Due to the spread of COVID-19, a key challenge was to reduce potential staff shortages in the healthcare sector. Besides recruiting retired healthcare workers, medical students were considered to support this task. Commitment of medical students in Germany during the COVID-19 pandemic was evaluated using an online survey, with particular focus on their burdens and anxieties. This survey was distributed to students within a 2-week period in April and May 2020. Ultimately, 1241 participants were included in the analysis. During the (...) pandemic, 67.9% of the participants reported that they had volunteered. Furthermore, 88.9% stated that they were against compulsory recruitment in this context. Students who volunteered had a significantly lower anxiety index than non-committed students. Additionally, students were more concerned about infecting other patients and relatives than themselves. Higher levels of anxiety were related to lower levels of commitment. A mandatory assignment during the pandemic was rejected by the students and does not seem to be necessary due to the large number of volunteers. (shrink)

Duality in Logic and Language [draft--do not cite this article] Duality phenomena occur in nearly all mathematically formalized disciplines, such as algebra, geometry, logic and natural language semantics.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)

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)

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)

French truc and machin (‘thing’) can function as placeholders, fillers or in general extender constructions. The aim of our paper is to investigate whether the prosodic characteristics of these three different uses may give a clue as to their respective status. For our analysis, we extracted 112 occurrences of truc and 57 occurrences of machin from the audio data of the PFC Corpus, which were analysed using Praat, focusing on the acoustic duration, the individual pitch contour and the integration of (...) machin and truc into the intonation contour of the utterance. As in previous studies, our results show that the prosodic patterns vary remarkably and show a highly heterogeneous picture so that the use of prosodic properties as cues for disambiguation is problematic. However, we are able to show some weak tendencies which point to a close functional link between placeholders and fillers reflecting their pragmatic functions. There is no evidence for prosodic weakening or even phonetic reduction in placeholders. Furthermore, we detect some evidence for the detachment typical of pragmatic markers in the case of fillers. The prosodic characteristics of truc and machin in general extender constructions diverge from both the placeholder and the filler functions. Their prosody seems to be largely determined by the particular respective construction into which both forms are strongly integrated. (shrink)

What unites the different studies in this volume is a corpus-based approach, in which various theoretical concepts and categories are applied to, and tested ...

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)

"Presents, and in part develops, a systematic philosophy as the universal science, or the theorization of the unrestricted universe of discourse, explicitly including being as such and as a whole. Argues that complete exploration of the theoretical domain requires such a science"--Provided by publisher.

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)

Martin Heidegger zählt zu den wirkmächtigsten Denkern des 20. Jahrhunderts - zugleich ist er einer der umstrittensten, nicht zuletzt aufgrund seiner Parteinahme für den Nationalsozialismus 1933. Basierend auf neuesten Quellen erzählt Lorenz Jäger das Leben des Philosophen, der den Menschen und sein Dasein in der Welt auf ganz neue Weise gedacht hat - von der katholischen Kindheit in Messkirch und den geistigen Auseinandersetzungen der zwanziger Jahre über den Nationalsozialismus bis weit in die Jahre des Wiederaufbaus hinein. Dabei begegnen uns (...) Lehrer wie Edmund Husserl, dem 1936 die Lehrerlaubnis entzogen wurde, Vertraute wie Karl Jaspers und Hannah Arendt, deren so schwieriges wie intensives Verhältnis zu Heidegger über historische Brüche hinweg anhielt, Intellektuelle und Dichter wie Ernst Jünger und Paul Celan, die ihn in seiner Schwarzwaldhütte besuchten, bis hin zu späten Interpreten wie Lacan und Derrida. Warum Heidegger jede Generation aufs Neue fasziniert und polarisiert, sein Denken auch heute nichts an Bedeutung eingebüsst hat: Auch das zeigt Lorenz Jäger in dieser Biographie, die meisterhaft das Leben Heideggers erzählt - und zugleich ein deutsches Jahrhundert"--Publisher's website. (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)

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)

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)

For a ⊆ b ⊆ ω with b\ a infinite, the set D = {x ∈ [ω]ω : a ⊆ x ⊆ b} is called a doughnut. A set S ⊆ [ω]ω has the doughnut property [MATHEMATICAL SCRIPT CAPITAL D] if it contains or is disjoint from a doughnut. It is known that not every set S ⊆ [ω]ω has the doughnut property, but S has the doughnut property if it has the Baire property ℬ or the Ramsey property ℛ. (...) In this paper it is shown that a finite support iteration of length ω1 of Cohen forcing, starting from L, yields a model for CH + equation image + equation image + equation image. (shrink)

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.

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)

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)

Ch. 1: Inadequate approaches to the question of God -- 1.1. Initial clarifications -- 1.2 Wholly unsystematic direct approaches -- 1.3. Semi-systematic indirect approaches -- 1.4. A wholly anti-systematic, anti-theoretical, and direct approach: Ludwig Wittgenstein -- 1.5. A characteristic example of a failed critique: Thomas Nagel's objections to God as "last point" -- Ch. 2. Heidegger's thinking of Being: the flawed development of a significant approach -- 2.1. Heidegger's failed and distorting interpretation and critique of the Christian metaphysics of Being (...) -- 2.2. Heidegger's four approaches to "retrieving" the "question of being" -- 2.3. What is unthought in Heidegger's thinking of Being I: Being-as-Ereignis -- 2.4. What is unthought in Heidegger's "thinking of Being" II: Being and being(s)- Ereignis and Ereignete(s) -- 2.5. The "overcoming [Überwinding] of metaphysics" as "transformational recovering [Verwindung]" of metaphysics and "the end of the history of Being" -- 2.6. The status of Heideggerian thinking I: thinking of Being as thinking within Ereignis, thinking that reaches its destination with Ereignis (Denken, das in das Ereignis einkehrt) -- 2.7. The status of Heideggerian thinking II: absolute claim, provisionality, the poverty of language, the language of thinking, the finitude of thinking -- 2.8. Heidegger's thinking and the topic "God" -- 2.9. Heidegger's "thinking": a fundamentally deficient and confused form of thinking -- Ch. 3:The structural-systematic approach to a theory of Being and God -- 3.1. The systematic context: the theoretical framework of the structural-systematic philosophy -- 3.2. The unrestricted universe of discourse as the universal dimension of primordial Being -- 3.3. Explication of the dimension of Being I: theory of Being as such -- 3.4. Explication of the dimension of Being II: theory of Being as a whole -- 3.5. Explication of the relation between absolutely necessary Being and the contingent dimension of Being as key to a conception of absolutely necessary Being as minded (as personal) -- 3.6. Absolutely necessary minded (personal) Being as creator of the world (as absolute creating) -- 3.7. The clarified relation between Being and God and the task of developing an integral theory about God -- Ch. 4: Critical examination of two counterpositions: Emmanuel Levinas and Jean-Luc Marion -- 4.1. Levinas's misguided conception of transcendence "beyond B/being" -- 4.2. Jean-Luc Marion's failed conception of "radical and non-metaphysical transcendence" and of "God without Being". (shrink)

In this article we give a forcing characterization for the Ramsey property of Σ 1 2 -sets of reals. This research was motivated by the well-known forcing characterizations for Lebesgue measurability and the Baire property of Σ 1 2 -sets of reals. Further we will show the relationship between higher degrees of forcing absoluteness and the Ramsey property of projective sets of reals.

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)

This paper intends to explore the prospects of a realistic view of scientific explanation, according to which the objects and structures occurring in the explanation must have real referents. Theories involving probability either lose their explanatory function or become counter-examples to this view, if real referents of probabilistic notions do not exist. It is argued that such referents can be found for statistical mechanics and quantum mechanics: the overall structure of mass phenomena that renders them capable of irreversible developments and (...) equilibrium states, and the inherent propensities of elementary systems. The present lack of a theoretical connection between these two referents impedes the recognition of the reality of probability in nature. (shrink)

What are the relationships between philosophy and the history of philosophy, the history of science and the philosophy of science? This selection of essays by Lorenz Krüger (1932-1994) presents exemplary studies on the philosophy of John Locke and Immanuel Kant, on the history of physics and on the scope and limitations of scientific explanation, and a realistic understanding of science and truth. In his treatment of leading currents in 20th century philosophy, Krüger presents new and original arguments for a (...) deeper understanding of the continuity and dynamics of the development of scientific theory. These result in significant consequences for the claim of the sciences that they understand reality in a rational manner. The case studies are complemented by fundamental thoughts on the relationship between philosophy, science, and their common history. (shrink)

The Sure-Thing Principle famously appears in Savage’s axiomatization of Subjective Expected Utility. Yet Savage introduces it only as an informal, overarching dominance condition motivating his separability postulate P2 and his state-independence postulate P3. Once these axioms are introduced, by and large, he does not discuss the principle any more. In this note, we pick up the analysis of the Sure-Thing Principle where Savage left it. In particular, we show that each of P2 and P3 is equivalent to a dominance condition; (...) that they strengthen in different directions a common, basic dominance axiom; and that they can be explicitly combined in a unified dominance condition that is a candidate formal statement for the Sure-Thing Principle. Based on elementary proofs, our results shed light on some of the most fundamental properties of rational choice under uncertainty. In particular they imply, as corollaries, potential simplifications for Savage’s and the Anscombe- Aumann axiomatizations of Subjective Expected Utility. Most surprisingly perhaps, they reveal that in Savage’s axiomatization, P3 can be weakened to a natural strengthening of so-called Obvious Dominance. (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)

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)

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)

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)