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Plato's Ghost: The Modernist Transformation of Mathematics
"Plato's Ghost" is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music. Jeremy Gray traces the growth of mathematical modernism from its roots in problem solving and theory to its interactions with physics, philosophy, theology, psychology, and ideas about real and artificial languages. He shows how mathematics was popularized, and explains how mathematical modernism not only gave expression to the work of mathematicians and the professional image they sought to create for themselves, but how modernism also introduced deeper and ultimately unanswerable questions.
"Plato's Ghost" evokes Yeats's lament that any claim to worldly perfection inevitably is proven wrong by the philosopher's ghost; Gray demonstrates how modernist mathematicians believed they had advanced further than anyone before them, only to make more profound mistakes. He tells for the first time the story of these ambitious and brilliant mathematicians, including Richard Dedekind, Henri Lebesgue, Henri Poincar, and many others. He describes the lively debates surrounding novel objects, definitions, and proofs in mathematics arising from the use of nave set theory and the revived axiomatic method--debates that spilled over into contemporary arguments in philosophy and the sciences and drove an upsurge of popular writing on mathematics. And he looks at mathematics after World War I, including the foundational crisis and mathematical Platonism.
"Plato's Ghost" is essential reading for mathematicians and historians, and will appeal to anyone interested in the development of modern mathematics.
528 pages, Hardcover
First published January 1, 2008
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Jeremy Gray
56 books8 followersLibrarian Note: There is more than one author in the Goodreads database with this name.
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August 6, 2020
As for the enigmatic title, see the poem by Yeats quoted in the frontispiece.
The recognized historian of science Jeremy Gray in Plato’s Ghost contends that mathematics in the late nineteenth and early twentieth centuries went through a modernist phase allied with contemporary movements in literature and the arts. In general, this reviewer has a pre-modern mentality, but in what concerns mathematics he is very much a modernist—little inconsistencies like this are what make life interesting! Modernism represents a legitimate development of the desire to know, and once the mind has been opened to it there can be no going back, as if it did not exist. Gray’s book is interesting as far as it goes, but frustrating in that he limits himself to description of other people’s work. To come up with philosophical arguments of one’s own is another gift entirely than scholarship.
Synopsis: what does modernism mean? As far as the mathematical context of concern to this author goes, it involves a handful of related elements: first, a commitment to an exploration of ideas dictated by strictly internal criteria. The role of external motivation, coming from physics say, is to be minimized. Second, greater attention to formal properties as against content, taken by itself. Third, a more demanding standard of rigor than was conventional up to then. As readers of the companion review by this recensionist on Amir Alexander’s Duel at Dawn will notice, some of these themes crop up even earlier, in what Alexander depicts as a Romanticist turn during the first half of the nineteenth century. Gray devotes some space to explaining why, in his judgment, his putative modernist transformation represents something new (investigation of the figure of Cauchy, who, though indeed associated with an increased stress on rigor, has a pre-modern mathematical ontology). A good illustration of the emerging style can be had in Lebesgue’s theory of measure, which he worked out for his doctoral thesis in 1902. Basing himself on research by Jordan and Borel from the 1880’s to 1890’s, Lebesgue sets forth a set of axioms by which to characterize the measure (or in Jordan’s terms, content) of a set, and then shows that the measure so defined is essentially unique and agrees with Jordan’s outer content. Armed with these definitions, Lebesgue introduces the notion of a measurable function and radically recasts the concept of the integral. The Lebesgue integral coincides with Riemann’s when the latter exists, as any reasonable concept of integral should, but is more versatile and has far more desirable properties with respect to its limit under a sequence of functions (vide Fatou’s lemma and the Lebesgue dominated convergence theorem) – so much so that mathematicians have adopted Lebesgue’s ideas as the de facto standard in real analysis ever since. Gray is correct to see this development as emblematic of the modernist spirit.
Gray’s book weighs in as a hefty tome, although he disclaims an ambition to write a complete history of mathematics around the turn of the twentieth century (1890-1930). The first chapter consists in a diachronic overview of modernism in various branches of mathematics, keeping in mind trends in ontology, epistemology, psychology and language. The change in philosophy, or path out of Kant to Fries and Herbart and other later figures, gets a short notice, as does the path to logic and logical formalism. The concluding sections of sociological observations on professionalization in the mathematical community elicit little response from this reviewer (as will be the case for corresponding sections in later chapters; it seems maladroit to mix intellectual with intrinsically less-interesting sociological history).
The reader will enjoy the detour in chapter two on the state of mathematics during the nineteenth century, prior to modernism. We get a précis of the work of numerous figures, both well known and obscure. All this merely sets the stage for the arrival of modernism proper in chapter three. Again, Gray surveys in a somewhat scattershot manner the trends in contemporary geometry, algebra, logic and set theory, with good coverage of the philosophical views of the principal players (not just names anyone would have heard of to some extent, such as Cantor, Dedekind, Kronecker, Hilbert and Frege, but also many others known only to specialists, such as du Bois-Reymond, Trendelenburg, Lotze and Erdmann). While, of course, it is pleasant to feast upon the ideas under contestation, it can also be tantalizing, in that space permits only a few pages each to sum up entire treatises.
Gray continues in much the same vein in the meatiest part of his book, chapter four on ‘modernism avowed’. Again, we get a whirlwind of names of mathematicians, both among those famous and those overlooked today, and discussion of a multiplicity of philosophical views. Topics include, inter alia, abstract Italian algebraic geometry, Poincaré’s geometric conventionalism and French modernism in analysis.
It is hard for this reviewer to discern Gray’s authorial intention in the succeeding two chapters, on connections to physics, language and psychology. Hasn’t he already established his thesis on the advent of a modernist movement in the lengthy fourth chapter? Isn’t Gray at odds with himself in these two further chapters, in as much as, supposedly, the modernist spirit is to set aside any connections to phenomena in the outside world and to proceed solely on internal criteria? Yet, as he acknowledges and documents, mathematicians were not content to relinquish contact with these external fields. So much, so good for them; but doesn’t this imply a retraction, or at the minimum a complication of Gray’s main thesis? Gray himself devotes such scant attention to this question that we cannot seek for an answer to it from him.
The remainder of the book is taken up with chapter seven on the interwar period, when a great debate on the foundations of mathematics raged. Gray implies that it is necessary to follow the history of modernism, well established before the first world war as the reader will have seen in chapter four, into the interwar period, but omits to say just why. Thus, the discussion of Brouwer, Weyl, Gödel and Turing, while interesting in its own right, fails to cast much light on the overall thesis Gray wishes to advance. For this reviewer, the best sections of this concluding chapter are the third and fourth, on the rise of mathematical Platonism and the question of whether modernism ‘won’ in the mathematical community, respectively. Unfortunately, the author declines to spell out what Platonism has to do with modernism, per se. Likewise, he cops out on the question of whether modernism won, merely suggesting that both modernist and non-modernist strands can persist in parallel and that the balance between the two can vary with prevailing fashions. Would that Gray would take a definite stand, but he is too much of a historian to want to commit himself to an evaluative judgment. Nevertheless, his discussion in these two sections is informative and he does close on a satisfying note, with three extended block quotations from participants in the developments Gray reviews, one by Emil Post and two by Gödel. This reviewer finds them very thought-provoking.
In all, the reader of Gray’s monograph can expect pericopes on many of the noteworthy developments in the mathematical world during its modernist phase, but exiguous conceptual analysis or critical argumentation (something at which Max Jammer excels when in good form). The organization of the work is somewhat diffuse and disconnected, in view of the large number of topics it treats with little in the way of systematic synthesis. To this recensionist, Gray does largely succeed in making his case for a modernist transformation of mathematics. It is a rather limited objective, though: why should we care? Gray himself appears to have no programmatic thesis of his own in mind, other than extensively to document the change to a modernist approach in the decades under study, which he duly accomplishes.
Gray, nevertheless, fails to make good on the promise implicit in the title of his book. Nowhere does he undertake a sustained comparison of the mathematical practice of his heroes with other cultural phenomena of the period in question, conventionally going under the name of modernism. Could he not have essayed an analysis, say, of the literary theory of a James Joyce, T.S. Eliot or Robert Musil, in order to highlight points of connection with Lebesgue et al.? Not everyone is polymathic enough to do this for himself. Besides, how many can there be who have immersed themselves in the arcane primary literature? A few great texts are still in circulation (Frege’s Grundlagen der Arithmetik or the early arithmetical and logical studies of Husserl), but for the most part Gray’s sources must be gathering dust on old library shelves. Thus, it counts as an inexcusable omission on the author’s part when he does not perform for us, the generally educated but not specialist public, the service he owes, viz., to spell out in clearer and ampler terms what his mathematical movement around the turn of the twentieth century has to do with the synchronic modernism in literature and in the arts with which most readers will be more familiar.
Another spur to reflection (granted, which Gray himself entirely misses) would be this question: could there now be a post-modernist turn in mathematics? What would that mean? No space here to enter into such a vast inquiry…
The recognized historian of science Jeremy Gray in Plato’s Ghost contends that mathematics in the late nineteenth and early twentieth centuries went through a modernist phase allied with contemporary movements in literature and the arts. In general, this reviewer has a pre-modern mentality, but in what concerns mathematics he is very much a modernist—little inconsistencies like this are what make life interesting! Modernism represents a legitimate development of the desire to know, and once the mind has been opened to it there can be no going back, as if it did not exist. Gray’s book is interesting as far as it goes, but frustrating in that he limits himself to description of other people’s work. To come up with philosophical arguments of one’s own is another gift entirely than scholarship.
Synopsis: what does modernism mean? As far as the mathematical context of concern to this author goes, it involves a handful of related elements: first, a commitment to an exploration of ideas dictated by strictly internal criteria. The role of external motivation, coming from physics say, is to be minimized. Second, greater attention to formal properties as against content, taken by itself. Third, a more demanding standard of rigor than was conventional up to then. As readers of the companion review by this recensionist on Amir Alexander’s Duel at Dawn will notice, some of these themes crop up even earlier, in what Alexander depicts as a Romanticist turn during the first half of the nineteenth century. Gray devotes some space to explaining why, in his judgment, his putative modernist transformation represents something new (investigation of the figure of Cauchy, who, though indeed associated with an increased stress on rigor, has a pre-modern mathematical ontology). A good illustration of the emerging style can be had in Lebesgue’s theory of measure, which he worked out for his doctoral thesis in 1902. Basing himself on research by Jordan and Borel from the 1880’s to 1890’s, Lebesgue sets forth a set of axioms by which to characterize the measure (or in Jordan’s terms, content) of a set, and then shows that the measure so defined is essentially unique and agrees with Jordan’s outer content. Armed with these definitions, Lebesgue introduces the notion of a measurable function and radically recasts the concept of the integral. The Lebesgue integral coincides with Riemann’s when the latter exists, as any reasonable concept of integral should, but is more versatile and has far more desirable properties with respect to its limit under a sequence of functions (vide Fatou’s lemma and the Lebesgue dominated convergence theorem) – so much so that mathematicians have adopted Lebesgue’s ideas as the de facto standard in real analysis ever since. Gray is correct to see this development as emblematic of the modernist spirit.
Gray’s book weighs in as a hefty tome, although he disclaims an ambition to write a complete history of mathematics around the turn of the twentieth century (1890-1930). The first chapter consists in a diachronic overview of modernism in various branches of mathematics, keeping in mind trends in ontology, epistemology, psychology and language. The change in philosophy, or path out of Kant to Fries and Herbart and other later figures, gets a short notice, as does the path to logic and logical formalism. The concluding sections of sociological observations on professionalization in the mathematical community elicit little response from this reviewer (as will be the case for corresponding sections in later chapters; it seems maladroit to mix intellectual with intrinsically less-interesting sociological history).
The reader will enjoy the detour in chapter two on the state of mathematics during the nineteenth century, prior to modernism. We get a précis of the work of numerous figures, both well known and obscure. All this merely sets the stage for the arrival of modernism proper in chapter three. Again, Gray surveys in a somewhat scattershot manner the trends in contemporary geometry, algebra, logic and set theory, with good coverage of the philosophical views of the principal players (not just names anyone would have heard of to some extent, such as Cantor, Dedekind, Kronecker, Hilbert and Frege, but also many others known only to specialists, such as du Bois-Reymond, Trendelenburg, Lotze and Erdmann). While, of course, it is pleasant to feast upon the ideas under contestation, it can also be tantalizing, in that space permits only a few pages each to sum up entire treatises.
Gray continues in much the same vein in the meatiest part of his book, chapter four on ‘modernism avowed’. Again, we get a whirlwind of names of mathematicians, both among those famous and those overlooked today, and discussion of a multiplicity of philosophical views. Topics include, inter alia, abstract Italian algebraic geometry, Poincaré’s geometric conventionalism and French modernism in analysis.
It is hard for this reviewer to discern Gray’s authorial intention in the succeeding two chapters, on connections to physics, language and psychology. Hasn’t he already established his thesis on the advent of a modernist movement in the lengthy fourth chapter? Isn’t Gray at odds with himself in these two further chapters, in as much as, supposedly, the modernist spirit is to set aside any connections to phenomena in the outside world and to proceed solely on internal criteria? Yet, as he acknowledges and documents, mathematicians were not content to relinquish contact with these external fields. So much, so good for them; but doesn’t this imply a retraction, or at the minimum a complication of Gray’s main thesis? Gray himself devotes such scant attention to this question that we cannot seek for an answer to it from him.
The remainder of the book is taken up with chapter seven on the interwar period, when a great debate on the foundations of mathematics raged. Gray implies that it is necessary to follow the history of modernism, well established before the first world war as the reader will have seen in chapter four, into the interwar period, but omits to say just why. Thus, the discussion of Brouwer, Weyl, Gödel and Turing, while interesting in its own right, fails to cast much light on the overall thesis Gray wishes to advance. For this reviewer, the best sections of this concluding chapter are the third and fourth, on the rise of mathematical Platonism and the question of whether modernism ‘won’ in the mathematical community, respectively. Unfortunately, the author declines to spell out what Platonism has to do with modernism, per se. Likewise, he cops out on the question of whether modernism won, merely suggesting that both modernist and non-modernist strands can persist in parallel and that the balance between the two can vary with prevailing fashions. Would that Gray would take a definite stand, but he is too much of a historian to want to commit himself to an evaluative judgment. Nevertheless, his discussion in these two sections is informative and he does close on a satisfying note, with three extended block quotations from participants in the developments Gray reviews, one by Emil Post and two by Gödel. This reviewer finds them very thought-provoking.
In all, the reader of Gray’s monograph can expect pericopes on many of the noteworthy developments in the mathematical world during its modernist phase, but exiguous conceptual analysis or critical argumentation (something at which Max Jammer excels when in good form). The organization of the work is somewhat diffuse and disconnected, in view of the large number of topics it treats with little in the way of systematic synthesis. To this recensionist, Gray does largely succeed in making his case for a modernist transformation of mathematics. It is a rather limited objective, though: why should we care? Gray himself appears to have no programmatic thesis of his own in mind, other than extensively to document the change to a modernist approach in the decades under study, which he duly accomplishes.
Gray, nevertheless, fails to make good on the promise implicit in the title of his book. Nowhere does he undertake a sustained comparison of the mathematical practice of his heroes with other cultural phenomena of the period in question, conventionally going under the name of modernism. Could he not have essayed an analysis, say, of the literary theory of a James Joyce, T.S. Eliot or Robert Musil, in order to highlight points of connection with Lebesgue et al.? Not everyone is polymathic enough to do this for himself. Besides, how many can there be who have immersed themselves in the arcane primary literature? A few great texts are still in circulation (Frege’s Grundlagen der Arithmetik or the early arithmetical and logical studies of Husserl), but for the most part Gray’s sources must be gathering dust on old library shelves. Thus, it counts as an inexcusable omission on the author’s part when he does not perform for us, the generally educated but not specialist public, the service he owes, viz., to spell out in clearer and ampler terms what his mathematical movement around the turn of the twentieth century has to do with the synchronic modernism in literature and in the arts with which most readers will be more familiar.
Another spur to reflection (granted, which Gray himself entirely misses) would be this question: could there now be a post-modernist turn in mathematics? What would that mean? No space here to enter into such a vast inquiry…
November 7, 2025
Platon-Regal
Trotz Platons berechtigter Kritik an der Schrift, wie er sie im „Phaidros“ darlegt, bleibt sie ein mächtiges Werkzeug des Denkens. Dort legt er Sokrates die Warnung in den Mund, die Schrift sei ein trügerisches pharmakon – Heilmittel und Gift zugleich: Sie stärke nicht das Gedächtnis – das wahre, innere Verstehen –, sondern erzeuge nur ein äußeres Erinnern und damit Scheinwissen. Ein geschriebener Text ist starr; er kann auf Fragen nicht antworten, sich nicht gegen Missverständnisse wehren und „treibt sich überall herum“, auch bei jenen, die ihn nicht verstehen. Platon sah in ihr daher nur ein „schwächeres Abbild“ des lebendigen, beseelten Gesprächs. Und doch liegt in diesem Abbild eine eigentümliche Macht: Die Schrift bewahrt, was das Gedächtnis zu verlieren droht, und erlaubt, Gedanken über Zeit, Raum und Generationen hinweg zu teilen.
Meine Vorfahren konnten weder lesen noch schreiben, und doch trugen sie Geschichten, Wissen und Gefühle in Liedern und Erzählungen – ihre Stimmen zogen wie Fäden durch die Zeit. Sie waren Hüter einer lebendigen, atmenden Tradition. Ich stehe zwischen diesen Welten: der mündlichen Überlieferung, die ich ehre, und der schriftlichen Reflexion, in der ich lebe. Vielleicht ist mein Schreiben nichts anderes als der Versuch, beiden gerecht zu werden – der flüchtigen Glut des gesprochenen Wortes und der stillen Glut der Schrift.
In den vergangenen siebenundvierzig Jahren habe ich unzählige Bücher gelesen – große Werke und solche, die kaum Beachtung fanden. Sie bilden den reichen Fundus, aus dem ich nun schöpfe. Denn ich habe beim Lesen stets annotiert – Randbemerkungen, Gedanken, kleine Spuren eines langen Zwiegesprächs mit den Toten und den Lebenden. Viele dieser Werke möchte ich nun würdigen; nicht weil sie vollkommen sind, sondern weil sie aufrichtig versuchen, etwas Wahres auszusprechen. Manche Bücher öffnen sich schon mit ihrem Titel – wie eine Tür in einen noch ungedachten Raum. Ein Wort, ein Klang, kann genügen, um etwas in uns zum Schwingen zu bringen. Selbst zweitrangige Werke können Funken schlagen, wenn sie zur rechten Zeit auf einen offenen Geist treffen.
Der Anlass, diese alten Annotationen nun „aus der Mottenkiste“ zu holen und die Bücher im Rahmen einer solchen Würdigung vorzustellen, ergab sich eher zufällig: Erst im November 2024 erfuhr ich durch meinen Sohn – der wiederum von seiner Schwester darauf gebracht worden war – von der Plattform Goodreads. Seither öffnet sich mir diese „digitale Mottenkiste der Leseratten“, in der jede Rezension ein Zettel im unendlichen Zettelkasten des globalen Lesens ist. Ich blättere darin wie in einem imaginären Archiv der Menschheit, in dem jeder Eintrag, jede Notiz, ein Flüstern aus einer anderen Zeit ist. Ich habe dort begonnen, Spuren zu hinterlassen – nicht um zu urteilen, sondern um zu danken. Denn jedes Buch, das ehrlich geschrieben und aufmerksam gelesen wird, fügt dem großen Gespräch der Menschheit eine eigene, unverwechselbare Stimme hinzu.
Es ist das Fundament dieser Bibliothek und wohl auch der gesamten abendländischen Philosophie, die Alfred North Whitehead einmal als „eine Reihe von Fußnoten zu Platon“ bezeichnete. In diesem Regal stehen die Dialoge selbst – Politeia, Phaidros, Symposion, Sophistes, Theaitetos – wie Stimmen eines fortwährenden Gesprächs, das über Jahrtausende hinweg wirkt.
Daneben lagern Bücher über ihn: Exegeten, Historiker, Kommentatoren, die versuchen, seine Gedanken zu erklären, zu deuten oder zu hinterfragen. Manche streiten, andere feiern; manche beleuchten Details, andere öffnen neue Horizonte. Zusammen bilden sie ein dichtes Netz, in dem das Denken Platons immer wieder aufscheint, nachklingt und neue Resonanzen erzeugt.
Die Regale dokumentieren meine über 4000 Bücher – meine persönliche Topographie des Lesens und Denkens. Was sind schon viertausend Bücher in achtundvierzig Jahren, wenn weltweit jedes Jahr rund 1,79 Millionen neue Bücher erscheinen? Diese Zahl relativiert meine Leseleistung, nicht jedoch die Bedeutung der Gedanken, die in den Büchern dieser Regale nachhallen.
Trotz Platons berechtigter Kritik an der Schrift, wie er sie im „Phaidros“ darlegt, bleibt sie ein mächtiges Werkzeug des Denkens. Dort legt er Sokrates die Warnung in den Mund, die Schrift sei ein trügerisches pharmakon – Heilmittel und Gift zugleich: Sie stärke nicht das Gedächtnis – das wahre, innere Verstehen –, sondern erzeuge nur ein äußeres Erinnern und damit Scheinwissen. Ein geschriebener Text ist starr; er kann auf Fragen nicht antworten, sich nicht gegen Missverständnisse wehren und „treibt sich überall herum“, auch bei jenen, die ihn nicht verstehen. Platon sah in ihr daher nur ein „schwächeres Abbild“ des lebendigen, beseelten Gesprächs. Und doch liegt in diesem Abbild eine eigentümliche Macht: Die Schrift bewahrt, was das Gedächtnis zu verlieren droht, und erlaubt, Gedanken über Zeit, Raum und Generationen hinweg zu teilen.
Meine Vorfahren konnten weder lesen noch schreiben, und doch trugen sie Geschichten, Wissen und Gefühle in Liedern und Erzählungen – ihre Stimmen zogen wie Fäden durch die Zeit. Sie waren Hüter einer lebendigen, atmenden Tradition. Ich stehe zwischen diesen Welten: der mündlichen Überlieferung, die ich ehre, und der schriftlichen Reflexion, in der ich lebe. Vielleicht ist mein Schreiben nichts anderes als der Versuch, beiden gerecht zu werden – der flüchtigen Glut des gesprochenen Wortes und der stillen Glut der Schrift.
In den vergangenen siebenundvierzig Jahren habe ich unzählige Bücher gelesen – große Werke und solche, die kaum Beachtung fanden. Sie bilden den reichen Fundus, aus dem ich nun schöpfe. Denn ich habe beim Lesen stets annotiert – Randbemerkungen, Gedanken, kleine Spuren eines langen Zwiegesprächs mit den Toten und den Lebenden. Viele dieser Werke möchte ich nun würdigen; nicht weil sie vollkommen sind, sondern weil sie aufrichtig versuchen, etwas Wahres auszusprechen. Manche Bücher öffnen sich schon mit ihrem Titel – wie eine Tür in einen noch ungedachten Raum. Ein Wort, ein Klang, kann genügen, um etwas in uns zum Schwingen zu bringen. Selbst zweitrangige Werke können Funken schlagen, wenn sie zur rechten Zeit auf einen offenen Geist treffen.
Der Anlass, diese alten Annotationen nun „aus der Mottenkiste“ zu holen und die Bücher im Rahmen einer solchen Würdigung vorzustellen, ergab sich eher zufällig: Erst im November 2024 erfuhr ich durch meinen Sohn – der wiederum von seiner Schwester darauf gebracht worden war – von der Plattform Goodreads. Seither öffnet sich mir diese „digitale Mottenkiste der Leseratten“, in der jede Rezension ein Zettel im unendlichen Zettelkasten des globalen Lesens ist. Ich blättere darin wie in einem imaginären Archiv der Menschheit, in dem jeder Eintrag, jede Notiz, ein Flüstern aus einer anderen Zeit ist. Ich habe dort begonnen, Spuren zu hinterlassen – nicht um zu urteilen, sondern um zu danken. Denn jedes Buch, das ehrlich geschrieben und aufmerksam gelesen wird, fügt dem großen Gespräch der Menschheit eine eigene, unverwechselbare Stimme hinzu.
Es ist das Fundament dieser Bibliothek und wohl auch der gesamten abendländischen Philosophie, die Alfred North Whitehead einmal als „eine Reihe von Fußnoten zu Platon“ bezeichnete. In diesem Regal stehen die Dialoge selbst – Politeia, Phaidros, Symposion, Sophistes, Theaitetos – wie Stimmen eines fortwährenden Gesprächs, das über Jahrtausende hinweg wirkt.
Daneben lagern Bücher über ihn: Exegeten, Historiker, Kommentatoren, die versuchen, seine Gedanken zu erklären, zu deuten oder zu hinterfragen. Manche streiten, andere feiern; manche beleuchten Details, andere öffnen neue Horizonte. Zusammen bilden sie ein dichtes Netz, in dem das Denken Platons immer wieder aufscheint, nachklingt und neue Resonanzen erzeugt.
Die Regale dokumentieren meine über 4000 Bücher – meine persönliche Topographie des Lesens und Denkens. Was sind schon viertausend Bücher in achtundvierzig Jahren, wenn weltweit jedes Jahr rund 1,79 Millionen neue Bücher erscheinen? Diese Zahl relativiert meine Leseleistung, nicht jedoch die Bedeutung der Gedanken, die in den Büchern dieser Regale nachhallen.
July 21, 2022
Himla intressant!
January 24, 2026
This book is essentially a history of analysis, geometry, logic and philosophy (of mathematics) in the period 1880 - 1910. It has some history of the before and after but very little. There are a few inaccuracies according to my own understanding of the topics, but in general it is a well written book that surveys a vast amount of history and makes the convincing argument that mathematics underwent a fundamental change during this period.
I wish that it spent just a little longer on dealing with the historical emergence of Platonism. I spends about 10 pages on Platonism total and most of it is summarising the debate around it (pros and cons), rather than how it emerged as the defacto position (according to Gray).
I wish that it spent just a little longer on dealing with the historical emergence of Platonism. I spends about 10 pages on Platonism total and most of it is summarising the debate around it (pros and cons), rather than how it emerged as the defacto position (according to Gray).
Displaying 1 - 4 of 4 reviews