Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, (...) focussing primarily on propositional logic, and to put them in their historical context. It is argued that truth-value semantics, syntactic ("Post-") and semantic completeness, decidability, and other results were first obtained by Hilbert and Bernays in 1918, and that Bernays's role in their discovery and the subsequent development of mathematical logic is much greater than has so far been acknowledged. (shrink)

Name der Zeitschrift: Nietzsche-Studien Jahrgang: 44 Heft: 1 Seiten: 490-493.

Name der Zeitschrift: Nietzsche-Studien Jahrgang: 46 Heft: 1 Seiten: 242-242.

ABSTRACT This article addresses shortcomings in the way that philosophers and cultural critics have considered propaganda by offering a new genealogical account. Looking at figures such as Marx, Adorno, Marcuse, Habermas, Bourdieu, and Stanley, this article finds that their consideration of propaganda has not necessarily been wrong but has missed some of the most significant and important functions of propaganda. This text draws on archival and published materials from propagandists, most notably Edward Bernays, to elaborate a new governmentality of (...) propaganda and public relations. Through focusing on the concept of public opinion, I argue that propaganda is best thought of as an apparatus whose function it is to construct, modify, counter, and destroy relations of force within public opinion in order to produce the subjectivities and conduct that propagandists and their clients desire. (shrink)

This article frames Trump's politics through a genealogy of propaganda, going back to P.T. Barnum in the 19th century and moving through the crowd psychologist Gustave Le Bon and the public relations counsel Edward Bernays in the 20th. This genealogy shows how propaganda was developed as a tool by eager professionals who would hire themselves to the elite to control the masses. Trump’s propaganda presents a break in that he has not only removed professionals from control over his propaganda, (...) he has mobilized it as a force against them. His lower and middle class supporters may not materially gain from Trump’s politics, but they get to vent their ressentiment on the professional class and see them too become the targets of propagandistic control. Ultimately, the conflict between working class whites, those without college degrees, and professionals earns little for its participants and occludes the role that elites play in class dynamics in the United States. This article adds substance and context to the claims that Trump’s appeal is anti-professional while showing that the claims that his supporters are ‘voting against their interests’ does not reflect the real psychological benefits many Trumpists get from supporting him. (shrink)

This study attempts to reconstruct Nietzsche’s reading of Aristotle in the 1860s and 1870s—the years before he left his career as a philologist. Against the popular view that Nietzsche read only one book by Aristotle, namely the Rhetoric, the present study hopes to show that he had direct knowledge of several of Aristotle’s main works, while much of his interest in Aristotle centred on the latter’s account of art. The particular aim of this study is to explore how Nietzsche’s reading (...) of Aristotle contributed to the formation of The Birth of Tragedy. It will show that, although Nietzsche mentions Aristotle in his first book only en passant, his theory of tragedy should be understood against the background of Aristotelian poetics, especially as interpreted by such contemporaries as Jacob Bernays, Joseph Hubert Reinkens, and Gustav Teichmüller. (shrink)

Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...) áreas fundamentales de la matemática, su aplicación en la lógica de primer orden, así como una breve descripción de las pruebas de consistencia relativa debidas a Gödel y Cohen, las cuales establecieron su independencia del sistema axiomático Zermelo-Fraenkel (ZF). Con todo lo anterior mostraremos cómo el quehacer matemático contemporáneo se adscribe al platonismo matemático en los términos de Bernays y Ferreirós. Revisaremos también los argumentos de Zermelo y Cantor para permitir el uso de asunciones en la matemática, los cuales se acercan a los planteamientos de la investigación científica y esbozan relaciones con la filosofía de la práctica matemática. Finalmente, justificamos el uso del axioma de elección en la contemporaneidad, abogando por unas relaciones de equidad entre la matemática y la filosofía, presentando además su plena vigencia, a través de la referencia a algunos problemas abiertos en la actualidad que vinculan el axioma de elección con la teoría de Ramsey. (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that the truth-paradoxes (...) and the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far (...) received little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

Most of the recent work on propaganda in philosophy has come from a narrowly epistemological standpoint that sees it as flawed messaging that negatively impacts public reasonableness and deliberation. This article posits two problems with this approach: first, it obscures the full range of propaganda's activities; and second, it prevents effective ameliorative measures by offering an overly truncated assessment of the problems to be addressed. Following Ellul and Hyska, I argue that propaganda aims at shaping actions and not just beliefs, (...) and that the propaganda activities that shape action include modifying beliefs but also much more. Examining this larger set of activities results in a shift in how we conceptualize the way that propaganda works. In particular, I add a novel argument that propaganda works by creating and reshaping publics, transforming who they are and their characteristic action. This article concludes that a more complete philosophical account of propaganda cannot just draw on epistemology but must also call on the tools of social ontology and political philosophy to create a more robust critical account. (shrink)

REVIEW OF: Automated Development of Fundamental Mathematical Theories by Art Quaife. (1992: Kluwer Academic Publishers) 271pp. Using the theorem prover OTTER Art Quaife has proved four hundred theorems of von Neumann-Bernays-Gödel set theory; twelve hundred theorems and definitions of elementary number theory; dozens of Euclidean geometry theorems; and Gödel's incompleteness theorems. It is an impressive achievement. To gauge its significance and to see what prospects it offers this review looks closely at the book and the proofs it presents.

Premier ouvrage de l’histoire de la philosophie à être totalement consacré au concept d’entéléchie, il ne s’agira pas de proposer un essai historique allant de la mise en place de cette notion chez Aristote jusqu’à la conception biologique développée par Hans Driesch. Inscrit dans un projet plus global de compréhension du temps aristotélicien, c’est à une véritable refondation métaphysique du concept que ce travail nous convie. Si Kant, à l’ultime fin de sa première critique, avait admis qu’il n’existait que deux (...) voies possibles de fondation de l’a priori - la voie historique (platonicienne) empruntée par Hegel et la voie physiologique (aristotélicienne) qui sera la nôtre - la première partie de ce second volume prendra pour acquis qu’il n’existe pas de théorie qui puisse unifier ces deux pôles du savoir. Cela impliquera une scission entre deux mouvements irrationnels que sont le mouvement entéléchique aristotélicien et le mouvement dialectique platonicien. A partir du corps a priori du surhomme, le premier mouvement sera à la racine de la théorie de la connaissance (De la science) alors que le second sera au fondement de la théorie des valeurs (De l’Idéologie). En circonscrivant le mouvement dialectique dorien autour du noûs perse (iranien), ce travail offrira une première définition totalement négative du mouvement entéléchique appuyé, lui, sur le noûs ionien (« phénicien ») dont la seconde partie sera l’objet. De l’analyse de la substance première en passant par l’étude phénoménologique des schèmes de la camusité et du membre moteur, cette étude reviendra sur l’élasticité du tendon afin d’approcher non-phénoménalement le concept lui-même et tenter ainsi une première symphyse avec les rythmes circadiens de la biologie contemporaine. (shrink)