also all have a rich structure satisfying many of the usual combinatorial principles and a definable wellorder of the reals. The inner model constructed using definability in the language augmented by the Härtig quantifier is thus also characterized. (shrink)

We review some fundamental questions concerning the real line of mathematical analysis, which, like the Continuum Hypothesis, are also independent of the axioms of set theory, but are of a less ‘problematic’ nature, as they can be solved by adopting the right axiomatic framework. We contend that any foundations for mathematics should be able to simply formulate such questions as well as to raise at least the theoretical hope for their resolution.The usual procedure in set theory is to add so-called (...) strong axioms of infinity to the standard axioms of Zermelo-Fraenkel, but then the question of their justification becomes to some people vexing. We show how the adoption of a view of the universe of sets with classes, together with certain kinds of Global Reflection Principles resolves some of these issues. (shrink)

A correction is needed to our paper: to the definition contained within the statement of Lemma 1.5 and thus arguments around it in §3.

We claim that a recent article of P. Cotogno ([2003]) in this journal is based on an incorrect argument concerning the non-computability of diagonal functions. The point is that whilst diagonal functions are not computable by any function of the class over which they diagonalise, there is no ?logical incomputability? in their being computed over a wider class. Hence this ?logical incomputability? regrettably cannot be used in his argument that no hypercomputation can compute the Halting problem. This seems to lead (...) him into a further error in his analysis of the supposed conventional status of the infinite time Turing machines of Hamkins and Lewis ([2000]). Theorem 1 refutes this directly. The diagonalisation misunderstanding Infinite computation Conclusion. (shrink)

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

We describe the solution of the Limit Rule Problem of Revision Theory and discuss the philosophical consequences of the fact that the truth set of Revision Theory is a complete 1/2 set.

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)

The logician Kurt Godel in 1951 established a disjunctive thesis about the scope and limits of mathematical knowledge: either the mathematical mind is equivalent to a Turing machine (i.e., a computer), or there are absolutely undecidable mathematical problems. In the second half of the twentieth century, attempts have been made to arrive at a stronger conclusion. In particular, arguments have been produced by the philosopher J.R. Lucas and by the physicist and mathematician Roger Penrose that intend to show that the (...) mathematical mind is more powerful than any computer. These arguments, and counterarguments to them, have not convinced the logical and philosophical community. The reason for this is an insufficiency if rigour in the debate. The contributions in this volume move the debate forward by formulating rigorous frameworks and formally spelling out and evaluating arguments that bear on Godel's disjunction in these frameworks. The contributions in this volume have been written by world leading experts in the field. (shrink)

This study investigated subjective experiences of nine men who had been psychiatrically hospitalized upon being assessed as "dangerous-to-others-due-to-a-mental-illness." Using a phenomenological interviewing approach, researchers helped subjects construct narratives of their pre-hospitalization experiences. The research illuminated aspects of life-contexts that were shared among all or nearly all subjects: feeling ostracized and alone; struggling with longstanding and pervasive feelings of inadequacy; experiencing a sense or a fear of having little or no control or options in life; and feeling emotionally depressed, misunderstood, and (...) uncared for. Situations immediately preceding hospitalization were characterized by subjects experiencing threats to their sense of self-esteem that were of heightened intensity. In five cases, subjects reported anxiety related to self-fragmentation or becoming "nothing." Perceived threats to self-worth and self-structure were accompanied by anger and aggressive acts or impulses. In all cases, aggressive impulses and threats, and violence appeared to be in the service of self-validation and self-empowerment. In cases of violent behavior, an apparent function of the subjects' behaviors was toward self-consolidation. Based on findings, the researchers discuss implications consistent with humanistic psychology and existential psychotherapy principles and practices. (shrink)

We show in ZFC, assuming all reals have sharps, that a countable collection of ▵ 1 3 -degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.

We show in ZFC, assuming all reals have sharps, that a countable collection of $\triangle^1_3$-degrees without a minimal upper bound implies the existence of inner models with measurable cardinals.

We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma _{1}$ -definability at uncountable regular cardinals. In particular we give its exact consistency strength first in terms of the second uniform indiscernible for bounded subsets of $\kappa $ : $u_2$, and secondly to give the consistency strength of a property of Lücke’s.TheoremThe following are equiconsistent:There exists $\kappa $ which is stably measurable;for some cardinal $\kappa $, $u_2=\sigma $ ;The $\boldsymbol {\Sigma }_{1}$ -club property holds (...) at a cardinal $\kappa $.Here $\sigma $ is the height of the smallest $M \prec _{\Sigma _{1}} H $ containing $\kappa +1$ and all of $H $. Let $\Phi $ be the assertion: TheoremAssume $\kappa $ is stably measurable. Then $\Phi $.And a form of converse:TheoremSuppose there is no sharp for an inner model with a strong cardinal. Then in the core model K we have: $\mbox {``}\exists \kappa \Phi \mbox {''}$ is -generically absolute ${\,\longleftrightarrow \,}$ There are arbitrarily large stably measurable cardinals.When $u_2 < \sigma $ we give some results on inner model reflection. (shrink)

We investigate the set S 2 of "quickly sharped" reals: \begin{align*}S_2 &= \{x \mid x \in M, M \text{the} <^\ast-\text{least mouse} \not\in L\lbrack x\rbrack\} \\ &= \{x \mid L\lbrack x\rbrack \models "V = K"\},\\ \end{align*} in the manner of [K] defining a natural hierarchy and quasi-hierarchy of constructibility degrees and identifying their termination points.

The use of Extended Logics to replace ordinary second order definability in Kleene’s Ramified Analytical Hierarchy is investigated. This mirrors a similar investigation of Kennedy, Magidor and Väänänen [11] where Gödel’s universe L of constructible sets is subjected to similar variance. Enhancing second order definability allows models to be defined which may or may not coincide with the original Kleene hierarchy in domain. Extending the logic with game quantifiers, and assuming strong axioms of infinity, we obtain minimal correct models of (...) analysis. A wide spectrum of models can be so generated from abstract definability notions: one may take an abstract Spector Class and extract an extended logic for it. The resultant structure is then a minimal model of the given kind of definability. (shrink)

We set $\mathscr{D} = \langle\mathscr{D}, \leq_L, \tt\#\rangle$ , where D is the set of degrees of nonconstructibility for countable sets of countable ordinals. We show how to define inductively over this structure the degrees of such sets of ordinals in K, the core model, and the next few core models thereafter, i.e. without reference to mice, premice or measurable cardinals.

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and (...) can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus. (shrink)

We prove that a form of the $Erd\H{o}s$ property (consistent with $V = L\lbrack H_{\omega_2}\rbrack$ and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle $\psi_{AC}$ holds, and therefore 2ℵ0 = ℵ2. We also prove that $\psi_{AC}$ implies that every function $f: \omega_1 \rightarrow \omega_1$ is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum (...) fails. (shrink)

We show that the predicate “x is the power set of y” is ‐definable, if V = L[E] is an extender model constructed from a coherent sequences of extenders, provided that there is no inner model with a Woodin cardinal. Here is a predicate true of just the infinite cardinals. From this we conclude: the validities of second order logic are reducible to, the set of validities of the Härtig quantifier logic. Further we show that if no L[E] model has (...) a cardinal strong up to one of its ℵ‐fixed points, and, the Löwenheim number of this logic, is less than the least weakly inaccessible δ, then (i) is a limit of measurable cardinals of K, and (ii) the Weak Covering Lemma holds at δ. (shrink)

We give the proof of a theorem of Jensen and Zeman on the existence of a global □ sequence in the Core Model below a measurable cardinal κ of Mitchell order ) equal to κ++, and use it to prove the following theorem on mutual stationarity at n.Let ω1 denote the first uncountable cardinal of V and set to be the class of ordinals of cofinality ω1.TheoremIf every sequence n m. In particular, there is such a model in which for (...) all sufficiently large m<ω, the class of measurables λ with oM≥ωm is, in V, stationary below m+2. (shrink)

This article explores ways in which the Revision Theory of Truth can be expressed in the object language. In particular, we investigate the extent to which semantic deficiency, stable truth, and nearly stable truth can be so expressed, and we study different axiomatic systems for the Revision Theory of Truth.

Gupta-Belnap-style circular definitions use all real numbers as possible starting points of revision sequences. In that sense they are boldface definitions. We discuss lightface versions of circular definitions and boldface versions of inductive definitions.

Welche Rolle spielt Sprache für eine kritische Theorie? Die Beiträger beantworten diese Frage vor dem Hintergrund gegenwärtiger Diskussionen in der Sprach- und Sozialphilosophie. Sie zeichnen so ein Bild epistemologischer, kommunikativer, sozialer und normativer Gefahren und Potenziale der Sprache. Mit Beiträgen von Robert B. Brandom, Alexander G. Düttmann, Martin Seel u.a.

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 119 Der Verf. bedient sieh in Verfolgung seines Ziels der fibliehen historischen Methode, die er mit Meistersehaft handhabt. Doch ist er keineswegs ein typischer Vertreter des modernen Historismus. Als Philosoph ist er gefesselt von den Problemen, die sich in der dreifachen Thematik seiner Untersuehung verbergen. Er begibt sich in die Gesehichte, aber doch nur, um yon Zeit zu Zeit aus ihr herauszutreten und i)berlegungen nachzugehen, die er (...) selbst, anlfifilieh einer methodologisehen Bemerkung in der Einleitung, als eine "Typologie yon LSsungen" (3) bezeiehnet. Aber das ist ein understatement, keine exakte Besehreibung. Die unbefangene und nfiehterne Kfihnheit dieser seiner trans-historisehen Reflexionen durehweht als ein frischer Luftzug die Welt der Gelehrsamkeit und Vielbelesenheit, die sich in diesen Seiten aufbaut. Freilieh, wo der Verf. selbst steht, gibt er uns nur gelegentlieh zu verstehen, so z.B. wenn er mit Entsehiedenheit die averroistisehe Depotenzierung des Einzelnen gegenfiber der Mensehheir zurfickweist. Aber, wiederum im Zusammenhang mit Averroes, legt er Gedanken zu der berfihmten oder auch berfiehtigten Lebre yon der doppelten Wahrheit vor, die uns in Zweifel darfiber lassen, ob und wie weit sich der Verf. hier verbirgt oder d~couvriert. M. gesellt sich nicht zu denen, die Averroes entlasten woUen, indem sie die fatale Lehre als eine spatere Zutat erkl~ren. Vielmehr mSchte er das Anathema dadurch fortnehmen, daB er die grobe und beleidigende Darstellung der Lehre dutch eine subtile Deutung ersetzt, die sie als konsequent, als vernfinftig und schlie61ich als wahr erscheinen l~Bt (107 ft.). Der Mensch, so argumentiert er, drfickt sich in einer Mehrheit yon "Sprachen" (universes of discourse) aus, die sich nieht ineinander fibersetzen lassen--der Sprache der Kunst, der Dichtung, der Philosophie, der Religion usw. So kann ein und derselbe Menseh ohne Selbstwidersprueh oder Unredliehkeit als Philosoph sagen: die individuelleSeele ist sterblich, als Gl~ubigerhingegen: sie ist unsterblich. Denn sowohl "Seele" wie "Individuum" wie aueh "Unsterblichkeit" meinen etwas anderes je nach dem universe of discourse, dem philosophischen oder religiSsen, in welchem sie gebraueht werden. Freilich, man kann den Versueh maehen, in langagestart in einer der vielen langues zu reden, und die Theologie kann nicht umhin, eben dies zu wagen. Ffir die Theologie aber~ so bekennt der Verf., ist kein Raum in seinem "scheme of things" (109). Das ist ein erschreckendes Wort, und nieht blofi ffir den, der die Theologie erhalten mSchte. Denn es besteht begrfindete Sorge, dab der Ruin der zwisehen den versehiedenen langues zerriebenen Theologie auch die Philosophiepulverisiert. Die verschiedenen"Spraehen" miissen doch wohl in der einen mensehlichen Person sinnvoll zusammengeordnet sein. Welche Wissenschaft aber wenn nicht die Philosophie darf sich diese Zusammenordnung zum Gegenstand ihres Forschens und Sagens machen? Wir schliefien also unseren Bericht fiber ein bedeutendes Buch mit einer Frage, nicht aber der Kritik oder gar des Besser-wissen-wollenswegen, sondern um auszudrficken, dab der Autor uns nicht nur als gelehrter Kenner unterrichtet, sondern als Philosoph zum Denken zwingt. Mi~nchen, Germany HELMUT KUHN Diogenis Laertii Vitae Philosophorum. Recognovit brevique adnotatione critica instruxit H. S. Long. 1 vol. in2. (Oxford: 1964.Pp. xx ~ xiv W 597. $11.20.) Der Hg erinnert uns, dass seit der Cobetsehen (1850), leider apparatlosen, keine kritische Ausgabe des Diogenes im ganzen ersehlenen ist. Immerhin gibt es abet die Ubersetzung yon M. Gigante (DiogeneLaerzio, Vite dei filosofi, Bari 1962), die so annotiert ist, dass sie vielfach anstatt einer Edition gebraucht werden kann. Man bedauert, dass der Hg sie offenbar noch nicht benutzen konnte (sein Buch ist wohl 1964erschienen, doch ist die Vorrede 1961datiert). Der Hg schliesst sich der Meinung an, dass nut 3 der existierenden Diogenes-Hss den Wert unabh~ngiger Zeugen besitzen. Vorsichtiger beurteilt den Sachverhalt z.B.H. Erbse in: Geschichte der Text~berlieferung, I. Band (1961), S. 306f., doch wollen wir die These des Hg akzeptieren. Wie allgemein zugestanden, gehen diese drei auf eine gemeinsame Vorlage zur~iek. Unter diesen Ums~nden ist es die Pflicht des Hg, uns verl~sslich und eindeutig fiber den Text dieser drei (BFP aus dem 12.u. 13.Jh.) zu informieren, eine Entscheidung zu treffen, wo diese 120 HISTORY OF PHILOSOPHY nicht tibereinstimmen, darfiber hinaus Textverderbnisse anzuzeigen und womSglich zu emendieren, entweder dureh eigene Vermutungen (in Buch VI und IX, e. 19% des Ganzen, habe ich nur zwei gefunden, beide einleuehtend... (shrink)

Zusammenfassung Hintergrund Advance Care Planning (ACP) wird auch in Deutschland zunehmend praktiziert. Aus klinisch-ethischer Perspektive bietet ACP eine Möglichkeit, Vorausverfügungen zu konkretisieren und auf diese Weise die Entscheidungsfindung bei fehlender Selbstbestimmungsfähigkeit von Patient:innen zu unterstützen. Während es für Gesprächsangebote im Sinne des ACP in Pflegeeinrichtungen und Einrichtungen der Eingliederungshilfe seit 2015 Finanzierungsmöglichkeiten gibt und erste Studien zu Angeboten veröffentlich wurden, fehlt es in Deutschland bisher an publizierten Evaluationsstudien zu ACP-Angeboten im Krankenhaus. Intervention und Methoden Im vorliegenden Beitrag erfolgt die strukturierte (...) Darstellung von ACP als ein Element des klinisch-ethischen Unterstützungsangebotes am Universitätsklinikum Halle (Saale) (UKH). Es erfolgte eine quantitative Inhaltsanalyse der schriftlichen Dokumentation von durchgeführten ACP-Gesprächsprozessen für den Zeitraum der Pilotphase von 01/2020 bis 08/2021 (20 Monate). Ergebnisse Im Zeitraum wurden 93 ACP-Gespräche angefragt. Mit 79 Patient:innen konnten 110 Gespräche geführt werden. 46 % der Anfragen kamen von Palliative Care betreuten Patient:innen. Im Durchschnitt dauerten die Beratungen 45 min. Der Gesprächsprozess zur Erstellung einer Patientenverfügung benötigte durchschnittlich 122 min und 2,5 Gespräche. Bei 23 % der Patient:innen endete der ACP-Prozess nach dem Erstgespräch. Die Inhalte der ACP-Prozesse tangierten verschiedene Bereiche anderer Professionen im Krankenhaus, insbesondere die Entscheidungsfindung über aktuelle Diagnostik und Therapie zwischen Ärzt:innen und Patient:innen. Diskussion Die Einführung eines ACP-Angebotes im Krankenhaus zeigt neben einer Vielzahl an Chancen auch Herausforderungen auf, welche es im gemeinsamen Diskurs zu bewältigen gilt. Bei der Einbettung eines ACP-Angebots im Krankenhaus müssen die Besonderheiten der Klinik und insbesondere die Abgrenzung von ACP zu anderen Arbeitsfeldern der Ethikberatung, wie beispielsweise die Ethikfallberatung, bedacht werden. (shrink)

There has recently been a revival of interest in panpsychism as a theory of consciousness. The hope of the contemporary proponents of panpsychism is that the view enables us to integrate consciousness into our overall theory of reality in a way that avoids the deep difficulties that plague the more conventional options of physicalism on the one hand and dualism on the other. However, panpsychism comes in two forms — strong and weak emergentist — and there are arguments that seem (...) to show that weak emergentist panpsychism faces problems analogous to those of physicalism whilst strong emergentist panpsychism faces problems analogous to those of dualism. In this paper, I will develop a new hybrid of the strong and weak emergentist forms of panpsychism, a view according to which subjects of experience are strongly emergent but their phenomenal properties are weakly emergent. I will argue that this hybrid view manages to avoid the challenges facing both physicalism and dualism, and the analogues of those challenges that seem to undermine standard forms of panpsychism. (shrink)

In this work, the prominent political philosopher Philip Pettit embarks on a massive undertaking to offers major new accounts of the foundations of the state and the nature of justice. In doing so Pettit builds a new theory of what the state is and what it ought to be, addresses the normative question of how justice serves as a measure of the success of a state, and the way it should operate in relation to its citizens and other people.

Since the 1970’s there has been a major increase in adventure sports participation but it seems that engagement in such sports comes with a stigma: adventure sports participants are often regarded as reckless ‘daredevils’. We approach the questions about people’s perception of risk and recklessness in adventure sports by combining empirical research with philosophical analysis. First, we provide empirical evidence that suggests that laypeople tend to assess the danger of adventure sports as greater than more mundane sports and judge adventure (...) sports participants as more reckless than participants in non-adventure sports. We contextualise these findings within existing psychological risk perception paradigms and outline new philosophical explanations of the identified pattern in laypeople’s risk perception. (shrink)

A person presented with adequate but not conclusive evidence for a proposition is in a position voluntarily to acquire a belief in that proposition, or to suspend judgment about it. The availability of doxastic options in such cases grounds a moderate form of doxastic voluntarism not based on practical motives, and therefore distinct from pragmatism. In such cases, belief-acquisition or suspension of judgment meets standard conditions on willing: it can express stable character traits of the agent, it can be responsive (...) to reasons, and it is compatible with a subjective awareness of the available options. (shrink)