First published in 1903, this volume revolutionized philosophy and forever altered the direction of ethical studies. A philosopher’s philosopher, G. E. Moore was the idol of the Bloomsbury group, and Lytton Strachey declared that Principia Ethica marked the rebirth of the Age of Reason. This work clarifies some of moral philosophy’s most common confusions and redefines the science’s terminology. Six chapters explore: the subject matter of ethics, naturalistic ethics, hedonism, metaphysical ethics, ethics in relation to conduct, and the ideal. (...) Moore's simplicity of style and precise use of everyday language exercised an enormous influence on the development of analytic philosophy, and they contribute to the continuing resonance of his compelling arguments. (shrink)

Motus quidem veros corporum singulorum cognofcere , & ab apparentibus actu diícriminare, difficillimum est ; propterca quod partes ípatij illius immobilis in quo corpora vere moventur, non incurrunt in sensus.

Principia Ethica is recognised as the definitive starting point for twentieth-century ethical theory. Its influence was first largely confined to the Bloomsbury Group - Maynard Keynes wrote that it was 'better than Plato' - who took it up for its celebration of the values of art and love; but later it achieved the widespread recognition it still retains as a classic text of analytic ethical theory. It is particularly renowned for Moore's argument that previous ethical theories have been guilty (...) of a fallacy - the 'naturalistic fallacy'. Principia Ethica is reprinted here with the previously unpublished Preface Moore wrote for a planned, but never completed, second edition. Though unfinished, it sets out clearly Moore's second thoughts about his own work. The volume also includes two important pieces from his later ethical writings, 'Free will' and 'The conception of intrinsic value', and a new introduction by Thomas Baldwin. (shrink)

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

The great three-volume Principia Mathematica is deservedly the most famous work ever written on the foundations of mathematics. Its aim is to deduce all the fundamental propositions of logic and mathematics from a small number of logical premisses and primitive ideas, and so to prove that mathematics is a development of logic. This abridged text of Volume I contains the material that is most relevant to an introductory study of logic and the philosophy of mathematics (more advanced students will (...) wish to refer to the complete edition). It contains the whole of the preliminary sections (which present the authors' justification of the philosophical standpoint adopted at the outset of their work); the whole of Part 1 (in which the logical properties of propositions, propositional functions, classes and relations are established); section 6 of Part 2 (dealing with unit classes and couples); and Appendices A and B (which give further developments of the argument on the theory of deduction and truth functions). (shrink)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects. This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex (...) terms is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics. Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. (shrink)

Principia Logico-Metaphysica contains a foundational logical theory for metaphysics, mathematics, and the sciences. It includes a canonical development of Abstract Object Theory [AOT], a metaphysical theory that distinguishes between ordinary and abstract objects.This article reports on recent work in which AOT has been successfully represented and partly automated in the proof assistant system Isabelle/HOL. Initial experiments within this framework reveal a crucial but overlooked fact: a deeply-rooted and known paradox is reintroduced in AOT when the logic of complex terms (...) is simply adjoined to AOT’s specially formulated comprehension principle for relations. This result constitutes a new and important paradox, given how much expressive and analytic power is contributed by having the two kinds of complex terms in the system. Its discovery is the highlight of our joint project and provides strong evidence for a new kind of scientific practice in philosophy, namely, computational metaphysics.Our results were made technically possible by a suitable adaptation of Benzmüller’s metalogical approach to universal reasoning by semantically embedding theories in classical higher-order logic. This approach enables one to reuse state-of-the-art higher-order proof assistants, such as Isabelle/HOL, for mechanizing and experimentally exploring challenging logics and theories such as AOT. Our results also provide a fresh perspective on the question of whether relational type theory or functional type theory better serves as a foundation for logic and metaphysics. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

If he had not been discouraged by the opposition of the farmers, Mein Herr could surely have done better still. He could have made his map into a relief map, with mountains and valleys represented on the scale of one foot to the foot; he could have represented every blade of grass and every pool of water, every pillar box and every fence, every mouse and every man, by a full-scale model in the appropriate and authentic materials. And all the (...) models could have been working models, programmed to represent exactly every waterfall and every thunderstorm, every birth, marriage anddeath, every renaissance and every reformation. If he had done all this the country would not simply do nearly as well, but just as well as the map. He could throw the country away, and still have the country. He could throw the map away, and still have all that he needed, unless for some reason he wanted to have two copies of his map. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

1. Teoria del diritto -- 2. Teoria della democrazia -- 3. La sintassi del diritto.

Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which we have explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's work (...) from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at the University of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties of fluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London, the National Medal of Science in the United States, and the Copley Medal from the Royal Society. His many publications include Radiative transfer, Hydrodynamic and hydromagnetic stability, and The mathematical theory of black holes, each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profound admiration for a scientist whose work he believed is unsurpassed, and unsurpassable. (shrink)

The prospect of organic unified knowledge challenges the increasing fragmentation of scientific disciplines which have become narrowly specialized with the accelerating rate of discoveries and the shaky status of many inductively obtained theories. Yet proof checkers which can control the logical correctness of reasoning offer the possibility of developing an integrative, deductive approach encompassing many branches of science within the same framework. The Principia Humanistica, developed by Krzysztof de Werszowec Rey, constitute such an attempt to apply the Mizar system (...) of verification to the human and related sciences as well as theology. Mizar is based on set theory whose terms may define the individual, value choices, the human person, culture, and religion. This essay explores the Mizar framework, including the definition of valuation and religion. It seeks to show the possibilities opened by such an integrated multidisciplinary approach for the study of free will, the definition of courage, and convergence towards unification with God. (shrink)

Abstract:I begin by asking whether there was a Fregean revolution in logic, and, if so, in what did it consist. I then ask whether, and if so, to what extent, Russell played a decisive role in carrying through the Fregean revolution, and, if so, how. A subsidiary question is whether it was primarily the influence of The Principles of Mathematics or Principia Mathematica, or perhaps both, that stimulated and helped consummate the Fregean revolution. Finally, I examine cases in which (...) logicians sought, in the years immediately following publication of the Principles and Principia, to integrate traditional logic into the Fregean paradigm, focusing on the case of Henry Bradford Smith. My proposed conclusion is that there were different means adopted for rewriting the syllogism, in terms of the logic of relations, in terms of the propositional calculus, or as formulas of the monadic predicate calculus. This suggests that the changes implemented as a result of the adoption of the Russello-Fregean conception of logic could more accurately be called by Grattan-Guinness’s term convolution, rather than revolution. (shrink)

Presents Newton's unifying idea of gravitation and explains how he converted physics from a science of explanation into a general mathematical system.

Newton certainly regarded his second law of motion in the Principia as a fundamental axiom of mechanics. Yet the works that came after the Principia, the major treatises on the foundations of mechanics in the eighteenth century—by Varignon, Hermann, Euler, Maclaurin, d’Alembert, Euler (again), Lagrange, and Laplace—do not record, cite, discuss, or even mention the Principia’s statement of the second law. Nevertheless, the present study shows that all of these scientists do in fact assume the principle that (...) the Principia’s second law asserts as a fundamental axiom in their mechanics. (For what that second law asserts, we rely on Newton’s own testimony.) Some, like Varignon and Hermann, assume the axiom implicitly, apparently unaware that any assumption is being made, while others, like Maclaurin and Euler, assume the axiom explicitly, apparently unaware that the assertion assumed is the second law as Newton himself understood it. But in every case these scientists employ the principle asserted by the Principia’s second law fundamentally, unaware that they should be citing Neutonus, Prin., Phil. Nat. Math., Lex II. (shrink)

This paper illustrates the main features of Luigi Ferrajoli’s theoretical approach to law, as they are developed in his Principia Juris . These include his opposition to the traditional perspective of natural law; his anti-cognitivist orientation; and, finally, his fundamentally normative approach. Among the numerous problems discussed in Ferrajoli’s compendious book, the paper focuses on his definition of constitutional democracy. In particular, the paper discusses the way in which Ferrajoli defines the complementarity between democracy and rights; Ferrajoli’s own criticism (...) of T. H. Marshall’s idea of citizenship; and the importance that the distinction between ‘decidable’ and ‘non-decidable’ rights have in Ferrajoli’s own system. Other issues of interests that are briefly discussed include the constitutionalisation of private law, and the defence of different kinds of liberty-rights. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The illuminating Guide to Newton's _Principia_ by I. Bernard Cohen makes this preeminent work truly accessible for today's scientists, scholars, and students. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students. (shrink)

One of the questions that any future history of British moral philosophy in the twentieth century should investigate and document is how it came about that Moore's Principia Ethica was appropriated by what we can call the Humean tradition of moral philosophy. I shall not trace that development now but only argue that there was no excuse or justification for it.

One of the questions that any future history of British moral philosophy in the twentieth century should investigate and document is how it came about that Moore's Principia Ethica was appropriated by what we can call theHumean tradition of moral philosophy. I shall not trace that development now but only argue that there was no excuse or justification for it.

Originally published in 1910, Principia Mathematica led to the development of mathematical logic and computers and thus to information sciences. It became a model for modern analytic philosophy and remains an important work. In the late 1960s the Bertrand Russell Archives at McMaster University in Canada obtained Russell's papers, letters and library. These archives contained the manuscripts for the new Introduction and three Appendices that Russell added to the second edition in 1925. Also included was another manuscript, 'The Hierarchy (...) of Propositions and Functions', which was divided up and re-used to create the final changes for the second edition. These documents provide fascinating insight, including Russell's attempts to work out the theorems in the flawed Appendix B, 'On Induction'. An extensive introduction describes the stages of the manuscript material on the way to print and analyzes the proposed changes in the context of the development of symbolic logic after 1910. (shrink)

In his monumental 1687 work, _Philosophiae Naturalis Principia Mathematica_, known familiarly as the _Principia_, Isaac Newton laid out in mathematical terms the principles of time, force, and motion that have guided the development of modern physical science. Even after more than three centuries and the revolutions of Einsteinian relativity and quantum mechanics, Newtonian physics continues to account for many of the phenomena of the observed world, and Newtonian celestial dynamics is used to determine the orbits of our space vehicles. (...) This authoritative, modern translation by I. Bernard Cohen and Anne Whitman, the first in more than 285 years, is based on the 1726 edition, the final revised version approved by Newton; it includes extracts from the earlier editions, corrects errors found in earlier versions, and replaces archaic English with contemporary prose and up-to-date mathematical forms. Newton's principles describe acceleration, deceleration, and inertial movement; fluid dynamics; and the motions of the earth, moon, planets, and comets. A great work in itself, the _Principia_ also revolutionized the methods of scientific investigation. It set forth the fundamental three laws of motion and the law of universal gravity, the physical principles that account for the Copernican system of the world as emended by Kepler, thus effectively ending controversy concerning the Copernican planetary system. The translation-only edition of this preeminent work is truly accessible for today's scientists, scholars, and students. (shrink)

This volume of Bertrand Russell's Collected Papers finds Russell focused on writing Principia Mathematica during 1905-08. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of Principia went to the printer.

FOR PLATO, PRINCIPLES WERE THE ROOT-SOURCE of being or of knowledge. For Aristotle, they were the “first cause” of being, of becoming, or of being known. Much the same conception is at issue in Thomas of Aquinas, for whom a principle was something primary in the being of a thing, or in its becoming, or in knowledge of it. As standard philosophical usage has evolved in the light of these ideas, a principle is as something basic—as a fundamentum or archê. (...) It either admits no proof or it needs not proof. Moreover, it must be abstract by way of applying to a broad range of cases. Thus, all concerned seem agreed that principles are fundamental generalities governing our understanding of the modus operandi of some knowledge-accessible domain. (shrink)

FOR PLATO, PRINCIPLES WERE THE ROOT-SOURCE of being or of knowledge. For Aristotle, they were the “first cause” of being, of becoming, or of being known. Much the same conception is at issue in Thomas of Aquinas, for whom a principle was something primary in the being of a thing, or in its becoming, or in knowledge of it. As standard philosophical usage has evolved in the light of these ideas, a principle is as something basic—as a fundamentum or archê. (...) It either admits no proof or it needs not proof. Moreover, it must be abstract by way of applying to a broad range of cases. Thus, all concerned seem agreed that principles are fundamental generalities governing our understanding of the modus operandi of some knowledge-accessible domain. (shrink)

On the occasion of the centenary of the publication of the first volume of Principia Mathematica, this article aims to shed some light on Whitehead’s philosophy of mathematics, to differentiate Whitehead’s version of logicism from Russell’s, and to show the unity of Whitehead’s thought. These aims rely on Whitehead’s basic insight that mathematics is the study of pattern.

It is generally acknowledged that the 1910 Principia does not deny the existence of classes, but claims only that the theory it advances can be developed so that any apparent commitment to them is eliminable by the method of contextual analysis. The application of contextual analysis to ontological questions is widely viewed as the central philosophical innovation of Russell’s theory of descriptions. Principia’s “no-classes theory of classes” is a striking example of such an application. The present paper develops (...) a reconstruction of Principia’s theory of functions and classes that is based on Russell’s epistemological applications of the method of contextual analysis. Such a reconstruction is not eliminativist—indeed, it explicitly assumes the existence of classes—and possesses certain advantages over the no–classes theory advocated by Whitehead and Russell. (shrink)

Here the concern is with the logic underlying Whitehead and Russell's Principia Mathematica and with the relation of that logic to Russell's underlying metaphysics. The author emphasizes the fact that work is, strictly speaking, a theory of propositional functions, not of classes; sentences containing symbols for classes are defined by means of propositional functions. It is terms of the latter sort of entity that Russell's Paradox must be solved; the theory of types is, strictly speaking, a theory of the (...) stratification of propositional functions. (shrink)

A. P. Rao is considered to be one of India's leading, modern philosophers. In this compelling new monograph, he discusses the unique philosophical energies and synergies between Russell and Wittgenstein's seminal works and re-interprets the logical-positivist thrust of language and mathematical philosophy in this century and into the next.