bluuebunny/crossref_metadata_2025_split huggingface dataset:
Zur Axiomatik der elementargeometrischen Verkniipfungsrelationen (1933d)
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Man sollte das System aller jener Aussagen iiber Felder untersuchen, die in der Normalform keine Existenzprafixe enthalten. Die Begriffe Punkt und Gerade, die unter Verwendung von Existenzprafixen definierbar sind (z. B. Punkt ist ein Element, zu dem kein nicht leeres Element existiert, das sein echter Teil ist), sind in diesem engeren System undefinierbar. Untersuchungen in dieser Richtung finden sich bei Wernick (1929).
Introductory note to 1933f
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
In this short note Gödel describes an interpretation of intuitionistic propositional logic IPC in a system of classical propositional logic enriched with an additional unary operator B. The letter B stands for “beweisbar”, i.e., provable, this being the intuitive interpretation of B. Here “provable” should be understood as “provable by any correct means” and not as “provable in a given formal system” (see below).
Review of Skolem 1933a: On the impossibility of a complete characterization of the number sequence by means of a finite axiom system (1934c)
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Consider the expressions that are built up from: (1) variables x, y, ... , ranging over the natural numbers; (2) + (addition) and · (multiplication); &gt; and=; (4) the operations of the propositional calculus; (5) the quantifiers, applied to number variables. (More complicated functions, as for example xY and x!, can be defined in terms of+, · and the logical concepts cited.) The author proves that there is a system N* of entities, with two operations, + and •, defined on it and with two relations, &gt; and =, that is not isomorphic to the system N of natural numbers, but for which nevertheless all statements hold that are expressible by means of the symbols mentioned at the outset and hold for the system N. From this it follows that there is no axiom system employing only the notions mentioned at the outset (and therefore none at all employing only number-theoretic notions) that uniquely determines the structure of the sequence of natural numbers, a result that also follows without difficulty from the investigations of the reviewer in his 1931.
Review of Chen 1933: Axioms for real numbers (1934d)
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
What is presented is merely an axiom system for the notion &lt; (addition and multiplication do not occur), that is, for the order type of the real numbers. It differs from the usual characterization of this order type only in that the existence of a countable dense subset is not demanded, which of course causes the loss of completeness (categoricity). It is claimed nonetheless that the system has this property (in what sense is not clear).
Review of Carnap 1934: The antinomies and the incompleteness of mathematics (1935b)
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
In this work the author derives the consequences that result from the construction of formally undecidable propositions for the problem of antinomies of the second kind (for instance that of Epimenides). Namely, the logical flaw in these antinomies lies not in the self-referential character of certain notions and propositions occurring in them (this self-referential character, after all, also attaches, for example, to the undecidable propositions mentioned), but rather in the use of the notion “true”. That is, more precisely, it is falsely assumed that there is a notion !2U (true) such that for each sentence A the formula is provable. From the occurrence of the antinomies it can be concluded that such a notion !2U cannot be expressed in a consistent language. To be sure, every language can be extended so as to contain a notion !2U that satisfies (1) for all sentences A of the original language, but not so that (1) holds for the sentences of the extended language as well. Every formal system is thus incomplete in two respects: 1° insofar as there are propositions undecidable within it, and 2° insofar as there are notions that cannot be defined within it (such as !2U or the number sequences constructed by the diagonal method). Thus we are led to conclude that, although everything mathematical is formalizable, it is nonetheless impossible to formalize all of mathematics in a single formal system, a fact that intuitionism has asserted all along.
Discussion remark (1936)
Authors: Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Actually, for each individual entrepreneur the demand also depends on his income, and that in turn depends on the price of the factors of production. One can formulate an appropriate system of equations and investigate whether it is solvable.
Collected Works
Authors: Gudel Kurt 
Published: November 2023

Abstract
Kurt Gudel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein’s equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gudel’s publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gudel’s Nachlass. These long-awaited final two volumes contain Gudel’s correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gudel’s Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gudel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gudel’s work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.
Introductory note to 1938, 1939, 1939a and 1940
Authors: Gudel Kurt 
Published: November 2023

Abstract
The papers discussed in this introductory note deal with Gudel’s proof of the relative consistency of the axiom of choice and of the generalized continuum hypothesis with the usual axioms for set theory. The note 1938 announces the results and gives a brief discussion of the ideas un derlying their proofs; 1939 is an abstract in which the results are again announced. The paper 1939a gives considerable technical detail con cerning the proofs; essentially complete proofs, along somewhat different lines, are presented in 1940.
The consistency of the axiom of choice and of the generalized continuum hypothesis (1938)
Authors: Gudel Kurt 
Published: November 2023

Abstract
The method of proof consists in constructing on the basis of the axioms of T a model for which the propositions 1-4 are true. This model, roughly speaking, consists of all “mathematically constructible” sets, where the term “constructible” is to be understood in the semi-intuitionistic sense which excludes impredicative procedures. This means “constructible” sets are defined to be those sets which can be obtained by Russell’s ramified hierarchy of types, if extended to include transfinite orders.
Introductory note to 1946
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
In 1946, the year of its bicentennial, Princeton University organized several conferences. The conference on problems of mathematics took place on 17-19 December 1946. Its more than seventy participants in cluded most of the leading American mathematicians and several from abroad. Its sessions included discussions of practically the whole range of pure mathematics. The university printed a pamphlet containing a summary of the discussion in each of the sessions (Princeton University 1947). Alfred Tarski was listed as “discussion leader” in the session on mathematical logic, held on 17 December, and evidently gave the principal invited talk. Gudel’s remarks took their point of departure from Tarski’s talk, and may have been invited or planned as a comment.
Remarks before the Princeton bicentennial conference on problems in mathematics (1946)
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Tarski has stressed in his lecture (and I think justly) the great importance of the concept of general recursiveness (or Turing’s computability). It seems to me that this importance is largely due to the fact that with this concept one has for the first time succeeded in giving an absolute definition of an interesting epistemological notion, i.e., one not depending on the formalism chosen. In all other cases treated previously, such as demonstrability or definability, one has been able to define them only relative to a given language, and for each individual language it is clear that the one thus obtained is not the one looked for. For the concept of computability, however, although it is merely a special kind of demonstrability or decidability, the situation is different. By a kind of miracle it is not necessary to distinguish orders, and the diagonal procedure does not lead outside the defined notion. This, I think, should encourage one to expect the same thing to be possible also in other cases (such as demonstrability or definability).
Introductory note to 1947 and 1964
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Cantor’s continuum problem served as one of the principal and periodic foci for Gudel’s research from 1935 until his death more than four decades later. His article 1947 (substantially revised and expanded to become 1964) originated from a request, made in 1945 by the editor of the American mathematical monthly, for a paper on the continuum problem. The result was an expository article written in the style for which the Monthly is well known, but having a flavor that reflected Gudel’s distinctive blend of mathematical and philosophical interests. Although 1947 contains no new technical results, it gives considerable insight into his philosophical views on set theory and on what would and would not, in his opinion, constitute a solution to the continuum problem. In one sense, 1947 can be regarded as a continuation, and as a variation in a different key, of his reflections in 1944 on Russell and mathematical logic.
Introductory note to 1958 and 1972
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
Gudel’s “Dialectica paper” appeared in 1958, in German, in honor of P. Bernays’ 70th birthday; it is reproduced, following this introductory note, together with a translation into English by Stefan Bauer Mengelberg and Jean van Heijenoort. The ideas in this paper date back at least as far as 1941, since Gudel lectured at that time on his interpretation at Princeton and Yale. (In Gudel’s Nachlass there is the text of a lecture, “In what sense is intuitionistic logic constructive?”, given at Yale University on 15 April 1941.)
Über e1ne bisher noch nicht benützte Erweiterung des finiten Standpunktes (1958)
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
P. Bernays hat wiederholt darauf hingewiesen, dass angesichts der Tat-sache der Unbeweisbarkeit der Widerspruchsfreiheit eines Systems mit geringeren Beweismitteln als denen des Systems selbst eine Überschreitung des Rahmens der im Hilbertschen Sinn finiten Mathematik nötig ist, um die Widerspruchsfreiheit der klassischen Mathematik, ja sogar um die der klassischen Zahlentheorie zu beweisen.
Postscript to Spector 1962 (1962)
Authors: Gudel Kurt , Feferman Solomon , Dawson John W , Kleene Stephen C , Moore Gregory H , Solovay Robert M , Heijenoort Jean van 
Published: November 2023

Abstract
This important paper [ Spector 1962] was written by Clifford Spector during his stay at the Institute for Advanced Study in 1960 1961 under a grant from the Office of Naval Research. The discussions P. Bernays and I had with Spector (see footnote 1) took place after the main result (contained in §10 of the paper) had been established already. However, it ought to be mentioned that during the time Spector first established this result he was in close contact with Kreisel. It was Spector’s express intention to give to Kreisel a good deal of credit for his work. Originally a joint publication by Spector and Kreisel was envisaged. This plan was dropped because Spector had taken over the elaboration by himself and because the version of the proof which was to be published was due to Spector. Also Spector alone, at that time, was working on an extension of the result in the direction of stricter constructivity which he hoped to include in his paper.
Introduction to the Expanded Edition
Authors: Davidson Cathy N 
Published: November 2023

Abstract
When I began the research for Revolution and the Word in the 1970s, two stereotypes prevailed about early American fiction. The first assumption was that it did not exist. This isn’t true. Although most survey courses and anthologies of American fiction at the time began with James Fenimore Cooper’s Leatherstocking Saga of the 1820s or sometimes with Wieland by Charles Brockden Brown, at least one hundred novels were produced in America between 1789 and 1820. Novelists of the early national period read one another and often responded to one another’s plots. Readers avidly sought out novels. Publishers and proprietors of lending libraries advertised novels prominently as a way to attract readers to buy or borrow other kinds of books. Nonfiction authors of advice books, primers, histories, tracts, or sermons took up novelistic techniques or even claimed to be novelists as a way to reach the wider novel-reading public.
Ideology And Genre
Authors: Davidson Cathy N 
Published: November 2023

Abstract
This wandering son of the new Republic come home again is especially struck by the “extreme avidity with which books of mere amusement [are] purchased and perused by all ranks.”1 And Tyler’s fictional comments are by no means thenly observations on this remarkable new interest in fiction. As the editor of New York Magazine decisively proclaimed in 1797, “This is a novel-reading age.” In chapter 2, I focused on the manufacture of fiction at the dawning of the Industrial Revolution and, correspondingly, on the economic origins of the American novel. I traced how the form first appeared in a transitional society, preindustrial in its modes of production yet protocapitalistic in its modes of consumption, and I surveyed how the new genre along with its early producers—individual authors and enterprising printers-survived financially in a postcolonial world that merely presaged mass book production and mass consumption. In this chapter, my focus is on the politics of genre and, more specifically, on the ideological position that the novel as a genre was perceived to take in the aftermath of the Revolutionary War—a vital and volatile time when the ideals of the nation had to be formulated and promulgated. I ask how the new form survived in a society that, on the highest levels, was intensely hostile to its appearance.
The Picaresque And The Margins Of Political Discourse
Authors: Davidson Cathy N 
Published: November 2023

Abstract
A number of novelists of the early national period turned the essentially conservative subgenre of the sentimental novel (with its fetishization of female virginity) to a subversive purpose by valorizing precisely those women whom the society had either overtly condemned (the fallen woman) or implicitly rendered invisible (woman as feme covert). Yet even the most progressive sentimental novels still focused primarily on women’s restricted familial role. Within the confines of the novel and the society, women only sporadically and peripherally entered into the political discourse of the era, either as objects of the debate or participants in it. Certainly a number of sentimental novels (such as The Coquette and The Power of Sympathy) include scenes in which female characters discuss political issues, but given the Constitutional silencing of women, this fictive act is just that-a fiction. Lacking any legal standing, women’s political opinions could be dismissed as easily as John Adams dismissed his wife’s plea. “Every man, by the Constitution, is born with an equal right to be elected to the highest office,” the Reverend John Cosens Ogden of Portsmouth, New Hampshire, declaimed in 1793. “And every woman, is born with an equal right to be the wife of the most eminent man.”1 No wonder sentimental fiction remained closeted, circumscribed by home and hearth.
Early American Gothic: The Limits Of Individualism
Authors: Davidson Cathy N 
Published: November 2023

Abstract
The humor and the title of Royall Tyler’s popular play The Contrast both derive from the sustained juxtaposition of innocent American values with urbane but corrupt European ones. That contrast is, in effect, an early American variation of what Raymond Williams has schematized in English literature as The Country and the City. In Tyler’s play Colonel Henry Manly (consistent with his name) is early portrayed as a representative American man—honest, direct, and forthright. He is compared to the more dubiously named Billy Dimple, who has been to Europe, where he has squandered his inheritance in the pursuit of fashion and European sophistication. This second character quotes Chesterfield and copies the forms of gentility but has little concern for the substance of morality. That same opposition is also played out in a minor key. Manly’s country servant, Jonathan, is, at first, tempted by luxury, but he remains essentially a good, earnest, solid, and stolid Yankee, while Billy’s servant, Jessamy, who is foppish and irresponsible, is a more openly materialistic and misogynistic parody of his master, Dimple. The unfolding play then complicates these contrasts, showing that Dimple is hardly the sophisticate he pretends to be and that Manly, more ambiguously, might not be all that he first seems either. He is, after all, a prig; his American patriotism is a self-parody; his speech, like the campaign slogans of the era, is too full of itself.
Afterword: Texts as Histories
Authors: Davidson Cathy N 
Published: November 2023

Abstract
Friedrich von Schiller, one of the most eminent historians of the late eighteenth century, was carried into the lecture hall in Jena upon the shoulders of enthusiastic admirers who deposited him at the podium where he would answer, once and for all, a question he had raised before: “What Is Universal History and Why Do We Study It?” Universal History, Schiller explained, discovered in the past a vast network of causal relationships that, with relentless logic, produced the present. It was the task of the Universal Historian to chart out those causalities in order that the reader might see the coherent whole that was modern Europe, might understand how previous events had produced a stable Continental society that enjoyed an enduring peace and that promised (history portended as much) to last forever. Schiller’s speech on that May day in 1789 was constantly interrupted by cheers from the crowd, who could not foresee, any more than the Universal Historian, that in less than two months another crowd would storm the Bastille and launch Europe into its most revolutionary epoch.
Mythic Timelines
Authors: Read Kay Almere , González Jason J 
Published: November 2023

Abstract
Mythic timelines are based in both tangible and intangible worlds. On the one hand, the idea of time is founded on actual human experiences of tangible change. After all, we all experience a great deal of unavoidable transformation from birth to death. As babies we are not the same as when we are children; and as children, we are not exactly like what we will be as young adults. We change when we marry and have children of our own, and again when we reach the age at which our children care for us.
Honor and Sacredness in the Roman and Christian Worlds
Authors: Barton Carlin 
Published: November 2023

Abstract
The Romans in the late Republic and early Empire endured, for the most part, a universe without salvation. The gladiator and the Christian who eyed one another across the colored sands of the arena were separated by a chasm as profound as that dividing mortal and immortal in the Iliad of Homer. Perpetua would receive eternal life; the gladiator who slew her would not. But when Perpetua guided the gladiator’s trembling hand to her throat, she was speaking to him in a language he knew well, one expressing the ancient and adamantine bond between honor and the sacred. The following essay will explore aspects of Roman concepts of honor, sacrifice, and the sacred that linked the condemned Roman to the imperishable Christian.
Contemplative Death in Jewish Mystical Tradition
Authors: Fine Lawrence 
Published: November 2023

Abstract
A feature normally assumed essential to martyrdom is that it results in physical death. This essay, however, focuses on a variety of traditions in which martyrdom has to do with something other than actual dying. In certain Jewish mystical traditions, particularly medieval Kabbalah and Eastern European Hasidism, we discover a range of rituals that encourage the practice of contemplative or imagined martyrdom. The study of such traditions expands our conception of the meaning of religious martyrdom.
The Name and the Scar
Authors: Ellmann Maud 
Published: November 2023

Abstract
According to Australian Aboriginal legend, the demigod Wondjina created the world of things by giving them names. Intoxicated with his power, he named and made so many things that the universe could not contain his nomenclature. His father “cut out his mouth” to stop the clutter. How does one cut out a mouth? Pictures of Wondjina show a holeless face, the mouth wiped out without a scar, but the eyes gape wide with horror.
The Pisan Cantos are haunted by the figure of this mouthless god, punished for the incontinence of his creations. At the time of their writing, Pound himself had been arrested for his crimes of speech, specifically his fascist propaganda broadcasts for Rome Radio. Caged by the Americans at Pisa at the end of World War II, he symbolically castrated his own mouth by taking a vow of silence. In Canto 74, Pound splits Wondjina's name into two halves—Ouan Jin—as if to re-inflict the mutilation of the namer on the name.