Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is (...) adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula Φ(λ, a) such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$ , there is a supertransitive inner model of Zermelo containing all ordinals in which for every λ A (...) λ = {α ∣Φ(λ, a)}. (shrink)

Working in Z + KP, we give a new proof that the class of hereditarily finite sets cannot be proved to be a set in Zermelo set theory, extend the method to establish other failures of replacement, and exhibit a formula $\Phi$ such that for any sequence $\langle A_{\lambda} \mid \lambda \text{a limit ordinal} \rangle$ where for each $\lambda, A_{\lambda} \subseteq ^{\lambda}2$, there is a supertransitive inner model of Zermelo containing all ordinals in which for every $\lambda A_{\lambda} = \{\alpha (...) \mid\Phi\}$. (shrink)

This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], as improved and extended by work of the second. We use the rudimentarily recursive functions and the slightly larger collection of gentle functions to initiate the study of provident sets, which are transitive models of $\mathsf{PROVI}$, a subsystem of $\mathsf{KP}$ whose minimal model is Jensen’s $J_{\omega}$. $\mathsf{PROVI}$ supports familiar definitions, such as rank, transitive closure and ordinal addition—though not ordinal multiplication—and Shoenfield’s unramified (...) forcing. Providence is preserved under directed unions. An arbitrary set has a provident closure, and the extension of a provident $M$ by a set-generic $\mathcal{G}$ is the provident closure of $M\cup\{\mathcal{G}\}$. The improvidence of many models of $\mathsf{Z}$ is shown. The final section uses similar but simpler recursions to show, in the weak system $\mathsf{MW}$, that the truth predicate for $\dot{\varDelta}_{0}$ formulæ is $\Delta_{1}$. (shrink)

Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.

We derive the schemes of from certain weak forms of the same.

Bourbaki suggest that their definition of the number 1 runs to some tens of thousands of symbols. We show that that is a considerable under-estimate, the true number of symbols being that in the title, not counting 1 179 618 517 981 links between symbols that are needed to disambiguate the whole expression.

We prove the existence of p-ideals that are nonmeagre subsets of P(ω) under various set-theoretic assumptions.

We recently examined gene expression during Xenopus tadpole tail appendage regeneration and found that carbohydrate regulatory genes were dramatically altered during the regeneration process. In this essay, we speculate that these changes in gene expression play an essential role during regeneration by stimulating the anabolic pathways required for the reconstruction of a new appendage. We hypothesize that during regeneration, cells use leptin, slc2a3, proinsulin, g6pd, hif1α expression, receptor tyrosine kinase (RTK) signaling, and the production of reactive oxygen species (ROS) to (...) promote glucose entry into glycolysis and the pentose phosphate pathway (PPP), thus stimulating macromolecular biosynthesis. We suggest that this metabolic shift is integral to the appendage regeneration program and that the Xenopus model is a powerful experimental system to further explore this phenomenon.Also watch the Video Abstract. (shrink)

Wie lassen sich die globalen Ökosysteme und damit auch die Lebensgrundlage zukünftiger Generationen dauerhaft vor ihrer Zerstörung bewahren? Weder bessere Technologien noch Effizienzsteigerungen reichen aus, es bedarf vielmehr der Hinwendung zu suffizienten Lebensstilen. Die Studie, die an der Schnittstelle von Naturphilosophie, angewandter Ethik und empirisch-ökologischer Forschung anzusiedeln ist, thematisiert eine der dringendsten Fragen der Zeitgeschichte: das Naturverständnis des Menschen angesichts einer "ökologischen Krise". Dabei geht es auch um die Frage, warum Natur als raumzeitliche Verflechtung aller Lebewesen einen Eigenwert besitzt, der (...) menschlichen Interessen Grenzen setzt. (shrink)

We introduce the Vital Sign Ontology (VSO), an extension of the Ontology for General Medical Science (OGMS) that covers the consensus human vital signs: blood pressure, body temperature, respiratory rate, and pulse rate. VSO provides a controlled structured vocabulary for describing vital sign measurement data, the processes of measuring vital signs, and the anatomical entities participating in such measurements. VSO is implemented in OWL-DL and follows OBO Foundry guidelines and best practices. If properly developed and extended, we believe the VSO (...) will find applications for the EMR, clinical informatics, and medical device communities. (shrink)

Recent arguments claim that behavioral science has focused – to its detriment – on the individual over the system when construing behavioral interventions. In this commentary, we argue that tackling economic inequality using both framings in tandem is invaluable. By studying individuals who have overcome inequality, “positive deviants,” and the system limitations they navigate, we offer potentially greater policy solutions.

Psychometrically sound instruments that assess temporal dynamics of creative abilities are limited. The Ambulatory Battery of Creativity is designed to assess creative ideation performance multiple times in everyday life and was proven to capture the intra-individual dynamic of creative abilities reliably and validly. The present ambulatory study aimed to replicate and extend the psychometric evidence of the novel ABC. Sixty-nine participants worked on the ABC during a 5-day ambulatory assessment protocol. Each day, participants completed six randomly presented items of the (...) verbal and the figural ABC. Matching previous psychometric analyses, the results indicated good between-person and good within-person reliability. Furthermore, evidence for between-person and within-person validity of the ABC was obtained. Performance in the verbal and the figural ABC were interrelated and correlated with an independent measure of creative potential. The verbal ABC was further associated with openness, self-reported creative behavior, creative activities, and creative achievements, thus providing additional evidence of construct validity, especially for the verbal ABC. Finally, the verbal and the figural ABC yielded convincing within-person validity: Longer response times and higher subjective originality ratings were associated with more original ideas. This replication and extension of the ABC’s psychometric properties indicates that it enables a reliable and valid assessment of moment-to-moment fluctuations of creative ideation abilities in everyday life, which may facilitate the investigation of exciting new research questions related to dynamic aspects of creative ability. (shrink)

I show that Albert Einstein’s distinction between principle and constructive theories was predated by Hendrik A. Lorentz’s equivalent distinction between mechanism- and principle-theories. I further argue that Lorentz’s views toward realism similarly prefigure what Arthur Fine identified as Einstein’s ‘‘motivational realism.’’ r 2005 Published by Elsevier Ltd.

In this paper I propose a reasonably sharp formulation of the temporal asymmetry of radiation. I criticize accounts that propose to derive the asymmetry from a low-entropy assumption characterizing the state of the early universe and argue that these accounts fail, since they presuppose the very asymmetry they are intended to derive. r 2006 Elsevier Ltd. All rights reserved.

Die im Reader versammelten Beiträge verstehen sich als Versuche zu einer Soziologie des Visuellen. Sie untersuchen am Beispiel des Mediums Stadtfilm, welche Rolle die dorterzeugten Bilder großer Städte bei der Produktion urbanistischer Repräsentanten spielen. Aus diesem Grund werden insbesondere Übergänge analysiert, die Spielfilme einerseits und urbanistische Diskurse andererseits miteinander verknüpfen. Gemeinsamer Ausgangspunkt ist die These, daß es vor allem Bilder sind, die solche Verknüpfungen gewährleisten. Es wird unterstellt, daß es das Medium Film erlaubt, gerade über den Einsatz von Bildern "näher" (...) an soziale Wirklichkeiten heranzukommen, als dies textzentrierter Praxis empirischer Sozialforschung möglich ist. Stadtfilme erzeugen wirkmächtige Bilder, auf die dann unter bestimmten Bedingungen in urbanistischen Kontexten zurückgegriffen wird. Die Autoren präsentieren konzeptionelle Überlegungen und Filminterpretationen zu Moebius (1991, Regie: Matti Geschonneck), Der Himmel über Berlin (1987, Regie: Wim Wenders), In weiter Ferne, so nah! (1993, Regie: Wim Wenders), Der Bauch des Architekten (1987, Regie: Peter Greenaway) und Hass (1995, Regie: Mathieu Kassovitz). Sie bedienen sich dabei sehr unterschiedlicher Verfahren. Gemeinsam sind ihnen allerdings die Anliegen, die größere Nähe der Filme zu sozialen Welten hervorzuheben und die Übergänge zwischen Stadtfilmen und Urbanistik herauszuarbeiten. -/- City and Film. Attempts at a 'Visual Sociology' Summary The contributions collected in this reader present attempts at a Visual sociology'. Based on a study on the medium 'city film' the author s determine which role the images of big cities evoked in such films can play for urbanistic representations. Therefore the analysis is, in particular, focussed on points of transition marking a connection of movies, on the one hand, and urbanistic discourse, on the othe r. The common point of departure is the hypothesis that images, more than anything else, do guarantee such connections. The authors assume that the medium film may lead 'closer' to social realities than the text- centered practices of empirical social research. City films produce powerful images which, under certain cond itions, can be utilized in urbanistic contexts. The authors present conceptual considerations and interpretations of the following films: Moebius (1991, director: Matti Geschonneck); Der Himmel über Berlin (1987, director: Wim Wenders); In weiter Ferne, so nah! (1993, director: Wim Wenders); The Belly of the Architect (1987, director: Peter Greenaway); and quite different methods they aim at the same goals: emphasizing the greater closeness of films to social worlds and bringing out the points of transition between city films and urbanistics. (shrink)

Elliot R. Wolfson intervenes in the debate over Martin Heidegger and Nazism from a unique perspective, as a scholar of Jewish mysticism and philosophy who has been profoundly influenced by Heidegger's work. He reveals crucial aspects of Heidegger's thinking that betray an affinity with dimensions of Jewish thought.

Despite All Critique (2014) -- World Politics and Western Reason (1980) -- The Doubled Outsides of the Modern International (2005) -- The Subject of Security (1995) -- The Protection of Nature and the Nature of Protection (2005) -- Social Movements/World Politics (1994) -- Europe is Not Where It is Supposed to Be (2000) -- They Seek it Here, They Seek it There : Looking for Politics in Clayoquot Sound (2003) -- Violence, Modernity, Silence : From Weber to International Relations (1993) (...) -- Hobbes, Origins, Limits (2011) -- War, Terror, Judgement (2002) -- International, Imperial, Exceptional (2005) -- Which Democracy for Which Demos? (2013) -- The Political Theory of Boundaries and the Boundaries of Political Theory : Interview With Raia Prokhovnik (2012). (shrink)

Trope theory is a leading metaphysical theory in analytic ontology. One of its classic statements is found in the work of Donald C. Williams who argued that tropes qua abstract particulars are the very alphabet of being. The concept of an abstract particular has been repeatedly attacked in the literature. Opponents and proponents of trope theory alike have levelled their criticisms at the abstractness of tropes and the associated act of abstraction. In this paper I defend the concept of a (...) trope qua abstract particular by rejecting arguments that purport to show that tropes should not be understood as abstract and by arguing that the abstractness of tropes plays an indispensable role in one of our more promising trope-theoretic analyses of universals and of concrete objects. (shrink)

Information can be public among a group. Whether or not information is public matters, for example, for accounts of interdependent rational choice, of communication, and of joint intention. A standard analysis of public information identifies it with (some variant of) common belief. The latter notion is stipulatively defined as an infinite conjunction: for p to be commonly believed is for it to believed by all members of a group, for all members to believe that all members believe it, and so (...) forth. This analysis is often presupposed without much argument in philosophy. Theoretical entrenchment or intuitions about cases might give some traction on the question, but give little insight about why the identification holds, if it does. The strategy of this paper is to characterize a practical-normative role for information being public, and show that the only things that play that role are (variants of) common belief as stipulatively characterized. In more detail: a functional role for “taking a proposition for granted” in non-isolated decision making is characterized. I then present some minimal conditions under which such an attitude is correctly held. The key assumption links this attitude to beliefs about what is public. From minimal a priori principles, we can argue that a proposition being public among a group entails common commitment to believe among that group. Later sections explore partial converses to this result, the factivity of publicity and publicity from the perspective of outsiders to the group, and objections to the aprioricity of the result deriving from a posteriori existential presuppositions. (shrink)

The concept of instantiation is realized differently across a variety of metaphysical theories. A certain realization of the concept in a given theory depends on what roles are specified and associated with the concept and its corresponding term as well as what entities are suited to fill those roles. In this paper, the classic realization of the concept of instantiation in a one-category ontology of abstract particulars or tropes is articulated in a novel way and defended against unaddressed objections.

Bu araştırma Hz. Peygamber’e izafe edilen “Dünya müminin zindanı, kâfirin cennetidir” rivayetini konu edinmektedir. Zikri geçen hadisle ilgili literatür taraması yapıldığında müstakil bir araştırmaya rastlanmamaktadır. Esasında ilim geleneğimizde tek bir hadisi bütün yönleriyle inceleyen pek çok araştırma vardır. Ancak söz konusu haberin müsellem ve mesajı açık kabul edilmesi hem Arap hem de Batı araştırmalarına konu edilmemesinin gerekçesi olabilir. İlgili rivayetin temel hadis kaynaklarında muhtelif metinlerle, beş ayrı sahâbîden aktarıldığı tespit edilmiştir. Araştırmamızda sözü edilen metin ve senedler ayrı ayrı incelenerek rivayetin (...) hadis ilmi açısından değeri tartışılmıştır. Rivayetin pek çok tariki olduğu için araştırma merfu‘ haberlerle sınırlandırılmıştır. Sözü edilen rivayete temel hadis metinlerinde hangi bâb başlığı altında yer verildiği ve klasik hadis şerhlerinde metne nasıl yaklaşıldığı tetkik edilmiştir. Rivayetin “zühd” konusunun ayrılmaz bir parçası haline geldiği ve buna bağlı olarak vaaz ve irşad literatüründe önemli bir yer tuttuğu tespit edilmiştir. Hadiste müminin dünya hayatıyla ilişkisine dair serdedilen ifadeler, kabaca “fâni olan her şeye yüz çevirmek” şeklinde tanımlayabileceğimiz zühdle ilişkilendirilmesine yol açmıştır. Hadis şârihleri ise mezkûr haberi dünya arzularının cezb ediciliğiyle, süreklilik arz eden meşakkatli ibadetlerle mükellef olmanın verdiği zorlukla ve dünyada bireylerin başına gelen musibetlere karşı sabretmesi gerektiğiyle ilişkilendirmişlerdir. Bu bakımdan musannifler ile şârihlerin hadisi benzer perspektifle değerlendirdikleri görülmüştür. Çalışmamızda, Kur’an ve hadis metinlerinde yer alan metaforik anlatı biçimi göz önünde tutulduğunda hadisi farklı bir bakış açısıyla değerlendirmenin mümkün olup olmadığı tespit edilmiştir. Zira metafor, retorik sanatların önemli bir unsuru olup, benzetme edatlarını kullanmadan farklı konular arasında anlam bağlantısı kurma sanatıdır. İstiare, teşbih, alegori ve kinaye gibi türlerle benzerlikler taşısa da anlatılan konudan ziyade anlatım tarzını vurgulayarak sözleri güçlendirmesiyle diğerlerinden ayrılmaktadır. Metaforlar düşünce dünyasına derinlik katmakla kalmaz, aynı zamanda karmaşık veya soyut kavramların daha anlaşılır ifade edilmesine imkân tanır. Dilin gücünü ortaya çıkarırken, yaratıcı düşünce ve duygusal bağlantılar kurma becerisini pekiştirerek anlatının içerdiği mesajın vurgusunu artırır ve muhatapta daha derin etki bırakmayı sağlar. Tüm bunlardan hareketle ilgili metinde yer alan “zindan” kavramının metaforik bir anlam içerdiği kabul edildiğinde yeni bir yorum denemesine açık olduğu söylenebilir. Özellikle modern dönemde belirgin, açık ve fark edilir düzeyde ortaya çıkan düşünce ve ahlak krizine karşı bir anlamlandırma yolu seçerek ilgili rivayeti “medeniyet ve sünnet” ilişkisini göz önünde tutarak metaforik bir yorum denemesiyle ele aldık. Zira bu sözleriyle Resûl-i Ekrem’in çökmüş ve çürümekte olan medeniyetlerin haksızlık ve sefaletin kaynağı haline getirdiği tek dünyacı anlayışı reddettiği, nimetlere ve mahrumiyetlere karşı gereğinden fazla ya da az değer atfetmeyi kabul etmediği ve ölümle her şeyini kaybedeceğini düşünenlere karşı bilinç uyandırmaya çalıştığı iddia edilmektedir. Bunun yanında modern insanın İslâm medeniyetini yeniden canlandırabilmesini engelleyen bir dizi kriz vardır. Bunlar ruhsal, bireysel, düşünsel, metafizik ve toplumsal krizlerdir. İnsan, ruhsal krizi manevi ilerleme ve aydınlanmayla; bireysel krizi değerleri arzulara bırakmamakla; düşünsel krizi farklı düşüncelere açık bir şekilde eleştirel düşünceyi geliştirmekle; metafizik krizi dünyevi cazibelerden arınarak varoluşsal kısıtlamalara sırt çevirip bilgi ve anlam arayışına yönelmekle; toplumsal krizi toplumdaki değişimlere katkıda bulunarak insan hakları mücadelesi vermekle alt edebilir. Araştırmamızda insanın bu krizlerle başa çıkıp zindandan kurtularak özgürlüğe kavuşacağı ve kendi medeniyetini kurabileceği fikri metaforik bir yorum denemesiyle ileri sürülmüştür. Modern dönemde karşımıza çıkan sorunların tespitinin ve bu sorunlara dair çözüm önerilerinin rivayet kültüründen beslenmek suretiyle yapılmasının mümkün olup olmadığı da bu sayede tetkik edilmiştir. Bu kapsamda “Dünya müminin zindanı, kâfirin cennetidir” rivayetinin ne şekilde anlaşıldığı veya anlaşılması gerektiği etrafındaki tartışmalara temas edilerek yeni bir yorum arayışına gidilmiştir. Söz konusu arayış “deneme” olarak isimlendirilmiş ve sonraki araştırmacıların çok daha kapsamlı denemelerde bulunması hedeflenmiştir. (shrink)

We provide a justification for political liberalism’s Reciprocity Principle, which states that political decisions must be justified exclusively on the basis of considerations that all reasonable citizens can reasonably be expected to accept. The standard argument for the Reciprocity Principle grounds it in a requirement of respect for persons. We argue for a different, but compatible, justification: the Reciprocity Principle is justified because it makes possible a desirable kind of political community. The general endorsement of the Reciprocity Principle, we will (...) argue, helps realize joint political rule and relationships of civic friendship. The main obstacle to the realization of these values is the presence of reasonable disagreement about religious, moral, and philosophical issues characteristic of liberal societies. We show the Reciprocity Principle helps to overcome this obstacle. (shrink)

Being a patient and living a life -- Clinical space and traits of healing -- False starts and frequent failures -- Three journeys : A.'Ibuprofen and love', B. 'Staying tuned up', C. 'We all want the same things' -- Being a patient : the moral field -- Rethinking healthcare ethics : the patient's moral authority.

1. Dans la belle série d’études proposée par Mathias Girel, trois mots, qui apparaissent régulièrement tout au long du volume, retiennent l’attention du lecteur: celui de “nuance,” celui d’“ambiguïté” et celui d’“ambivalence.” De fait, l’histoire de la philosophie telle que la pratique Girel est avant tout un art de la nuance et de l’ambiguïté: on ne trouvera pas ici de jugements à l’emporte-pièce, et encore moins les amalgames stratégiques si chers à ces adeptes du “name-dropping” que sont R...

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite subsets of $\omega (...) $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

The authors of this paper earlier argued that concrete objects, such as things or persons, may have final value, which is not reducible to the value of states of affairs that concern the object in question. Our arguments have been challenged. This paper is an attempt to respond to some of these challenges, viz. those that concern the reducibility issue. The discussion presupposes a Brentano-inspired account of value in terms of fitting responses to value bearers. Attention is given to a (...) yet another type of reduction proposal, according to which the ultimate bearers of final value are abstract particulars rather than abstract states or facts. While the proposal is attractive, it confronts serious difficulties. To recognise tropes as potential bearers of final value, along with other objects, is one thing; but to reduce the final value of concrete objects to the final value of tropes is another matter. (shrink)