This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are (...) covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence. (shrink)

In the March 1927 number of this Journal Mr. Klaas, who is studying abroad, showed the lack of opposition between science and religion. In May he gave the reason. His newest contribution striking contribution striking points out their recognized relations. The Editor.

Wat is toeval? Bestaat het? Hoe moeten we toeval interpreteren? Is alles logisch te verklaren, of is er meer tussen hemel en aarde? In dit boek kijken we naar een vakantieganger die op Bali onverwacht zijn buurman tegenkomt, de Shakespeare-onderzoeker die per toeval de sleutel tot de ware identiteit van de bard in diens teksten denkt te ontwaren, de man die altijd gezond leefde maar plotseling een ongeneeslijke vorm van kanker krijgt, gelovigen die de hand van God denken te zien (...) in het perfecte samenspel van de natuurconstanten dat leven mogelijk maakt, fysici die de grondslagen van de kwantummechanica of de richting van de tijd onderzoeken, biologen die Darwins evolutietheorie proberen te doorgronden, de filosofie van de vrije wil, en ten slotte Jezus als een toevallig of een noodzakelijk fenomeen. In zijn nieuwste boek geeft mathematisch fysicus Klaas Landsman zowel een inleiding als een visie op al deze onderwerpen, die iedereen met belangstelling voor de combinatie van wetenschap en levensbeschouwing zal raken en op nieuwe gedachten zal brengen. (shrink)

This book presents a multidisciplinary perspective on chance, with contributions from distinguished researchers in the areas of biology, cognitive neuroscience, economics, genetics, general history, law, linguistics, logic, mathematical physics, statistics, theology and philosophy. The individual chapters are bound together by a general introduction followed by an opening chapter that surveys 2500 years of linguistic, philosophical, and scientific reflections on chance, coincidence, fortune, randomness, luck and related concepts. A main conclusion that can be drawn is that, even after all this time, (...) we still cannot be sure whether chance is a truly fundamental and irreducible phenomenon, in that certain events are simply uncaused and could have been otherwise, or whether it is always simply a reflection of our ignorance. Other challenges that emerge from this book include a better understanding of the contextuality and perspectival character of chance (including its scale-dependence), and the curious fact that, throughout history (including contemporary science), chance has been used both as an explanation and as a hallmark of the absence of explanation. As such, this book challenges the reader to think about chance in a new way and to come to grips with this endlessly fascinating phenomenon. (shrink)

Anselmian theism holds that there necessarily exists a being, God, who is essentially unsurpassable in power, knowledge, goodness, and wisdom. This being is also understood to be the creator and sustainer of all that is. In contemporary analytic philosophy of religion, this role is generally understood as follows: God surveys the array of possible worlds, and in his wisdom selects exactly one for actualization, based on its axiological properties. In this paper, I discuss an under-appreciated challenge for this account of (...) the Anselmian God’s selection of a world. In particular, I urge that there are failures of comparability between various possible worlds, and I argue that, given certain assumptions, these failures threaten the rationality of God’s choice of a world. To the extent that rationality is deemed necessary for unsurpassability, this result also challenges the core Anselmian notion that God is an unsurpassable being. (shrink)

ZusammenfassungDieser Beitrag konzentriert sich auf eine starke und auf eine schwache Seite von Bayers Zugang zu Luthers Theologie. So wird als Stärke angesehen, dass das Thema der Rechtfertigung in Luthers Theologie als allumfassend angesetzt wird. Dagegen besteht eine Schwäche in der Art und Weise, wie Bayer durch Luthers Dialektik der zwei Arten, in denen Gott sich verbirgt – also verborgen »unter dem Gegenteil« und absolut verborgen – hindurch bricht, indem er die beiden trennt und diese Aufteilung als Kriterium verwendet, um (...) zwischen einer Periode, in der Luther die reformatorische Einsicht vollständig ausarbeitet, und einem vor-reformatorischen Luther zu unterscheiden. Diese Luther-Interpretation sollte nochmals überdacht werden, denn sie verneint die Entsprechung und die kontrapunktisch zu verstehende Beziehung zwischen dieser doppelten Verborgenheit im Lichte des »offenbaren Gottes«. Ein ähnliches Problem taucht dann auf, wenn Bayer die Rede vom dreieinigen Gott, die ausschließlich am Evangelium orientiert ist, unterscheidet von einer allgemeinen Art und Weise, von Gott zu reden, die allein auf dem Gesetz basiert. Luthers Vorstellung, dass die Unterscheidung zwischen Gesetz und Evangelium vollständig in Gottes Offenbarung des Evangeliums integriert ist, widerspricht einer solchen Unterscheidung. Dieser Beitrag betrachtet nicht nur die Unterscheidung zwischen einem unreifen und einem reifen Luther, der alle Implikationen der reformatorischen Einsicht ausgearbeitet hat, als unnötig, sondern er würdigt den jungen Luther als einen Theologen, der in der Lage ist, dasjenige zusammen zu halten, was beim späten Luther auseinander zu fallen droht. Glücklicherweise beinhaltet Bayers Studie auch Anknüpfungsmöglichkeiten für eine solche Interpretation Luthers, die die positiven ebenso wie die negativen Aspekte beider Arten der Verborgenheit ebenso wie Gesetz und Evangelium in einem einzigen kontinuierlichen Prozess integriert.SummaryThis contribution concentrates on one strong and one weak side of Bayer's approach to Luther's theology. It finds a strength in the universally implemented theme of justification in Luther's theological thought. A weakness is however found in the way Bayer breaks through Luther's dialectics concerning the dual way God hides himself – i. e. hidden ‘under the opposite’ and absolutely hidden – by separating them and using this division as a criterion to distinguish between the period where Luther had fully worked out the insight of the Reformation and the pre-Reformation Luther. Such an interpretation of Luther needs to be reconsidered because it neglects the correspondence and the contrapuntal relation between this double hiddeness in the light of the ‘revealed God’.A similar problem arises when Bayer divides speaking about the triune God, which is exclusively orientated towards the Gospel, from a general way of speaking about God, which is only based on the Law. Luther's idea that the distinction between Law and Gospel is fully integrated into God's revelation of the Gospel contradicts such a division.This contribution considers not only a distinction between an immature and a mature Luther who has worked out all the implications of the reformation insight unnecessary, but appreciates the young Luther as a theologian who is capable of holding together what the later Luther is in danger of letting fall apart. Fortunately, in Bayer's study there are also openings for a Luther interpretation that includes the positive as well as the negative aspect of both kinds of hiddeness and of Law and Gospel in a single continuous process. (shrink)

Aumann and Serrano :810–836, 2008) introduce the axiom of duality, which ensures that risk measures respect comparative risk aversion. This paper characterizes all dual risk measures by a simple equivalent condition. This equivalence provides a decomposition result and a construction method, which is used to analyze concrete dual measures. Moreover, this paper aims to extend this characterization to the most general setting. Compared with Aumann and Serrano, it, therefore, relaxes the axiom of positive homogeneity, and allows for risk-neutral and risk-seeking (...) agents, as well as for all integrable gambles. (shrink)

_The Ethics and Religious Philosophy of Etty Hillesum_ offers a comprehensive account of international scholarship on the life, works and vision of the Dutch Jewish writer Etty Hillesum, and her struggle to come to terms with her personal life in the context of the Holocaust.

If one formulates Helmholtz’s ideas about perception in terms of modern-day theories one arrives at a model of perceptual inference and learning that can explain a remarkable range of neurobiological facts. Using constructs from statistical physics it can be shown that the problems of inferring what cause our sensory inputs and learning causal regularities in the sensorium can be resolved using exactly the same principles. Furthermore, inference and learning can proceed in a biologically plausible fashion. The ensuing scheme rests on (...) Empirical Bayes and hierarchical models of how sensory information is generated. The use of hierarchical models enables the brain to construct prior expectations in a dynamic and context-sensitive fashion. This scheme provides a principled way to understand many aspects of the brain’s organisation and responses. In this paper, we suggest that these perceptual processes are just one emergent property of systems that conform to a free-energy principle. The free-energy considered here represents a bound on the surprise inherent in any exchange with the environment, under expectations encoded by its state or configuration. A system can minimise free-energy by changing its configuration to change the way it samples the environment, or to change its expectations. These changes correspond to action and perception, respectively, and lead to an adaptive exchange with the environment that is characteristic of biological systems. This treatment implies that the system’s state and structure encode an implicit and probabilistic model of the environment. We will look at models entailed by the brain and how minimisation of free-energy can explain its dynamics and structure. (shrink)

This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low probability, their very existence implies that the no-signaling (...) principle used in proofs of randomness of outcomes of quantum-mechanical measurements should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness that in various guises was investigated by Kolmogorov and others and treat Bell’s Theorem and the Free Will Theorem with their implications for randomness. (shrink)

English summary: German linguistics, formerly internationally inspiring, fell into a deep crisis at the beginning of the twentieth century. Since the First World War, those in the field have been looking for ways to regain its lost scientific and social recognition. This desire for relevance was particularly clear when practitioners of the different approaches to linguistic innovation competed for the scarce resources of public research funding. The remaining funding documents of the German Research Foundation demonstrate which specific linguistic approaches were (...) proclaimed as critical by researchers, and which were honored by outside funders during changing political contexts. Thus, the history of German philology and the development of its dynamics is here - for the first time - traced from the perspective of public support for research, from the time of the Weimar Republic until the first decades of the Federal Republic. German text. German description: Die ehemals international impulsgebende deutsche Sprachwissenschaft geriet am Anfang des zwanzigsten Jahrhunderts in eine tiefe Krise. Seit dem Ersten Weltkrieg suchte das Fach nach Wegen, die verlorene wissenschaftliche und gesellschaftliche Anerkennung wieder zu erlangen.Dieser Wille zur Relevanz zeigte sich besonders deutlich, wo die verschiedenen Neuerungsansatze der Sprachforschung um die knappen Mittel der staatlichen Forschungsforderung konkurrierten. An den erhaltenen Forderakten der Deutschen Forschungsgemeinschaft ist abzulesen, welche spezifischen Aufgabenstellungen die Sprachwissenschaft in wechselnden politischen Kontexten jeweils 'nach aussen' proklamierte und 'von aussen' honoriert bekam.So wird hier aus der Perspektive der staatlichen Forschungsforderung die Geschichte der deutschen Sprachforschung in ihrer Entwicklungsdynamik erstmals von der Weimarer Republik bis in die ersten Jahrzehnte der Bundesrepublik nachgezeichnet. (shrink)

I argue that Bohmian mechanics cannot reasonably be claimed to be a deterministic theory. If one assumes the “quantum equilibrium distribution” provided by the wave function of the universe, Bohmian mechanics requires an external random oracle in order to describe the algorithmic randomness properties of typical outcome sequences of long runs of repeated identical experiments. This oracle lies beyond the scope of Bohmian mechanics, including the impossibility of explaining the randomness property in question from “random” initial conditions. Thus the advantages (...) of Bohmian mechanics over other interpretations of quantum mechanics, if any, must lie at an ontological level, and in its potential to derive the quantum equilibrium distribution and hence the Born rule. (shrink)

Bell’s Theorem from Physics 36:1–28 (1964) and the (Strong) Free Will Theorem of Conway and Kochen from Notices AMS 56:226–232 (2009) both exclude deterministic hidden variable theories (or, in modern parlance, ‘ontological models’) that are compatible with some small fragment of quantum mechanics, admit ‘free’ settings of the archetypal Alice and Bob experiment, and satisfy a locality condition akin to parameter independence. We clarify the relationship between these theorems by giving reformulations of both that exactly pinpoint their resemblance and their (...) differences. Our reformulation imposes determinism in what we see as the only consistent way, in which the ‘ontological state’ initially determines both the settings and the outcome of the experiment. The usual status of the settings as ‘free’ parameters is subsequently recovered from independence assumptions on the pertinent (random) variables. Our reformulation also clarifies the role of the settings in Bell’s later generalization of his theorem to stochastic hidden variable theories. (shrink)

Much attention has been paid to ‘deictic shifts’ in Ancient Greek literary texts. In this article I show that similar phenomena can be found in documentary texts. Contracts in particular display unexpected shifts from the first to the third person or vice versa. Rather than constituting a narrative technique, I argue that such shifts should be related to the existence of two major types of stylization, called the ‘objective’ and the ‘subjective’ style. In objectively styled contracts, subjective intrusions may occur (...) as a result of the scribe temporarily assuming himself to be the deictic center, whereas in subjectively styled contracts objective intrusions may occur as a result of the contracting parties dictating to the scribe, and the scribe not modifying the personal references. There are also a couple of texts which display more extensive deictic alter­nations, which suggests that generic confusion between the two major types of stylization may have played a role. (shrink)

The article offers an edition, translation and commentary of eight so-called book epigrams. They all stem from eleventh-century manuscripts containing the New Testament or commentaries on it, more specifically the Paris. Coisl. 199, the Vindobon. Theol. Gr. 302, the Paris. Coisl. 26, and the Vatic. Gr. 363. While most of them are unedited, the second one is a conflation of known epigrams, and the third an unknown version of a previously edited epigram. Although book epigrams are frequently encountered in Byzantine (...) manuscripts, the genre has not received much attention. In the track of the recently increasing interest in manuscripts as cultural artifacts in their own right, our commentary focuses on the relationship between epigram and manuscript, and the process of copying. It also discusses textual problems, structure, content, function, vocabulary, and metrical features of the poems. The analysis is enriched by parallels from other, mostly contemporary, book epigrams, which were collected during an ongoing database project at Ghent University. The comparison shows, among other things, that the material belonging to this genre is ‘recyclable’: it is constantly re-used, sometimes with slight but meaningful modifications. (shrink)

Journal Name: Philologus Issue: Ahead of print.

God is traditionally taken to be a perfect being, and the creator and sustainer of all that is. So, if theism is true, what sort of world should we expect? To answer this question, we need an account of the array of possible worlds from which God is said to choose. It seems that either there is (a) exactly one best possible world; or (b) more than one unsurpassable world; or (c) an infinite hierarchy of increasingly better worlds. Influential arguments (...) for atheism have been advanced on each hierarchy, and these jointly comprise a daunting trilemma for theism. In this paper, I argue that if theism is true, we should expect the actual world to be a multiverse comprised of all and only those universes which are worthy of creation and sustenance. I further argue that this multiverse is the unique best of all possible worlds. Finally, I explain how his unconventional view bears on the trilemma for theism. (shrink)

Theism is the view that God exists; naturalism is the view that there are no supernatural beings, processes, mechanisms, or forces. This Element explores whether things are better, worse, or neither on theism relative to naturalism. It introduces readers to the central philosophical issues that bear on this question, and it distinguishes a wide range of ways it can be answered. It critically examines four views, three of which hold that things are better on theism than on naturalism, and one (...) of which holds just the opposite. (shrink)

Using side-by-side Sacks forcing, it is shown that it is consistent that $2^\omega$ be large and that there be many types of ultrafilters of character $\omega_1$.

Using side-by-side Sacks forcing, it is shown that it is consistent that 2 ω be large and that there be many types of ultrafilters of character ω 1.

The growing scholarly debate on emotions and the development of Pentecostal and Charismatic churches in the Global South are just two reasons that urge systematic theology to relate more concretely to faith experiences. Potkay and others present joy as a typical Christian emotion, but it is not a key theme in systematic theology, although it plays far more prominent a role in spiritual and practical theological works. In this paper, the author presents the understandings of joy from the perspectives of (...) Blaise Pascal, A.A. van Ruler and Pentecostals from Ecuador and explores the implications for theological anthropology. Based on the study of these three perspectives, the author defends the thesis that joy offers a new focus in the field of theological anthropology that places different traditional theological perspectives on the human being in a fresh relation to each other and lays a foundation for a theological contribution to emotion studies. (shrink)

The question of whether God exists has long preoccupied philosophers. Many accounts of God have been proposed, and many arguments for and against God’s existence have been offered and discussed. But while philosophers have been busy trying to determine whether or not God exists, they have generally neglected to ask this question: "Does it _matter _whether God exists?" _Does God Matter?_ features ten original essays written by prominent philosophers of religion that address this very important, yet surprisingly neglected, question. One (...) natural way to approach this question is to seek to understand what difference God’s existence would—or does—make to the value of the world and the well-being of its inhabitants. The three essays in Section I defend versions of _pro-theism_: the view that God’s existence would, or does, make things better than they would otherwise be. The three subsequent essays in Section II defend _anti-theism_: the view that God’s existence would, or does, make things worse than they would otherwise be. The final four essays in Section III consider the interplay between the existential and axiological debates concerning the existence of God. This book presents important research on a growing topic in philosophy of religion that will also be of keen interest to scholars working in other areas of philosophy, and in other disciplines. (shrink)

Historians of science and the philosophy of science find the substance and stance of Isaac Beeckman's thought highly interesting, for it represented an early attempt to develop a comprehensive picture of the world by means of mechanistic theory, that is, forces acting upon one another. Besides possibly influencing Descartes, this view broke away from medieval religious assumptions and belief in occult forces. Berkel teases out Beeckman's evolving approach to nature by means of his extensive journals, explaining the leading concept of (...) "picturability." Beeckman supplied a stepping stone (one still not widely appreciated) on the path that led to the scientific revolution. (shrink)

ZUSAMMENFASSUNGDer vorliegende Beitrag beschreibt das Gefühl der Gier als die misslungene Antwort auf die existenzielle Grundangst und Grundsorge des Menschen. Literatur deutet der Autor als Archiv der Gefühle, hier der Gier. Im zweiten Teil diskutiert der Essay die Deutung von Goethes Faust durch den Wirtschaftswissenschaftler Hans Christoph Binswanger, der die magische Struktur des Wirtschaftens und damit die Habgier als Motor einer auf Wachstum ausgerichteten Wirtschaft entdeckt. Über das Gleichnis vom reichen Kornbauern erschließt der Autor den biblischen Phänomenbestand der Gier: Die (...) Gier dokumentiert ein falsches Selbstverständnis. Ziel kann heute nur ein Selbstverständnis sein, das dem magischen Kern des Wirtschaftens entkommt.SUMMARYThis article describes the feeling of greed as an unsuccessful response to the existential fear and worry inherent to human existence. The author interprets literature as an archive of emotions, including that of greed. The second part of the essay discusses the economist Christoph Binswanger's interpretation of Goethe's ‘Faust’. He discovers the magical structure of the economy and thus describes greed as the impetus for a growth-directed economy. Interacting with the Parable of the Rich Fool , the author deduces the biblical understanding of the phenomenon of greed: greed documents a false understanding of the self. Our contemporary aim, then, should be reaching a conception of the self which escapes the magical core of the economy. (shrink)

God is traditionally taken to be a necessarily existing being who is unsurpassably powerful, knowledgeable, and good. The familiar problem of actual evil claims that the presence of gratuitous suffering in the actual world constitutes evidence against the existence of such a being. In contrast, the problem of possible evil claims that the possibility of bad worlds constitutes evidence against theism. How? It seems plausible to suppose that there are very bad possible worlds. But if God exists in every world, (...) then God exists in those, too. And if God exists in very bad worlds, some say, God is culpable for not ensuring that they are better. In what follows, I consider this argument, survey some responses, and offer a novel solution. Along the way, I argue that theists should maintain that the actual world is a multiverse featuring all and only universes worthy of being created and sustained by God, and – more controversially – I suggest that theists should embrace modal collapse: the claim that this multiverse is the only possible world. (shrink)

For many centuries, philosophers have debated this question: “Does God exist?” Surprisingly, they have paid rather less attention to this distinct – but also very important – question: “Would God’s existence be a good thing?” The latter is an axiological question about the difference in value that God’s existence would make (or does make) in the actual world. Perhaps the most natural position to take, whether or not one believes in God, is to hold that it would be a very (...) good thing if such a being were to exist. After all, God is traditionally thought to be perfectly powerful and good, and it might seem obvious that such a being’s existence would make things better than they would otherwise be. But this judgment has been contested: some philosophers have held that God’s existence would make things worse, and that, on this basis, one can reasonably prefer God’s non-existence. We first distinguish a wide array of axiological positions concerning the value of God’s existence which might be held by theists, atheists, and agnostics alike. We next construe these positions as comparative judgments about the axiological status of various possible worlds. We then criticize an important recent attempt to show that God’s existence would make things worse, in various ways, than they would otherwise be. (shrink)

The author defends the thesis that Pascal’s use of sentir offers an important entrance to his perception of the human being, while explaining Pascal’s anthropology as an experience-oriented and love-focused understanding of human existence. This understanding of Pascal is based on the reconstruction of an alternative context of interpretation. Not the early modern debates on rationality, but the medieval authors that inspired Port-Royal is taken as the main reference. Reading Pascal’s texts from the use of sentire by Bernard of Clairvaux, (...) Bonaventure and Duns Scotus, offers a different perspective on the relation between body, will and knowledge in his thought. This alternative interpretation leads to a re-orientation on the relevance of his thought for actual debates on modernity. (shrink)