This text prepares undergraduate mathematics students to meet two challenges in the study of mathematics, namely, to read mathematics independently and to understand and write proofs. The book begins by teaching how to read mathematics actively, constructing examples, extreme cases, and non-examples to aid in understanding an unfamiliar theorem or definition (a technique famililar to any mathematician, but rarely taught); it provides practice by indicating explicitly where work with pencil and paper must interrupt reading. The book then turns to proofs, (...) showing in detail how to discover the structure of a potential proof from the form of the theorem (especially the conclusion). It shows the logical structure behind proof forms (especially quantifier arguments), and analyzes, thoroughly, the often sketchy coding of these forms in proofs as they are ordinarily written. The common introductroy material (such as sets and functions) is used for the numerous exercises, and the book concludes with a set of "Laboratories" on these topics in which the student can practice the skills learned in the earlier chapters. Intended for use as a supplementary text in courses on introductory real analysis, advanced calculus, abstract algebra, or topology, the book may also be used as the main text for a "transitions" course bridging the gab between calculus and higher mathematics. (shrink)

2021 jährte sich zum zwanzigsten Mal die Einführung des Lebenspartnerschaftsgesetzes und damit der Eingetragenen Lebenspartnerschaft als das erste Rechtsinstitut für gleichgeschlechtliche Paare. 2017 löste die Ehe die Lebenspartnerschaft ab, allerdings nicht mit allen Rechten einer Ehe wie zwischen heterosexuellen Personen. Der Aushandlungsprozess zur sogenannten Ehe für alle ist insbesondere für religionswissenschaftliche Fragestellungen erkenntnisreich. Am Beispiel des Diskurses um die Einführung der gleichgeschlechtliche Ehe in Deutschland 2015 und dem Referendum in Irland als diskursivem Ereignis zeigt die Autorin, wie politische Akteur*innen in (...) einem zeitgenössischen Deutungskampf um die Bedeutung von Ehe wetteifern und dabei mit der Diskursprämisse einer angenommenen Moderne die Dichotomie von religiös vs. säkular sowie weitere Narrative von und über Religion(en) zur Selbst- und Fremdpositionierungen sowie für ihre Koalitions- und Oppositionsbildungen einsetzen. Die Analyse verwendet einen zeit-, akteurs- und arenaspezifischen Ansatz und verknüpft methodologisch die Wissenssoziologische Diskursanalyse (WDA) mit einem religionswissenschaftlichen Erkenntnisinteresse. (shrink)

"This accessible, applications-related introductory treatment explores some of the structure of modern symbolic logic useful in the exposition of elementary mathematics. Topics include axiomatic structure and the relation of theory to interpretation. No prior training in logic is necessary, and numerous examples and exercises aid in the mastery of the language of logic. 1959 edition"--.

ABSTRACTIn the present study, attentional bias was investigated as a potential predisposing mechanism for the contamination-related subtype of obsessive-compulsive disorder. Fifty healthy participants with varying degrees of subclinical C-OC symptoms performed a visual search task to measure differential attentional biases elicited by neutral, disgust-, and fear-specific pictorial material. Participants had to find a target picture within five neutral distractor pictures randomly presented on different locations in an array. The task was to decide whether the array contained an unpleasant target picture (...) or not. In randomly-selected emotional trials, participants were further asked about the content of the picture and the confidence of their answer. The results show that the reaction times significantly differed between the emotional and neutral pictures. Participants were significantly more confident in answering questions referring to fear compared to disgust pictures. This effect was mar... (shrink)

The book provides a comprehensive overview on the state of the art of the quantum part of mathematical physics. In particular, it contains contributions to the spectral theory of Schrödinger and random operators, quantum field theory, relativistic quantum mechanics and interacting many-body systems.It also presents an overview on the achievements in mathematical physics since the last conference QMath11 held at Hradec Kralove, Czechia in 2010.

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and (...) objective ideas), intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

Analytical philosophy begins with the first mathematical and philosophical works of Bolzano published between 1804 and 1817. There, Bolzano set out a project for the global reform of mathematics by means of the axiomatic method. Having completed the Wissenschaftslehre, Bolzano wrote a summary of his logic for the Größenlehre, which he sent to Exner in 1833. The correspondence between Bolzano and Exner covered some of the main subjects treated by analytical philosophy: the status of abstract objects (propositions and (...) objective ideas), intuitions, objectless ideas, the concept of object and many others. While Bolzano argued in favor of abstract entities independent of mind and of language, Exner considered them as abstractions obtained from the subjective judgments and representations. During the XlXth century, Bolzano's philosophy spread over Bohemia and Austria through manuscripts and through the first edition of Zimmermann's textbook of philosophy. The most important Brentanians, Kerry, Twardowski, Meinong and Husserl, discussed his doctrines which may also have influenced Wittgenstein and the Polish school. (shrink)

The present paper studies a specific way of addressing the question whether the laws involving the basic constituents of nature are statistical. While most German physicists, above all Planck, treated the issues of determinism and causality within a Kantian framework, the tradition which I call Vienna Indeterminism began from Mach’s reinterpretation of causality as functional dependence. This severed the bond between causality and realism because one could no longer avail oneself of a priori categories as a criterion for empirical reality. (...) Hence, an independent reality criterion had to be sought, a problem which all three physicists to be studied solved in different ways that were mainly conditioned by their different concepts of probability. In order to prevent a dissipation of intuited facts, Mach had to resort to a principle of unique determination as his reality criterion, especially when discussing the Principle of Least Action. Giving theories more independence, Boltzmann understood atomism as property reduction to precisely defined theoretical entities and their interactions. While this served as a relative reality criterion, he also advocated a constructivist one because atomism was already implied by our finitary reasoning power. Finally, Exner contemplated the idea that all apparently deterministic laws are only a macroscopic limit of an irreducible indeterminism, because by adopting the frequency interpretation, observable collectives could be considered as the real basic entities. (shrink)

This paper continues an earlier investigation into the philosophical tradition of Vienna Indeterminism until the formation of the Vienna Circle in 1929. It focuses in particular on how Philipp Frank and Richard von Mises were able to contemplate genuine indeterminism in physics before the advent of quantum mechanics. On this account, all apparently deterministic laws could well be the macroscopic limit of indeterministic basic laws valid for the single mirco-events. Philosophically Vienna Indeterminism was launched by Mach's redefinition of causality in (...) terms of functional dependencies. This severed the rigid bond between causality and empirical realism characteristic of the Kantian conception and made possible to adjust the ontology according to the needs of a single theory. The debates between Max Planck and Franz Serafin Exner teach that the indeterminism issue was also a struggle about Boltzmann's philosophical legacy between Vienna and Berlin. Quite in line with Mach's firm empiricism, Vienna Indeterminists rejected any final decision between determinism and indeterminism on the metaphysical level. Once the frequency interpretation had won favor, the empiricist stance, moreover, permitted them to consider mass phenomena as generic observational facts coordinated to statistical collectives and to treat them on a par with moving point particles. The only condition imposed on this ontology was the uniqueness of this coordination, a condition that could be viewed as a late heir of Mach's principle of unique determination which had complemented his relational ontology. (shrink)

The Prague Philosopher Bernard Bolzano (1781-1848) has long been admired for his groundbreaking work in mathematics: his rigorous proofs of fundamental theorems in analysis, his construction of a continuous, nowhere-differentiable function, his investigations of the infinite, and his anticipations of Cantor's set theory. He made equally outstanding contributions in philosophy, most notably in logic and methodology. One of the greatest mathematician-philosophers since Leibniz, Bolzano is now widely recognised as a major figure of nineteenth-century philosophy. Praised by Husserl as “one of (...) the greatest logicians of all times,” he has also been recognised by Michael Dummett as one of the first modern analytic philosophers and by Alberto Coffa as the founder of the “semantic tradition.” This volume contains English translations of the essay “On the Mathematical Method,” a concise introduction to Bolzano’s logic and philosophy of mathematics, as well as substantial selections from his correspondence with Franz Exner, Professor of Philosophy at the Charles University in Prague in the 1830s and 40s. It will be of interest to students of Austrian philosophy, the development of analytic philosophy, the philosophy of language, and the history and philosophy of logic and mathematics. (shrink)

The paper presents philosophical views which have been propagated in the first decade of the 20 th -century by Austrian experimental physicist Franz-Serafin Exner. According to Exner all apparently deterministic laws are only a kind of the macroscopic limit of the indeterministic random events and processes in nature. The paper attempts to show whether Exner’s ideas have influenced the views on randomness and probability developed by renowned Polish physicist Marian Smoluchowski who belonged to informal circle of (...) class='Hi'>Exner’s students and assistants. (shrink)

Bernard Bolzano (1781-1848) a passe toute sa vie en Boheme, qui faisait encore partie de l'Empire autrichien. Apres des etudes de philosophie, mathematique et theologie, il est devenu pretre et professeur de Science de la religion a l'Universite de Prague. Heritier de l'Aufklarung, il a consacre sa vie a la reforme de la semi-feodale societe autrichienne et a la reforme des sciences a priori: logique, mathematique et theologie. Ses critiques de la constitution et de l'ordre existant lui valurent d'etre destitue (...) de sa chaire en 1819 et de passer le reste de sa vie en exil interieur entoure d'un petit cercle d'amis, ecrivant ses grands traites: le Traite de science de la religion (1834), la Theorie de la science (1837), la Theorie des grandeurs ainsi que l'utopie Du meilleur Etat et les Paradoxes de l'infini (1851). Le texte De la methode mathematique, extrait de l'Introduction a la Theorie des grandeurs, resume quelques unes de ses plus importantes innovations en logique et presente sa philosophie des mathematiques, concue en opposition a Kant. Bolzano l'a choisi pour l'envoyer a Franz Exner, nomme professeur de philosophie a l'Universite de Prague en 1831. L'echange epistolaire qui s'en est suivi tourne autour des deux theses controversees de la logique de Bolzano: sa conception des objets logiques en soi, independants de la pensee et de la langue, et son concept d'intuition. Dans cette controverse s'est joue le sort de la philosophie autrichienne. Bolzano n'a pas reussi a convaincre Exner, qui lui oppose avec tenacite les idees de Herbart. (shrink)

The explanation of the phenomenon of Brownian motion, given by Einstein in 1905 and based on the kinetic–molecular conception of matter, is considered one of the fundamental pillars supporting atomism in its victorious struggle against phenomenological physics in the early years of this century. Despite the importance of the subject, there exists no specific study on it of sufficient depth. Generally speaking, most histories of physics repeat the following scheme: the discovery made by Robert Brown in 1827 , of the (...) continuous movement of small particles suspended in a fluid did not arouse interest for a long time. Finally, at the close of the century, Gouy's research brought it to the attention of the physicists. Gouy was convinced that Brownian motion constituted a clear demonstration of the existence of molecules in continuous movement. Nevertheless, he did not work out any mathematized theory that could be subjected to quantitative confirmation. All nineteenth-century research remained at the qualitative level and yet it was able to clarify some general characteristics of the phenomenon: the completely irregular, unceasing, motion of the particles is not produced by external causes. It does not depend on the nature of the particles but only on their size. The first significant measurements, carried out by Felix Exner in 1900, appeared to deny the possibility of reconciling the kinetic theory with Brownian motion. The discovery of the ultra-microscope then allowed Zsigmondy to perceive the presence of movements, which were completely analogous to Brown's, in the particles of the colloids; these movements were rather smaller in size than those invesigated up to then. Thus Zsigmondy aroused interest in the phenomenon. Finally, in 1905, Einstein succeeded in stating the mathematical laws governing the movements of particles on the basis of the principles of the kinetic–molecular theory. The following year Smoluchowski arrived at conclusions which corresponded to Einstein's. These laws received a first, rough confirmation in the years immediately following by the work of The Svedberg, Seddig and, for some historians, Henri. Then in 1908 Jean Perrin gave it a definitive confirmation. (shrink)

This essay argues for the relevance of the history of family life to the history of science, taking the example of the Exners of Vienna. The Exners were an influential case of the nineteenth‐century European phenomenon of the “scientific dynasty.” The focus here is on their collaborative research on color theory at the turn of the twentieth century. At first glance, this project looks like a reactionary strike against aesthetic innovation, a symptom of what historians assume was an unbridgeable gulf (...) between scientific reason and artistic modernism. We can better understand the Exners’ motivations by situating this research at the intersection of the family's public and private lives. The domestic context sheds light on their use of such scientific terms as “subjective,” “normal,” and “universal,” providing a more nuanced sense of what rationality really meant in fin‐de‐siècle Vienna. (shrink)

Inhaltsverzeichnis/Table of Contents: Vorbemerkung/Preface. Dagfin FØLLESDAL: Bolzano's Legacy. Jan BERG: Bolzano, the Prescient Encyclopedist. Jan SEBESTIK: Bolzano, Exner and the Origins of Analytical Philosophy. Paul RUSNOCK: Bolzano and the Traditions of Analysis. Peter SIMONS: Bolzano on Collections. Ali BEHBOUD: Remarks on Bolzano's Collections. Mark SIEBEL: Variation, Derivability and Necessity. Edgar MORSCHER: Bolzano's Method of Variation: Three Puzzles. Rolf GEORGE: Bolzano's Programme andObjects. Mark TEXTOR: Bolzano's Sententialism. Wolfgang KÜNNE: Propositions in Bolzano and Frege. Michael DUMMETT: Comments on Wolfgang Künne's Paper. (...) Carsten Uwe GIESKE: Bolzano's Notion of Testifying. (shrink)

ArgumentAfter having measured the velocity of the nervous impulse in the 1850s, Helmholtz began doing research on the temporal dimensions of visual perception. Experiments dealing with the velocity of propagation in nerves were carried out occasionally for some fifteen years until their final publication in 1871. Although the temporal dimension of perception seems to have interested Helmholtz less than problems of geometry and space, his experiments on the time of perception were technically rather subtle and seminal, especially compared with experiments (...) performed by his contemporaries, such as Sigmund Exner, William James, Rudolf Hermann Lotze, Ernst Mach, Wilhelm Volkmann, and Wilhelm Wundt. Helmholtz’s conception of the temporal aspects of perception reflects the continuity that holds between psychophysiological research and the Kantian philosophical background. (shrink)

First authoritative and comprehensive study in the field of Inkblot Personality Test, this book describes the historical roots of the three major projective inkblot measures: the Rorschach, the Holtzman Inkblot Technique (HIT) and the Somatic Inkblot Series (SIS). It presents the extensive psychometric background work accompanying the normative data and diagnostic indicators along with indices for selecting executives in a business organization. The book begins with a detailed history of Hermann Rorschach and his early experiments with inkblots in the diagnosis (...) of mentally ill patients. Special attention is given to the administration and scoring of the Rorschach, with the sections detailing the systems developed by Klopfer and Exner. The HIT and SIS are also reviewed in detail, emphasizing their psychometric qualities. (shrink)

Se realizó una investigación descriptiva con el objetivo de caracterizar la esfera afectiva de mujeres diagnosticadas con trastornos depresivos, en el período comprendido entre 2012 y 2015. La muestra estuvo conformada por 46 mujeres residentes en la provincia de Camagüey, seleccionadas de manera intencional, a partir de los criterios establecidos por los autores del estudio. Se aplicó el Psicodiagnóstico de Rorschach, según la codificación e interpretación del Sistema Comprehensivo de Exner. Como principales resultados se obtuvo que, en la mayoría (...) de las mujeres, predominó la combinación del Índice de depresión negativo y el Índice de inhabilidad social positivo, el estilo vivencial coartado e introversivo, proporción afectiva baja y Lambda alta. A descriptive study was conducted to characterize the affective sphere of women diagnosed with depressive disorders during a period between 2012 and 2015. The sample consisted of 46 women living in Camagüey, who were selected intentionally using criteria established by the investigation authors. A Rorschach Test was applied, with regard to the encoding and interpretation of Exner´s Comprehensive System. Results suggested that most women exhibited a combination of the negative depression index and the positive social disability index, constricted and introversive experiential style, low affective proportion and high Lambda. (shrink)

Objective: The present study examines the validity of 11 new Holtzman Inkblot Technique indices. These were chosen from Exner’s Comprehensive System indices using two criteria: first, they had to be valid according to meta-analysis, and second, they must be computed using the HIT standard scoring system.Methods: Both techniques were administrated with a retest interval from 1 to 7days to a sample of 139 subjects from the general population. The validity of the new indices was studied through Pearson correlation with (...) the corresponding RCS indices.Results: Nine of the 11 new indices showed significant correlations with Rorschach scales, confirming our hypotheses. The correlation ranged from a minimum of 0.144 to a maximum of 0.414.Conclusions: The results provide support for the validity of the new HIT indices and have important implications for both clinical and research fields. (shrink)

As recent scholarship has repeatedly shown, the history of Vienna Circle is to some extent rooted in the tradition of Austrian Philosophy which Neurath considered as not involved in the “Kantian interlude”. Nevertheless, it seems that the heritage of Leibniz and, in particular, of his “reform of logic” has been hitherto neglected. Indeed, Leibnizianism (along with Herbartianism) represents a main feature of this tradition stretching from Bolzano to quite forgotten figures as Exner and Zimmermann, and still influent on the (...) Brentano circle. This paper attempt to highlight the role played by Leibniz in framing of the “scientific world conception”, focusing in particular both on Carnap’s and Neurath’s stance towards the characteristica universalis underlying the project of the encyclopedia Leibniz aimed to realize. (shrink)

English summary: This volume contains a mixture of essays by Bolzano on mechanics, its mathematical basis, on logic and aesthetics. German description: Der Band enthalt vermischte Abhandlungen Bolzanos zur Mechanik, zu ihren mathematischen Grundlagen, zur Logik und zur Asthetik: a. Versuch einer objectiven Begrundung der Lehre vom Zusammenhang der Krafte, 1842 - b. Versuch einer objectiven Begrundung der Lehre von den drei Dimensionen des Raumes, 1843 - c. Uber den Begriff des Schonen, 1845 - d. Aufsatz, worin eine von Hrn. (...) Exner in seiner Abhandlung: Ueber den Nominalismus und Realismus angeregte logische Frage beantwortet wird, 1843 - e. Ein Paar Bemerkungen uber die neue Theorie in Herrn Chr. Doppler's Schrift: Ueber das farbige Licht der Doppelsterne und einiger Gestirne des Himmels, 1843. (shrink)