scholarly journals The Motives behind Cantor's Set Theory – Physical, Biological, and Philosophical Questions

2004 ◽  
Vol 17 (1-2) ◽  
pp. 49-83 ◽  
Author(s):  
José Ferreirós
Keyword(s):  
Nineteenth Century ◽  
General Theory ◽  
Set Theory ◽  
Research Program ◽  
Georg Cantor ◽  
German Science ◽  
Detailed Interpretation ◽  
Philosophical Questions

The celebrated “creation” of transfinite set theory by Georg Cantor has been studied in detail by historians of mathematics. However, it has generally been overlooked that his research program cannot be adequately explained as an outgrowth of the mainstream mathematics of his day. We review the main extra-mathematical motivations behind Cantor's very novel research, giving particular attention to a key contribution, the Grundlagen (Foundations of a general theory of sets) of 1883, where those motives are articulated in some detail. Evidence from other publications and correspondence is pulled out to provide clarification and a detailed interpretation of those ideas and their impact upon Cantor's research. Throughout the paper, a special effort is made to place Cantor's scientific undertakings within the context of developments in German science and philosophy at the time (philosophers such as Trendelenburg and Lotze, scientists like Weber, Riemann, Vogt, Haeckel), and to reflect on the German intellectual atmosphere during the nineteenth century.

Dedekind, Julius Wilhelm Richard (1831–1916)

2018 ◽  
Author(s):  
Howard Stein
Keyword(s):  
Nineteenth Century ◽  
Set Theory ◽  
Mathematical Knowledge ◽  
Mathematical Structure ◽  
Georg Cantor ◽  
General Notion ◽  
Algebraic Numbers ◽  
Integral Calculus ◽  
Foundational Work ◽  
First Time

Dedekind is known chiefly, among philosophers, for contributions to the foundations of the arithmetic of the real and the natural numbers. These made available for the first time a systematic and explicit way, starting from very general notions (which Dedekind himself regarded as belonging to logic), to ground the differential and integral calculus without appeal to geometric ‘intuition’. This work also forms a pioneering contribution to set theory (further advanced in Dedekind’s correspondence with Georg Cantor) and to the general notion of a ‘mathematical structure’. Dedekind’s foundational work had a close connection with his advancement of substantive mathematical knowledge, particularly in the theories of algebraic numbers and algebraic functions. His achievements in these fields make him one of the greatest mathematicians of the nineteenth century.

scholarly journals Georg Cantor (1845-1918): la locura del infinito o el infinito de la locura

2013 ◽  
Vol 14 (1) ◽  
Author(s):  
Vernor Arguedas
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Set Theory ◽  
Cantor Set ◽  
Mathematical Work ◽  
Georg Cantor ◽  
Font Size ◽  
Early Twentieth Century ◽  
Palabras Clave ◽  
Siglo Xix

<p><strong><span style="font-family: 'Palatino Linotype'; font-size: x-small;">Resumen:</span> </strong><span style="font-family: Arial; font-size: x-small;">Georg Cantor es uno de los más distinguidos matemáticos de mediados del siglo XIX y comienzos del XX, en este artículo tocamos algunos aspectos de su vida y su quehacer matemático.</span></p><p><span style="font-family: 'Palatino Linotype'; font-size: x-small;"><strong>Palabras clave: </strong></span><span style="font-family: Arial; font-size: x-small;"> Cantor, teoría de conjuntos, infinito, números transfinitos.</span></p><p><span style="font-family: 'Palatino Linotype'; font-size: x-small;"><strong>Abstract:</strong> </span><span style="font-family: Arial; font-size: x-small;"> Georg Cantor is one of the most distinguished mathematicians of the mid-nineteenth century and early twentieth century. This article refers to some aspects of his life and his mathematical work<br /></span></p><p><strong><span style="font-family: 'Palatino Linotype'; font-size: x-small;">KeyWords:</span><span style="font-family: Arial; font-size: x-small;"> </span></strong><span style="font-family: Arial; font-size: x-small;">Cantor, set theory, infinite, transfinite numbers.</span></p>

THE INFLUENCE OF SCOTTISH ACCOUNTANTS IN THE UNITED STATES: THE EARLY CASE OF THE SOCIETY OF ACCOUNTANTS IN EDINBURGH

1997 ◽  
Vol 24 (1) ◽  
pp. 117-141 ◽  
Author(s):  
T. A. LEE
Keyword(s):  
United States ◽  
General Theory ◽  
Research Program ◽  
The United States ◽  
The World ◽  
Early Case ◽  
The Impact ◽  
Chartered Accountants ◽  
The U.S

This study represents part of a long-term research program to investigate the influence of U.K. accountants on the development of professional accountancy in other parts of the world. It examines the impact of a small group of Scottish chartered accountants who emigrated to the U.S. in the late 1800s and early 1900s. Set against a general theory of emigration, the study's main results reveal the significant involvement of this group in the founding and development of U.S. accountancy. The influence is predominantly with respect to public accountancy and its main institutional organizations. Several of the individuals achieved considerable eminence in U.S. public accountancy.

PARETO’S INFLUENCE ON SCHOLARS FROM THE ITALIAN TRADITION IN PUBLIC FINANCE

2012 ◽  
Vol 34 (1) ◽  
pp. 43-66 ◽  
Author(s):  
AMEDEO FOSSATI
Keyword(s):  
Public Finance ◽  
General Theory ◽  
Research Program ◽  
Time Span ◽  
Three Generations ◽  
Original Contribution ◽  
Specific Influence

The paper discusses the influence of Pareto’s methodological revolution on the Italian scientific tradition in public finance. To that end, the works of the most celebrated scholars from within the first, second, and final generations of this tradition are reviewed with reference to their reactions to Pareto’s idea of science as logico-experimental activities, and his contributions to the development of marginalism and theoretical sociology. The particular scholars considered across the three generations’ time span include Pantaleoni, De Viti, Barone, Einaudi, Sensini, Griziotti, Borgatta, Murray, and Fasiani. The main original contribution of this paper is the marshaling of evidence in support of the author’s proposition that Fasiani’s research program is characterized by a clearly Paretian mode of enquiry with regard to methodology and the economic investigation of fiscal activities, although the specific influence of Pareto’s sociology on Fasiani’s approach to fiscal studies was relatively modest. It is provisionally concluded that, in taking the best and most relevant of Pareto’s work for fiscal studies, Fasiani’s contributions came to represent the highest point in the evolution of the general theory of public finance in the Italian tradition.

scholarly journals DIALOGICAL LINGUISTICS IN RUSSIA: THE HISTORY OF FORMATION AND THE CURRENT STATUS

2021 ◽  
pp. 159-173
Author(s):  
N. N. Shpilnaya ◽  
Keyword(s):  
General Theory ◽  
Research Program ◽  
Linguistic Theory ◽  
Final Part ◽  
Current Status ◽  
Interactional Theory ◽  
Current State ◽  
The Status ◽  
History Of ◽  
History Of Formation

The article is an outline of the development of Dialogical Linguistics in Russia. It represents its milestones of formation and the current state. Dialogical Linguistics is considered to be an integral linguistic branch, claiming the status of a distinct «research program» and comprises such sections as follows: Linguistics of Dialogical Text, Linguistic Theory of Replication, Interactional Theory of Dialogue, General Theory of Dialogue. In the final part of the article, the principles of dialogical modeling of linguistic objects are being formulated.

Charles Sanders Peirce: An Overview

1996 ◽  
pp. 1-16
Author(s):  
Vincent G. Potter
Keyword(s):  
Nineteenth Century ◽  
Charles Sanders Peirce ◽  
Alfred North Whitehead ◽  
Bertrand Russell ◽  
Gottlob Frege ◽  
Georg Cantor ◽  
Academic World ◽  
American Pragmatism ◽  
George Boole

This chapter provides an overview of the life of Charles Sander Peirce—philosopher, logician, scientist, and father of American pragmatism. This man, unappreciated in his lifetime, virtually ignored by the academic world of his day, is now recognized as perhaps America's most original philosopher and her greatest logician. Indeed, on the latter score, he is surely one of the logical giants of the nineteenth century, which produced such geniuses as Georg Cantor, Gottlob Frege, George Boole, Augustus De Morgan, Bertrand Russell, and Alfred North Whitehead. Today, more than eighty years after his death, another generation of scholars is beginning to pay him the attention he deserves. The chapter shows the brilliant and tragic career of Peirce. Though he never published a book on philosophy, his articles and drafts fill volumes.

Funding the Faiths

2011 ◽  
pp. 322-340
Author(s):  
Laurence R. Iannaccone ◽  
Feler Bose
Keyword(s):  
Nineteenth Century ◽  
General Theory ◽  
Religious Commitment ◽  
Religious Institutions ◽  
Material Support ◽  
Economics Of Religion ◽  
Religious Competition ◽  
American Judaism ◽  
Government Production ◽  
The Impact

Of all the things that sustain formal religious institutions, none is more essential than material support. Without adequate income, congregations fold, denominations fail, and the faithful flock to greener pastures. Nor is any facet of religious commitment more concrete and quantifiable. Faced with skepticism about the accuracy and consistency of attendance and membership rates reported by individuals or institutions, the obvious alternative is to follow the money. Strange as it may seem, the economics of religion has yet to pay much attention to financial matters. The basic argument of this article, which suggests some first steps toward a general theory of religious finance, rests on a series of observations concerning the impact of government, production, religious beliefs, and religious competition. The article also applies the outlined principles across many different times, places, and traditions, including modern Europe, nineteenth-century Christian America, American Judaism, Buddhism, paganism, and Hinduism.

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