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[GÖDEL] & CARNAP, RUDOLF + AREND HEYTING + JOHANN v. NEUMANN, etc.

[Bericht uber die 2. Tagung für Erkenntnislehre der exakten Wissenschaften Königsberg 1930]. Die Logizistische Grundlegung der Mathematik + Die intuitionistische Grundlegung der Mathematik + Die formalistische Grundlegung der Mathematik. [In: Erkenntn... - [ENDING THE FOUNDATIONAL CRISIS OF MATHEMATICS]

Herman H. J. Lynge & Søn A/S
lyn38312
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 three papars that pave the way for the discussion that follows, "Diskussion zur Grundlegung der Mathematik", between Gödel, Hahn, Carnap, Heyting, von Neumann, Reidemeister, and Scholz. They all presented their positions in the most conciliatory manner, out of the comprehension that all parties who had contributed to the crisis had also contributed because they wanted to solve it, and because they were also searching for the best possible foundation. It is also this comprehension that Hilbert takes over, when he, in his program, sets out to prove the contradiction-freedom of infinite mathematics on the basis of finite arithmetic.Thus, the seminal papers in the present volume once and for all ended the foundational crisis of mathematics and any fear of new antinomies.
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Orations on Philosophy and Education. (Cambridge…
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MELANCHTHON, PHILIP. - SACHIKO KUSUKAWA (ED.) & CHRISTINE F. SALAZAR (TRANSL.)
Herman H. J. Lynge & Søn A/S
lyn62729
Cambridge University Press, 1999. 8vo. Hardback. Slight wear to capitals. Ownership signature and notes in pencil to inside of front board. A few scattered marginal notes and underlinings in text in pencil. XXXIX, 272 pp.
Vorträge und Aufsätze.  - [PRESENTATION-COPY OF…
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HEIDEGGER, MARTIN.
Herman H. J. Lynge & Søn A/S
lyn62680
Pfullingen, Günter Neske, (1954). 8vo. Original full black cloth with white lettering to spine. Very clean, bright, and fresh, also internally. Original orange dust-jacket with black lettering to spine and white lettering to front. Minimal edge wear. An excellent and clean dust-jacket with just minor signs of wear. Very slight soiling to title-page, otherwise no wear or markings to text. Letter from Heidegger inserted to inside of front board. Front free end-paper signed and dated by Heidegger and with an inserted note in ink from the person that Heidegger gave the book to stating that this highly personal memento from his student time in Freiburg and his memorable encounters with Heidegger was given to his son Matthias for his 40th birthday, in 1995. 283, (1) pp. First edition, presentation-copy signed by Heidgger and with an inserted letter, also signed and dated by Heidegger, of this seminal collection of lectures and essays, which was of decisive importance to the immense influence of Heidegger’s thinking upon post World War Europe. This collection of Heidegger’s lectures and essays contains such groundbreaking works as “Die Frage nach der Technik” (The Question Concerning Technology) and “Wissenschaft und Besinnung” (Science and Reflection), “”Dichterisch Wohnet der Mensch…” “, along with other important works written between 1936 and 1953 collected here for the first time. This collection would later be reprinted and serve as volume 7 of Heidegger’s collected works (the Gesamtausgabe). This copy is signed “Martin Heidegger” and dated (1954 – the year of publication) to the front free end-paper, and on the inside of the front board is inserted an autograph signed letter in Heidegger’s hand to “Sehr geehrter Herr Doktor” (honourable doctor), in which Heidegger asks to meet up the following day, suggesting different times of the day. The letter is dated Freiburg 10th of February, 1954, which is two days before Heidegger gave his groundbreaking lecture “The Question Concerning Technology” at the University of Freiburg, suggesting that the letter was given to someone attending the lecture, possibly someone with whom he wanted to discuss it beforehand. “The Question Concerning Technology” still serves as one of the most pertinent philosophical essays of modern time, foreshadowing what is arguably the greatest philosophical and moral dilemmas that we struggle with today due to modern technology. Heidegger begins with asking the question what technology is, in an attempt to fully understand its essence and to ultimately prepare a free relationship to it – a theme that could hardly be more relevant today. “As relevant now as ever before, this accessible collection is an essential landmark in the philosophy of science from one of the most profound thinkers of the twentieth century (New York Times). The advent of machine technology has given rise to some of the deepest problems of modern thought. Featuring the celebrated essay The Question Concerning Technology, this prescient volume contains Martin Heidegger's groundbreaking investigation into the pervasive enframing character of our understanding of ourselves and the world.” (Harper Collins: The Question Concerning Technology And Other Essays By Martin Heidegger, 2013). “Science and Reflection” (here published for the first time), a lecture delivered on August 4, 1953, to a small circle of attendees, is Heidegger’s meditation on the difference between science and “mindfulness”, and an as-relevant-as-ever attempt at uniting science as such, in itself, with its application and meaning, combatting scientific fragmentation. In line with the other foreshadowing lectures, “Dichterisch wohnet der Mensch”, given on October 6, 1951, in Bühlerhöhe, seeks to explore how to reach a peace or dwelling in a modern, technological world. Heidegger uses the quote by Hölderlin to explore how human existence is deeply intertwined with language and poetry and reaches the conclusion that to truly dwell is to live in a poetic way, allowing for the meaningful unfolding of the world through language. The other essays/lectures printed in this seminal volume are: Überwindung der Metaphysik (1936-1946) Wer ist Nietzsches Zarathustra (1953) Was heißt Denken? (1952) Bauen Wohnen Denken (1951) Das Ding (1950) Logos (Heraklit, Fragment 50) (1951) Moira (Parmenides, Fragment VIII, 34-41) (1952) Aletheia (Heraklit, Fragment 16) (1954)
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CHRISTIANSON, JOHN ROBERT.
Herman H. J. Lynge & Søn A/S
lyn62730
Cambridge University Press, 2000. 8vo. In the original blue cloth publisher's binding with gilt title to spine and front board. With the original dust jacket. Insignificant wear to capitals. Ownership signature to inside of front board. Internally clean. XII, 451 pp.
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BAXTER, RICHARD. - WILLIAM LAMONT (ED.)
Herman H. J. Lynge & Søn A/S
lyn62731
Cambridge University Press, 1994. 8vo. In the original red cloth publisher's binding with gilt title to spine. With the original dust jacket. Ownership signature to inside of front board. Internally clean. XXXI, 254, (2) pp.
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FONTENELLE
Herman H. J. Lynge & Søn A/S
lyn62726
Dijon, Imprimerie de P Causse, An 2 (1793). 8vo. In contemporary half calf. Wear to extremities. Ex-libris pasted down to pasted down front end-paper and previous owner's name to front free end-paper. First and last leaves with light browning and a small stain to upper margin, but generally internally nice and clean. (4), 291 pp.
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SMITH, L.
Herman H. J. Lynge & Søn A/S
lyn62722
Fridericia, Kongl. privil. Adressecontoirs Bogtrykkerie, 1787. 8vo. In contemporary full sprinkled calf with five raised bands and richly gilt spine. Edges of boards with wear and leather on spine cracked. (32), 368, (1) pp. First edition of this scarce publication issued in the aftermath of the catastrophic Vejle fire of 23 April 1786, which destroyed much of the town. The book is a collection of religious sermons, published with the purpose of raising funds to aid the impoverished citizens of Vejle who had lost their homes and livelihoods in the fire.
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