Arkady Plotnitsky
Apostolos Doxiadis and Barry Mazur (eds)
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691149042
- eISBN:
- 9781400842681
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691149042.003.0012
- Subject:
- Mathematics, History of Mathematics
This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the ...
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This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the question of the potentially uncircumventable limits of thought and knowledge; and second, to the question of a certain heterogeneous and yet interactive multiplicity of concepts and of different fields such as algebra and geometry. The chapter starts with the Pythagoreans' discovery of the concept of “incommensurability,” or the irrationality of certain numbers, specifically the side and the diagonal of the square, and the narrative associated with this discovery. It then examines the transition from non-Euclidean physics to non-Euclidean mathematics by focusing on quantum mechanics and its relation to non-Euclidean epistemology. It also discusses the algebraic aspects of non-Euclidean geometry and concludes with the suggestion that non-Euclidean thinking retains the essential, shaping role of the movement of thought.Less
This chapter explores the relationship between narrative and non-Euclidean mathematics. It considers how non-Euclidean mathematics and the narratives accompanying it are linked: first, to the question of the potentially uncircumventable limits of thought and knowledge; and second, to the question of a certain heterogeneous and yet interactive multiplicity of concepts and of different fields such as algebra and geometry. The chapter starts with the Pythagoreans' discovery of the concept of “incommensurability,” or the irrationality of certain numbers, specifically the side and the diagonal of the square, and the narrative associated with this discovery. It then examines the transition from non-Euclidean physics to non-Euclidean mathematics by focusing on quantum mechanics and its relation to non-Euclidean epistemology. It also discusses the algebraic aspects of non-Euclidean geometry and concludes with the suggestion that non-Euclidean thinking retains the essential, shaping role of the movement of thought.
Bas C. van Fraassen
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199278220
- eISBN:
- 9780191707926
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199278220.003.00010
- Subject:
- Philosophy, Philosophy of Mind, Philosophy of Science
The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on ...
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The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on mathematical logic. He founded theoretical physics in a mathematics constructed along logicist lines, which is also what proved his undoing at the hands of a famous review by Newman that set the pattern for later objections to structuralist views.Less
The first sustained, rigorous development of a structuralist view of science appeared in the writings of Bertrand Russell, where the philosophical motivation precedes a precise formulation drawing on mathematical logic. He founded theoretical physics in a mathematics constructed along logicist lines, which is also what proved his undoing at the hands of a famous review by Newman that set the pattern for later objections to structuralist views.
Andrea Henderson
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198809982
- eISBN:
- 9780191860140
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809982.003.0002
- Subject:
- Literature, 19th-century Literature and Romanticism
Edwin Abbott’s Flatland dramatizes the implications of dethroning what Victorians regarded as the preeminent representational system: Euclidean geometry. The displacement of the singular Euclidean ...
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Edwin Abbott’s Flatland dramatizes the implications of dethroning what Victorians regarded as the preeminent representational system: Euclidean geometry. The displacement of the singular Euclidean account of space with a multiplicity of non-referential spatial regimes did more than introduce the possibility of varying perspectives on the world; the challenge to the “sacredness” of Euclid met with resistance partly because it suggested the ideal of a transparent representational system was inherently untenable. Flatland explores the repercussions of this problem for the novel, shifting emphasis from the revelation of the content of character to focus on the vagaries of point of view. The characters are Euclidean figures shown the limitations of their constructions of the world, and epistemic certainty is unavailable because all representational systems are contingent. Abbott finds consolation for this loss of certainty in the formalist, aesthetic character of projective geometry, insisting on the beauty of signs in and of themselves.Less
Edwin Abbott’s Flatland dramatizes the implications of dethroning what Victorians regarded as the preeminent representational system: Euclidean geometry. The displacement of the singular Euclidean account of space with a multiplicity of non-referential spatial regimes did more than introduce the possibility of varying perspectives on the world; the challenge to the “sacredness” of Euclid met with resistance partly because it suggested the ideal of a transparent representational system was inherently untenable. Flatland explores the repercussions of this problem for the novel, shifting emphasis from the revelation of the content of character to focus on the vagaries of point of view. The characters are Euclidean figures shown the limitations of their constructions of the world, and epistemic certainty is unavailable because all representational systems are contingent. Abbott finds consolation for this loss of certainty in the formalist, aesthetic character of projective geometry, insisting on the beauty of signs in and of themselves.
Thomas C. Vinci
- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780199381166
- eISBN:
- 9780199381234
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199381166.003.0005
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
Chapter 4 has three main parts. The first develops an account of Kant’s mathematical method, based partly on work by Philip Kitcher, called the KV account. This account allows for epistemically ...
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Chapter 4 has three main parts. The first develops an account of Kant’s mathematical method, based partly on work by Philip Kitcher, called the KV account. This account allows for epistemically independent applications of geometrical method to objects in pure space—the mind-dependent space of imagination—as well as to objects in a putatively mind-independent empirical space. The a priori synthetic necessity of geometry is understood as counterfactual necessity. Objections from Friedman and Waxman are considered. In the former case the application constitutes pure geometry, in the latter, physical geometry. In the second part we see that Kant compares the theorems of both kinds of geometry, finds them identical, and seeks to explain this coincidence in a Second Geometrical Argument. The explanation is Transcendental Idealism. In the final part, I consider how Kant’s Euclidean theory of pure geometry fares in light of modern non-Euclidean theories of physical geometry.Less
Chapter 4 has three main parts. The first develops an account of Kant’s mathematical method, based partly on work by Philip Kitcher, called the KV account. This account allows for epistemically independent applications of geometrical method to objects in pure space—the mind-dependent space of imagination—as well as to objects in a putatively mind-independent empirical space. The a priori synthetic necessity of geometry is understood as counterfactual necessity. Objections from Friedman and Waxman are considered. In the former case the application constitutes pure geometry, in the latter, physical geometry. In the second part we see that Kant compares the theorems of both kinds of geometry, finds them identical, and seeks to explain this coincidence in a Second Geometrical Argument. The explanation is Transcendental Idealism. In the final part, I consider how Kant’s Euclidean theory of pure geometry fares in light of modern non-Euclidean theories of physical geometry.
Ta-Pei Cheng
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199573639
- eISBN:
- 9780191722448
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573639.003.0005
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
Einstein's new theory of gravitation is formulated in a geometric framework of curved spacetime. Here the subject of non-Euclidean geometry is introduced by way of Gauss's theory of curved surfaces. ...
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Einstein's new theory of gravitation is formulated in a geometric framework of curved spacetime. Here the subject of non-Euclidean geometry is introduced by way of Gauss's theory of curved surfaces. Generalized (Gaussian) coordinates: A systematic way to label points in space without reference to any objects outside this space. Metric function: For a given coordinate choice, the metric determines the intrinsic geometric properties of a curved space. Geodesic equation: It describes the shortest and the straightest possible curve in a warped space and is expressed in terms of the metric function. Curvature: It is a nonlinear second derivative of the metric. As the deviation from Euclidean relations is proportional to the curvature, it measures how much the space is warped.Less
Einstein's new theory of gravitation is formulated in a geometric framework of curved spacetime. Here the subject of non-Euclidean geometry is introduced by way of Gauss's theory of curved surfaces. Generalized (Gaussian) coordinates: A systematic way to label points in space without reference to any objects outside this space. Metric function: For a given coordinate choice, the metric determines the intrinsic geometric properties of a curved space. Geodesic equation: It describes the shortest and the straightest possible curve in a warped space and is expressed in terms of the metric function. Curvature: It is a nonlinear second derivative of the metric. As the deviation from Euclidean relations is proportional to the curvature, it measures how much the space is warped.
John P. Burgess
- Published in print:
- 2015
- Published Online:
- May 2015
- ISBN:
- 9780198722229
- eISBN:
- 9780191789076
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722229.003.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
This chapter explains what heuristic methods, ubiquitous and indispensable in the context of discovery in mathematics, are prohibited in the context of justification by the requirement of rigor as ...
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This chapter explains what heuristic methods, ubiquitous and indispensable in the context of discovery in mathematics, are prohibited in the context of justification by the requirement of rigor as now understood. The chapter describes, with special attention to the role of infinities and infinitesimals and of spatiotemporal intuition in the eighteenth-century calculus, how the requirement of rigor, honored in principle but slighted in practice during the early modern period, came to be enforced as never before during the nineteenth century. The question why such new higher standards, ultimately going far beyond the ancient level of rigor represented by Euclid, came to be insisted upon is broached, and several factors discussed that provide partial answers, especially the role of non-Euclidean geometry. But it is not pretended that any answer can be given that would completely rationalize all the historical decisions of the mathematical community.Less
This chapter explains what heuristic methods, ubiquitous and indispensable in the context of discovery in mathematics, are prohibited in the context of justification by the requirement of rigor as now understood. The chapter describes, with special attention to the role of infinities and infinitesimals and of spatiotemporal intuition in the eighteenth-century calculus, how the requirement of rigor, honored in principle but slighted in practice during the early modern period, came to be enforced as never before during the nineteenth century. The question why such new higher standards, ultimately going far beyond the ancient level of rigor represented by Euclid, came to be insisted upon is broached, and several factors discussed that provide partial answers, especially the role of non-Euclidean geometry. But it is not pretended that any answer can be given that would completely rationalize all the historical decisions of the mathematical community.
Tony Robbin
- Published in print:
- 2006
- Published Online:
- October 2013
- ISBN:
- 9780300110395
- eISBN:
- 9780300129625
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110395.003.0005
- Subject:
- Society and Culture, Technology and Society
This chapter serves as a brief lesson on projective geometry. It starts by discussing two basic theorems of projective geometry, which are concerned with perspectives from a point and perspectives ...
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This chapter serves as a brief lesson on projective geometry. It starts by discussing two basic theorems of projective geometry, which are concerned with perspectives from a point and perspectives from a line. The discussion then looks at projectivities and perspectivities, which result from several perspectivities and relate a range, respectively. This is followed by the study of analytic projective geometry and the connection between projective and projection. The chapter concludes with a discussion on the complex projective line, the projective three-space, and Felix Klein's thoughts on the presence of non-Euclidean geometries in projective geometry, specifically the topology of the projective plane.Less
This chapter serves as a brief lesson on projective geometry. It starts by discussing two basic theorems of projective geometry, which are concerned with perspectives from a point and perspectives from a line. The discussion then looks at projectivities and perspectivities, which result from several perspectivities and relate a range, respectively. This is followed by the study of analytic projective geometry and the connection between projective and projection. The chapter concludes with a discussion on the complex projective line, the projective three-space, and Felix Klein's thoughts on the presence of non-Euclidean geometries in projective geometry, specifically the topology of the projective plane.
Waxman Wayne
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199328314
- eISBN:
- 9780199369348
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199328314.003.0007
- Subject:
- Philosophy, History of Philosophy
This chapter focuses on Kant’s account of the possibility of mathematics in relation to the transcendental expositions of space and time in the Transcendental Aesthetic, that is, the role of ...
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This chapter focuses on Kant’s account of the possibility of mathematics in relation to the transcendental expositions of space and time in the Transcendental Aesthetic, that is, the role of sensibility therein rather than understanding (which is discussed in Chapter 15). It is argued that Kant was nothing like the Euclidean dogmatist he is commonly portrayed as being by showing that and how his account of sensibility is perfectly capable of accommodating mathematical spaces of any curvature and number of dimensions. It is also shown how this account enabled him to explain the possibility not only of geometry, but even the most abstract, purely symbolic varieties of mathematics, among which post-Fregean mathematical logic should probably be included.Less
This chapter focuses on Kant’s account of the possibility of mathematics in relation to the transcendental expositions of space and time in the Transcendental Aesthetic, that is, the role of sensibility therein rather than understanding (which is discussed in Chapter 15). It is argued that Kant was nothing like the Euclidean dogmatist he is commonly portrayed as being by showing that and how his account of sensibility is perfectly capable of accommodating mathematical spaces of any curvature and number of dimensions. It is also shown how this account enabled him to explain the possibility not only of geometry, but even the most abstract, purely symbolic varieties of mathematics, among which post-Fregean mathematical logic should probably be included.
Ian F. A. Bell
- Published in print:
- 2012
- Published Online:
- June 2013
- ISBN:
- 9781846318092
- eISBN:
- 9781846317743
- Item type:
- chapter
- Publisher:
- Liverpool University Press
- DOI:
- 10.5949/UPO9781846317743.009
- Subject:
- Literature, Poetry
This chapter describes how Ezra Pound discovered the aesthetic potential of the concept of Vorticism and fourth-dimensional thought and integrated this into his writings. In his ‘Vorticism’ essay, ...
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This chapter describes how Ezra Pound discovered the aesthetic potential of the concept of Vorticism and fourth-dimensional thought and integrated this into his writings. In his ‘Vorticism’ essay, Pound emphasized the extent to which the Vorticist surface belongs to advances in Euclidean geometry, offering ‘Descartian’ or analytic geometry as the creative idiom. It is suggested that modernist poetics availed itself of trajectories within fourth-dimensional thought through a telling of obliquity, and that Vorticism and its allied activities provide the most generative ground.Less
This chapter describes how Ezra Pound discovered the aesthetic potential of the concept of Vorticism and fourth-dimensional thought and integrated this into his writings. In his ‘Vorticism’ essay, Pound emphasized the extent to which the Vorticist surface belongs to advances in Euclidean geometry, offering ‘Descartian’ or analytic geometry as the creative idiom. It is suggested that modernist poetics availed itself of trajectories within fourth-dimensional thought through a telling of obliquity, and that Vorticism and its allied activities provide the most generative ground.
Olivier Darrigol
- Published in print:
- 2014
- Published Online:
- June 2014
- ISBN:
- 9780198712886
- eISBN:
- 9780191781360
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198712886.003.0004
- Subject:
- Physics, History of Physics
This chapter deals with the foundations of geometry, with emphasis on Helmholtz’s approach to this problem in the late 1860s. It is first recalled how the ancient belief in the apodictic truth of the ...
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This chapter deals with the foundations of geometry, with emphasis on Helmholtz’s approach to this problem in the late 1860s. It is first recalled how the ancient belief in the apodictic truth of the axioms of geometry came under attack at the turn of the eighteenth and nineteenth centuries, making room for the new geometries of Gauss, Bolyai, Lobachevski, and Riemann. This opening of possibilities raised the question of the necessary structural kernel of any physical geometry. The central section of this chapter is a detailed account of Helmholtz’s answer to this question, according to which the locally Euclidean character of space follows from its measurability by freely mobile rigid bodies. This argument has difficulties, due to a seeming circularity in the definition of rigid bodies and to the strictness of the assumed rigidity, which requires spaces of constant curvature. It is shown how these difficulties can be circumvented, leading to the necessity of the Riemannian structure of space (with any curvature) for measurable space.Less
This chapter deals with the foundations of geometry, with emphasis on Helmholtz’s approach to this problem in the late 1860s. It is first recalled how the ancient belief in the apodictic truth of the axioms of geometry came under attack at the turn of the eighteenth and nineteenth centuries, making room for the new geometries of Gauss, Bolyai, Lobachevski, and Riemann. This opening of possibilities raised the question of the necessary structural kernel of any physical geometry. The central section of this chapter is a detailed account of Helmholtz’s answer to this question, according to which the locally Euclidean character of space follows from its measurability by freely mobile rigid bodies. This argument has difficulties, due to a seeming circularity in the definition of rigid bodies and to the strictness of the assumed rigidity, which requires spaces of constant curvature. It is shown how these difficulties can be circumvented, leading to the necessity of the Riemannian structure of space (with any curvature) for measurable space.
David D. Nolte
- Published in print:
- 2018
- Published Online:
- August 2018
- ISBN:
- 9780198805847
- eISBN:
- 9780191843808
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198805847.003.0005
- Subject:
- Physics, History of Physics
This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who ...
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This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.Less
This chapter reviews the history of modern geometry with a focus on the topics that provided the foundation for the new visualization of physics. It begins with Carl Gauss and Bernhard Riemann, who redefined geometry and identified the importance of curvature for physics. Vector spaces, developed by Hermann Grassmann, Giuseppe Peano and David Hilbert, are examples of the kinds of abstract new spaces that are so important for modern physics, such as Hilbert space for quantum mechanics. Fractal geometry developed by Felix Hausdorff later provided the geometric language needed to solve problems in chaos theory. Motion cannot exist without space—trajectories are the tracks of points, mathematical or physical, through it.
Andrea Henderson
- Published in print:
- 2018
- Published Online:
- May 2018
- ISBN:
- 9780198809982
- eISBN:
- 9780191860140
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198809982.001.0001
- Subject:
- Literature, 19th-century Literature and Romanticism
Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth ...
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Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wave-like stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.Less
Algebraic Art explores the invention of a peculiarly Victorian account of the nature and value of aesthetic form, and it traces that account to a surprising source: mathematics. The nineteenth century was a moment of extraordinary mathematical innovation, witnessing the development of non-Euclidean geometry, the revaluation of symbolic algebra, and the importation of mathematical language into philosophy. All these innovations sprang from a reconception of mathematics as a formal rather than a referential practice—as a means for describing relationships rather than quantities. For Victorian mathematicians, the value of a claim lay not in its capacity to describe the world but its internal coherence. This concern with formal structure produced a striking convergence between mathematics and aesthetics: geometers wrote fables, logicians reconceived symbolism, and physicists described reality as consisting of beautiful patterns. Artists, meanwhile, drawing upon the cultural prestige of mathematics, conceived their work as a “science” of form, whether as lines in a painting, twinned characters in a novel, or wave-like stress patterns in a poem. Avant-garde photographs and paintings, fantastical novels like Flatland and Lewis Carroll’s children’s books, and experimental poetry by Swinburne, Rossetti, and Patmore created worlds governed by a rigorous internal logic even as they were pointedly unconcerned with reference or realist protocols. Algebraic Art shows that works we tend to regard as outliers to mainstream Victorian culture were expressions of a mathematical formalism that was central to Victorian knowledge production and that continues to shape our understanding of the significance of form.
Frederick C. Beiser
- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780198722205
- eISBN:
- 9780191789052
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198722205.003.0008
- Subject:
- Philosophy, History of Philosophy
Chapter 7 discusses the early philosophical works and development of Otto Liebmann. It focuses upon the contents and motives behind his early Kant und die Epigonen and his early critique of ...
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Chapter 7 discusses the early philosophical works and development of Otto Liebmann. It focuses upon the contents and motives behind his early Kant und die Epigonen and his early critique of Schopenhauer. I attempt to rescue Liebmann’s reputation from Klaus Christian Köhnke’s severe criticisms. Liebmann is shown to be a classic 19th-century German liberal rather than a proto-national-socialist. Liebmann is treated as a crucial figure in the neo-Kantian critique of positivism and in the development of a non-psychological interpretation of Kant.Less
Chapter 7 discusses the early philosophical works and development of Otto Liebmann. It focuses upon the contents and motives behind his early Kant und die Epigonen and his early critique of Schopenhauer. I attempt to rescue Liebmann’s reputation from Klaus Christian Köhnke’s severe criticisms. Liebmann is shown to be a classic 19th-century German liberal rather than a proto-national-socialist. Liebmann is treated as a crucial figure in the neo-Kantian critique of positivism and in the development of a non-psychological interpretation of Kant.
Waxman Wayne
- Published in print:
- 2013
- Published Online:
- January 2014
- ISBN:
- 9780199328314
- eISBN:
- 9780199369348
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199328314.003.0001
- Subject:
- Philosophy, History of Philosophy
This introductory text signals what is new and noteworthy in the book and provides guidance for comprehending and evaluating it. It opens with some general remarks regarding the book’s relation to ...
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This introductory text signals what is new and noteworthy in the book and provides guidance for comprehending and evaluating it. It opens with some general remarks regarding the book’s relation to the same author’s Kant and the Empiricists. Understanding Understanding (2005), and recapitulates some of the themes common to both books. It then states the thesis that most directly sets this interpretation of Kant apart from others—that the categories presuppose apperception (pure self-consciousness) and not vice versa—and describes how its acceptance leads to privileging questions that seldom get asked. The Memo concludes with a part-by-part, chapter-by-chapter synopsis of the whole.Less
This introductory text signals what is new and noteworthy in the book and provides guidance for comprehending and evaluating it. It opens with some general remarks regarding the book’s relation to the same author’s Kant and the Empiricists. Understanding Understanding (2005), and recapitulates some of the themes common to both books. It then states the thesis that most directly sets this interpretation of Kant apart from others—that the categories presuppose apperception (pure self-consciousness) and not vice versa—and describes how its acceptance leads to privileging questions that seldom get asked. The Memo concludes with a part-by-part, chapter-by-chapter synopsis of the whole.
