Jan Olof Bengtsson
- Published in print:
- 2006
- Published Online:
- January 2007
- ISBN:
- 9780199297191
- eISBN:
- 9780191711374
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199297191.001.0001
- Subject:
- Philosophy, Philosophy of Religion
The book challenges the current view that personalism is primarily an early 20th-century phenomenon. The established definitions of personalism, mainly in terms of the American school of B. P. Bowne, ...
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The book challenges the current view that personalism is primarily an early 20th-century phenomenon. The established definitions of personalism, mainly in terms of the American school of B. P. Bowne, are shown to fit broadly the positions of much earlier continental European and Scandinavian philosophers and theologians. The beginnings of specifically personalistic thought are traced to F. H. Jacobi’s criticism of pantheism, first set forth in the 1780s, and the work of the later F. W. J. Schelling. Its development is then identified in the work of selected, representative thinkers who, throughout the 19th century, build on or develop further positions established by Jacobi and Schelling, primarily the thinkers belonging to the broad current of so-called ‘speculative theism’ in Germany and in Sweden. The development of idealistic personalism in Britain by A. S. Pringle-Pattison, J. R. Illingworth, C. C. J. Webb and others is shown to be parallel to the emergence of the American school. It is argued that these should be seen as a continuation of the earlier European movement. Both the American and the British schools drew on the work of H. Lotze, but the book points to the neglected continental European background to Lotze, the current of personalistic, partly idealistic, and theistic philosophy of which Lotze’s work was only one, late variation. Discerning the central themes of the emerging worldview of personalism, the book establishes that they developed consistently in a broad, unitary movement with a distinct historical profile from the late 18th to the early 20th centuries, the nature and importance of which has heretofore been neglected in the history of philosophy and in historical theology.Less
The book challenges the current view that personalism is primarily an early 20th-century phenomenon. The established definitions of personalism, mainly in terms of the American school of B. P. Bowne, are shown to fit broadly the positions of much earlier continental European and Scandinavian philosophers and theologians. The beginnings of specifically personalistic thought are traced to F. H. Jacobi’s criticism of pantheism, first set forth in the 1780s, and the work of the later F. W. J. Schelling. Its development is then identified in the work of selected, representative thinkers who, throughout the 19th century, build on or develop further positions established by Jacobi and Schelling, primarily the thinkers belonging to the broad current of so-called ‘speculative theism’ in Germany and in Sweden. The development of idealistic personalism in Britain by A. S. Pringle-Pattison, J. R. Illingworth, C. C. J. Webb and others is shown to be parallel to the emergence of the American school. It is argued that these should be seen as a continuation of the earlier European movement. Both the American and the British schools drew on the work of H. Lotze, but the book points to the neglected continental European background to Lotze, the current of personalistic, partly idealistic, and theistic philosophy of which Lotze’s work was only one, late variation. Discerning the central themes of the emerging worldview of personalism, the book establishes that they developed consistently in a broad, unitary movement with a distinct historical profile from the late 18th to the early 20th centuries, the nature and importance of which has heretofore been neglected in the history of philosophy and in historical theology.
Jacqueline Mariña
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199206377
- eISBN:
- 9780191709753
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199206377.003.0003
- Subject:
- Religion, Philosophy of Religion
This chapter examines the grounds for the younger Schleiermacher's claim in Spinozism that there are no genuine individuals. Making extensive use of Kant's philosophy, Schleiermacher defends ...
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This chapter examines the grounds for the younger Schleiermacher's claim in Spinozism that there are no genuine individuals. Making extensive use of Kant's philosophy, Schleiermacher defends Spinoza's claim that there can be only one genuine substance. His argument is conducted in light of Jacobi's presentation of Leibniz' system. The first part of the chapter discusses Schleiermacher's epistemological arguments against the knowability of Leibniz' principle of individuation. The second part of the chapter provides an analysis of Schleiermacher's metaphysical arguments against the existence of a genuine plurality of individuals.Less
This chapter examines the grounds for the younger Schleiermacher's claim in Spinozism that there are no genuine individuals. Making extensive use of Kant's philosophy, Schleiermacher defends Spinoza's claim that there can be only one genuine substance. His argument is conducted in light of Jacobi's presentation of Leibniz' system. The first part of the chapter discusses Schleiermacher's epistemological arguments against the knowability of Leibniz' principle of individuation. The second part of the chapter provides an analysis of Schleiermacher's metaphysical arguments against the existence of a genuine plurality of individuals.
A.D. Neate and A. Truman
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780199239252
- eISBN:
- 9780191716911
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239252.003.0013
- Subject:
- Mathematics, Probability / Statistics, Analysis
This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces ...
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This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.Less
This chapter summarises a selection of results on the inviscid limit of the stochastic Burgers equation emphasising geometric properties of the caustic, Maxwell set and Hamilton-Jacobi level surfaces and relating these results to a discussion of stochastic turbulence. It shows that for small viscosities there exists a vortex filament structure near to the Maxwell set. It is discussed how this vorticity is directly related to the adhesion model for the evolution of the early universe, and new explicit formulas for the distribution of mass within the shock are included.
J. C. Gower and G. B. Dijksterhuis
- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198510581
- eISBN:
- 9780191708961
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198510581.003.0004
- Subject:
- Mathematics, Probability / Statistics
This chapter discusses the principal forms of T, specifically the case where T is an orthogonal matrix Q; then X1 and X2 must have the same number of columns P. ...
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This chapter discusses the principal forms of T, specifically the case where T is an orthogonal matrix Q; then X1 and X2 must have the same number of columns P. If the rows of X1 and X2 are regarded as giving the coordinates of points, then the orthogonal transformation leaves the distances between the points of each configuration unchanged; then the orthogonal Procrustes problem can be considered as rotating the configuration X1 to match the configuration X2 . The chapter also considers the special cases of orthogonal matrices that represent reflections in a plane (Householder transforms) and rotations in a plane (Jacobi rotations).Less
This chapter discusses the principal forms of T, specifically the case where T is an orthogonal matrix Q; then X1 and X2 must have the same number of columns P. If the rows of X1 and X2 are regarded as giving the coordinates of points, then the orthogonal transformation leaves the distances between the points of each configuration unchanged; then the orthogonal Procrustes problem can be considered as rotating the configuration X1 to match the configuration X2 . The chapter also considers the special cases of orthogonal matrices that represent reflections in a plane (Householder transforms) and rotations in a plane (Jacobi rotations).
Andrea Braides
- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198507840
- eISBN:
- 9780191709890
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507840.003.0004
- Subject:
- Mathematics, Applied Mathematics
Homogenization problems for a general class of integrals are solved by a direct approach. Different homogenization formulas are given, both in an asymptotic form and as a cell problem (in the convex ...
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Homogenization problems for a general class of integrals are solved by a direct approach. Different homogenization formulas are given, both in an asymptotic form and as a cell problem (in the convex case). These are applied in the study of the asymptotic behaviour of Riemannian metrics and Hamilton-Jacobi equations.Less
Homogenization problems for a general class of integrals are solved by a direct approach. Different homogenization formulas are given, both in an asymptotic form and as a cell problem (in the convex case). These are applied in the study of the asymptotic behaviour of Riemannian metrics and Hamilton-Jacobi equations.
Moody T. Chu and Gene H. Golub
- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198566649
- eISBN:
- 9780191718021
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198566649.003.0004
- Subject:
- Mathematics, Applied Mathematics
The feasibility conditions for a physical system often mandate specific structural stipulations on the inverse problems. This chapter focuses on eight selected structures: Jacobi matrices, Toeplitz ...
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The feasibility conditions for a physical system often mandate specific structural stipulations on the inverse problems. This chapter focuses on eight selected structures: Jacobi matrices, Toeplitz matrices, nonnegative matrices, stochastic matrices, unitary matrices, matrices with prescribed entries, matrices with prescribed singular values, and matrices with prescribed singular values and eigenvalues.Less
The feasibility conditions for a physical system often mandate specific structural stipulations on the inverse problems. This chapter focuses on eight selected structures: Jacobi matrices, Toeplitz matrices, nonnegative matrices, stochastic matrices, unitary matrices, matrices with prescribed entries, matrices with prescribed singular values, and matrices with prescribed singular values and eigenvalues.
Karl Ameriks
- Published in print:
- 2006
- Published Online:
- September 2007
- ISBN:
- 9780199205349
- eISBN:
- 9780191709272
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199205349.003.0008
- Subject:
- Philosophy, History of Philosophy
This chapter explains how Reinhold's Letters took the form of a ‘short’ Critique, which immediately after its publication was much more influential than the complex details of Kant's lengthy ...
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This chapter explains how Reinhold's Letters took the form of a ‘short’ Critique, which immediately after its publication was much more influential than the complex details of Kant's lengthy original. In the Letters, Reinhold simplified matters hugely by not venturing at all into the complexities of the Transcendental Aesthetic and Transcendental Analytic. He jumped ahead to the moral and historical implications of the end of the Dialectic, arguing that Kant's espousal of a Critical and moral form of rational religion was the ideal solution to the battles between supernaturalism and naturalism that were raging in Germany after Jacobi had ignited the Pantheism Dispute. Admitting that he was not yet tracing Kant's notion of pure practical reason and rational religion back to its ‘grounds’ in the first Critique, Reinhold satisfied himself and his audience with the claim that the ‘results’ of the Critique met the fundamental ‘need’ of the time (fully to satisfy popular Enlightenment morality through a hope in a ‘highest good’ warranted by rational religion) — just as Jesus had satisfied the ‘common sense’ of his time by turning dogmatic religion into rational morality.Less
This chapter explains how Reinhold's Letters took the form of a ‘short’ Critique, which immediately after its publication was much more influential than the complex details of Kant's lengthy original. In the Letters, Reinhold simplified matters hugely by not venturing at all into the complexities of the Transcendental Aesthetic and Transcendental Analytic. He jumped ahead to the moral and historical implications of the end of the Dialectic, arguing that Kant's espousal of a Critical and moral form of rational religion was the ideal solution to the battles between supernaturalism and naturalism that were raging in Germany after Jacobi had ignited the Pantheism Dispute. Admitting that he was not yet tracing Kant's notion of pure practical reason and rational religion back to its ‘grounds’ in the first Critique, Reinhold satisfied himself and his audience with the claim that the ‘results’ of the Critique met the fundamental ‘need’ of the time (fully to satisfy popular Enlightenment morality through a hope in a ‘highest good’ warranted by rational religion) — just as Jesus had satisfied the ‘common sense’ of his time by turning dogmatic religion into rational morality.
Alfonso Sorrentino
- Published in print:
- 2015
- Published Online:
- October 2017
- ISBN:
- 9780691164502
- eISBN:
- 9781400866618
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691164502.003.0005
- Subject:
- Mathematics, Applied Mathematics
This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the ...
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This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the functional analytic counterpart of the variational methods discussed in the previous chapters. The starting point is the relation between KAM tori (or more generally, invariant Lagrangian graphs) and classical solutions and subsolutions of the Hamilton–Jacobi equation. It introduces the notion of weak (non-classical) solutions of the Hamilton–Jacobi equation and a special class of subsolutions (critical subsolutions). In particular, it highlights their relation to Aubry–Mather theory.Less
This chapter describes another interesting approach to the study of invariant sets provided by the so-called weak KAM theory, developed by Albert Fathi. This approach can be considered as the functional analytic counterpart of the variational methods discussed in the previous chapters. The starting point is the relation between KAM tori (or more generally, invariant Lagrangian graphs) and classical solutions and subsolutions of the Hamilton–Jacobi equation. It introduces the notion of weak (non-classical) solutions of the Hamilton–Jacobi equation and a special class of subsolutions (critical subsolutions). In particular, it highlights their relation to Aubry–Mather theory.
Toshimasa Yasukata
- Published in print:
- 2003
- Published Online:
- November 2003
- ISBN:
- 9780195144949
- eISBN:
- 9780199834891
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195144945.003.0008
- Subject:
- Religion, Philosophy of Religion
Argues the question of Lessing's alleged “Spinozism.” The discussion shows that Lessing's hen kai pan [One and All] signifies not a Spinozistic pantheism but a panentheism of spiritualistic stamp. It ...
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Argues the question of Lessing's alleged “Spinozism.” The discussion shows that Lessing's hen kai pan [One and All] signifies not a Spinozistic pantheism but a panentheism of spiritualistic stamp. It is also pointed out that for Lessing's hen kai pan there are three different Greek formulas: hen kai pan, as Friedrich Heinrich Jacobi reports in his letter to Moses Mendelssohn; hen ego kai panta, as Lessing's own 1780 handwritten epigram suggests; and hen ego kai pan, as introduced in recent years by Alexander Altmann and Erwin Quapp. Religious‐philosophical as well as linguistic observation recommends taking the phrase hen ego kai panta [I am One and All] as Lessing's most authentic formula, thus suggesting that the world (panta and God (theos) are mediated through the first person “I” (ego). In view of this “panta” formula, our concluding proposal is to characterize Lessing's view of God and the world as “pantaentheism.”Less
Argues the question of Lessing's alleged “Spinozism.” The discussion shows that Lessing's hen kai pan [One and All] signifies not a Spinozistic pantheism but a panentheism of spiritualistic stamp. It is also pointed out that for Lessing's hen kai pan there are three different Greek formulas: hen kai pan, as Friedrich Heinrich Jacobi reports in his letter to Moses Mendelssohn; hen ego kai panta, as Lessing's own 1780 handwritten epigram suggests; and hen ego kai pan, as introduced in recent years by Alexander Altmann and Erwin Quapp. Religious‐philosophical as well as linguistic observation recommends taking the phrase hen ego kai panta [I am One and All] as Lessing's most authentic formula, thus suggesting that the world (panta and God (theos) are mediated through the first person “I” (ego). In view of this “panta” formula, our concluding proposal is to characterize Lessing's view of God and the world as “pantaentheism.”
Thomas Holden
- Published in print:
- 2010
- Published Online:
- May 2010
- ISBN:
- 9780199579945
- eISBN:
- 9780191722776
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199579945.003.0008
- Subject:
- Philosophy, History of Philosophy, Philosophy of Religion
This concluding chapter summarizes Hume's overall case for divine amorality and assesses the significance of his commitment to moral atheism, both for our wider understanding of his theoretical and ...
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This concluding chapter summarizes Hume's overall case for divine amorality and assesses the significance of his commitment to moral atheism, both for our wider understanding of his theoretical and practical philosophy, and for our understanding of the philosophical history of irreligion in the early modern period. It is argued that a proper understanding of Hume's commitment to moral atheism casts light on his general epistemology as well as the precise scope and force of his sceptical critique of traditional natural theology. Hume's moral atheism also has the important practical consequence of ruling out the fideistic proposal (found in Hamann, Jacobi, and Kant) that we might responsibly believe in or at least hope for a moral God even in the absence of knowledge.Less
This concluding chapter summarizes Hume's overall case for divine amorality and assesses the significance of his commitment to moral atheism, both for our wider understanding of his theoretical and practical philosophy, and for our understanding of the philosophical history of irreligion in the early modern period. It is argued that a proper understanding of Hume's commitment to moral atheism casts light on his general epistemology as well as the precise scope and force of his sceptical critique of traditional natural theology. Hume's moral atheism also has the important practical consequence of ruling out the fideistic proposal (found in Hamann, Jacobi, and Kant) that we might responsibly believe in or at least hope for a moral God even in the absence of knowledge.
Jörg Liesen and Zdenek Strakos
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199655410
- eISBN:
- 9780191744174
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199655410.001.0001
- Subject:
- Mathematics, Applied Mathematics, Algebra
This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov ...
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This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss–Christoffel quadrature, continued fractions, and, more generally, of Vorobyev method of moments. Using the concept of cyclic invariant subspaces conditions are studied that allow generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the practically important distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples. The book emphasises that algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation, and computation cannot be separated from each other. Moreover, the book underlines the importance of the historical context and it demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are therefore included as an inherent part of the text. The book ends with formulating some omitted issues and challenges which need to be addressed in future work. The book is intended as a research monograph which can be used in a wide scope of graduate courses on related subjects. It can be beneficial also for readers interested in the history of mathematics.Less
This book offers a detailed treatment of the mathematical theory of Krylov subspace methods with focus on solving systems of linear algebraic equations. Starting from the idea of projections, Krylov subspace methods are characterised by their orthogonality and minimisation properties. Projections onto highly nonlinear Krylov subspaces can be linked with the underlying problem of moments, and therefore Krylov subspace methods can be viewed as matching moments model reduction. This allows enlightening reformulations of questions from matrix computations into the language of orthogonal polynomials, Gauss–Christoffel quadrature, continued fractions, and, more generally, of Vorobyev method of moments. Using the concept of cyclic invariant subspaces conditions are studied that allow generation of orthogonal Krylov subspace bases via short recurrences. The results motivate the practically important distinction between Hermitian and non-Hermitian problems. Finally, the book thoroughly addresses the computational cost while using Krylov subspace methods. The investigation includes effects of finite precision arithmetic and focuses on the method of conjugate gradients (CG) and generalised minimal residuals (GMRES) as major examples. The book emphasises that algebraic computations must always be considered in the context of solving real-world problems, where the mathematical modelling, discretisation, and computation cannot be separated from each other. Moreover, the book underlines the importance of the historical context and it demonstrates that knowledge of early developments can play an important role in understanding and resolving very recent computational problems. Many extensive historical notes are therefore included as an inherent part of the text. The book ends with formulating some omitted issues and challenges which need to be addressed in future work. The book is intended as a research monograph which can be used in a wide scope of graduate courses on related subjects. It can be beneficial also for readers interested in the history of mathematics.
Michah Gottlieb
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780195398946
- eISBN:
- 9780199894499
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195398946.001.0001
- Subject:
- Religion, Judaism, Philosophy of Religion
Moses Mendelssohn (1729–1786) is often considered the founder of modern Jewish philosophy or even of modern Judaism. For many, Mendelssohn's commitment to enlightened values appeared to be ...
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Moses Mendelssohn (1729–1786) is often considered the founder of modern Jewish philosophy or even of modern Judaism. For many, Mendelssohn's commitment to enlightened values appeared to be irreconcilable with his life-long adherence to Judaism. This book approaches this problem by placing Mendelssohn's moderate enlightenment in three contexts: Maimonides' medieval enlightenment, Spinoza's radical enlightenment, and F.H. Jacobi's Christian counter-Enlightenment. This books argues that Mendelssohn breaks from Maimonides because he faces problems never encountered by Maimonides—namely how to remain an observant Jew in a modern state where Jews could be citizens with their Christian neighbors. Through an original, selective reading of Jewish tradition, Mendelssohn is able to achieve remarkable harmony between Judaism and enlightenment. But at the end of his life Mendelssohn confronts a profound challenge to his religious principles in the “Pantheism Controversy” that he wages with Jacobi over Lessing's alleged Spinozism. To defend his enlightened religious position, Mendelssohn develops a pragmatic religious idealism that inaugurates an anthropocentric turn in religious thought later developed by thinkers such as Hermann Cohen and Mordecai Kaplan.Less
Moses Mendelssohn (1729–1786) is often considered the founder of modern Jewish philosophy or even of modern Judaism. For many, Mendelssohn's commitment to enlightened values appeared to be irreconcilable with his life-long adherence to Judaism. This book approaches this problem by placing Mendelssohn's moderate enlightenment in three contexts: Maimonides' medieval enlightenment, Spinoza's radical enlightenment, and F.H. Jacobi's Christian counter-Enlightenment. This books argues that Mendelssohn breaks from Maimonides because he faces problems never encountered by Maimonides—namely how to remain an observant Jew in a modern state where Jews could be citizens with their Christian neighbors. Through an original, selective reading of Jewish tradition, Mendelssohn is able to achieve remarkable harmony between Judaism and enlightenment. But at the end of his life Mendelssohn confronts a profound challenge to his religious principles in the “Pantheism Controversy” that he wages with Jacobi over Lessing's alleged Spinozism. To defend his enlightened religious position, Mendelssohn develops a pragmatic religious idealism that inaugurates an anthropocentric turn in religious thought later developed by thinkers such as Hermann Cohen and Mordecai Kaplan.
Robert Stern
- Published in print:
- 2009
- Published Online:
- September 2009
- ISBN:
- 9780199239108
- eISBN:
- 9780191716942
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199239108.003.0011
- Subject:
- Philosophy, General
This chapter concerns Peirce's claim that Hegel neglected to give sufficient weight to what Peirce called ‘Firstness’, by which Peirce meant immediacy or individuality. Peirce's concerns are compared ...
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This chapter concerns Peirce's claim that Hegel neglected to give sufficient weight to what Peirce called ‘Firstness’, by which Peirce meant immediacy or individuality. Peirce's concerns are compared to a worry that surfaces in the German Idealist tradition with the later Schelling, and goes on to play a crucial role in the thought of many of Hegel's subsequent critics, from Kierkegaard to Deleuze: namely, has Hegel succeeded in addressing Jacobi's worry that our relation to the world must involve an immediacy that cannot be grasped in conceptual terms? Where Peirce's position is interesting, however, is that while he wants to do justice to this concern, he also wants to balance it with a commitment to what he calls Thirdness, and thus to mediation and generality, so that (this chapter argues) Peirce's outlook cannot represent a complete break with Hegel (as Peirce himself thought), but may rather provide a model for thinking about what a properly Hegelian treatment of this issue should really be.Less
This chapter concerns Peirce's claim that Hegel neglected to give sufficient weight to what Peirce called ‘Firstness’, by which Peirce meant immediacy or individuality. Peirce's concerns are compared to a worry that surfaces in the German Idealist tradition with the later Schelling, and goes on to play a crucial role in the thought of many of Hegel's subsequent critics, from Kierkegaard to Deleuze: namely, has Hegel succeeded in addressing Jacobi's worry that our relation to the world must involve an immediacy that cannot be grasped in conceptual terms? Where Peirce's position is interesting, however, is that while he wants to do justice to this concern, he also wants to balance it with a commitment to what he calls Thirdness, and thus to mediation and generality, so that (this chapter argues) Peirce's outlook cannot represent a complete break with Hegel (as Peirce himself thought), but may rather provide a model for thinking about what a properly Hegelian treatment of this issue should really be.
Adam M. Bincer
- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199662920
- eISBN:
- 9780191745492
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199662920.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Generalities refers to the definition of basic concepts. The goal here is to define group, field, vector space and algebra. The chapter starts with the definitions of associativity, identity, inverse ...
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Generalities refers to the definition of basic concepts. The goal here is to define group, field, vector space and algebra. The chapter starts with the definitions of associativity, identity, inverse and closure and use these to define group. This is followed by the definition of subgroup and invariant subgroup. The cyclic group is introduced to provide an example of a finite group. Next, homomorphism, isomorphism, realization and representation are defined. A canonical description of an N-dimensional vector space is given in terms of Nx1 column matrices. In conclusion, the commutator of two matrices is defined and the Jacobi identity is presented. Biographical notes on Galois, Abel and Jacobi are given.Less
Generalities refers to the definition of basic concepts. The goal here is to define group, field, vector space and algebra. The chapter starts with the definitions of associativity, identity, inverse and closure and use these to define group. This is followed by the definition of subgroup and invariant subgroup. The cyclic group is introduced to provide an example of a finite group. Next, homomorphism, isomorphism, realization and representation are defined. A canonical description of an N-dimensional vector space is given in terms of Nx1 column matrices. In conclusion, the commutator of two matrices is defined and the Jacobi identity is presented. Biographical notes on Galois, Abel and Jacobi are given.
Michah Gottlieb
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780195398946
- eISBN:
- 9780199894499
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195398946.003.0004
- Subject:
- Religion, Judaism, Philosophy of Religion
This chapter analyzes of Jacobi's critique of Mendelssohn's moderate religious enlightenment. For Jacobi, the very structure of reason is inimical to freedom and undermines individuality since reason ...
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This chapter analyzes of Jacobi's critique of Mendelssohn's moderate religious enlightenment. For Jacobi, the very structure of reason is inimical to freedom and undermines individuality since reason operates by means of logically necessary, universal judgments. Mendelssohn's support of enlightened absolutism is anti-humanistic since it levels the differences between all citizens and demands uncompromising obedience to the sovereign. For Jacobi, Spinoza's anti-humanistic philosophy is the culmination of enlightened reasoning as expressed by Lessing's confession of Spinozism and involves fatalism, which denies human free choice, pantheism, which denies the substantiality of the individual ego, and atheism. For Jacobi, in theological matters one must rely on individual faith, which rescues human individuality and freedom. Faith is an enemy of despotism for in making God's revelation to the individual the overriding determining principle of action, it gives the believer an Archimedean point from which to resist despotic rule.Less
This chapter analyzes of Jacobi's critique of Mendelssohn's moderate religious enlightenment. For Jacobi, the very structure of reason is inimical to freedom and undermines individuality since reason operates by means of logically necessary, universal judgments. Mendelssohn's support of enlightened absolutism is anti-humanistic since it levels the differences between all citizens and demands uncompromising obedience to the sovereign. For Jacobi, Spinoza's anti-humanistic philosophy is the culmination of enlightened reasoning as expressed by Lessing's confession of Spinozism and involves fatalism, which denies human free choice, pantheism, which denies the substantiality of the individual ego, and atheism. For Jacobi, in theological matters one must rely on individual faith, which rescues human individuality and freedom. Faith is an enemy of despotism for in making God's revelation to the individual the overriding determining principle of action, it gives the believer an Archimedean point from which to resist despotic rule.
Michah Gottlieb
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780195398946
- eISBN:
- 9780199894499
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195398946.003.0005
- Subject:
- Religion, Judaism, Philosophy of Religion
Mendelssohn sees Jacobi's favoring of republicanism as a rhetorical subterfuge aimed at promoting religious despotism. For Mendelssohn, Jacobi's rejection of the authority of reason in metaphysics ...
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Mendelssohn sees Jacobi's favoring of republicanism as a rhetorical subterfuge aimed at promoting religious despotism. For Mendelssohn, Jacobi's rejection of the authority of reason in metaphysics leads to religious oppression and Mendelssohn argues that when obeying the demands of reason we are most free. Mendelssohn holds that reason confirms the existence of a providential, good God and secures human individuality. Spinoza's error stems from his misunderstanding the principle of sufficient reason. Mendelssohn interprets Lessing's Spinozism as an innocuous type that is grounded in an attempt to give rational sense to Christian mysteries. Mendelssohn contrasts his Jewish concept of faith with Jacobi's Christian faith. Judaism seeks to unite of religion and reason, while Jacobi's Christianity creates a dichotomy between the two. In defending theism, Mendelssohn adopts a form of pragmatic religious idealism based on the efficacy of religious belief in promoting human flourishing.Less
Mendelssohn sees Jacobi's favoring of republicanism as a rhetorical subterfuge aimed at promoting religious despotism. For Mendelssohn, Jacobi's rejection of the authority of reason in metaphysics leads to religious oppression and Mendelssohn argues that when obeying the demands of reason we are most free. Mendelssohn holds that reason confirms the existence of a providential, good God and secures human individuality. Spinoza's error stems from his misunderstanding the principle of sufficient reason. Mendelssohn interprets Lessing's Spinozism as an innocuous type that is grounded in an attempt to give rational sense to Christian mysteries. Mendelssohn contrasts his Jewish concept of faith with Jacobi's Christian faith. Judaism seeks to unite of religion and reason, while Jacobi's Christianity creates a dichotomy between the two. In defending theism, Mendelssohn adopts a form of pragmatic religious idealism based on the efficacy of religious belief in promoting human flourishing.
S. G. Rajeev
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0005
- Subject:
- Physics, Atomic, Laser, and Optical Physics
In this chapter, the moment of inertia is defined and Euler's equations for the rigid body are derived. They can be solved in terms of Jacobi elliptic functions.
In this chapter, the moment of inertia is defined and Euler's equations for the rigid body are derived. They can be solved in terms of Jacobi elliptic functions.
S. G. Rajeev
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0009
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation ...
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This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation of optics as well as to the Schrödinger equation of quantum mechanics is explained.Less
This chapter derives the Hamilton-Jacobi equation. Euler's two centre problem is solved by using separation of variables in the elliptical co-ordinate system. The connection to the eikonal equation of optics as well as to the Schrödinger equation of quantum mechanics is explained.
S. G. Rajeev
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0011
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with ...
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This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with inverse cube force is shown to be more symmetric. Montgomery's ‘pair of pants’ metric is derived. The orbits are geodesics in a metric of negative curvature on the plane with three points removed. The Virial Theorem is suggested as an exercise.Less
This chapter derives the consequences of scale invariance in the three body problem. Jacobi co-ordinates are introduced. The orbits are geodesics in a certain metric. The three body problem with inverse cube force is shown to be more symmetric. Montgomery's ‘pair of pants’ metric is derived. The orbits are geodesics in a metric of negative curvature on the plane with three points removed. The Virial Theorem is suggested as an exercise.
S. G. Rajeev
- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199670857
- eISBN:
- 9780191775154
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199670857.003.0012
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter includes a detailed study of the three body problem where one of the bodies is infinitesimal and the other two are in circular motion. This applies to the Sun-Jupiter-Asteroid, ...
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This chapter includes a detailed study of the three body problem where one of the bodies is infinitesimal and the other two are in circular motion. This applies to the Sun-Jupiter-Asteroid, Earth-Moon-Satellite systems. Lagrange's surprising discovery of stable equilibrium points and orbits around them is explained. Jacobi's integral and Hill's regions are derived. A spin-off is a theory of stability in the presence of velocity dependent (Coriolis) forces: sometimes a maximum of the potential can be a stable equilibrium.Less
This chapter includes a detailed study of the three body problem where one of the bodies is infinitesimal and the other two are in circular motion. This applies to the Sun-Jupiter-Asteroid, Earth-Moon-Satellite systems. Lagrange's surprising discovery of stable equilibrium points and orbits around them is explained. Jacobi's integral and Hill's regions are derived. A spin-off is a theory of stability in the presence of velocity dependent (Coriolis) forces: sometimes a maximum of the potential can be a stable equilibrium.
