Paolo Mancosu
- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780198746829
- eISBN:
- 9780191809095
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198746829.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics, History of Philosophy
The book provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. The notion of abstraction in question is that ...
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The book provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. The notion of abstraction in question is that related to the use of abstraction principles in neo-logicism. The most familiar abstraction principle in this context is Hume’s Principle. Hume’s Principle says that two concepts have the same number if and only if the objects falling under each one of them can be put in one–one correspondence. Chapter 1 shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege’s discussion of them. The second chapter provides the first contextual analysis of Frege’s discussion of abstraction principles in section 64 of the Grundlagen; the second part investigates the foundational reflection on abstraction principles in the Peanosets not by using school and Russell. Chapter 3 discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities. This theory assigns numerosities to infinite sets not by using one–one correspondence but by preserving the part–whole principle, namely the principle according to which if a set A is strictly included in a set B, then the numerosity of A is strictly smaller than the numerosity of B. Mancosu shows how this new development leads to deep mathematical, historical, and philosophical problems. Chapter 4 brings the previous strands together by offering some surprising novel perspectives on neo-logicism.Less
The book provides an original investigation of historical and systematic aspects of the notions of abstraction and infinity and their interaction. The notion of abstraction in question is that related to the use of abstraction principles in neo-logicism. The most familiar abstraction principle in this context is Hume’s Principle. Hume’s Principle says that two concepts have the same number if and only if the objects falling under each one of them can be put in one–one correspondence. Chapter 1 shows that abstraction principles were quite widespread in the mathematical practice that preceded Frege’s discussion of them. The second chapter provides the first contextual analysis of Frege’s discussion of abstraction principles in section 64 of the Grundlagen; the second part investigates the foundational reflection on abstraction principles in the Peanosets not by using school and Russell. Chapter 3 discusses a novel approach to measuring the size of infinite sets known as the theory of numerosities. This theory assigns numerosities to infinite sets not by using one–one correspondence but by preserving the part–whole principle, namely the principle according to which if a set A is strictly included in a set B, then the numerosity of A is strictly smaller than the numerosity of B. Mancosu shows how this new development leads to deep mathematical, historical, and philosophical problems. Chapter 4 brings the previous strands together by offering some surprising novel perspectives on neo-logicism.
Jay F. Rosenberg
- Published in print:
- 2005
- Published Online:
- September 2011
- ISBN:
- 9780199275816
- eISBN:
- 9780191699849
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199275816.001.0001
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
This book introduces Immanuel Kant's masterwork, the Critique of Pure Reason, from a ‘relaxed’ problem-oriented perspective which treats Kant as an especially insightful practising philosopher, from ...
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This book introduces Immanuel Kant's masterwork, the Critique of Pure Reason, from a ‘relaxed’ problem-oriented perspective which treats Kant as an especially insightful practising philosopher, from whom we still have much to learn, intelligently and creatively responding to significant questions that transcend his work's historical setting. The book's main project is to command a clear view of how Kant understands various perennial problems, how he attempts to resolve them, and to what extent he succeeds. The constructive portions of the First Critique—the Aesthetic and Analytic—are explored in detail; the Paralogisms and Antinomies more briefly. At the same time the book is an introduction to the challenges of reading the text of Kant's work and, to that end, selectively adopts a more rigorous historical and exegetical stance.Less
This book introduces Immanuel Kant's masterwork, the Critique of Pure Reason, from a ‘relaxed’ problem-oriented perspective which treats Kant as an especially insightful practising philosopher, from whom we still have much to learn, intelligently and creatively responding to significant questions that transcend his work's historical setting. The book's main project is to command a clear view of how Kant understands various perennial problems, how he attempts to resolve them, and to what extent he succeeds. The constructive portions of the First Critique—the Aesthetic and Analytic—are explored in detail; the Paralogisms and Antinomies more briefly. At the same time the book is an introduction to the challenges of reading the text of Kant's work and, to that end, selectively adopts a more rigorous historical and exegetical stance.
Eric Schliesser
- Published in print:
- 2017
- Published Online:
- October 2017
- ISBN:
- 9780190690120
- eISBN:
- 9780190690151
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190690120.001.0001
- Subject:
- Philosophy, History of Philosophy
This book treats Adam Smith as a systematic philosopher. Smith was a giant of the Scottish Enlightenment with polymath interests. The book explores Smith’s economics and ethics in light of his other ...
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This book treats Adam Smith as a systematic philosopher. Smith was a giant of the Scottish Enlightenment with polymath interests. The book explores Smith’s economics and ethics in light of his other commitments on the nature of knowledge, the theory of emotions, the theory of mind, his account of language, the nature of causation, and his views on methodology. It places Smith’s ideas in the context of a host of other philosophers, especially David Hume, Rousseau, and Isaac Newton; it draws on the reception of Smith’s ideas by Sophie de Grouchy, Mary Wollstonecraft, and other philosophers and economists to sketch the elements of and the detailed connections within Smith’s system. The book traces out Smith’s system and puts it in the context of his highly developed views on the norms that govern responsible speech. In particular, the book articulates Smith’s concerns with the impact of his public policy recommendations, especially on the least powerful in society. In so doing, the book offers new interpretations of Smith’s views on the invisible hand, Wealth of Nations, his treatment of virtue, the nature of freedom, the individual’s relationship to society, his account of the passions, the moral roles of religion, and his treatment of the role of mathematics in economics. While the book offers a single argument, it is organized in modular fashion and includes a helpful index; readers with a more focused interest in Smith’s achievements can skip ahead to the section of interest.Less
This book treats Adam Smith as a systematic philosopher. Smith was a giant of the Scottish Enlightenment with polymath interests. The book explores Smith’s economics and ethics in light of his other commitments on the nature of knowledge, the theory of emotions, the theory of mind, his account of language, the nature of causation, and his views on methodology. It places Smith’s ideas in the context of a host of other philosophers, especially David Hume, Rousseau, and Isaac Newton; it draws on the reception of Smith’s ideas by Sophie de Grouchy, Mary Wollstonecraft, and other philosophers and economists to sketch the elements of and the detailed connections within Smith’s system. The book traces out Smith’s system and puts it in the context of his highly developed views on the norms that govern responsible speech. In particular, the book articulates Smith’s concerns with the impact of his public policy recommendations, especially on the least powerful in society. In so doing, the book offers new interpretations of Smith’s views on the invisible hand, Wealth of Nations, his treatment of virtue, the nature of freedom, the individual’s relationship to society, his account of the passions, the moral roles of religion, and his treatment of the role of mathematics in economics. While the book offers a single argument, it is organized in modular fashion and includes a helpful index; readers with a more focused interest in Smith’s achievements can skip ahead to the section of interest.
Lee M. Brown (ed.)
- Published in print:
- 2004
- Published Online:
- February 2006
- ISBN:
- 9780195114409
- eISBN:
- 9780199785827
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/019511440X.001.0001
- Subject:
- Philosophy, History of Philosophy
This book features a collection of essays that seek to provide accurate and well-developed characterizations of the epistemological and metaphysical concerns that shaped the conceptual languages and ...
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This book features a collection of essays that seek to provide accurate and well-developed characterizations of the epistemological and metaphysical concerns that shaped the conceptual languages and philosophical thought of sub-Saharan Africa. A common theme between the essays is that a word shared by different cultures can have different extensions while being taken to have the same sense. It is argued that the ability to appreciate or understand the conceptual languages of others is influenced by the extent to which this content is viewed from the perspectives of the native users of the language. Among the topics covered by the essays are conceptions of the person, truth, destiny, personal identity, and metaphysics.Less
This book features a collection of essays that seek to provide accurate and well-developed characterizations of the epistemological and metaphysical concerns that shaped the conceptual languages and philosophical thought of sub-Saharan Africa. A common theme between the essays is that a word shared by different cultures can have different extensions while being taken to have the same sense. It is argued that the ability to appreciate or understand the conceptual languages of others is influenced by the extent to which this content is viewed from the perspectives of the native users of the language. Among the topics covered by the essays are conceptions of the person, truth, destiny, personal identity, and metaphysics.
Robert Pasnau
- Published in print:
- 2017
- Published Online:
- December 2017
- ISBN:
- 9780198801788
- eISBN:
- 9780191840371
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198801788.001.0001
- Subject:
- Philosophy, History of Philosophy, Metaphysics/Epistemology
No part of philosophy is as disconnected from its history as is epistemology. After Certainty offers a reconstruction of that history as the story of an epistemic ideal first formulated by Plato and ...
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No part of philosophy is as disconnected from its history as is epistemology. After Certainty offers a reconstruction of that history as the story of an epistemic ideal first formulated by Plato and Aristotle, later developed throughout the Middle Ages, and then dramatically reformulated in the seventeenth century. In watching these debates unfold over the centuries, we come to understand why epistemology has traditionally been embedded within a much wider sphere of concerns about human nature and the reality of the world we live in. We also come to see why epistemology has become today a much narrower and specialized field, concerned with the conditions under which it is true to say, in English, that someone knows something. Looking back to earlier days, this study makes its way through the various and changing ideals of inquiry that have been pursued over the centuries, from the expectations of certainty and explanatory depth to the rising concern over evidence and precision, as famously manifested in the new science. At both the sensory and the intellectual levels, the initial expectation of infallibility is seen to give way to mere subjective indubitability, and in the end it is unclear whether anything remains of the epistemic ideals that philosophy has long pursued. All we may ultimately be left with is hope.Less
No part of philosophy is as disconnected from its history as is epistemology. After Certainty offers a reconstruction of that history as the story of an epistemic ideal first formulated by Plato and Aristotle, later developed throughout the Middle Ages, and then dramatically reformulated in the seventeenth century. In watching these debates unfold over the centuries, we come to understand why epistemology has traditionally been embedded within a much wider sphere of concerns about human nature and the reality of the world we live in. We also come to see why epistemology has become today a much narrower and specialized field, concerned with the conditions under which it is true to say, in English, that someone knows something. Looking back to earlier days, this study makes its way through the various and changing ideals of inquiry that have been pursued over the centuries, from the expectations of certainty and explanatory depth to the rising concern over evidence and precision, as famously manifested in the new science. At both the sensory and the intellectual levels, the initial expectation of infallibility is seen to give way to mere subjective indubitability, and in the end it is unclear whether anything remains of the epistemic ideals that philosophy has long pursued. All we may ultimately be left with is hope.
Richard Tieszen
- Published in print:
- 2011
- Published Online:
- May 2011
- ISBN:
- 9780199606207
- eISBN:
- 9780191725500
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199606207.001.0001
- Subject:
- Philosophy, History of Philosophy
This book contains an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic, with reference to his three ...
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This book contains an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic, with reference to his three philosophical heroes, Plato, Leibniz, and Husserl, and to his engagement with Kant. Close readings of Gödel's texts on foundations are supplemented with materials from the Gödel Nachlass and from Hao Wang's discussions with Gödel. Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed‐up theorems, and independence proofs are discussed throughout the book. A detailed analysis of his critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959, is provided. On this basis, a new type of platonic rationalism that requires rational intuition, called ‘constituted platonism’, is developed and defended. It is shown how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. The implications of the position for the claim that human minds (‘monads’) are machines are considered in some detail. Issues about pragmatic holism and rationalism are discussed in a final chapter.Less
This book contains an analysis, development, and defense of a number of central ideas in Kurt Gödel's writings on the philosophy and foundations of mathematics and logic, with reference to his three philosophical heroes, Plato, Leibniz, and Husserl, and to his engagement with Kant. Close readings of Gödel's texts on foundations are supplemented with materials from the Gödel Nachlass and from Hao Wang's discussions with Gödel. Gödel's views on the philosophical significance of his technical results on completeness, incompleteness, undecidability, consistency proofs, speed‐up theorems, and independence proofs are discussed throughout the book. A detailed analysis of his critique of Hilbert and Carnap, and of his subsequent turn to Husserl's transcendental philosophy in 1959, is provided. On this basis, a new type of platonic rationalism that requires rational intuition, called ‘constituted platonism’, is developed and defended. It is shown how constituted platonism addresses the problem of the objectivity of mathematics and of the knowledge of abstract mathematical objects. The implications of the position for the claim that human minds (‘monads’) are machines are considered in some detail. Issues about pragmatic holism and rationalism are discussed in a final chapter.
Andrews Reath
- Published in print:
- 2006
- Published Online:
- May 2006
- ISBN:
- 9780199288830
- eISBN:
- 9780191603648
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199288836.001.0001
- Subject:
- Philosophy, History of Philosophy
This book contains chapters on various features of Kant's moral psychology and moral theory, with particular emphasis on a conception of rational agency autonomy. The opening chapters explore ...
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This book contains chapters on various features of Kant's moral psychology and moral theory, with particular emphasis on a conception of rational agency autonomy. The opening chapters explore different elements of Kant's views about motivation, including an account of respect for morality as the distinctive moral motive and a view of the principle of happiness as a representation of the shared structure of non-moral choice. These chapters stress the unity of Kant's moral psychology by arguing that moral and non-moral considerations motivate in essentially the same way. Several of the chapters develop an original approach to Kant's conception of autonomy that emphasizes the political metaphors found throughout Kant's writings on ethics. They argue that autonomy is best interpreted not as a psychological capacity, but as a kind of sovereignty: in claiming that moral agents have autonomy, Kant regards them as a kind of sovereign legislator with the power to give moral law through their willing. The final chapters explore some of the implications of this conception of autonomy elsewhere in Kant's moral thought, arguing that his Formula of Universal Law uses this conception of autonomy to generate substantive moral principles and exploring the connection between Kantian self-legislation and duties to oneself.Less
This book contains chapters on various features of Kant's moral psychology and moral theory, with particular emphasis on a conception of rational agency autonomy. The opening chapters explore different elements of Kant's views about motivation, including an account of respect for morality as the distinctive moral motive and a view of the principle of happiness as a representation of the shared structure of non-moral choice. These chapters stress the unity of Kant's moral psychology by arguing that moral and non-moral considerations motivate in essentially the same way. Several of the chapters develop an original approach to Kant's conception of autonomy that emphasizes the political metaphors found throughout Kant's writings on ethics. They argue that autonomy is best interpreted not as a psychological capacity, but as a kind of sovereignty: in claiming that moral agents have autonomy, Kant regards them as a kind of sovereign legislator with the power to give moral law through their willing. The final chapters explore some of the implications of this conception of autonomy elsewhere in Kant's moral thought, arguing that his Formula of Universal Law uses this conception of autonomy to generate substantive moral principles and exploring the connection between Kantian self-legislation and duties to oneself.
Russell B. Goodman
- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199577545
- eISBN:
- 9780191802621
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199577545.001.0001
- Subject:
- Philosophy, History of Philosophy
This study of five American thinkers—Jonathan Edwards, Benjamin Franklin, Thomas Jefferson, Ralph Waldo Emerson, and Henry David Thoreau—considers their work in relation to the philosophers and other ...
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This study of five American thinkers—Jonathan Edwards, Benjamin Franklin, Thomas Jefferson, Ralph Waldo Emerson, and Henry David Thoreau—considers their work in relation to the philosophers and other thinkers they found important: to the deism of John Toland and Matthew Tindal, the moral sense theories of Francis Hutcheson, Adam Smith, and David Hume, the political and religious philosophy of John Locke, the romanticism of William Wordsworth and Samuel Taylor Coleridge, and the transcendental idealism of Immanuel Kant. The book considers Edwards’s condemnation and Franklin’s acceptance of deism, argues that Jefferson was an Epicurean in his metaphysical views and a Christian, Stoic, and Epicurean in his moral outlook, traces Emerson’s debts to writers from Madame de Staël to William Ellery Channing, and considers Thoreau’s orientation to the universe through sitting and walking. The morality of American slavery is a major theme in the book, introduced not to excuse or condemn, but to study how five formidably intelligent people thought about the question when it was—as it no longer is for us—open. Edwards, Franklin, and Jefferson owned slaves, though Franklin and Jefferson played important roles in disturbing the uneasy American moral equilibrium that included slavery, even as they approved an American constitution that incorporated it. Emerson and Thoreau were prominent public opponents of slavery in the 1840s and 1850s. The book contains an interlude on the concept of a republic and concludes with an epilogue documenting some continuities in American philosophy, particularly between Emerson’s Philosophy and pragmatism.Less
This study of five American thinkers—Jonathan Edwards, Benjamin Franklin, Thomas Jefferson, Ralph Waldo Emerson, and Henry David Thoreau—considers their work in relation to the philosophers and other thinkers they found important: to the deism of John Toland and Matthew Tindal, the moral sense theories of Francis Hutcheson, Adam Smith, and David Hume, the political and religious philosophy of John Locke, the romanticism of William Wordsworth and Samuel Taylor Coleridge, and the transcendental idealism of Immanuel Kant. The book considers Edwards’s condemnation and Franklin’s acceptance of deism, argues that Jefferson was an Epicurean in his metaphysical views and a Christian, Stoic, and Epicurean in his moral outlook, traces Emerson’s debts to writers from Madame de Staël to William Ellery Channing, and considers Thoreau’s orientation to the universe through sitting and walking. The morality of American slavery is a major theme in the book, introduced not to excuse or condemn, but to study how five formidably intelligent people thought about the question when it was—as it no longer is for us—open. Edwards, Franklin, and Jefferson owned slaves, though Franklin and Jefferson played important roles in disturbing the uneasy American moral equilibrium that included slavery, even as they approved an American constitution that incorporated it. Emerson and Thoreau were prominent public opponents of slavery in the 1840s and 1850s. The book contains an interlude on the concept of a republic and concludes with an epilogue documenting some continuities in American philosophy, particularly between Emerson’s Philosophy and pragmatism.
Anthony J. Lisska
- Published in print:
- 2016
- Published Online:
- August 2016
- ISBN:
- 9780198777908
- eISBN:
- 9780191823374
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198777908.001.0001
- Subject:
- Philosophy, History of Philosophy
This book presents an analysis of the principal texts used by Thomas Aquinas in developing his theory of perception. Little work has been devoted principally to his theory of perception and less ...
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This book presents an analysis of the principal texts used by Thomas Aquinas in developing his theory of perception. Little work has been devoted principally to his theory of perception and less still to inner sense. The thesis of intentionality serves as the philosophical backdrop of this analysis, which incorporates the insights not only of Franz Brentano but also of Anthony Kenny and John Haldane. The principal emphasis is on the importance of inner sense, with special reference to the vis cogitativa. By means of this faculty of inner sense, Aquinas offers an account of a direct awareness of individuals of natural kinds. By using this awareness, he can make better sense out of the process of abstraction using the active intellect (intellectus agens). Were it not for the vis cogitativa, Aquinas would be unable to account for an awareness of the principal ontological category in his metaphysics.Less
This book presents an analysis of the principal texts used by Thomas Aquinas in developing his theory of perception. Little work has been devoted principally to his theory of perception and less still to inner sense. The thesis of intentionality serves as the philosophical backdrop of this analysis, which incorporates the insights not only of Franz Brentano but also of Anthony Kenny and John Haldane. The principal emphasis is on the importance of inner sense, with special reference to the vis cogitativa. By means of this faculty of inner sense, Aquinas offers an account of a direct awareness of individuals of natural kinds. By using this awareness, he can make better sense out of the process of abstraction using the active intellect (intellectus agens). Were it not for the vis cogitativa, Aquinas would be unable to account for an awareness of the principal ontological category in his metaphysics.
Thomas Holden
- Published in print:
- 2004
- Published Online:
- January 2005
- ISBN:
- 9780199263264
- eISBN:
- 9780191601743
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199263264.001.0001
- Subject:
- Philosophy, History of Philosophy
Examines the debate in early modern philosophy over the composition and internal architecture of matter, focussing on problems concerning the structure of continua, the metaphysics of parts and ...
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Examines the debate in early modern philosophy over the composition and internal architecture of matter, focussing on problems concerning the structure of continua, the metaphysics of parts and wholes, and the individuation of material beings. Are the parts of material bodies actual or potential entities? Is matter divisible to infinity? Do material bodies resolve to atoms? All the leading figures of the period address this cluster of issues, including Galileo, Descartes, Hobbes, Leibniz, Newton, Hume, Boscovich, Reid, and Kant. Presents a historical and critical study of these discussions, and offers an overarching interpretation of the controversy. Locates the central problem in the tension between the early moderns’ actual parts ontology on the one hand, and the programme of the geometrization of nature on the other.Less
Examines the debate in early modern philosophy over the composition and internal architecture of matter, focussing on problems concerning the structure of continua, the metaphysics of parts and wholes, and the individuation of material beings. Are the parts of material bodies actual or potential entities? Is matter divisible to infinity? Do material bodies resolve to atoms? All the leading figures of the period address this cluster of issues, including Galileo, Descartes, Hobbes, Leibniz, Newton, Hume, Boscovich, Reid, and Kant. Presents a historical and critical study of these discussions, and offers an overarching interpretation of the controversy. Locates the central problem in the tension between the early moderns’ actual parts ontology on the one hand, and the programme of the geometrization of nature on the other.
“A Gentleman and an Officer”
‘A Nation of Beggars’?
The A Priori in Philosophy
A. J. Appasamy and his Reading of Rāmānuja
A. J. Tomlinson
Aaron Hill
The Abbey Theatre, 1899-1999
The Abbots and Priors of Late Medieval and Reformation England
Abelard and Heloise
