Stewart Shapiro
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780198250296
- eISBN:
- 9780191598388
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198250290.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal ...
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A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.Less
A language is second‐order, or higher‐order, if it has bound variables that range over properties or sets of the items in the range of the ordinary, first‐order variables. This book presents a formal development of second‐ and higher‐order logic and an extended argument that higher‐order systems have an important role to play in the philosophy and foundations of mathematics. The development includes the languages, deductive systems, and model‐theoretic semantics for higher‐order languages, and the basic and advanced results in its meta‐theory: completeness, compactness, and the Löwenheim–Skolem theorems for Henkin semantics, and the failure of those results for standard semantics. Argues that second‐order theories and formalizations, with standard semantics, provide better models of important aspects of mathematics than their first‐order counterparts. Despite the fact that Quine is the main opponent of second‐order logic (arguing that second‐order logic is set‐theory in disguise), the present argument is broadly Quinean, proposing that there is no sharp line dividing mathematics from logic, especially the logic of mathematics. Also surveys the historical development in logic, tracing the emergence of first‐order logic as the de facto standard among logicians and philosophers. The connection between formal deduction and reasoning is related to Wittgensteinian issues concerning rule‐following. The book closes with an examination of several alternatives to second‐order logic: first‐order set theory, infinitary languages, and systems that are, in a sense, intermediate between first order and second order.
Charles S. Chihara
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.001.0001
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the ...
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A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.Less
A continuation of the study of mathematical existence begun in Ontology and the Vicious‐Circle Principle (published in 1973); in the present work, Quine's indispensability argument is rebutted by the development of a new nominalistic version of mathematics (the Constructibility Theory) that is specified as an axiomatized theory formalized in a many‐sorted first‐order language. What is new in the present work is its abandonment of the predicative restrictions of the earlier work and its much greater attention to the applications of mathematics in science and everyday life. The book also contains detailed discussions of rival views (Mathematical Structuralism, Field's Instrumentalism, Burgess's Moderate Realism, Maddy's Set Theoretical Realism, and Kitcher's Ideal Agent account of mathematics), in which many comparisons with the Constructibility Theory are made.
Thomas Koshy
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780195334548
- eISBN:
- 9780199868766
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195334548.003.0005
- Subject:
- Mathematics, Combinatorics / Graph Theory / Discrete Mathematics
This chapter presents Catalan numbers in an interesting, historical perspective, beginning with the well-known triangulation problem. In addition, it develops three recursive formulas for Cn, an ...
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This chapter presents Catalan numbers in an interesting, historical perspective, beginning with the well-known triangulation problem. In addition, it develops three recursive formulas for Cn, an approximate value for Cn, a relationship with the gamma function, and Shapiro's identity. It also shows how the parenthesization and triangulation problems are closely related.Less
This chapter presents Catalan numbers in an interesting, historical perspective, beginning with the well-known triangulation problem. In addition, it develops three recursive formulas for Cn, an approximate value for Cn, a relationship with the gamma function, and Shapiro's identity. It also shows how the parenthesization and triangulation problems are closely related.
Graham Priest
- Published in print:
- 2006
- Published Online:
- May 2007
- ISBN:
- 9780199263301
- eISBN:
- 9780191718823
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199263301.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The study of formal inconsistent arithmetics has already occasioned a number of interesting technical results, as well as philosophical spin-offs. This chapter looks at some of these. It shows how ...
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The study of formal inconsistent arithmetics has already occasioned a number of interesting technical results, as well as philosophical spin-offs. This chapter looks at some of these. It shows how inconsistent arithmetics are delivered by certain kinds of inconsistent models, and what such models are like. It then turns to more philosophical issues. These concern, importantly, the way that inconsistent arithmetics relate to some of the limitative results of classical metamathematics.Less
The study of formal inconsistent arithmetics has already occasioned a number of interesting technical results, as well as philosophical spin-offs. This chapter looks at some of these. It shows how inconsistent arithmetics are delivered by certain kinds of inconsistent models, and what such models are like. It then turns to more philosophical issues. These concern, importantly, the way that inconsistent arithmetics relate to some of the limitative results of classical metamathematics.
Michele Maggiore
- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780198570745
- eISBN:
- 9780191717666
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198570745.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter discusses the experimental evidence for the existence of GWs, which was first obtained from the Hulse-Taylor binary pulsar, PSR B1913+16, and which is now further confirmed by ...
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This chapter discusses the experimental evidence for the existence of GWs, which was first obtained from the Hulse-Taylor binary pulsar, PSR B1913+16, and which is now further confirmed by observations in other relativistic binary systems. These binary pulsars are remarkable, allowing for high precision verification of various predictions of general relativity. Hulse and Taylor were awarded the Nobel Prize in 1993, ‘for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation’, which included a demonstration of the emission of gravitational radiation, achieved by Taylor and co-workers in the late 1970s and early 1980s. The full pulsar timing formula, including various special- and general-relativistic effects such as Roemer, Einstein, and Shapiro time delay, is then derived. The recently discovered double pulsar is also discussed.Less
This chapter discusses the experimental evidence for the existence of GWs, which was first obtained from the Hulse-Taylor binary pulsar, PSR B1913+16, and which is now further confirmed by observations in other relativistic binary systems. These binary pulsars are remarkable, allowing for high precision verification of various predictions of general relativity. Hulse and Taylor were awarded the Nobel Prize in 1993, ‘for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation’, which included a demonstration of the emission of gravitational radiation, achieved by Taylor and co-workers in the late 1970s and early 1980s. The full pulsar timing formula, including various special- and general-relativistic effects such as Roemer, Einstein, and Shapiro time delay, is then derived. The recently discovered double pulsar is also discussed.
Jeffrey Brand-Ballard
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780195342291
- eISBN:
- 9780199867011
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195342291.003.0017
- Subject:
- Philosophy, Political Philosophy
This chapter examines more restrictive theories of rule guidance, including those of legal formalists such as Larry Alexander and Frederick Schauer, and that of an exclusive positivist, Scott J. ...
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This chapter examines more restrictive theories of rule guidance, including those of legal formalists such as Larry Alexander and Frederick Schauer, and that of an exclusive positivist, Scott J. Shapiro. The chapter shows that their arguments do not impugn selective optimization. Shapiro’s constraint model of rule guidance is examined and found to be partially compatible with selective optimization. Shapiro’s practical difference thesis is also reconciled with selective optimization, albeit not in a way Shapiro is likely to favor. The chapter concludes by briefly contrasting selective optimization with Richard A. Posner’s legal pragmatism and Lawrence Solum’s theory of equity.Less
This chapter examines more restrictive theories of rule guidance, including those of legal formalists such as Larry Alexander and Frederick Schauer, and that of an exclusive positivist, Scott J. Shapiro. The chapter shows that their arguments do not impugn selective optimization. Shapiro’s constraint model of rule guidance is examined and found to be partially compatible with selective optimization. Shapiro’s practical difference thesis is also reconciled with selective optimization, albeit not in a way Shapiro is likely to favor. The chapter concludes by briefly contrasting selective optimization with Richard A. Posner’s legal pragmatism and Lawrence Solum’s theory of equity.
Stewart Alan
- Published in print:
- 2008
- Published Online:
- October 2011
- ISBN:
- 9780199549276
- eISBN:
- 9780191701504
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199549276.003.0009
- Subject:
- Literature, Shakespeare Studies
The letters that this book has examined operate in a bewildering variety of ways, but a theme emerges. As Mary Poovey and Barbara Shapiro have argued, the culture in which and for which William ...
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The letters that this book has examined operate in a bewildering variety of ways, but a theme emerges. As Mary Poovey and Barbara Shapiro have argued, the culture in which and for which William Shakespeare wrote his plays had an increasing interest in and reliance on bureaucratic record-keeping, documentary evidence, and verifiable proofs. Letters were part of this trend, not merely a means to maintain communication across distances, but increasingly taken as documentary evidence of transactions, of responsibility, and ultimately of guilt. This impulse is registered repeatedly throughout Shakespeare's plays. Indeed, an account focused on the sheer incidence of these letters in the plays might well conclude that Shakespeare was admitting the priority of written documents. However this verdict ignores the fact that these are plays performed in a theatre in front of an audience: the audience does not read the letters, but instead sees the transactions they produce.Less
The letters that this book has examined operate in a bewildering variety of ways, but a theme emerges. As Mary Poovey and Barbara Shapiro have argued, the culture in which and for which William Shakespeare wrote his plays had an increasing interest in and reliance on bureaucratic record-keeping, documentary evidence, and verifiable proofs. Letters were part of this trend, not merely a means to maintain communication across distances, but increasingly taken as documentary evidence of transactions, of responsibility, and ultimately of guilt. This impulse is registered repeatedly throughout Shakespeare's plays. Indeed, an account focused on the sheer incidence of these letters in the plays might well conclude that Shakespeare was admitting the priority of written documents. However this verdict ignores the fact that these are plays performed in a theatre in front of an audience: the audience does not read the letters, but instead sees the transactions they produce.
Joseph P. Tomain
- Published in print:
- 2009
- Published Online:
- May 2009
- ISBN:
- 9780195333411
- eISBN:
- 9780199868841
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195333411.003.0002
- Subject:
- Law, Philosophy of Law
The Allegory of the Cave is both more familiar and complex than it might first appear. The familiar part of this allegory is that a prisoner is unshackled and works his way into the warmth and light ...
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The Allegory of the Cave is both more familiar and complex than it might first appear. The familiar part of this allegory is that a prisoner is unshackled and works his way into the warmth and light of sun where he “sees” the Good, the True, the Beautiful, and the Just. But now comes the complex part. Neither the prisoner nor we can literally or figuratively see the sun. Nor can we know Justice beyond having a sense of it. This chapter argues that Plato gives us less of a definition of the higher law than he provides a method, the dialectic, for trying to find it. The Allegory of the Cave confirms the notion that we all have a sense of Justice, that we must be educated to it, but that we can never completely obtain it.Less
The Allegory of the Cave is both more familiar and complex than it might first appear. The familiar part of this allegory is that a prisoner is unshackled and works his way into the warmth and light of sun where he “sees” the Good, the True, the Beautiful, and the Just. But now comes the complex part. Neither the prisoner nor we can literally or figuratively see the sun. Nor can we know Justice beyond having a sense of it. This chapter argues that Plato gives us less of a definition of the higher law than he provides a method, the dialectic, for trying to find it. The Allegory of the Cave confirms the notion that we all have a sense of Justice, that we must be educated to it, but that we can never completely obtain it.
H. Asada, T. Futamase, and P. A. Hogan
- Published in print:
- 2010
- Published Online:
- January 2011
- ISBN:
- 9780199584109
- eISBN:
- 9780191723421
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199584109.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
For a binary star system the periastron advance per orbit period is calculated as well as the Shapiro time delay in radar arrival time due to the passage of the signal through the gravitational field ...
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For a binary star system the periastron advance per orbit period is calculated as well as the Shapiro time delay in radar arrival time due to the passage of the signal through the gravitational field of the binary. The effect of gravitational radiation reaction on the orbital period and on the shape of the orbit is derived by studying the perturbations of the osculating elements of the orbit and alternatively by using traditional energy and angular momentum balance arguments. The gravitational interaction of spin is also discussed.Less
For a binary star system the periastron advance per orbit period is calculated as well as the Shapiro time delay in radar arrival time due to the passage of the signal through the gravitational field of the binary. The effect of gravitational radiation reaction on the orbital period and on the shape of the orbit is derived by studying the perturbations of the osculating elements of the orbit and alternatively by using traditional energy and angular momentum balance arguments. The gravitational interaction of spin is also discussed.
Fraser MacBride
- Published in print:
- 2005
- Published Online:
- July 2005
- ISBN:
- 9780195148770
- eISBN:
- 9780199835560
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195148770.003.0018
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of ...
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The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of anapparently different kind, and what, if any, intrinsic properties mathematical objects possess. According to one influential interpretation of mathematical discourse, this is because the objects under study are themselves incomplete; they are positions or akin to positions in patterns or structures. Two versions of this idea are examined (Resnik, Shapiro). It is argued that the evidence adduced in favor of the incompleteness of mathematical objects underdetermines whether it is the objects themselves or our knowledge of them that is incomplete. Also, holding that mathematical objects are incomplete conflicts with the practice of mathematics. The objection that structuralism is committed to the identity of indiscernibles is evaluated and it is also argued that the identification of objects with positions is metaphysically suspect.Less
The basic relations and functions that mathematicians use to identify mathematical objects fail to settle whether mathematical objects of one kind are identical to or distinct from objects of an
apparently different kind, and what, if any, intrinsic properties mathematical objects possess. According to one influential interpretation of mathematical discourse, this is because the objects under study are themselves incomplete; they are positions or akin to positions in patterns or structures. Two versions of this idea are examined (Resnik, Shapiro). It is argued that the evidence adduced in favor of the incompleteness of mathematical objects underdetermines whether it is the objects themselves or our knowledge of them that is incomplete. Also, holding that mathematical objects are incomplete conflicts with the practice of mathematics. The objection that structuralism is committed to the identity of indiscernibles is evaluated and it is also argued that the identification of objects with positions is metaphysically suspect.
Matthew H. Kramer
- Published in print:
- 2008
- Published Online:
- January 2009
- ISBN:
- 9780199546138
- eISBN:
- 9780191705434
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546138.003.0003
- Subject:
- Law, Philosophy of Law
This chapter develops further the positions taken in Chapter 1, and it explains how moral principles can enter into the law of a legal system even if legal officials are mistaken in many of the ...
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This chapter develops further the positions taken in Chapter 1, and it explains how moral principles can enter into the law of a legal system even if legal officials are mistaken in many of the concrete moral judgments which they reach during their adjudicative and administrative determinations. It replies to criticisms directed by Scott Shapiro and Jules Coleman against an early version of Chapter 1.Less
This chapter develops further the positions taken in Chapter 1, and it explains how moral principles can enter into the law of a legal system even if legal officials are mistaken in many of the concrete moral judgments which they reach during their adjudicative and administrative determinations. It replies to criticisms directed by Scott Shapiro and Jules Coleman against an early version of Chapter 1.
Antony Hatzistavrou
- Published in print:
- 2007
- Published Online:
- January 2009
- ISBN:
- 9780199237159
- eISBN:
- 9780191705427
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199237159.003.0007
- Subject:
- Law, Philosophy of Law
This chapter presents an epistemic account of the internal point of view. It argues that to have the internal point of view towards law is to be epistemically guided by law and especially by the rule ...
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This chapter presents an epistemic account of the internal point of view. It argues that to have the internal point of view towards law is to be epistemically guided by law and especially by the rule of recognition. The chapter is divided in the four parts. The first part argues contra Shapiro that Hart accepts a variety of motives for one's conformity, which do not include the consideration that a legal rule applies. The second part argues contra Holton that the inconsistency in Hart's account of the internal point of view arises only on Holton's assumption that the internal point of view has motivational clout and that this assumption is ungrounded. The third part constructs an account of the internal point of view on which it provides only epistemic guidance. Finally, the fourth part explains how, on the proposed account, the internal point of view is distinguished from the external point of view.Less
This chapter presents an epistemic account of the internal point of view. It argues that to have the internal point of view towards law is to be epistemically guided by law and especially by the rule of recognition. The chapter is divided in the four parts. The first part argues contra Shapiro that Hart accepts a variety of motives for one's conformity, which do not include the consideration that a legal rule applies. The second part argues contra Holton that the inconsistency in Hart's account of the internal point of view arises only on Holton's assumption that the internal point of view has motivational clout and that this assumption is ungrounded. The third part constructs an account of the internal point of view on which it provides only epistemic guidance. Finally, the fourth part explains how, on the proposed account, the internal point of view is distinguished from the external point of view.
Lamed Shapiro
Leah Garrett (ed.)
- Published in print:
- 2007
- Published Online:
- October 2013
- ISBN:
- 9780300110692
- eISBN:
- 9780300134698
- Item type:
- book
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110692.001.0001
- Subject:
- Literature, American, 20th Century Literature
Lamed Shapiro (1878–1948) was the author of groundbreaking and controversial short stories, novellas, and essays. Himself a tragic figure, Shapiro led a life marked by frequent ocean crossing, ...
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Lamed Shapiro (1878–1948) was the author of groundbreaking and controversial short stories, novellas, and essays. Himself a tragic figure, Shapiro led a life marked by frequent ocean crossing, alcoholism, and failed ventures, yet his writings are models of precision, psychological insight, and daring. Shapiro focuses intently on the nature of violence: the mob violence of pogroms committed against Jews; the traumatic after-effects of rape, murder, and powerlessness; and, the murderous event that transforms the innocent child into witness and the rabbi's son into agitator. Within a society on the move, Shapiro's refugees from the shtetl and the traditional way of life are in desperate search of food, shelter, love, and things of beauty. Remarkably, and against all odds, they sometimes find what they are looking for. More often than not, the climax of their lives is an experience of ineffable terror. This book also reveals Lamed Shapiro as an American master. His writings depict the Old World struggling with the New, extremes of human behaviour combined with the pursuit of normal happiness. Through the perceptions of a remarkable gallery of men, women, children—even of animals and plants—Shapiro successfully reclaimed the lost world of the shtetl as he negotiated East Broadway and the Bronx, Union Square, and vaudeville.Less
Lamed Shapiro (1878–1948) was the author of groundbreaking and controversial short stories, novellas, and essays. Himself a tragic figure, Shapiro led a life marked by frequent ocean crossing, alcoholism, and failed ventures, yet his writings are models of precision, psychological insight, and daring. Shapiro focuses intently on the nature of violence: the mob violence of pogroms committed against Jews; the traumatic after-effects of rape, murder, and powerlessness; and, the murderous event that transforms the innocent child into witness and the rabbi's son into agitator. Within a society on the move, Shapiro's refugees from the shtetl and the traditional way of life are in desperate search of food, shelter, love, and things of beauty. Remarkably, and against all odds, they sometimes find what they are looking for. More often than not, the climax of their lives is an experience of ineffable terror. This book also reveals Lamed Shapiro as an American master. His writings depict the Old World struggling with the New, extremes of human behaviour combined with the pursuit of normal happiness. Through the perceptions of a remarkable gallery of men, women, children—even of animals and plants—Shapiro successfully reclaimed the lost world of the shtetl as he negotiated East Broadway and the Bronx, Union Square, and vaudeville.
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/9780199573639.003.0007
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
A spherically symmetric metric has two unknown scalar metric functions. The Schwarzschild solution to the GR field equation is presented. An embedding diagram is used to visualize such a warp space. ...
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A spherically symmetric metric has two unknown scalar metric functions. The Schwarzschild solution to the GR field equation is presented. An embedding diagram is used to visualize such a warp space. GR predicts a solar deflection of a light ray that is twice as large as that implied by the equivalence principle. We present a brief discussion of gravitational lensing, with the lens equation derived. The precession of Mercury's perihelion and the Shapiro time delay of a light ray are worked out as successful tests of general relativity.Less
A spherically symmetric metric has two unknown scalar metric functions. The Schwarzschild solution to the GR field equation is presented. An embedding diagram is used to visualize such a warp space. GR predicts a solar deflection of a light ray that is twice as large as that implied by the equivalence principle. We present a brief discussion of gravitational lensing, with the lens equation derived. The precession of Mercury's perihelion and the Shapiro time delay of a light ray are worked out as successful tests of general relativity.
Stewart Shapiro
- Published in print:
- 2000
- Published Online:
- November 2003
- ISBN:
- 9780199241279
- eISBN:
- 9780191597107
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0199241279.003.0014
- Subject:
- Philosophy, Metaphysics/Epistemology
It seems that if a thinker in an argument arrives at an empirical conclusion, then some of the belief‐formation or reasoning principles she employs must be a priori if the reasoning is to be ...
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It seems that if a thinker in an argument arrives at an empirical conclusion, then some of the belief‐formation or reasoning principles she employs must be a priori if the reasoning is to be knowledgeable. Stewart Shapiro accepts this claim, and investigates the way in which the basic principles of logic must have an a priori status if the process of empirical confirmation of propositions reasoning that involves such principles of logic is to make sense.Less
It seems that if a thinker in an argument arrives at an empirical conclusion, then some of the belief‐formation or reasoning principles she employs must be a priori if the reasoning is to be knowledgeable. Stewart Shapiro accepts this claim, and investigates the way in which the basic principles of logic must have an a priori status if the process of empirical confirmation of propositions reasoning that involves such principles of logic is to make sense.
Peter Redford (ed.)
- Published in print:
- 2016
- Published Online:
- May 2017
- ISBN:
- 9781526104489
- eISBN:
- 9781526121127
- Item type:
- chapter
- Publisher:
- Manchester University Press
- DOI:
- 10.7228/manchester/9781526104489.003.0002
- Subject:
- Literature, 16th-century and Renaissance Literature
The collection was assembled by William Parkhurst in the first decades of the seventeenth century, and later passed into the hands of the Finch family, at whose seat of Burley-on-the-Hill it was ...
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The collection was assembled by William Parkhurst in the first decades of the seventeenth century, and later passed into the hands of the Finch family, at whose seat of Burley-on-the-Hill it was examined in the nineteenth century by Alfred J Horwood of the Historical Manuscripts Commission, and in the early twentieth by the scholar Logan Pearsall Smith, who caused transcripts to be made of some of the material. These were used by later scholars, the manuscript itself being believed to have been destroyed by fire. The circumstances of this fire, and of the manuscript’s mysterious survival and subsequent discovery by I A Shapiro are described, as are its disappearance once again and rediscovery by Peter Beal. The survival was still not widely publicised and, until now, no detailed study of the Burley manuscript has been published.Less
The collection was assembled by William Parkhurst in the first decades of the seventeenth century, and later passed into the hands of the Finch family, at whose seat of Burley-on-the-Hill it was examined in the nineteenth century by Alfred J Horwood of the Historical Manuscripts Commission, and in the early twentieth by the scholar Logan Pearsall Smith, who caused transcripts to be made of some of the material. These were used by later scholars, the manuscript itself being believed to have been destroyed by fire. The circumstances of this fire, and of the manuscript’s mysterious survival and subsequent discovery by I A Shapiro are described, as are its disappearance once again and rediscovery by Peter Beal. The survival was still not widely publicised and, until now, no detailed study of the Burley manuscript has been published.
Charles S. Chihara
- Published in print:
- 1991
- Published Online:
- November 2003
- ISBN:
- 9780198239758
- eISBN:
- 9780191597190
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198239750.003.0007
- Subject:
- Philosophy, Logic/Philosophy of Mathematics
The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) ...
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The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik. A number of difficulties with these two views are detailed and it is explained how the Constructibility Theory is not troubled by the problems that Structuralism was explicitly developed to resolve.Less
The first of six chapters in which rival views are critically evaluated and compared with the Constructibility view described in earlier chapters. The views considered here (forms of ‘Structuralism’) are those of Stewart Shapiro and Michael Resnik. A number of difficulties with these two views are detailed and it is explained how the Constructibility Theory is not troubled by the problems that Structuralism was explicitly developed to resolve.
Lamed Shapiro
- Published in print:
- 2007
- Published Online:
- October 2013
- ISBN:
- 9780300110692
- eISBN:
- 9780300134698
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110692.003.0005
- Subject:
- Literature, American, 20th Century Literature
This chapter presents the text of Lamed Shapiro's short fiction titled The Kiss. It explains that the story is about a pogromist who kills a Jew because of his refusal to kiss the pogromist's feet. ...
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This chapter presents the text of Lamed Shapiro's short fiction titled The Kiss. It explains that the story is about a pogromist who kills a Jew because of his refusal to kiss the pogromist's feet. It suggests that the pogromist's act is a mockery of Christ's humility in washing the feet of John the Baptist.Less
This chapter presents the text of Lamed Shapiro's short fiction titled The Kiss. It explains that the story is about a pogromist who kills a Jew because of his refusal to kiss the pogromist's feet. It suggests that the pogromist's act is a mockery of Christ's humility in washing the feet of John the Baptist.
Lamed Shapiro
- Published in print:
- 2007
- Published Online:
- October 2013
- ISBN:
- 9780300110692
- eISBN:
- 9780300134698
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110692.003.0011
- Subject:
- Literature, American, 20th Century Literature
This chapter presents the text of Lamed Shapiro's short fiction titled The Rebbe and the Rebbetsin. It explains that the story is about a Jewish couple with the wife claiming to hear angels chanting ...
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This chapter presents the text of Lamed Shapiro's short fiction titled The Rebbe and the Rebbetsin. It explains that the story is about a Jewish couple with the wife claiming to hear angels chanting when they study the Torah and smell the odors of Paradise when the husband is cooking fish. It contends that the loving portrait of a traditional Jewish couple, suggests a future as barren as the rabbinic couple itself.Less
This chapter presents the text of Lamed Shapiro's short fiction titled The Rebbe and the Rebbetsin. It explains that the story is about a Jewish couple with the wife claiming to hear angels chanting when they study the Torah and smell the odors of Paradise when the husband is cooking fish. It contends that the loving portrait of a traditional Jewish couple, suggests a future as barren as the rabbinic couple itself.
Lamed Shapiro
- Published in print:
- 2007
- Published Online:
- October 2013
- ISBN:
- 9780300110692
- eISBN:
- 9780300134698
- Item type:
- chapter
- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300110692.003.0012
- Subject:
- Literature, American, 20th Century Literature
This chapter presents the text of Lamed Shapiro's short fiction titled The Man and His Servant. It explains that the story is about a man in a wheelchair being pushed by his young servant. It ...
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This chapter presents the text of Lamed Shapiro's short fiction titled The Man and His Servant. It explains that the story is about a man in a wheelchair being pushed by his young servant. It highlights the people's fear for this man and mentions that he never talks to his servant. It also discusses the servant's “fight for freedom”.Less
This chapter presents the text of Lamed Shapiro's short fiction titled The Man and His Servant. It explains that the story is about a man in a wheelchair being pushed by his young servant. It highlights the people's fear for this man and mentions that he never talks to his servant. It also discusses the servant's “fight for freedom”.
