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)

This study shows that professional identity should not be viewed as a composed variable with a uniform structure. Based on the literature and previous research, we view teachers? job satisfaction, self?efficacy, occupational commitment and change in the level of motivation as indicators of teachers? professional identity. Using two?step cluster analysis, three distinct professional identity profiles have empirically been identified, based on data of 1214 teachers working in secondary education in the Netherlands. These profiles differed significantly regarding the indicators of teachers? (...) professional identity. Teachers belonging to the found profiles did not significantly differ in their amount of experience. (shrink)

The purpose of this study was to examine student perceptions of teaching behavior. Additionally the aim was to examine if teacher characteristics (educational level, gender, and teaching experience) could explain differences in student perceptions of their teachers. Teaching behavior was studied from the research on teaching and teacher effectiveness perspective. Secondary students (N = 7,114), taught by 410 teachers in Spain, participated in the study. Survey data were analyzed using non-parametric tests, Kruskal-Wallis, U Mann-Whitney with Bonferroni correction, and the analysis (...) of effect sizes. Furthermore, a regression model was applied. Results showed that teaching behavior was perceived as sufficient to good, depending on the teaching behavior domain. Results indicated interesting differences between lower secondary education, upper secondary education and vocational education and training teachers. The effect size values (rU statistic) ranged between 0.43 and 0.63, highlighting the significant effect of teachers’ teaching experience on the six teaching skills domains: learning climate, efficient classroom management, clarity of instruction, activating teaching, differentiation, and teaching learning strategies. Those teachers with less teaching experience were the ones who showed higher scores. Findings from the regression model showed that educational level had a significant predictive effect on the six teaching skills domains, mainly for male teachers. However, in several domains female teachers were perceived by students to outperform their male counterparts. (shrink)

Erwin Panofsky explicitly states that the first half of the opening chapter of Studies in Iconology—his landmark American publication of 1939—contains ‘the revised content of a methodological article published by the writer in 1932’, which is now translated for the first time in this issue of Critical Inquiry.1 That article, published in the philosophical journal Logos, is among his most important works. First, it marks the apogee of his series of philosophically reflective essays on how to do art history,2 that (...) reach back, via a couple of major pieces on Alois Riegl, to the 1915 essay on Heinrich Wölfflin.3 Under the influence of his colleague at Hamburg Ernst Cassirer, the principal interpreter of Kant in the 1920s, Panofsky from 1915 on exhibits in his work ever more Kantian thinking and language.4 But Logos was not an art-historical review or one dedicated to aesthetics but a principal mainstream journal of the philosophy of culture. So ‘On the Problem of Describing and Interpreting Works of the Visual Arts’ has a good claim to be the culmination of Panofsky's philosophical thinking in his German period under the Weimar Republic. · 1. Erwin Panofsky, Studies in Iconology: Humanistic Themes in the Art of the Renaissance , p. xv; hereafter abbreviated SI. See Panofsky, ‘Zum Problem der Beschreibung und Inhaltsdeutung von Werken der bildenden Kunst’, Logos 21 : 103–19; trans. Jaś Elsner and Katharina Lorenz under the title ‘On the Problem of Describing and Interpreting Works of the Visual Arts’, Critical Inquiry 38 : 467–82; hereafter abbreviated ‘P’.· 2. See the discussion in Carlo Ginzburg, ‘From Aby Warburg to E. H. Gombrich: A Problem of Method’, Myths, Emblems, Clues, trans. John and Anne C. Tedeschi , pp. 17–59, esp. pp. 36–41.· 3. See Panofsky, ‘Das Problem des Stils in der bildenden Kunst’, Deutschsprachige Aufsätze, ed. Karen Michels and Martin Warnke, 2 vols. , 2:1009–18; ‘Der Begriff des Kunstwollens’,Deutschsprachige Aufsätze, 2:1019–34, trans. Kenneth J. Northcott and Joel Snyder under the title ‘The Concept of Artistic Volition’, Critical Inquiry 8 : 17–33; and ‘Über das Verhältnis der Kunstgeschichte zur Kunsttheorie: Ein Beitrag zu der Erörterung über die Möglichkeit kunstwissenschaftlicher Grundbegriffe’, Deutschsprachige Aufsätze, 2: 1035–63, trans. Lorenz and Elsner under the title ‘On the Relationship of Art History and Art Theory: Towards the Possibility of a Fundamental System of Concepts for a Science of Art’, Critical Inquiry 35 : 43–71.· 4. On neo-Kantianism in pre-Nazi Germany, see Michael Friedman, A Parting of the Ways: Carnap, Cassirer, and Heidegger , pp. 25–37; Éric Dufour and T. Z. R. Créteil, ‘Le Statue du singulier: Kant et le néokantisme de l’École de Marbourg', Kantstudien 93 : 324–50; Edward Skidelsky, Ernst Cassirer: The Last Philosopher of Culture , pp. 22–51; and Peter E. Gordon, Continental Divide: Heidegger, Cassirer, Davos , pp. 52–86. Specifically on the Cassirerian Kantianism of Panofsky, see Michael Podro, The Critical Historians of Art , pp. 181–82; Michael Ann Holly, Panofsky and the Foundations of Art History , pp. 91–92, 147–52; Silvia Ferretti, Cassirer, Panofsky, and Warburg: Symbol, Art, and History, trans. Richard Pierce , pp. 174–77, 182–84; David Summers, ‘Meaning in the Visual Arts as a Humanistic Discipline’, in Meaning in the Visual Arts: Views from the Outside, ed. Irving Lavin , pp. 9–24; Mark A. Cheetham, Kant, Art, and Art History: Moments of Discipline , pp. 68–77; Paul Crowther, The Transhistorical Image: Philosophizing Art and Its History , pp. 70–73; Allister Neher, ‘“The Concept of Kunstwollen”, Neo-Kantianism, and Erwin Panofsky's Early Art Theoretical Essays', Word and Image 20 : 41–51; Georges Didi-Huberman,Confronting Images: Questioning the Ends of a Certain History of Art, trans. John Goodman , pp. 4–6, 90–138; and Lorenz and Elsner, ‘Translators’ Introduction', Critical Inquiry35 : 33–42, esp. pp. 38, 40–42. (shrink)

Recently there has been a resurgence of philosophical interest in love, resulting in a wide variety of accounts. Central to most accounts of love is the notion of caring about your beloved for his sake. Yet such a notion needs to be carefully articulated in the context of providing an account of love, for it is clear that the kind of caring involved in love must be carefully distinguished from impersonal modes of concern for particular others for their sakes, such (...) as moral concern or concern grounded in compassion. That is, we might say, the kind of caring that is central to love must be somehow distinctly intimate. The trouble is to cash out these firm intuitions in a satisfactory way. (shrink)

The wide reflective equilibrium (WRE) is considered the most important method of ethical justification and is intensively discussed in the scientific community. However, it is unclear to what extent it is actually applied in the ethical literature. The objective of this paper is to fill this gap by providing a critical overview of its explicit applications. Explicit application refers to studies that, following Daniels’ definition, contain three levels, name their elements, and provide a connection between the levels. Philosophers Index, ProQuest, (...) PubMed, Web of Science, and Scopus were searched for studies that explicitly used the WRE method and were written in German or English. All topics, disciplines, and publication forms were considered. Nineteen studies were found in which the WRE was applied 23 times. In the 23 applications, 50 equilibria were discussed, and 19 times it was reported that an equilibrium state was reached. The authors applied the WRE in various disciplines, for different purposes, and to diverse topics. The applications themselves differed considerably regarding the application procedure and the scope. Differences can be seen in particular with regard to the presentation of the adjustment process and the WRE criteria used. The results indicate that the WRE can be successfully applied, but the number of explicit applications is still very low. Further research is needed to develop the WRE into an established method of justification. In particular, standards are needed for adjustment and for WRE criteria. (shrink)

... PREFACE Paul Gochet (Liege) "[...] une entite physique ne peut etre envisagee que comme une sorte de concretisation, de consolidation locale dans un ...

Schopenhauer’s invective is legendary among philosophers, and is unmatched in the historical canon. But these complaints are themselves worthy of careful consideration: they are rooted in Schopenhauer’s philosophy of language, which itself reflects the structure of his metaphysics. This short chapter argues that Schopenhauer’s vitriol rewards philosophical attention; not because it expresses his critical take on Fichte, Hegel, Herbart, Schelling, and Schleiermacher, but because it neatly illustrates his philosophy of language. Schopenhauer’s epithets are not merely spiteful slurs; instead, they reflect (...) deep-seated theoretical and methodological commitments to transparency of exposition. (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.

Authenticity, it is plausible to suppose, is a feature of one's identity as a person---of one's sense of the kind of life worth living. Most attempts to explicate this notion of a person's identity do so in terms of an antecedent understanding of what it is for a person to value something. This is, I argue, a mistake: a concern is not intelligible as a value apart from the place it has within a larger identity that the value serves in (...) turn to constitute; to assume otherwise is to risk leaving out the very person whose identity these values allegedly constitute. By contrast, I offer an account of values as always already a part of one's identity. I do so by providing an analysis of values in terms of what I call 'person-focused emotions,' emotions like pride and shame. Such emotions, I argue, involve a commitment to the import of a person primarily and, only secondarily, to things valued, and in this way enable us to understand what it is to value these things *for the sake of* the person. The upshot is a more satisfying account of a person's identity and values, an account that can provide the necessary background for a more thorough investigation of authenticity. (shrink)

‘Philosophical dialogue’ indicates both a form of philosophical inquiry and its corresponding literary genre. In its written form, it typically features two or more characters who engage in a discussion concerning morals, knowledge, as well as a variety of topics that can be widely labelled as ‘philosophical’. Our philosophical dialogue takes place in Krakow, Poland. It is a rainy morning and two strangers are waiting at a tram stop. One of them is dressed neatly, and cannot stop fidgeting with his (...) closed umbrella. The other was caught unprepared by the morning downpour and water is dripping from his worn, soaked jacket. (shrink)

Michel Weber, Éléments de routine ayurvédique. Autonomie, rituel et ascèse, Les Éditions Chromatika, 2021. (978-2-930517-82-7 ; pdf 978-2-930517-83-4 ; 104 pp., 14€) -/- L’Ayurvéda propose une philosophie de vie qui articule un vaste système métaphysique (une cosmologie théorique) avec une visée thérapeutique profonde (une anthropologie pratique). -/- À la croisée de la théorie et de la pratique, on trouve la routine (« dinacharya ») dont le but est de susciter l’individuation et la solidarité, c’est-à-dire l’autonomie (de chacun) respectueuse de la (...) communauté (de tous). Ce faisant, elle constitue une ascèse dont l’efficacité a été longuement éprouvée et rarement égalée. (shrink)

Love, Friendship, and the Self presents a reexamination of our common understanding of ourselves as persons in light of the phenomena of love and friendship. It argues that the individualism that is implicit in that understanding cannot be sustained if we are to understand the kind of distinctively personal intimacy that love and friendship essentially involve. For love is a matter of identifying with someone: sharing for his sake the concerns and values that make up his identity as the person (...) he is. Moreover, in friendship the friends share not only a concern for each other but also their activity, their lives, and even potentially their selves. By providing a detailed analysis of these notions, Bennett Helm argues for an understanding of persons as essentially social. (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 →.

Philosophical accounts of freedom typically fail to capture an important kind of freedom—freedom to change what one cares about—that is central to our understanding of what it is to be a person. This paper articulates this kind of freedom more clearly, distinguishing it from freedom of action and freedom of the will, and gives an account of how it is possible. Central to this account is an understanding of the role of emotions in determining what we value, thus motivating a (...) rethinking of the importance of emotions in the mental lives of persons. (shrink)

My aim is to understand at least some of the non-instrumental reasons we can have for action in a way that can provide a satisfying non-egoist account of 'social actions' - actions undertaken for the sake of others. I do this in part by presenting, in terms of a discussion of the rationality of emotions, an account of what it is for something to have import to an agent . I then extend this account to include our caring about others (...) as agents, in part by revealing the way in which one's emotional and desiderative responsiveness to another agent one cares about must be sensitive to her cares, so that one comes to share her cares. The upshot is substantial revision in our understanding of agency, both in terms of our understanding of the role emotions play in our agency and in terms of a careful extension of the scope of practical rationality to include what I call a 'rationality of import'. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Rationality is the constitutive ideal of the mental. Therefore it is important to understand the sort of rationality at issue here. It is often assumed that rationality just is instrumental rationality, but this leaves us with too thin a notion of desire: Desires centrally involve the notion of things mattering or being significant, for their objects must normally be worth pursuing to the subject. Such significance is simply unintelligible in terms of instrumental rationality. Consequently, understanding significance and its rational connections (...) to desire and action is essential to understanding rationality as a constitutive ideal. In particular, it is a crucial step in vindicating the idea of animal thought. ;I argue that significance, as well as desire, must be understood in part in terms of the emotions. Many prominent theories of emotions illegitimately conceive of significance as conceptually prior to the capacity for having emotions, in that things can be significant to a creature that does not have any emotions at all. In contrast, I argue first that a creature must have the capacity for emotions in order to be a subject of significance because to be significant is in part to be a suitable object of emotions generally. Second, emotions are essentially feelings not because they "involve" bodily sensations but because they are a distinctive kind of awareness of the significance of the world to the subject; particular occurrent emotions therefore presuppose that things are already significant to the subject. Consequently, emotions and significance form a conceptual package, with neither being prior to the other: Significance and the emotions emerge together in a pattern of instrumental and non-instrumental rationality that can be articulated in terms of their interconnected explanatory roles. ;Being a subject of beliefs and desires therefore requires more than simply rationally mediated goal-directedness, as Dennett believes. Rather, it requires being open, through the emotions, to the significance of the world and to the reasons that significance provides for action. This conclusion is shown to have important ramifications for our understanding both of a minimal sense of agency and of what it is to be a person. (shrink)

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)

It is widely held that Locke propounded a theory of personal identity in terms of consciousness and memory. By ‘theory’ here is meant a set of necessary and sufficient conditions indicating what personal identity consists in. It is also held that this theory is open to obvious and damaging objections, so much so that it has to be supplemented in terms of bodily continuity, either because memory alone is not sufficient, or because the concept of memory is itself dependent upon (...) considerations of bodily continuity. Alternatively it has been suggested that Locke's theory could be modified by allowing that for the purposes of personal identity ‘remember’ should be regarded as a transitive relation. So if A remembers the experiences of B but not those of C, and B remembers the experiences of C, then A, B and C can be regarded as belonging to the same unit of consciousness. (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)

To identify oneself with something is for it to be a source of meaning and worth in one's life. Normally such identification is constituted by a certain holistic rational pattern both in one's judgments and will and in one's emotions and desires. However, one's identity can be fragmented into conflicting sources of meaning when the pattern in one's judgments becomes disconnected from that in one's emotions. By analyzing these kinds of fragmentation, I articulate some of the rational connections there are (...) between emotional attitudes and evaluative judgments and so ultimately the kinds of accord or integrity that are possible for persons. (shrink)

‘Actions are by their very nature temporary and perishing; and where they proceed not from some cause in the characters and disposition of the person, who perform'd them, they infix not themselves upon him, and can neither redound to his honour, if good, nor infamy, if evil. The action itself may be blameable; it may be contrary to all the rules of morality and religion: But the person is not responsible for it; and as it proceeded from nothing in him, (...) that is durable or constant, and leaves nothing of that nature behind it, 'tis impossible he can, upon its account, become the object of punishment or vengeance.'. (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)