rudolf carnap arend heyting johann (4 Ergebnisse)

Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Very Good + Jacket. 1st Edition. Vii, 536 Pp. Blue Cloth, Gilt. First Edition, Fifth Printing (Indicated, But Not Dated; Code 1169 On Rear Flap May Indicate A November 1969 Printing). Book Near Fine, Slight Usage, Gilt Brilliant, Ownership Signature Of Professor John T. Kearns. Dj With Some Rubbing. The Book Brings Together For The First Time An Extensive Collection Of Essays By Both Philosophers And Mathematicians On The Nature Of Mathematics; Philosophical Questions Are Discussed By Leaders In Each Field. The Selections Include The First English Translations Of Several Important Works, As Well As New Translations Of Others, And Several Articles Have Been Extensively Revised By Their Authors For This Anthology.

Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Very Good + Jacket. 1st Edition. Vii, 536 Pp. Blue Cloth, Gilt. First Edition, Second Printing (August 1964). Book Near Fine, Slight Usage, Gilt Brilliant, No Marks. Dj With Slight Rubbing. The Book Brings Together For The First Time An Extensive Collection Of Essays By Both Philosophers And Mathematicians On The Nature Of Mathematics; Philosophical Questions Are Discussed By Leaders In Each Field. The Selections Include The First English Translations Of Several Important Works, As Well As New Translations Of Others, And Several Articles Have Been Extensively Revised By Their Authors For This Anthology.

Hardcover. Zustand: Near Fine. Zustand des Schutzumschlags: Very Good + Jacket. First UK Edition. Vii, 536 Pp. Blue Cloth, Gilt. First Uk Printing (1964). The Book Brings Together For The First Time An Extensive Collection Of Essays By Both Philosophers And Mathematicians On The Nature Of Mathematics; Philosophical Questions Are Discussed By Leaders In Each Field. The Selections Include The First English Translations Of Several Important Works, As Well As New Translations Of Others, And Several Articles Have Been Extensively Revised By Their Authors For This Anthology. Book Near Fine, Slight Usage. Dj Priced 63S. Net. With Slight Rubbing.

Leipzig, Felix Meiner, 1931. The entire volume present. 8vo. Orig. printed green wrappers. Sunning to spine, and a bit of soiling and minor wear to front wrapper w. minor loss of upper layer of paper at two pages, not gone through paper. A few leaves w. marginal markings, quite discreet. Library marking to inside of front wrapper, library stamp to title-page (Mathematical Institute of the University of Amsterdam). Overall a fine and nice copy. Pp. (91) - 105 + (106) - 115 + (116) - 121. The entire volume: (2) pp., Pp. (91) - 190. First edition of the Erkenntnis-volume from the Königsberg congress of 1930, where Gödel introduced his incompleteness results and Carnap, Heyting and von Neumann held the seminal papers (here printed for the first time) that ended the "Grundlagenkrise der Mathematik" (foundational crisis of mathematics). It is also in this volume that the seminal discussions following Gödel's announcements of his results are printed for the first time ("Discussion on the Foundation of Mathematics", between Gödel, von Neumann, Carnap, Hahn, Reidemeister, Heyting, and Scholz) (Gödel, Collected Works, 1931a) as well as the article which inaugurated the logicist foundation of mathematics, in which the modern sense of "logicism" is introduced (Carnap's contribution).In Königsberg in September 1930, Gödel presented his incompleteness results, a landmark in mathematical logic, at the second congress of scientific epistemology, -a congress which proved to be a turning point in the history of philosophical and mathematical logic. It is the papers presented at this congress which are printed in the present volume, apart from the contributions by Gödel and Scholtz (which were printed elsewhere) together with the seminal discussions that followed the presentation of the papers. The groundbreaking papers that are printed here include Carnap's "Die Logizistische Grundlegung der Mathematik", which furthermore introduced the modern sense of the term "logicism", Arend Heyting's "Die intuitionistische Grundlegung der Mathematik" and Johann von Neumann's "Die formalistische Grundlegung der Mathematik" as well as papers by Neugebauer, Reichenbach and Heisenberg. The present papers, as well as the following discussion, mark a turning point in the history of logic and a cornerstone in the future development of the field. The so-called "Foundational Crisis of Mathematics" was a phase within mathematics begun in the early 20th century due to the search for proper foundations of mathematics and the uncertainty of this quest, which was supported by the many difficulties that philosophy of mathematics faced at the end of the 19th and beginning of the 20th century . The crisis took its actual beginning with the publication of Russell's "principles of Mathematics" of 1903, culminated in the 1920'ies with the main advocates of Formalism and Intuitionism respectively, Hilbert and Brouwer, in what is called the "foundational struggle of mathematics", and ended with the present volume in 1931, following the congress of 1930.With the discovery of non-Euclidean geometry in the 18th century, it became evident that not only one sort of mathematics was possible, and even that some propositions could be true in one mathematical system, but false in another. This was the actual basis for the awareness of a mathematical foundation in the mathematical public, which again was the basis for the fact that the question of the foundation of mathematics could develop -and could develop into an actual crisis. During the first 30 years of the 20th century, almost all great mathematicians worked on their answer to the question of the correct foundation of mathematics, and thus it came to a crisis that developed into a struggle. It is this struggle and crisis that Carnap, Heyting and von Neumann break in 1930, where they present the three great positions of the struggling years: logicism (Carnap), intuitionism (Heyting) and formalism (von Neumann), and it is these thr.