Brouwer versus Hilbert: 1907–1928

1998 ◽  
Vol 11 (2) ◽  
pp. 291-325 ◽  
Author(s):  
J. Posy Carl
Keyword(s):  
Twentieth Century ◽  
Current Literature ◽  
Philosophy Of Mathematics ◽  
Formal Logic ◽  
Foundations Of Mathematics ◽  
Theory Of Meaning ◽  
Classical Mathematics ◽  
And Behavior ◽  
Shed Light ◽  
The Way

The ArgumentL. E. J. Brouwer and David Hubert, two titans of twentieth-century mathematics, clashed dramatically in the 1920s. Though they were both Kantian constructivists, their notorious Grundlagenstreit centered on sharp differences about the foundations of mathematics: Brouwer was prepared to revise the content and methods of mathematics (his “Intuitionism” did just that radically), while Hilbert's Program was designed to preserve and constructively secure all of classical mathematics.Hilbert's interests and polemics at the time led to at least three misconstruals of intuitionism, misconstruals which last to our own time: Current literature often portrays popular views of intuitionism as the product of Brouwer's idiosyncratic subjectivism; modern logicians view intuitionism as simply applying a non-standard formal logic to mathematics; and contemporary philosophers see that logic as based upon a pure assertabilist theory of meaning. These pictures stem from the way Hilbert structured the controversy.Even though Brouwer's own work and behavior occasionally reinforce these pictures, they are nevertheless inaccurate accounts of his approach to mathematics. However, the framework provided by the Brouwer-Hilbert debate itself does not supply an adequate correction of these inaccuracies. For, even if we eliminate these mistakes within that framework, Brouwer's position would still appear fragmented and internally inconsistent. I propose a Kantian framework — not from Kant's philosophy of mathematics but from his general metaphysics — which does show the coherence and consistency of Brouwer's views. I also suggest that expanding the context of the controversy in this way will illuminate Hilbert's views as well and will even shed light upon Kant's philosophy.

Raqqa: The Forgotten Excavation of an Islamic Site in Syria by the Ottoman Imperial Museum in the Early Twentieth Century

2014 ◽  
Vol 30 (1) ◽  
pp. 73-93 ◽  
Author(s):  
Ayşin Yoltar-Yildirim
Keyword(s):  
Twentieth Century ◽  
Medieval Period ◽  
Archaeological Excavation ◽  
Early Twentieth Century ◽  
Archival Documents ◽  
History Of ◽  
Late Nineteenth ◽  
Islamic Archaeology ◽  
Shed Light ◽  
The Way

Raqqa, in Syria, was the only Islamic site excavated by the Ottoman Imperial Museum during its existence in the late nineteenth and early twentieth century. Although the Imperial Museum may not have been searching specifically for an Islamic site of the medieval period to excavate, its response to the plundering of Raqqa, which began as early as 1899, was to pursue an archaeological excavation in a systematic manner. Two campaigns were conducted, under the directorships of Macridy and Haydar Bey, in 1905–6 and 1908 respectively. Although not lasting more than a couple of months, they were relatively important from the perspective of the Imperial Museum and Islamic archaeology at that time. This article focuses on the history of these Raqqa excavations, namely, the reasons the Imperial Museum began excavating there, how it conducted its excavations, and, finally, the finds and the way they were displayed at the Museum. Existing archival documents on the excavation, along with the earliest inventories of the finds in the Imperial Museum and the personal letters of Macridy, all hitherto unpublished, are analyzed in order to shed light on these long forgotten excavations.

‘Grey Dawn’ in the British Pacific: Race, Security and Colonial Sovereignty on the Eve of World War I

2016 ◽  
Vol 9 (1) ◽  
pp. 32-54 ◽  
Author(s):  
Jesse Tumblin
Keyword(s):  
Twentieth Century ◽  
World War I ◽  
Military Force ◽  
Royal Navy ◽  
World War ◽  
Building Projects ◽  
Cooperative Security ◽  
Strategic Defense ◽  
Racial Discourses ◽  
The Way

This article examines the way a group of colonies on the far reaches of British power – Australia, New Zealand, Canada, and India, dealt with the imperatives of their own security in the early twentieth century. Each of these evolved into Dominion status and then to sovereign statehood (India lastly and most thoroughly) over the first half of the twentieth century, and their sovereignties evolved amidst a number of related and often countervailing problems of self-defence and cooperative security strategy within the British Empire. The article examines how security – the abstracted political goods of military force – worked alongside race in the greater Pacific to build colonial sovereignties before the First World War. Its first section examines the internal-domestic dimension of sovereignty and its need to secure territory through the issue of imperial naval subsidies. A number of colonies paid subsidies to Britain to support the Royal Navy and thus to contribute in financial terms to their strategic defense. These subsidies provoked increasing opposition after the turn of the twentieth century, and the article exlpores why colonial actors of various types thought financial subsidies threatened their sovereignties in important ways. The second section of the article examines the external-diplomatic dimension of sovereignty by looking at the way colonial actors responded to the Anglo-Japanese Alliance. I argue that colonial actors deployed security as a logic that allowed them to pursue their own bids for sovereignty and autonomy, leverage racial discourses that shaped state-building projects, and ultimately to attempt to nudge the focus of the British Empire's grand strategy away from Europe and into Asia.

Breeding Better Babies in the Eugenic Garden City: ‘Municipal Darwinism’ and the (Anti)Cosmopolitan Utopia in the early Twentieth Century

2010 ◽  
Vol 5 (2) ◽  
pp. 267-290 ◽  
Author(s):  
Susan Currell
Keyword(s):  
Twentieth Century ◽  
City Planning ◽  
Comparative Approach ◽  
Core Beliefs ◽  
Garden City ◽  
New Town ◽  
Early Twentieth Century ◽  
National Body ◽  
Practical Level ◽  
The Way

Showing how ‘modernist cosmopolitanism’ coexisted with an anti-cosmopolitan municipal control this essay looks at the way utopian ideals about breeding better humans entered into new town and city planning in the early twentieth century. An experiment in eugenic garden city planning which took place in Strasbourg, France, in the 1920s provided a model for modern planning that was keenly observed by the international eugenics movement as well as city planners. The comparative approach taken in this essay shows that while core beliefs about degeneration and the importance of eugenics to improve the national ‘body’ were often transnational and cosmopolitan, attempts to implement eugenic beliefs on a practical level were shaped by national and regional circumstances that were on many levels anti-cosmopolitan. As a way of assuaging the tensions between the local and the global, as well as the traditional with the modern, this unique and now forgotten experiment in eugenic city planning aimed to show that both preservation and progress could succeed at the same time.

Géographie et cartographie fictionnelles dans l’Utopie (1516) de Thomas More

Moreana ◽  
2010 ◽  
Vol 47 (Number 181- (3-4) ◽  
pp. 9-68
Author(s):  
Jean Du Verger
Keyword(s):  
Complex Network ◽  
Narrative Strategies ◽  
Thomas More ◽  
The Third ◽  
Editio Princeps ◽  
Shed Light ◽  
The Way

The philosophical and political aspects of Utopia have often shadowed the geographical and cartographical dimension of More’s work. Thus, I will try to shed light on this aspect of the book in order to lay emphasis on the links fostered between knowledge and space during the Renaissance. I shall try to show how More’s opusculum aureum, which is fraught with cartographical references, reifies what Germain Marc’hadour terms a “fictional archipelago” (“The Catalan World Atlas” (c. 1375) by Abraham Cresques ; Zuane Pizzigano’s portolano chart (1423); Martin Benhaim’s globe (1492); Martin Waldseemüller’s Cosmographiae Introductio (1507); Claudius Ptolemy’s Geographia (1513) ; Benedetto Bordone’s Isolario (1528) ; Diogo Ribeiro’s world map (1529) ; the Grand Insulaire et Pilotage (c.1586) by André Thevet). I will, therefore, uncover the narrative strategies used by Thomas More in a text which lies on a complex network of geographical and cartographical references. Finally, I will examine the way in which the frontispiece of the editio princeps of 1516, as well as the frontispiece of the third edition published by Froben at Basle in 1518, clearly highlight the geographical and cartographical aspect of More’s narrative.

Poetic Trespass

2014 ◽  
Author(s):  
Lital Levy
Keyword(s):  
Twentieth Century ◽  
Visual Art ◽  
Prose Poetry ◽  
Old World ◽  
History And Literature ◽  
Political Boundaries ◽  
Depth Study ◽  
Emile Habiby ◽  
The Relationship ◽  
The Way

A Palestinian-Israeli poet declares a new state whose language, “Homelandic,” is a combination of Arabic and Hebrew. A Jewish-Israeli author imagines a “language plague” that infects young Hebrew speakers with old world accents, and sends the narrator in search of his Arabic heritage. This book brings together such startling visions to offer the first in-depth study of the relationship between Hebrew and Arabic in the literature and culture of Israel/Palestine. More than that, the book presents a captivating portrait of the literary imagination's power to transgress political boundaries and transform ideas about language and belonging. Blending history and literature, the book traces the interwoven life of Arabic and Hebrew in Israel/Palestine from the turn of the twentieth century to the present, exposing the two languages' intimate entanglements in contemporary works of prose, poetry, film, and visual art by both Palestinian and Jewish citizens of Israel. In a context where intense political and social pressures work to identify Jews with Hebrew and Palestinians with Arabic, the book finds writers who have boldly crossed over this divide to create literature in the language of their “other,” as well as writers who bring the two languages into dialogue to rewrite them from within. Exploring such acts of poetic trespass, the book introduces new readings of canonical and lesser-known authors, including Emile Habiby, Hayyim Nahman Bialik, Anton Shammas, Saul Tchernichowsky, Samir Naqqash, Ronit Matalon, Salman Masalha, A. B. Yehoshua, and Almog Behar. By revealing uncommon visions of what it means to write in Arabic and Hebrew, the book will change the way we understand literature and culture in the shadow of the Israeli–Palestinian conflict.

Sed ubi Socrates currit? On the Gettier Problem before Gettier

2017 ◽  
Author(s):  
Risto Hilpinen
Keyword(s):  
Twentieth Century ◽  
True Belief ◽  
Belief System ◽  
Gettier Problem ◽  
Current Belief ◽  
The Future ◽  
Late Nineteenth ◽  
The Gettier Problem ◽  
The Way ◽  
Forward Looking

Medieval philosophers presented Gettier-type objections to the commonly accepted view of knowledge as firmly held true belief, and formulated additional conditions that meet the objections or analyzed knowledge in a way that is immune to the Gettier-type objections. The proposed conditions can be divided into two kinds: backward-looking conditions and forward-looking conditions. The former concern an inquirer’s current belief system and the way the inquirer acquired her beliefs, the latter refer to what the inquirer may come to learn in the future and how she can respond to objections. Some conditions of knowledge proposed in late nineteenth- and twentieth-century epistemology can be regarded as variants of the conditions put forward by medieval authors.

Veiling Esther, Unveiling Her Story

2018 ◽  
Author(s):  
Adam J. Silverstein
Keyword(s):  
Nineteenth Century ◽  
Twentieth Century ◽  
Case Studies ◽  
Muslim World ◽  
Historical Narratives ◽  
Modern Times ◽  
Religious Background ◽  
Literary Context ◽  
Shed Light ◽  
Selection Of

This book examines the ways in which the biblical book of Esther was read, understood, and used in Muslim lands, from ancient to modern times. It zeroes-in on a selection of case studies, covering works from various periods and regions of the Muslim world, including the Qur’an, premodern historical chronicles and literary works, the writings of a nineteenth-century Shia feminist, a twentieth-century Iranian dictionary, and others. These case studies demonstrate that Muslim sources contain valuable materials on Esther, which shed light both on the Esther story itself and on the Muslim peoples and cultures that received it. The book argues that Muslim sources preserve important, pre-Islamic materials on Esther that have not survived elsewhere, some of which offer answers to ancient questions about Esther, such as the meaning of Haman’s epithet in the Greek versions of the story, the reason why Mordecai refused to prostrate himself before Haman, and the literary context of the “plot of the eunuchs” to kill the Persian king. Furthermore, throughout the book we will see how each author’s cultural and religious background influenced his or her understanding and retelling of the Esther story: In particular, it will be shown that Persian Muslims (and Jews) were often forced to reconcile or choose between the conflicting historical narratives provided by their religious and cultural heritages respectively.

Why Phenomenology?

2018 ◽  
Author(s):  
George Pattison
Keyword(s):  
Twentieth Century ◽  
Subject Matter ◽  
Alternative Model ◽  
Phenomenological Approach ◽  
Human Existence ◽  
Present Approach ◽  
The Self ◽  
Existence Of God ◽  
Pure Intuition ◽  
The Way

This chapter sets out the rationale for adopting a phenomenological approach to the devout life literature. Distinguishing the present approach from versions of the phenomenology of religion dominant in mid-twentieth-century approaches to religion, an alternative model is found in Heidegger’s early lectures on Paul. These illustrate that alongside its striving to achieve a maximally pure intuition of its subject matter, phenomenology will also be necessarily interpretative and existential. Although phenomenology is limited to what shows itself and therefore cannot pass judgement on the existence of God, it can deal with God insofar as God appears within the activity and passivity of human existence. From Hegel onward, it has also shown itself open to seeing the self as twofold and thus more than a simple subjective agent, opening the way to an understanding of the self as essentially spiritual.

Shadow Sites

2007 ◽  
Author(s):  
Kitty Hauser
Keyword(s):  
Twentieth Century ◽  
Wizard Of Oz ◽  
The Way ◽  
John Piper

In mid-twentieth-century Britain, an archaeological vision of the British landscape reassured and enchanted a number of writers, artists, photographers, and film-makers. From John Piper, Eric Ravilious and Shell guide books, to photographs of bomb damage, aerial archaeology, and The Wizard of Oz, Kitty Hauser delves into these evocative interpretations and looks at how they affected the way the landscape was seen.

Hegel's Conception of the Study of Human Nature

1970 ◽  
Vol 4 ◽  
pp. 32-47
Author(s):  
H. B. Acton
Keyword(s):  
Twentieth Century ◽  
Human Nature ◽  
Dialectical Materialism ◽  
Philosophy Of History ◽  
Formal Logic ◽  
Human Society ◽  
Royal Family ◽  
Dialectical Method ◽  
English Speaking ◽  
The Creation

It is easy to understand why Hegel's philosophy should be little studied by English-speaking philosophers today. Those who at the beginning of the twentieth century initiated the movement we are now caught up in presented their earliest philosophical arguments as criticisms of the prevailing Anglo-Hegelian views. It may now be thought illiberal to take much interest in this perhaps excusably slaughtered royal family, and positively reactionary to hanker after the foreign dynasty from which it sometimes claimed descent. Hegel was a systematic philosopher with a scope hardly to be found today, and men who, as we say, wish to keep up with their subject may well be daunted at the idea of having to understand a way of looking at philosophy which they suspect would not repay them for their trouble anyway. Furthermore, since Hegel wrote, formal logic has advanced in ways he could not have foreseen, and has, it seems to many, destroyed the whole basis of his dialectical method. At the same time, the creation of a science of sociology, it is supposed, has rendered obsolete the philosophy of history for which Hegel was at one time admired. In countries where there are Marxist intellectuals, Hegel does get discussed as the inadvertent forerunner of historical and dialectical materialism. But in England, where there is no such need or presence, there do not seem to be any very strong ideological reasons for discussing him. In what follows I shall be asking you to direct your thoughts to certain forgotten far-off things which I hope you will find historically interesting even if you do not agree with me that they give important clues for an understanding of human nature and human society.

Sign in / Sign up

Export Citation Format

Share Document