Vorlesungen über die Algebra der Logik ist ein unveränderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1890. Hansebooks ist Herausgeber von Literatur zu unterschiedlichen Themengebieten wie Forschung und Wissenschaft, Reisen und Expeditionen, Kochen und Ernährung, Medizin und weiteren Genres. Der Schwerpunkt des Verlages liegt auf dem Erhalt historischer Literatur. Viele Werke historischer Schriftsteller und Wissenschaftler sind heute nur noch als Antiquitäten erhältlich. Hansebooks verlegt diese Bücher neu und trägt damit zum Erhalt selten gewordener Literatur und historischem Wissen auch für die (...) Zukunft bei. (shrink)

Ernst Schröder, Parafrasi Schröderiane. Ovvero: Ernst Schröder, Leoperazioni del Calcolo Logico. Original German text with Italian translation, commentary and annotations by Davide Bondoni, LED Edizioni, Milan, 2010, pp. 208, 15,5 × 22 cm, ISBN 978-88-7916-474-0.

In this paper articulated in two parts we propose a structural interpretation of Schröder’s work, pointing out his insistence on the priority of a whole in comparison with its parts. The examples are taken from the diverse areas in which Schröder was active, with a particular interest in his project of an absolute algebra. I am regretting for the bad quality of my English, hoping that notwithstanding the reader can grasp at least the fundamental tracts of my reasoning.

In this paper (the second of two parts) we propose a structural interpretation of Schröder’s work, pointing out his insistence on the priority of a whole in comparison with its parts. The examples are taken from the diverse areas in which Schröder was active, with a particular interest in his project of an absolute algebra.

English summary: Deism, the "Religionsphilosophie der Aufklarung" (religious philosophy of the Enlightenment, Ernst Troeltsch) played a significant role in the modernization of philosophy in the early modern age and of European culture in a broader sense. Although this has been known for a long time, there is still the need for a differentiated overall picture of the subject. Therefore, on the occasion of Gunter Gawlick's 80th birthday in June 2010, a seminar on the manifestations of Deism in Europe was (...) held at the "Herzog August Bibliothek Wolfenbuttel" (library of Duke August of Brunswick-Wolfenbuttel). The resulting anthology, edited by Winfried Schroder, assembles the partial results of current research on Deism, thereby providing a definition of Deism's role in the cultural, ideological and intellectual history of early modern times. German description: Zu den philosophie- und theologiegeschichtlichen Formationen, denen in der Zeitspanne zwischen dem spaten 16. und dem 18. Jahrhundert die Uberwindung der vormodernen Welt die wichtigsten Impulse verdankt, gehort ohne Zweifel der Deismus. Seine Leitideen sind der Gedanke der Suffizienz einer um moralische Vorschriften zentrierten 'naturlichen' Religion, die aus blosser Vernunft zuganglich ist, die Uberflussigkeit einer ubernaturlichen Offenbarung und die daraus abgeleitete Forderung nach Toleranz und Denkfreiheit. Diese Ideen weisen den Deismus geradezu als "die Religionsphilosophie der Aufklarung" (Ernst Troeltsch) aus. Diese massgebliche Rolle, die der Deismus im Modernisierungsprozess der fruhneuzeitlichen Philosophie und der europaischen Kultur im weiteren Sinne gespielt hat, ist seit langem bekannt - und doch fehlt es an einem differenzierten Gesamtbild. In den letzten Jahrzehnten sind zum einen wichtige Forschungsertrage erzielt worden, zum anderen hat die Deismus-Forschung etliche Desiderate festgestellt, denen sie teilweise bereits nachgegangen ist. Aus Anlass des 80. Geburtstags von Gunter Gawlick fand deshalb im Juni 2010 ein Arbeitsgesprach zu den Gestalten des Deismus in Europa in der Herzog August Bibliothek Wolfenbuttel statt. Der zugehorige von Winfried Schroder herausgegebene Sammelband bundelt die Teilergebnisse der bisherigen Desismus-Forschung zu einer Positionsbestimmung des Deismus in der Kultur-, Ideen- und Geistesgeschichte der Fruhen Neuzeit. (shrink)

History and Philosophy of Logic, Volume 33, Issue 3, Page 291-293, August 2012.

We aim at clarifying to what extent the work of the German mathematician Ernst Schröder on the algebra of logic is taken into consideration and rehashed in the work of the early Husserl, focusing on Husserl’s 1891 Review of the first volume of Schröder’s monumental Vorlesungen über die Algebra der Logik and on Husserl’s text Der Folgerungskalkül und die Inhaltslogik written in the same year. We will try to show how and why Husserl, while praising Schröder’s calculus, strongly criticizes (...) Schröder’s attempt at a philosophical clarification and justification of it. (shrink)

Les contributions à la logique de MacColl et Charles Sanders Peirce (1839-1914) ont été les deux plus profondes influences sur le travail de Ernst Schröder (1841-1902) en logique algébrique. Dans son Vorlesungen über dieAlgebra der Logik, Schröder a cité MacColl comme l’un de ses précurseurs les plus importants. Schröder a comparé les travaux de Peirce avec les premières parties de la série d’articles intitulés « The calculus of equivalent statements » que MacColl publie entre 1877 et 1880. Schröder a (...) attribué la priorité à MacColl pour avoir anticipé les résultats de Peirce. Pour Schröder, MacColl était une phase préliminaire à l’algèbre de la logique de Peirce. (shrink)

Les contributions à la logique de MacColl et Charles Sanders Peirce (1839-1914) ont été les deux plus profondes influences sur le travail de Ernst Schröder (1841-1902) en logique algébrique. Dans son Vorlesungen über dieAlgebra der Logik, Schröder a cité MacColl comme l’un de ses précurseurs les plus importants. Schröder a comparé les travaux de Peirce avec les premières parties de la série d’articles intitulés « The calculus of equivalent statements » que MacColl publie entre 1877 et 1880. Schröder a (...) attribué la priorité à MacColl pour avoir anticipé les résultats de Peirce. Pour Schröder, MacColl était une phase préliminaire à l’algèbre de la logique de Peirce. (shrink)

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic –Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical (...) inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schröder, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism. (shrink)

The calculus of relations was created and developed in the second half of the nineteenth century by Augustus De Morgan, Charles Sanders Peirce, and Ernst Schröder. In 1940 Alfred Tarski proposed an axiomatization for a large part of the calculus of relations. In the next decade Tarski's axiomatization led to the creation of the theory of relation algebras, and was shown to be incomplete by Roger Lyndon's discovery of nonrepresentable relation algebras. This paper introduces the calculus of relations and (...) the theory of relation algebras through a review of these historical developments. (shrink)

This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schroder, Leopold Lowenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.

This chapter discusses the complex conditions for the emergence of 19th-century symbolic logic. The main scope will be on the mathematical motives leading to the interest in logic; the philosophical context will be dealt with only in passing. The main object of study will be the algebra of logic in its British and German versions. Special emphasis will be laid on the systems of George Boole and above all of his German follower Ernst Schröder.

In what follows, the difference between Frege’s and Schröder’s understanding of logical connectives will be investigated. It will be argued that Frege thought of logical connectives as concepts, whereas Schröder thought of them as operations. For Frege, logical connectives can themselves be connected. There is no substantial difference between the connectives and the concepts they connect. Frege’s distinction between concepts and objects is central to this conception, because it allows a method of concept formation which enables us to form concepts (...) from the logical connectives alone. Schröder in contrast unifies the distinction between concepts and objects, but keeps the distinction between logical connectives and what they connect. It will be argued that Frege’s particular way of perceiving logical connectives is crucial for his foundational project. (shrink)

It is shown that David Hilbert's formalistic approach to axiomaticis accompanied by a certain pragmatism that is compatible with aphilosophical, or, so to say, external foundation of mathematics.Hilbert's foundational programme can thus be seen as areconciliation of Pragmatism and Apriorism. This interpretation iselaborated by discussing two recent positions in the philosophy ofmathematics which are or can be related to Hilbert's axiomaticalprogramme and his formalism. In a first step it is argued that thepragmatism of Hilbert's axiomatic contradicts the opinion thatHilbert style (...) axiomatical systems are closed systems, a reproachposed by Carlo Cellucci. In the second section the question isdiscussed whether Hilbert's pragmatism in foundational issuescomes close to an a-philosophical ``naturalism in mathematics'' assuggested by Penelope Maddy. The answer is ``no'', because forHilbert philosophy had its specific tasks in the general projectto found mathematics. This is illuminated in the concludingsection giving further evidence for Hilbert's foundationalapriorism by discussing his ``axiom of the existence of mind'' andrelating it to the ``one and only axiom'' of the German algebraistof logic, Ernst Schröder, postulating the inherence of signs onthe paper. (shrink)

Karl Eugen Müller's contribution to the development of the algebra of logic is perhaps the most important part of his scientific work. Müller, who became Gymnasialprofessor after his university studies, was a student of Ernst Schröder's friend, the mathematician Jakob Lüroth. As a result of publishing two papers on problems related to Schröder's monumental Vorlesungen iiber die Algebra der Logik, Müller was commissioned by the Deutsche Mathematiker- Vereinigung with the editing of the unpublished parts of the Vorlesungen from Schröder's (...) Nachla?. Müller worked on Schröder's papers until 1910, but did not bring this work to a conclusion. Müller's own Nachla?, including those parts of Schröder's papers still in his possession, was destroyed in Frankfurt a.M. in 1943, so there remains no hope of finding through Müller any part of the missing Nachla? of Schröder. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Correspondence of Charles S. Peirce and the Open Court Publishing Company, 1890–1913 ed. by Stetson J. RobinsonCornelis de WaalEdited by Stetson J. RobinsonThe Correspondence of Charles S. Peirce and the Open Court Publishing Company, 1890–1913 Berlin: De Gruyter, 2022. 666pp., incl. indexThe fifth volume in the Peirceana series brings us the extensive correspondence between Peirce and the Open Court Publishing Company (abbreviated to OCP by Robinson). The (...) double-barreled opening shot consists of two letters (one by Francis Russell and one by Open Court’s Editor Paul Carus) aimed at soliciting a contribution from [End Page 109] Peirce for the inaugural issue of a new quarterly journal to be published by the Open Court, called The Monist. Carus had been particularly impressed by Peirce’s Illustrations of the Logic of Science papers, which had appeared over a decade earlier in Popular Science Monthly, and to which Russell had drawn Carus’s attention.1 Peirce quickly responded, suggesting not one but an entire series of articles, the first of which to be titled “The Architecture of Theories.” It proved the beginning of a productive but also turbulent relationship between Peirce and the publishing company. The final letter in the exchange comes again from Carus, written September 10, 1913, about seven months before Peirce died.The Open Court Collection at Southern Illinois University Carbondale, from which much of the correspondence is drawn, is a truly magnificent collection. It contains not only business correspondence and financial records, but also the various stages of the publishing process. It includes the original texts that Peirce sent to the publisher, as well as the often heavily corrected galleys and proofs—material that is used appreciatively by the Peirce Edition Project for its critical edition of Peirce’s Writings. When we combine this record with the Nachlass of a philosopher who lived in a continuously expanding mansion with a penchant for keeping each and every scrap of paper, we get a remarkably full picture of everything that went into the publication of Peirce’s work with the Open Court. In contrast, we know painfully little of what went on at the Century Company, which published the Century Dictionary to which Peirce so heavily contributed, or of James Mark Baldwin’s treatment of Peirce’s submissions when he compiled his Dictionary of Philosophy and Psychology. Neither venture seems to have left any records, apart from what survived within Peirce’s own papers— at least no such records have so far been found. We know a bit more about Peirce’s dealings with The Nation, but again, almost exclusively because of what has been preserved in Peirce’s papers.Robinson’s hefty tome makes the correspondence between Peirce and the Open Court widely available for the first time. The book opens with a short explanation of the editorial method, a helpful chronology, and a brief historical introduction describing Peirce’s relationship with the Open Court. The work also contains fourteen illustrations, mostly of letters. The introduction to the volume is brief and largely piggybacks on a handful of sources, such as the Introduction to Volume 8 of the Writings, rather than that it was inspired by the collection of letters that follows it, or by a closer familiarity with the archival holdings of the Open Court.2 In his introduction, Robinson divides Peirce’s relationship with the publishing company in four periods: A very active 1890–1894, which includes Peirce’s familiar Monist Metaphysical papers, his contributions to the fortnightly The Open Court, and his [End Page 110] attempts at writing an elementary arithmetic. This period ends with a falling out between Peirce and Hegeler. It is followed by a far more subdued 1894–1897, where the relationship with the publisher is largely restored by Russell, and which results in an extensive discussion by Peirce of the third volume of Ernst Schröder’s Vorlesungen über die Algebra der Logik, which appeared in two parts in The Monist. This period too ends with a falling out. The activity picks up again in 1904, resulting in Peirce’s famous pragmatism papers as well as the “Some Amazing Mazes” series of 1908... (shrink)

Ernst Friedrich Ferdinand Zermelo transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set theory. (...) Two decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory and championed the use of infinitary logic, anticipating broad modern developments. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the awareness of what has endured in the subsequent development of set theory. Elaborating formulations and results are provided, and special emphasis is placed on the to and fro surrounding the Schröder-Bernstein Theorem and the correspondence and comparative approaches of Zermelo and Gödel. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details. (shrink)

Ernst Friedrich Ferdinand Zermelo (1871–1953) transformed the set theory of Cantor and Dedekind in the first decade of the 20th century by incorporating the Axiom of Choice and providing a simple and workable axiomatization setting out generative set-existence principles. Zermelo thereby tempered the ontological thrust of early set theory, initiated the delineation of what is to be regarded as set-theoretic, drawing out the combinatorial aspects from the logical, and established the basic conceptual framework for the development of modern set (...) theory. Two decades later Zermelo promoted a distinctive cumulative hierarchy view of models of set theory and championed the use of infinitary logic, anticipating broad modern developments. In this paper Zermelo's published mathematical work in set theory is described and analyzed in its historical context, with the hindsight afforded by the awareness of what has endured in the subsequent development of set theory. Elaborating formulations and results are provided, and special emphasis is placed on the to and fro surrounding the Schröder-Bernstein Theorem and the correspondence and comparative approaches of Zermelo and Gödel. Much can be and has been written about philosophical and biographical issues and about the reception of the Axiom of Choice, and we will refer and defer to others, staying the course through the decidedly mathematical themes and details. (shrink)

New forms of artificial intelligence on the one hand and the ubiquitous networking of “everything with everything” on the other hand characterize the fourth industrial revolution. This results in a changed understanding of human–machine interaction, in new models for production, in which man and machine together with virtual agents form hybrid teams. The empirical study “Socializing with robots” aims to gain insight especially into conditions of development and processes of hybrid human–machine teams. In the experiment, human–robot actions and interactions were (...) closely observed in a virtual environment. Robots as partners differed in shape and behavior. Participants were instructed to achieve an objective that could only be achieved via close teamwork. This paper unites different aspects from core disciplines of social robotics and psychology contributing to anthropomorphization with the empirical insights of the experiment. It focuses on the psychological effects on anthropomorphization and mechanization, taking the inter- and transdisciplinary field of social robotics as a starting point. (shrink)

I have based my psychological hypotheses on studies in perception and in personality. Research in these two areas began independently, but by the late forties the supposedly unconnected processes came to be seen as different aspects of one process. For instance, a low tolerance for perceptual ambiguity and cognitive dissonance was found to be significantly correlated with lack of emotional responsiveness, dogmatism, and authoritarianism; conversely, a high tolerance for perceptual ambiguity and cognitive dissonance was found to be significantly correlated with (...) tolerance of emotional ambivalence, openness to new experience, and a liberal world view.1 Later studies, primarily those conducted in the sixties, then established strong correlations between these findings and information-processing styles. Information processing involves three stages: first, stimuli are selected from the environment ; these stimuli are then arranged into "dimensions"; finally, if two or more dimensions result, they are compared and/or combined according to certain rules. H. M. Schroder and his colleagues have established correlations between personality styles and styles of information processing.2 For example, an intolerant personality—that is, one with a low integration index—"identifies and organizes stimuli in a fixed way, and the rules derived from existing schemata are explicit in defining this one way" . What psychologists call an "abstract personality" and identify in terms of "flexibility" or "tolerance of ambiguity"—what in literary studies is most conveniently called "negative capability"—is not necessarily characterized as lacking rules but rather as possessing a greater number of conflicting rules on a lower level which may be accommodated by rules on a higher level. · 1. See Jerome S. Bruner and David Krech, eds., Perception and Personality, 2nd ed. and Robert R. Blake and Glenn V. Ramsey, eds., Perception: An Approach to Personality . Although, as Else Frenkel-Brunswick says, "rigidity in one respect may go with flexibility in another," she also adds: "There is some indication that in the case of distinct intolerance of emotional ambivalence one may as a rule be able to locate at least some aspects of intolerance of cognitive ambiguity although these may often be more apparent on a higher level than that of perception proper" The present essay, since it is one section of a projected larger study, deals with the issues inherent in this approach in only a limited fashion. One could, for instance, quote whole essays in this branch of psychology dealing with ambiguity and point to their relevance for some aspects of literary study and the teaching of literature. Ambiguity, of course, is also a central term in New Criticism. See William Empson, Seven Types of Ambiguity and Ernst Kris and Abraham Kaplan, "Aesthetic Ambiguity," in Psychoanalytic Explorations in Art, ed. Kris , pp. 243-64.· 2. H. M. Schroder, M. J. Driver, and S. Streufert, "Levels of Information Processing," in Thought and Personality, ed. Peter B. Warr , pp. 174-91. All citations to this work will appear in the text. Reuven Tsur, senior lecturer in Hebrew literature at Tel-Aviv University, is the author of several books in Hebrew on medieval and modern Hebrew poetry and, in English, A Perception-Oriented Theory of Metre. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Complementary and alternative medicine has become an important section of healthcare. Its high level of acceptance among the general population represents a challenge to healthcare professionals of all disciplines and raises a host of ethical issues. This article is an attempt to explore some of the more obvious or practical ethical aspects of complementary and alternative medicine.

"Nicht die Bedingungen der Moglichkeit irgendwelcher Erkenntnisse, nicht die Voraussetzungen des Erkennens, weder die formalen noch die materialen, sondern das Erkennen selbst zu untersuchen ist die Aufgabe dieser Erkenntnistheorie. Dass etwas erkannt wird, d. h. dass in Wahrnehmungen, Erinnerungen, Gedanken, im Zweifeln, Glauben und Wissen Gegenstande erfasst werden, diese Tatsache bildet den Ausgangspunkt der folgenden Betrachtungen. Wie die verschiedenen Arten des Erkennens sich voneinander unterscheiden, aus welchen Elementarprozessen sie sich zusammensetzen und welche Gesetze ihre Entwickelung beherrschen, das sind die Fragen, (...) die von der Psychologie des Erkennens zu beantworten sind." Der Verlag der Wissenschaften verlegt historische Literatur bekannter und unbekannter wissenschaftlicher Autoren. Dem interessierten Leser werden so teilweise langst nicht mehr verlegte Werke wieder zugangig gemacht. Dieses Buch uber die Erkenntnistheorie von Dr. Ernst Durr ist ein unveranderter, hochwertiger Nachdruck der Originalausgabe aus dem Jahr 1910.". (shrink)

Die geschichtliche Entwicklung des Philosophieunterrichts am Gymnasium verlief in Deutschland bis in die heutige Zeit sehr different. Auf diesem Hintergrund erfolgt die Darstellung, Analyse und Kommentierung der Lehrplane und Curricula zum Philosophie- und Ethikunterricht in den Bundeslandern und vermittelt Informationen uber den Verlauf und aktuellen Stand der Curriculumstrategien.".

Name der Zeitschrift: Klio Jahrgang: 96 Heft: 1 Seiten: 287-288.