A long-awaited edition of Zermelo’s works Content Type Journal Article Pages 1-4 DOI 10.1007/s11016-011-9548-y Authors José Ferreirós, Instituto de Filosofia, CCHS-CSIC, Albasanz, 26-28, 28037 Madrid, Spain Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.
This paper aims to outline an analysis and interpretation of the process that led to First-Order Logic and its consolidation as a core system of modern logic. We begin with an historical overview of landmarks along the road to modern logic, and proceed to a philosophical discussion casting doubt on the possibility of a purely rational justification of the actual delimitation of First-Order-Logic. On this basis, we advance the thesis that a certain historical tradition was essential to the emergence of (...) modern logic; this traditional context is analyzed as consisting in some guiding principles and, particularly, a set of exemplares (i.e., paradigmatic instances). Then, we proceed to interpret the historical course of development reviewed in section 1, which can broadly be described as a two-phased movement of expansion and then restriction of the scope of logical theory. We shall try to pinpoint ambivalencies in the process, and the main motives for subsequent changes. Among the latter, one may emphasize the spirit of modern axiomatics, the situation of foundational insecurity in the 1920s, the resulting desire to find systems well-behaved from a proof-theoretical point of view, and the metatheoretical results of the 1930s. Not surprisingly, the mathematical and, more specifically, the foundational context in which Firs-Order-Logic matured will be seen to have played a primary role in its shaping. (shrink)
David Hilbert’s early foundational views, especially those corresponding to the 1890s, are analysed here. I consider strong evidence for the fact that Hilbert was a logicist at that time, following upon Dedekind’s footsteps in his understanding of pure mathematics. This insight makes it possible to throw new light on the evolution of Hilbert’s foundational ideas, including his early contributions to the foundations of geometry and the real number system. The context of Dedekind-style logicism makes it possible to offer a new (...) analysis of the emergence of Hilbert’s famous ideas on mathematical existence, now seen as a revision of basic principles of the “naive logic” of sets. At the same time, careful scrutiny of his published and unpublished work around the turn of the century uncovers deep differences between his ideas about consistency proofs before and after 1904. Along the way, we cover topics such as the role of sets and of the dichotomic conception of set theory in Hilbert’s early axiomatics, and offer detailed analyses of Hilbert’s paradox and of his completeness axiom (Vollständigkeitsaxiom). (shrink)
Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...) is meant by definability and by “arbitrariness,” a first historical part discusses the strong motives why set theory was conceived as a theory of arbitrary sets, emphasizing connections with analysis and particularly with the continuum of real numbers. Judged from this perspective, the axiom of choice stands out as a most central and natural set-theoretic principle (in the sense of quasi-combinatorialism). A second part starts by considering the potential mismatch between the formal systems of mathematics and their motivating conceptions, and proceeds to offer an elementary discussion of how far the Zermelo—Fraenkel system goes in laying out principles that capture the idea of “arbitrary sets”. We argue that the theory is rather poor in this respect. (shrink)
El artículo intenta promover una recepción más amplia de los trabajos recientes sobre filosofía de la actividad científica experimental. Primero se comentarán los orígenes y las características de la tradición teoreticista predominante, criticando sus presupuestos y sus "miserias". Se analizará luego la función de los instrumentos, proponiendo una tipología de la actividad experimental, aunque elemental --esperamos-- útil. Tras analizar la estructura del experimento, empleando contribuciones de Pickering y otros, discutiremos la dinámica de la experimentación: los procesos de formación de datos. (...) Ésta es, obviamente, la cuestión más crucial y debatida, de la que depende la especificidad y fiabilidad de los métodos científicos. /// This paper attempts to promote a more widespread reception of recent work on the philosophy of experimental scientific activity. First, we comment on the origins and character of the predominant theoreticist tradition, offering critical remarks on its assumptions and "poverty". Then we analyze the function of instruments, proposing a coarse but hopefully useful typology of experimental activity. After analyzing the structure of experiment, drawing on work by Pickering and others, we discuss the dynamics of experimentation --the processes of data formation. This is obviously the most crucial and disputed issue, on which the specificity and reliability of scientific methods depends. (shrink)
RESUMEN: Se ofrece un análisis de las transformaciones disciplinares que ha experimentado la lógica matemática o simbólica desde su surgimiento a fines del siglo XIX. Examinaremos sus orígenes como un híbrido de filosofía y matemáticas, su madurez e institucionalización bajo la rúbrica de “lógica y fundamentos”, una segunda ola de institucionalización durante la Posguerra, y los desarrollos institucionales desde 1975 en conexión con las ciencias de la computación y con el estudio de lenguaje e informática. Aunque se comenta algo de (...) la “historia interna”, nos centraremos en la emergencia, consolidación y convoluciones de la lógica como disciplina, a través de varias asociaciones profesionales y revistas, en centros como Turín, Gotinga, Varsovia, Berkeley, Princeton, Carnegie Mellon, Stanford y Amsterdam.ABSTRACT: We offer an analysis of the disciplinary transformations underwent by mathematical or symbolic logic since its emergence in the late 19th century. Examined are its origins as a hybrid of philosophy and mathematics, the maturity and institutionalisation attained under the label “logic and foundations”, a second wave of institutionalisation in the Postwar period, and the institutional developments since 1975 in connection with computer science and with the study of language and informatics. Although some “internal history” is discussed, the main focus is on the emergence, consolidation and convolutions of logic as a discipline, through various professional associations and journals, in centers such as Torino, Göttingen, Warsaw, Berkeley, Princeton, Carnegie Mellon, Stanford, and Amsterdam. (shrink)
The present paper is a contribution to the history of logic and its philosophy toward the mid-20th century. It examines the interplay between logic, type theory and set theory during the 1930s and 40s, before the reign of first-order logic, and the closely connected issue of the fate of logicism. After a brief presentation of the emergence of logicism, set theory, and type theory (with particular attention to Carnap and Tarski), Quine’s work is our central concern, since he was seemingly (...) the most outstanding logicist around 1940, though he would shortly abandon that viewpoint and promote first-order logic as all of logic. Quine’s class-theoretic systems NF and ML, and his farewell to logicism, are examined. The last section attempts to summarize the motives why set theory was preferred to other systems, and first orderlogic won its position as the paradigm logic system after the great War. (shrink)
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. (shrink)
Today, more corporations disclose information about their environmental performance in response to stakeholder demands of environmental responsibility and accountability. What information do corporations disclose on their websites? This paper investigates the environmental management policies and practices of the 200 largest corporations in the world. Based on a content analysis of the environmental reports of Fortune’s Global 200 companies, this research analyzes the content of corporate environmental disclosures with respect to the following seven areas: environmental planning considerations, top management support to (...) the institutionalization of environmental concerns, environmental structures and organizing specifics, environmental leadership activities, environmental control, external validations or certifications of environmental programs, and forms of corporate environmental disclosures. (shrink)
Corporate America is institutionalizing ethics through a variety of structures, systems, and processes. This study sought to identify managerial perceptions regarding the institutionalization of ethics in organizations. Eighty-six corporate level marketing and human resource managers of American multi-national corporations responded to a mail survey regarding the various implicit and explicit ways by which corporations institutionalize ethics. The results revealed that managers found ethics to be good for the bottom line of the organizations, they did not perceive the need for additional (...) formalization of ethics, and that they perceived implicit forms of institutionalizing ethics (e.g., leadership, corporate culture, top management support) to be more effective than the explicit forms of institutionalizing ethics (e.g., ethics ombudspeople, ethics committees, ethics newsletters). Implications of the survey and future research directions conclude the paper. (shrink)
In this book, as in various earlier studies of the author, she uses the three-dimensional method, which facilitates a stratified focus in agreement with three ...
: The history of modern feminist political theories is often framed in terms of the already existing theories of a number of radical nineteenth-century men philosophers such as James Mill, John Stuart Mill, Charles Fourier, Karl Marx, and Friedrich Engels. My argument takes issue with this way of framing feminist political theory by demonstrating that it rests on a derivation that remains squarely within the logic of malestream political theory. Each of these philosophers made use of a particular discursive trope (...) that linked the idea of women's emancipation with the idea of social progress. I argue that this trope reproduced the masculinist signification and symbolism inherent in their particular political philosophies. I argue for a more positive, less masculinist, account of the history of feminist political thought. (shrink)
: Liberal philosopher James Mill has been understood as being unambiguously antifeminist. However, Terence Ball, supposedly informed by a feminist perspective, has argued for a new interpretation. Ball has reconceptualized Mill as a feminist and the sole source of the feminism of his son (J. S. Mill), suggesting a revision of the received wisdom about their relationship to the development of nineteenth century feminist thought. This paper takes issue with Ball's "new interpretation" and its presumed feminist basis.
This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
Dedekind used to refer to Riemann as his main model concerning mathematical methodology, particularly regarding the use of abstract notions as a basis for mathematical theories. So, in passages written in 1876 and 1895 he compared his approach to ideal theory with Riemann’s theory of complex functions. In this paper, I try to make sense of those declarations, showing the role of abstract notions in Riemann’s function theory, its influence on Dedekind, and the importance of the methodological principle of avoiding (...) ‘forms of representation’ in shaping ideal theory. In order to emphasize the abstract viewpoint of Riemann and Dedekind, I compare their work with that of their great german contemporaries, Weierstrass and Kronecker; so, an influential ‘Göttingen group’ is confronted with the ‘Berlin school’ of mathematics. Some light is also thrown on the relation between Riemann and Dedekind, particularly with respect to Dedekind’s interest on Riemann’s ideas --in function theory, geometry and topology--, beginning in the 1850s and through later works. The abstract approach of the ‘Göttingen group’ was determinant for the turn to abstract mathematics in our century, and the direct influence of Riemann on Dedekind shows how this approach developed. (shrink)
Resenha de: Normal 0 21 false false false MicrosoftInternetExplorer4 /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Tabela normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font-family:"Times New Roman"; mso-ansi-language:#0400; mso-fareast-language:#0400; mso-bidi-language:#0400;} ORTEGA Y GASSET, José. Una interpretación de la historia universal: en torno a Toynbee . Obras Completas . v. IX. Madrid: Alianza, 1997.
Se propone una lectura de Simbólico retorno, 1955, primer libro de Delia Domínguez, en términos de dar cuenta de la representación estética de la naturaleza nativa del sur chileno profundo y del sujeto lírico femenino que la habita y la vive como experiencia de plenitud que contrasta con la orfandad familiar y social de éste. El tono elegíaco y sombrío del libro atestigua el dolor de la autora por la temprana pérdida de su madre, dolor que alimenta una cierta (...) visión anticipatoria de la decadencia de su clase social de origen: la burguesía agraria germana del sur de Chile de entonces. We propose a reading of Simbólico retorno, 1955, Delia Domínguez’s first book, in the interest of offering an evaluation of the aesthetic representation of Chile’s deep south living nature and of the feminine lyric subject which inhabits it and lives it, as an experience of plenitude that contrasts with the familial and social orphanhood. The elegiac and somber tone of the text, testifies of the author’s pain due to the early loss of her mother, a pain that feeds a certain anticipatory cision of decadence of her social class and origin: the gemanic agrarian bourgeoisie of the south of Chile of that time. (shrink)
"Estos dos modos de ver la explicación no son incompatibles entre sí; cada uno ofrece un modo razonable de analizar la explicación. De hecho, pueden ser tomados como representando dos aspectos diferentes pero compatibles de la explicación científica" (1989, p. 183). "[estos dos enfoques] se han desarrollado hasta el punto en que pueden coexistir pacíficamente como dos aspectos distintos de la explicación científica" (1992, p. 39). "No rechazo la posibilidad de una teoría [unificacionista] de este tipo; creo que ella no (...) entraría en conflicto con la explicación causal sino que la complementaría " (2001a, p. 10). (shrink)
Este libro nos presenta un «Ortega desde dentro», es decir, no como él había observado a Goethe, con catalejo, sino reconstruido a base de sus testimonios personales esparcidos en artículos, libros, cartas, clases y conferencias, a los que habría que sumar los que sobre él dejaron familiares, colaboradores, discípulos, amigos y enemigos. Estamos pues ante una biografía con ropaje autobiográfico, no sólo de su persona, sino también de su obra, íntimamente unidas a la España de la primera mitad del siglo (...) xx, a la que quiso guiar bajo los más diversos regímenes antes de ser arrastrado por su tragedia como nación. En cierto modo, es la historia de un amor imposible, porque la España que soñó no existía y puede que ni siquiera llegue a existir. Sin embargo y paradójicamente, también es la historia de cómo Ortega, al iluminar sus carencias, logró dejar su impronta en ella. (shrink)
España, inicios del siglo XX. José Ortega, armado de razón, busca un ideal que guíe su vida, oriente su acción pública e ilumine lo que le rodea. En su demanda se enfrentará con Don Quijote, Unamuno o Baroja; descifrará el neokantismo, la fenomenología, el psicoanálisis; investigará la leyenda milenarista, la prehistoria del criticismo, la anatomía del alma; descubrirá la mujer, la política, el compromiso; predicará el socialismo, la construcción de Europa, la recreación de España y recorrerá Castilla, Marburgo o (...) Asturias para asentarse en El Escorial, donde ya estaba. Los edificios conceptuales se asientan sobre vidas concretas; bajo toda construcción universal transpira una biografía particular. El joven José Ortega propone un recorrido atento por el pensamiento de juventud de Ortega y Gasset, reconstruyendo sus peripecias intelectuales hasta encontrar la razón vital de la razón vital. (shrink)
In the Spanish-Indian controversies, special attention was given to the subject of the education of the Indians, understood in a first approach as the necessary procedure to enable them to overcome their barbarianism, that is, to better adapt themselves to the natural law. This generated a philosophy of education which, in spite of being directly inspired by the circumstances of the Indians, nonetheless had permanent value by virtue of its anthropological soundness and its classical approach. This article deals with the (...) notions of barbarianism, education, natural law, and their interplay in the educational works of Bartolomé de las Casas and José de Acosta. (shrink)
This collection of essays explores what makes modern mathematics ‘modern’, where ‘modern mathematics’ is understood as the mathematics done in the West from roughly 1800 to 1970. This is not the trivial matter of exploring what makes recent mathematics recent. The term ‘modern’ (or ‘modernism’) is used widely in the humanities to describe the era since about 1900, exemplified by Picasso or Kandinsky in the visual arts, Rilke or Pound in poetry, or Le Corbusier or Loos in architecture (a building (...) by the latter graces the cover of this book’s dust jacket). (shrink)
: This introduction highlights two of Mondzain's contributions in the chapter reproduced here, "Iconic Space and the Rule of Lands." The first is her discussion of a link between images and power, which stresses the formal characteristics of paintings rather than their narratives. The second is her examination of the specific task which representation is called on to perform in religious as opposed to secular contexts, where spiritual, otherworldly figures are given physical shape and form.
It is an honor and also a pleasure to respond to the three philosophers who have devoted so much time and careful attention to reading and critiquing my paper "Nations of Immigrants: Do Words Matter?" As an interdisciplinary scholar who interacts more often with specialists in the social sciences, history, and Italian studies than with philosophers, I was unsure what to expect from the Coss Dialogue. Would it be possible to find words common enough to all that we could begin (...) to address the complex issues raised by national mythology about the United States as a nation of immigrants? I believe that our panel discussions revealed the common ground we rather quickly found. But they also uncovered a few gaping chasms .. (shrink)
