L’Empire romain atteint à la fin de la République une étendue géographique qui englobe des aires culturelles très diverses, ce qui a une influence sur la typologie et les fonctions des maisons dans les différentes régions de la Méditerranée. Dans l’impossibilité de pouvoir donner une vue d’ensemble et laissant de côté pour cette même raison les provinces occidentales de l’Afrique du Nord et du Levant, nous allons évoquer, après un regard sur la description de la maison urbaine chez Vitruve, quelques (...) exemples de Pompéi pour nous concentrer par la suite sur quelques maisons dans les provinces orientales, en particulier en Grèce et en Asie Mineure, pour mesurer l’influence ou non des Romains dans l’architecture privée. Il s’avère que cette dernière est bien restreinte, et que l’intégration de l’atrium est plutôt une référence qu’un élément structurel des maisons dont le péristyle reste l’élément central. L’étude est complétée par un excursus sur plusieurs maisons de l’Antiquité tardive à Athènes. (shrink)

Cette recension a déjà paru dans Critique d'art, le 4 novembre 2014. Renate LORENZ, Not Now! Now! Chronopolitics, Art & Research, Berlin, Sternberg Press, 2014, 187 p. Not Now! Now! prolonge les réflexions engagées lors du colloque international éponyme à l'Academy of Fine Arts de Vienne en 2013 qui réunissait théoriciens et artistes autour des chronopolitics. Si la durée, le rythme et l'ordonnancement du temps sont des enjeux majeurs dans la compréhension des évènements - Recensions.

Das heutige, mehr und mehr vom Aspekt des Werdens beherrschte Wirklichkeitsverständnis (Geschichtlichkeit, Evolution) verlangt nach einem ihm entsprechenden, von Grund auf dynamisch bestimmten Seinsbegriff, damit es philosophisch aufgearbeitet werden kann. Ein solcher Seinsbegriff findet sich in der sog. Prozess- bzw. Organismusphilo- sophie von A.N. Whitehead (1861-1947). Es ist das Ziel der vorliegen- den Arbeit, diesen herauszuarbeiten und für die weitere philosophische und theologische Diskussion bereitzustellen.

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics. However, many of these disciplines use the term ‘duality’ in vastly different senses, and while some of these senses are intimately connected to each other, others seem to be entirely … Continue reading Duality in Logic and Language →.

In this paper, we consider certain cardinals in ZF (set theory without AC, the axiom of choice). In ZFC (set theory with AC), given any cardinals C and D, either C ≤ D or D ≤ C. However, in ZF this is no longer so. For a given infinite set A consider $\operatorname{seq}^{1 - 1}(A)$ , the set of all sequences of A without repetition. We compare $|\operatorname{seq}^{1 - 1}(A)|$ , the cardinality of this set, to |P(A)|, the cardinality of (...) the power set of A. What is provable about these two cardinals in ZF? The main result of this paper is that $ZF \vdash \forall A(|\operatorname{seq}^{1 - 1}(A)| \neq|\mathscr{P}(\mathscr{A})|)$ , and we show that this is the best possible result. Furthermore, it is provable in ZF that if B is an infinite set, then $|\operatorname{fin}(B)| <|\mathscr{P}(B)|$ even though the existence for some infinite set B* of a function f from $\operatorname{fin}(B^\ast)$ onto P(B*) is consistent with ZF. (shrink)

The theory of Participatory Discrepancies (or PDs) claims that minute temporal asynchronies (microtiming) in music performance are crucial for prompting bodily entrainment in listeners, which is a fundamental effect of the “groove” experience. Previous research has failed to find evidence to support this theory. The present study tested the influence of varying PD magnitudes on the beat-related body movement behavior of music listeners. 160 participants (79 music experts, 81 non-experts) listened to twelve music clips in either Funk or Swing style. (...) These stimuli were based on two audio recordings (one in each style) of expert drum and bass duo performances. In one series of six clips, the PDs were downscaled from their originally performed magnitude to complete quantization in steps of 20%. In another series of six clips, the PDs were upscaled from their original magnitude to double magnitude in steps of 20%. The intensity of the listeners’ beat-related head movement was measured using video-based motion capture technology and Fourier analysis. A mixed-design four-factor ANOVA showed that the PD manipulations had a significant effect on the expert listeners’ entrainment behavior. The experts moved more when listening to stimuli with PDs that were downscaled by 60% compared to completely quantized stimuli. This finding offers partial support for PD theory: PDs of a certain magnitude do augment entrainment in listeners. But the effect was found to be small to moderately sized, and it affected music expert listeners only. (shrink)

In recent years, a number of authors have started studying Aristotelian diagrams containing metalogical notions, such as tautology, contradiction, satisfiability, contingency, strong and weak interpretations of contrariety, etc. The present paper is a contribution to this line of research, and its main aims are both to extend and to deepen our understanding of metalogical diagrams. As for extensions, we not only study several metalogical decorations of larger and less widely known Aristotelian diagrams, but also consider metalogical decorations of another type (...) of logical diagrams, viz. duality diagrams. At a more fundamental level, we present a unifying perspective which sheds new light on the connections between new and existing metalogical diagrams, as well as between object- and metalogical diagrams. Overall, the paper studies two types of logical diagrams and four kinds of metalogical decorations. (shrink)

This paper studies the Lockean thesis from the perspective of contemporary epistemic logic. The Lockean thesis states that belief can be defined as ‘sufficiently high degree of belief’. Its main problem is that it gives rise to a notion of belief which is not closed under conjunction. This problem is typical for classical epistemic logic: it is single-agent and static. I argue that from the perspective of contemporary epistemic logic, the Lockean thesis fares much better. I briefly mention that it (...) can successfully be extended from single-agent to multi-agent settings. More importantly, I show that accepting the Lockean thesis (and a more sophisticated version for conditional beliefs) leads to a significant and unexpected unification in the dynamic behavior of (conditional) belief and high (conditional) probability with respect to public announcements. This constitutes a methodological argument in favor of the Lockean thesis. Furthermore, if one accepts Baltag’s Erlangen program for epistemology, this technical observation has even stronger philosophical implications: because belief and high probability display the same dynamic behavior, it is plausible that they are indeed one and the same epistemic notion. (shrink)

The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.

Law is an ontologically ideal entity. This feature shall be explored in order to explain why law cannot be perceived by the senses, why its contents can remain constant over time, why it can in principle be translated and why it does not have a dual nature. Due to law’s ontologically ideal nature it is independent from time and space, normative in kind and open for rational arguments. Although law can in many regards be abstract, its ontologically ideal nature has (...) to be distinguished from abstractness. (shrink)

For a set M, let \\) denote the set of all finite sequences which can be formed with elements of M, and let \ denote the set of all 2-element subsets of M. Furthermore, for a set A, let Open image in new window denote the cardinality of A. It will be shown that the following statement is consistent with Zermelo–Fraenkel Set Theory \: There exists a set M such that Open image in new window and no function Open image (...) in new window is finite-to-one. (shrink)

This paper explores the interplay between logic-sensitivity and bitstring semantics in the square of opposition. Bitstring semantics is a combinatorial technique for representing the formulas that appear in a logical diagram, while logic-sensitivity entails that such a diagram may depend, not only on the formulas involved, but also on the logic with respect to which they are interpreted. These two topics have already been studied extensively in logical geometry, and are thus well-understood by themselves. However, the precise details of their (...) interplay turn out to be far more complicated. In particular, the paper describes an elegant and natural interaction between bitstrings and logic-sensitivity, which makes perfect sense when bitstrings are viewed as purely combinatorial entities. However, when we view bitstrings as semantically meaningful entities (which is actually the standard perspective, cf. the term ‘bitstring semantics’!), this interaction does not seem to have a full and equally natural counterpart. The paper describes some attempts to address this situation, but all of them are ultimately found wanting. For now, it thus remains an open problem to capture this interaction between bitstrings and logic-sensitivity from a semantic (rather than merely a combinatorial) perspective. (shrink)

If we assume the axiom of choice, then every two cardinal numbers are comparable, In the absence of the axiom of choice, this is no longer so. For a few cardinalities related to an arbitrary infinite set, we will give all the possible relationships between them, where possible means that the relationship is consistent with the axioms of set theory. Further we investigate the relationships between some other cardinal numbers in specific permutation models and give some results provable without using (...) the axiom of choice. (shrink)

For \(n\in \omega \), the weak choice principle \(\textrm{RC}_n\) is defined as follows: _For every infinite set_ _X_ _there is an infinite subset_ \(Y\subseteq X\) _with a choice function on_ \([Y]^n:=\{z\subseteq Y:|z|=n\}\). The choice principle \(\textrm{C}_n^-\) states the following: _For every infinite family of_ _n_-_element sets, there is an infinite subfamily_ \({\mathcal {G}}\subseteq {\mathcal {F}}\) _with a choice function._ The choice principles \(\textrm{LOC}_n^-\) and \(\textrm{WOC}_n^-\) are the same as \(\textrm{C}_n^-\), but we assume that the family \({\mathcal {F}}\) is linearly orderable (...) (for \(\textrm{LOC}_n^-\) ) or well-orderable (for \(\textrm{WOC}_n^-\) ). In the first part of this paper, for \(m,n\in \omega \) we will give a full characterization of when the implication \(\textrm{RC}_m\Rightarrow \textrm{WOC}_n^-\) holds in \({\textsf {ZF}}\). We will prove the independence results by using suitable Fraenkel-Mostowski permutation models. In the second part, we will show some generalizations. In particular, we will show that \(\textrm{RC}_5\Rightarrow \textrm{LOC}_5^-\) and that \(\textrm{RC}_6\Rightarrow \textrm{C}_3^-\), answering two open questions from Halbeisen and Tachtsis (Arch Math Logik 59(5):583–606, 2020). Furthermore, we will show that \(\textrm{RC}_6\Rightarrow \textrm{C}_9^-\) and that \(\textrm{RC}_7\Rightarrow \textrm{LOC}_7^-\). (shrink)

For an integer \, Ramsey Choice\ is the weak choice principle “every infinite setxhas an infinite subset y such that\ has a choice function”, and \ is the weak choice principle “every infinite family of n-element sets has an infinite subfamily with a choice function”. In 1995, Montenegro showed that for \, \. However, the question of whether or not \ for \ is still open. In general, for distinct \, not even the status of “\” or “\” is known. (...) In this paper, we provide partial answers to the above open problems and among other results, we establish the following:1.For every integer \, if \ is true for all integers i with \, then \ is true for all integers i with \.2.If \ are any integers such that for some prime p we have \ and \, then in \: \ and \.3.For \, \\\ implies \, and \ implies neither \ nor \ in \.4.For every integer \, \ implies “every infinite linearly orderable family of k-element sets has a partial Kinna–Wagner selection function” and the latter implication is not reversible in \ ). In particular, \ strictly implies “every infinite linearly orderable family of 3-element sets has a partial choice function”.5.The Chain-AntiChain Principle implies neither \ nor \ in \, for every integer \. (shrink)

Preface to Volumes 1 and 2 Lorenz Krüger xv Introduction to Volume 1 Lorraine J. Daston 1 I Revolution 1 What Are Scientific Revolutions? Thomas S. Kuhn 7 2 Scientific Revolutions, Revolutions in Science, and a Probabilistic Revolution 1800-1930 I. Bernard Cohen 23 3 Was There a Probabilistic Revolution 1800-1930? Ian Hacking 45 II Concepts 4 The Slow Rise of Probabilism: Philosophical Arguments in the Nineteenth Century Lorenz Krüger 59 5 The Decline of the Laplacian Theory of Probability: (...) A Study of Stumpf, von Kries, and Meinong Andreas Kamlah 91 6 Fechner’s Indeterminism: From Freedom to Laws of Chance Michael Heidelberger 117 7 The Saint Petersburg Paradox 1713-1937 Gerard Jorland 157 8 Laplace and Thereafter: The Status of Probability Calculus in the Nineteenth Century Ivo Schneider 191 9 Emile Borel as a Probabilist Eberhard Knobloch 215 III Uncertainty 10 The Domestication of Risk: Mathematical Probability and Insurance 1650-1830 237 11 The Objectification of Observation: Measurement and Statistical Methods in the Nineteenth Century Zeno G. Swijtink 261 12 The Measurement of Uncertainty in Nineteenth-Century Social Science Stephen M. Stigler 287 IV Society 13 Rational Individuals versus Laws of Society: From Probability to Statistics Lorraine J. Daston 295 14 Decrire, Compter, Calculer: The Debate over Statistics during the Napoleonic Period Marie-Noelle Bourguet 305 15 Probability in Vital and Social Statistics: Quetelet, Farr, and the Bertillons Bernard-Pierre Lécuyer 317 16 Paupers and Numbers: The Statistical Argument for Social Reform in Britain during the Period of Industrialization Karl H. Metz 337 17 Lawless Society: Social Science and the Reinterpretation of Statistics in Germany, 1850-1880 Theodore M. Porter 351 18 Prussian Numbers 1860-1882 Ian Hacking 377 19 How Do Sums Count? On the Cultural Origins of Statistical Causality M. Norton Wise 395. (shrink)

This paper studies John Buridan's octagons of opposition for the de re modal propositions and the propositions of unusual construction. Both Buridan himself and the secondary literature have emphasized the strong similarities between these two octagons (as well as a third one, for propositions with oblique terms). In this paper, I argue that the interconnection between both octagons is more subtle than has previously been thought: if we move beyond the Aristotelian relations, and also take Boolean considerations into account, then (...) the strong analogy between Buridan's octagons starts to break down. These differences in Boolean structure can already be discerned within the octagons themselves; on a more abstract level, they lead to these two octagons having different degrees of Boolean complexity (i.e. Boolean closures of different sizes). These results are obtained by means of bitstring analysis, which is one of the key tools from contemporary logical geometry. Finally, I argue that this historical investigation is directly relevant for the theoretical framework of logical geometry, and discuss how it helps us to address certain open questions in this framework. (shrink)

The aim of this paper is to initiate a systematic exploration of the model theory of epistemic plausibility models (EPMs). There are two subtly different definitions in the literature: one by van Benthem and one by Baltag and Smets. Because van Benthem's notion is the most general, most of the paper is dedicated to this notion. We focus on the notion of bisimulation, and show that the most natural generalization of bisimulation to van Benthem-type EPMs fails. We then introduce parametrized (...) bisimulations, and prove various bisimulationimplies- equivalence theorems, a Hennessy-Milner theorem, and several (un)definability results. We discuss the problems arising from the fact that these bisimulations are syntax-dependent (and thus not fully structural), and we present and compare two different ways of coping with this issue: adding a modality to the language, and putting extra constraints on the models. We argue that the most successful solution involves restricting to uniform and locally connected (van Benthem-type) EPMs: for this subclass the intuitively most natural notion of bisimulation and the technically sound notion coincide. Such EPMs turn out to correspond exactly with Baltag/Smets-type EPMs, which can be interpreted as constituting a methodological argument, favoring Baltag and Smets's definition of EPM over that of van Benthem. (shrink)

In the recent debate on future contingents and the nature of the future, authors such as G. A. Boyd, W. L. Craig, and E. Hess have made use of various logical notions, such as the Aristotelian relations of contradiction and contrariety, and the ‘open future square of opposition.’ My aim in this paper is not to enter into this philosophical debate itself, but rather to highlight, at a more abstract methodological level, the important role that Aristotelian diagrams can play in (...) organizing and clarifying the debate. After providing a brief survey of the specific ways in which Boyd and Hess make use of Aristotelian relations and diagrams in the debate on the nature of the future, I argue that the position of open theism is best represented by means of a hexagon of opposition. Next, I show that on the classical theist account, this hexagon of opposition ‘collapses’ into a single pair of contradictory statements. This collapse from a hexagon into a pair has several aspects, which can all be seen as different manifestations of a single underlying change. (shrink)

This paper studies Aumann’s agreeing to disagree theorem from the perspective of dynamic epistemic logic. This was first done by Dégremont and Roy (J Phil Log 41:735–764, 2012) in the qualitative framework of plausibility models. The current paper uses a probabilistic framework, and thus stays closer to Aumann’s original formulation. The paper first introduces enriched probabilistic Kripke frames and models, and various ways of updating them. This framework is then used to prove several agreement theorems, which are natural formalizations of (...) Aumann’s original result. Furthermore, a sound and complete axiomatization of a dynamic agreement logic is provided, in which one of these agreement theorems can be derived syntactically. These technical results are used to show the importance of explicitly representing the dynamics behind the agreement theorem, and lead to a clarification of some conceptual issues surrounding the agreement theorem, in particular concerning the role of common knowledge. The formalization of the agreement theorem thus constitutes a concrete example of the so-called dynamic turn in logic. (shrink)

Information technology (IT) is continuously making astounding progress in technical efficiency. The time, space, material and energy needed to provide a unit of IT service have decreased by three orders of magnitude since the first personal computer (PC) was sold. However, it seems difficult for society to translate IT’s efficiency progress into progress in terms of individual, organizational or socio-economic goals. In particular it seems to be difficult for individuals to work more efficiently, for organizations to be more productive and (...) for the socio-economic system to be more sustainable by using increasingly efficient IT. This article provides empirical evidence and potential explanations for this problem. Many counterproductive effects of IT can be explained economically by rebound effects. Beyond that, we conclude that the technological determinism adopted by decision-makers is the main obstacle in translating IT’s progress into non-technical goals. (shrink)

This article describes a specific pedagogical context for an advanced logic course and presents a strategy that might facilitate students’ transition from the object-theoretical to the metatheoretical perspective on logic. The pedagogical context consists of philosophy students who in general have had little training in logic, except for a thorough introduction to syllogistics. The teaching strategy tries to exploit this knowledge of syllogistics, by emphasizing the analogies between ideas from metalogic and ideas from syllogistics, such as existential import, the distinction (...) between contradictories and contraries, and the square of opposition. This strategy helps to improve students’ understanding of metalogic, because it allows the students to integrate these new ideas with their previously acquired knowledge of syllogistics. (shrink)

Excerpt from Die Kunst der Rechtsanwendung: Zugleich ein Beitrag zur Methodenlehre der Geisteswissenschaften Eine hnliche Definition der Philosophie geben Wundt ("system der Philosophie, S. 21) und Friedrich Paulsen, ("einleitung in die Philo sophie, S. W hrend Riehl ("philosophie der Gegenwart, S. 23) die Phi1030phie mit der Erkenntnistheorie indentif'rziert. Wesentlich enger fa t auch Windelband die Philosophie, indem er sie als die kritische Wissenschaft von den allgemeing ltigen Werten definiert, S. 1-irrtumer geworden. Daher unterscheidet sich die Philosophie im weiteren Sinne weder (...) im Objekt noch in der Methode von den positiven Einzelwissenschaften, vielmehr kann man alle Theorie als philosophisch bezeichnen, welche nicht im blo en empiristischen Kleinkram befangen bleibt, sondern sich der Einheit und des Zusammenhangs alles Wissens bewu t ist.1) Gew hnlich werden die theoretischen Disziplinen in Natur und Geisteswissenschaften eingeteilt. Hiernach haben die letz teren es mit der Erforschung des Seelenlebens zu tun, w hrend die ersteren die r umlichen Objekte betrachten. Neuerdings ist von Windelband in seiner Rede ber Geschichte und Natur wissenschaft und von Rickert in seinem Vortrag ber "kultur wissen schaft und Naturwissenschaft ein abweichender Ge sichtspunkt zur Klassifikation benutzt worden. Die genannten Autoren unterscheiden die sogenannten Gesetzeswissenschaften, denen es ausschlie lich um die Auffindung m glichst exakter Regeln zu tun ist, von den historischen Wissenschaften, denen die Schilderung des Einmaligen und Einzigartigen am Herzen liegt. Die Hervorhebung dieses Moments ist zweifellos sehr verdienstlich und fruchtbringend. Man darf aber nicht uber sehen, da sich diese Einteilung mit der alteren in "natur und Geisteswissenschaften kreuzt, denn es gibt sowohl nomotheti sche Geisteswissenschaften, wie vor allem die exakte Psycho logie als N aturwissenschaften, die auch idiographisch vorgehen, wie die Astronomie, wenn sie Mondgebirge und Sonnenflecken schildert, oder die Geologie, oder die Biologie, die von der Ent wicklung der Erde und ihrer Organismen berichten. Daher ist es verwirrend, wenn Rickert (s. 46) diejenigen Wissenschaften, deren Inhalt sich auf ein Besonderes und Individuelles bezieht, als Kulturwissenschaften bezeichnet, denn es ist nicht notwendig, da die idiographisch verfahrenden Disziplinen Werte oder Kulturbestrebungen als Objekte ins Auge fassen. Freilich mu die Darstellung des Individuellen und Einmaligen einen Wert besitzen, denn sonst w rde sich niemand mit ihnen besch ftigen. Aber das gleiche gilt von den nomothetischen Wissenschaften. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Induction arrangements are implemented in schools all over the world to support beginning teachers (BTs) (novices) in gradually growing into their profession. The aim of this study is to gain more insight into two key psychological processes involved in the work of a qualified beginning teacher, namely perceived stress and self-efficacy. This unfolding is necessary to find a path of influence to lead the way to meaningful support interventions. Support in the form of induction arrangements is hypothesised to decrease perceived (...) stress and to increase self-efficacy and, thus, decrease stress outcomes. To test our hypotheses 30 BTs and their school-based educators, working in 13 different schools, were surveyed. The analyses revealed that stress causes and stress outcomes are indeed interrelated and that self-efficacy affects this relationship in a mediating way. However, besides decreasing a beginning teachers? perceived lack of learning opportunities, no other influences of induction arrangements were obtained. Implications and suggestions for future research are discussed. (shrink)

Name der Zeitschrift: Zeitschrift für Religionswissenschaft Jahrgang: 24 Heft: 1 Seiten: 1-16.

ZusammenfassungDer folgende Beitrag geht Verhältnisbestimmungen von Religion und Staat in der zweiten Hälfte des 19. Jahrhunderts am Beispiel der Religionsgeschichtsschreibung von Jacob Burckhardt nach. An der Schnittstelle von Religionswissenschaft, Historik und Historiographiegeschichte wird Geschichtsschreibung der Religion dazu als spezifische Form historischer Sinnbildung in den Blick genommen. Burckhardts Diagnose einer Veränderung des Staatsverständnisses verweist auf eine semantische Verhältnisbestimmung von Religion und Kirche, die Aufschluss über eine Verschiebung des Religionsverständnisses in der zweiten Hälfte des 19. Jahrhunderts gibt. Darüber hinaus wird eine Ähnlichkeit (...) zwischen Verhältnisbestimmungen von Religion und Staat im öffentlichen Religionsdiskurs der Gegenwart und in der Religionsgeschichtsschreibung im 19. Jahrhundert aufgezeigt. (shrink)