Gottlob Frege. Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl. Centenary edition of 495. With supplementary text critically edited by Christian Thiel. Felix Meiner Verlag, Hamburg1986, LXIII + 187 pp. - Christian Thiel. Einleitung des Herausgebers. Therein, pp. XXI–LXIII. - Ernst Reinhold Eduard Hoppe. Review of Frege's Die Grundlagen der Arithmetik (495). Therein, pp. 109–117. (Reprinted from Archiv der Mathematik und Physik, ser. 2 part 2 (1885), Litterarischer Bericht VII, pp. 28–35.) - Georg Cantor. Review of the same. A reprint of 651. Therein, pp. 117–119. - Ernst Zermelo. Anmerkung. A reprint of 1257. Therein, p. 119. - Gottlob Frege. Erwiderung. Therein, p. 120. (Reprinted from Deutsche Litteraturzeitung, vol. 6 (1885), col. 1030.) - Anonymous. Review of the same. Therein, pp. 120–121. (Reprinted from Literarisches Centralblatt für Deutschland, vol. 36 (1885), cols. 1514–1515.) - Rudolf Eucken. Review of the same. Therein, pp. 122–123. (Reprinted from Philosophische Monatshefte, vol. 22 (1886), pp. 421–422.) - Kurd Laßwitz. Review of the same. Therein, pp. 123–128. (Reprinted from Zeitschrift für Philosophic und philosophische Kritik, n.s., supplement to vol. 89 (1886), pp. 143–148.) - Ernst Schröder. Stellungnahme. A reprint of p. 704 of 427. Therein, pp. 128–129. - Edmund Husserl. Frege's Versuch. A reprint of VIII 59. Therein, pp. 129–134. - Heinrich Scholz. Review of the same. A reprint of 35319. Therein, pp. 134–142.

1988 ◽  
Vol 53 (3) ◽  
pp. 993-999
Author(s):  
Matthias Schirn
Keyword(s):  
Edmund Husserl ◽  
Gottlob Frege ◽  
Georg Cantor ◽  
Supplementary Text ◽  
Ernst Schröder ◽  
Ernst Zermelo

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.

Ignacio Angelelli. Vorbemerkung. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, p. VI. - Gottlob Frege. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. A reprint of 491. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. VII-XVI, 1–88. - Gottlob Frege. Anwendungen der Begriffsschrift. A reprint of 492. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 89–93. - Gottlob Frege. Ueber den Briefwechsel Leibnizens und Huygens mit Papin. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 93–96. (Reprinted from Sitzungsberichte der Jenaischen Gesellschaft für Medicin und Naturwissenschaft für das Jahr 1881, pp. 29–32.) - Gottlob Frege, Ueber den Zweck der Begriffsschrift. A reprint of 493. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 97–106. - Gottlob Frege. Ueber die wissenschaftliche Berechtigung einer Begriffsschrift. A reprint of 494. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 106–114. - H. Scholz. Anmerkungen zur “Begriffsschrift.” With explanation by the editor. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 115–116. - Edmund Husserl. Anmerkungen zur Begriffsschrift. With explanation by the editor. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 117–121. - Ignacio Angelelli. Textkritische Bemerkungen. Begriffsschrift und andere Aufsätze, by Gottlob Frege, 2nd edn., edited by Ignacio Angelelli, Georg Olms Verlagsbuchhandlung, Hildesheim1964, pp. 122–124.

1967 ◽  
Vol 32 (2) ◽  
pp. 240-242 ◽  
Author(s):  
Benson Mates
Keyword(s):  
Edmund Husserl ◽  
Gottlob Frege

Set theory

2018 ◽  
Author(s):  
John P. Burgess
Keyword(s):  
Set Theory ◽  
Georg Cantor ◽  
Late Nineteenth Century ◽  
The Status ◽  
Reverse Situation ◽  
Ernst Zermelo ◽  
Relationship Of ◽  
The Relationship ◽  
Infinite Set ◽  
Modern Mathematics

In the late nineteenth century, Georg Cantor created mathematical theories, first of sets or aggregates of real numbers (or linear points), and later of sets or aggregates of arbitrary elements. The relationship of element a to set A is written a∈A; it is to be distinguished from the relationship of subset B to set A, which holds if every element of B is also an element of A, and which is written B⊆A. Cantor is most famous for his theory of transfinite cardinals, or numbers of elements in infinite sets. A subset of an infinite set may have the same number of elements as the set itself, and Cantor proved that the sets of natural and rational numbers have the same number of elements, which he called ℵ0; also that the sets of real and complex numbers have the same number of elements, which he called c. Cantor proved ℵ0 to be less than c. He conjectured that no set has a number of elements strictly between these two. In the early twentieth century, in response to criticism of set theory, Ernst Zermelo undertook its axiomatization; and, with amendments by Abraham Fraenkel, his have been the accepted axioms ever since. These axioms help distinguish the notion of a set, which is too basic to admit of informative definition, from other notions of a one made up of many that have been considered in logic and philosophy. Properties having exactly the same particulars as instances need not be identical, whereas sets having exactly the same elements are identical by the axiom of extensionality. Hence for any condition Φ there is at most one set {x|Φ(x)} whose elements are all and only those x such that Φ(x) holds, and {x|Φ(x)}={x|Ψ(x)} if and only if conditions Φ and Ψ hold of exactly the same x. It cannot consistently be assumed that {x|Φ(x)} exists for every condition Φ. Inversely, the existence of a set is not assumed to depend on the possibility of defining it by some condition Φ as {x|Φ(x)}. One set x0 may be an element of another set x1 which is an element of x2 and so on, x0∈x1∈x2∈…, but the reverse situation, …∈y2∈y1∈y0, may not occur, by the axiom of foundation. It follows that no set is an element of itself and that there can be no universal set y={x|x=x}. Whereas a part of a part of a whole is a part of that whole, an element of an element of a set need not be an element of that set. Modern mathematics has been greatly influenced by set theory, and philosophies rejecting the latter must therefore reject much of the former. Many set-theoretic notations and terminologies are encountered even outside mathematics, as in parts of philosophy: pair {a,b} {x|x=a or x=b} singleton {a} {x|x=a} empty set ∅ {x|x≠x} union ∪X {a|a∈A for some A∈X} binary union A∪B {a|a∈A or a∈B} intersection ∩X {a|a∈A for all A∈X} binary intersection A∩B {a|a∈A and a∈B} difference A−B {a|a∈A and not a∈B} complement A−B power set ℘(A) {B|B⊆A} (In contexts where only subsets of A are being considered, A-B may be written -B and called the complement of B.) While the accepted axioms suffice as a basis for the development not only of set theory itself, but of modern mathematics generally, they leave some questions about transfinite cardinals unanswered. The status of such questions remains a topic of logical research and philosophical controversy.

Derrida and Frege

Paragraph ◽  
2018 ◽  
Vol 41 (2) ◽  
pp. 184-195
Author(s):  
Marian Hobson
Keyword(s):  
Gottlob Frege

Derrida, for reasons which he never made clear publicly, published his mémoire for the diplôme d'études supérieures only in 1990, some thirty-five years after it had been written. Had it been published much earlier, some of the dispiritingly ill-informed remarks about his work might have been avoided. The mémoire, entitled The Problem of Genesis in Husserl's Philosophy, reveals that he is, when required, perfectly able to write a standard thesis in straightforward French. And that, in particular, he is aware of the work of the great logician Gottlob Frege in its relation to Husserl.

Consciência e Intencionalidade na Fenomenologia de Edmund Husserl

2020 ◽  
Vol 20 (1) ◽  
pp. 95
Author(s):  
Ricardo Pinho Souto ◽  
José De Sá de Araújo Neto
Keyword(s):  
Edmund Husserl

O presente artigo visa discorrer sobre um dos conceitos centrais na fenomenologia husserliana: o conceito de intencionalidade. De saída, ressalta-se que a consciência é necessariamente intencional por partir da relação básica constituída pelo par indissociável sujeito/objeto. Tal conceito - intencionalidade -, põe em destaque o movimento da consciência em direção ao objeto e, mais ainda, essa propriedade cumpre um caráter universal, fazendo-se presente no funcionamento psíquico do homem.

Kontrast und Wissen

2009 ◽  
Vol 54 (1) ◽  
pp. 69-102
Author(s):  
Robin Rehm
Keyword(s):  
19Th Century ◽  
Edmund Husserl ◽  
Specific Knowledge ◽  
Max Scheler ◽  
Black And White ◽  
Black Circle ◽  
Black Cross ◽  
Definition Of ◽  
And Function ◽  
The 19Th Century

Kasimir Malewitschs suprematistische Hauptwerke ›Schwarzes Quadrat‹, ›Schwarzer Kreis‹ und ›Schwarzes Kreuz‹ von 1915 setzen sich aus schwarzen Formen auf weißem Grund zusammen. Der Typus des Schwarzweißbildes weist überraschende Parallelen zu den bildlichen Wahrnehmungsinstrumenten auf, die vom ausgehenden 18. bis Anfang des 20. Jahrhunderts in den Experimenten der Farbenlehre, physiologischen Optik und Psychologie verwendet worden sind. Die vorliegende Studie untersucht diese Parallelen in drei Schritten: Zunächst erfolgt eine allgemeine Charakterisierung des Schwarzweißbildes mit Hilfe des Kontrastbegriffs von Edmund Husserl. Des weiteren wird die Entstehung und Funktion des schwarzweißen Kontrastbildes in den Wissenschaften des 19. Jahrhunderts typologisch herausgearbeitet. Unter Berücksichtigung des Wissensbegriffs von Max Scheler wird abschließend die Spezifik des Wissens eruiert, das die Schwarzweißbilder sowohl in der Malerei Malewitschs als auch in den genannten Wissenschaften generieren. Malevich’s main Suprematist works, such as ›Black Square‹, ›Black Circle‹, and ›Black Cross‹ from 1915, consist of black shapes on white ground. Surprisingly this series of shapes strongly resembles scientific black-and-white images used for research on colour theory, physiological optics, and psychology throughout the 19th century. This paper examines the parallels between Malevich’s paintings and the scientific drawings in three steps: It first characterizes black-and-white images in general, using Edmund Husserl’s definition of the term ›contrast‹. Secondly, the paper investigates the development and function of black-and-white images as tools of perception in the sciences. It finally discusses the specific knowledge generated through Malevich’s art and through scientific black-and-white images, following Max Scheler’s phenomenological identification of knowledge.

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