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.
To mark the centenary of the 1910 to 1913 publication of the monumental Principia Mathematica by Alfred N. Whitehead and Bertrand Russell, this collection of fifteen new essays by distinguished scholars considers the influence and history of PM over the last hundred years.
The evolution of gravitational tests from an epistemological perspective framed in the concept of rational reconstruction of Imre Lakatos, based on his methodology of research programmes. Unlike other works on the same subject, the evaluated period is very extensive, starting with Newton's natural philosophy and up to the quantum gravity theories of today. In order to explain in a more rational way the complex evolution of the gravity concept of the last century, I propose a natural extension of the methodology of the research programmes of Lakatos that I then use during the paper. I believe that this approach offers a new perspective on how evolved over time the concept of gravity and the methods of testing each theory of gravity, through observations and experiments. I argue, based on the methodology of the research programmes and the studies of scientists and philosophers, that the current theories of quantum gravity are degenerative, due to the lack of experimental evidence over a long period of time and of self-immunization against the possibility of falsification. Moreover, a methodological current is being developed that assigns a secondary, unimportant role to verification through observations and/or experiments. For this reason, it will not be possible to have a complete theory of quantum gravity in its current form, which to include to the limit the general relativity, since physical theories have always been adjusted, during their evolution, based on observational or experimental tests, and verified by the predictions made. Also, contrary to a widespread opinion and current active programs regarding the unification of all the fundamental forces of physics in a single final theory, based on string theory, I argue that this unification is generally unlikely, and it is not possible anyway for a unification to be developed based on current theories of quantum gravity, including string theory. In addition, I support the views of some scientists and philosophers that currently too much resources are being consumed on the idea of developing quantum gravity theories, and in particular string theory, to include general relativity and to unify gravity with other forces, as long as science does not impose such research programs. CONTENTS: Introduction Gravity Gravitational tests Methodology of Lakatos - Scientific rationality The natural extension of the Lakatos methodology Bifurcated programs Unifying programs 1. Newtonian gravity 1.1 Heuristics of Newtonian gravity 1.2 Proliferation of post-Newtonian theories 1.3 Tests of post-Newtonian theories 1.3.1 Newton's proposed tests 1.3.2 Tests of post-Newtonian theories 1.4 Newtonian gravity anomalies 1.5 Saturation point in Newtonian gravity 2. General relativity 2.1 Heuristics of the general relativity 2.2 Proliferation of post-Einsteinian gravitational theories 2.3 Post-Newtonian parameterized formalism (PPN) 2.4 Tests of general relativity and post-Einsteinian theories 2.4.1 Tests proposed by Einstein 2.4.2 Tests of post-Einsteinian theories 2.4.3 Classic tests 2.4.3.1 Precision of Mercury's perihelion 2.4.3.2 Light deflection 2.4.3.3 Gravitational redshift 2.4.4 Modern tests 2.4.4.1 Shapiro Delay 2.4.4.2 Gravitational dilation of time 2.4.4.3 Frame dragging and geodetic effect 2.4.4.4 Testing of the principle of equivalence 2.4.4.5 Solar system tests 2.4.5 Strong field gravitational tests 2.4.5.1 Gravitational lenses 2.4.5.2 Gravitational waves 2.4.5.3 Synchronization binary pulsars 2.4.5.4 Extreme environments 2.4.6 Cosmological tests 2.4.6.1 The expanding universe 2.4.6.2 Cosmological observations 2.4.6.3 Monitoring of weak gravitational lenses 2.5 Anomalies of general relativity 2.6 The saturation point of general relativity 3. Quantum gravity 3.1 Heuristics of quantum gravity 3.2 The tests of quantum gravity 3.3 Canonical quantum gravity 3.3.1 Tests proposed for the CQG 3.3.2. Loop quantum gravity 3.4 String theory 3.4.1 Heuristics of string theory 3.4.2. Anomalies of string theory 3.5 Other theories of quantum gravity 3.6 Unification (The Final Theory) 4. Cosmology Conclusions Notes Bibliography DOI: 10.13140/RG.2.2.35350.70724
Charles Chihara's new book develops and defends a structural view of the nature of mathematics, and uses it to explain a number of striking features of mathematics that have puzzled philosophers for centuries. The view is used to show that, in order to understand how mathematical systems are applied in science and everyday life, it is not necessary to assume that its theorems either presuppose mathematical objects or are even true. Chihara builds upon his previous work, in which he presented a new system of mathematics, the constructibility theory, which did not make reference to, or presuppose, mathematical objects. Now he develops the project further by analysing mathematical systems currently used by scientists to show how such systems are compatible with this nominalistic outlook. He advances several new ways of undermining the heavily discussed indispensability argument for the existence of mathematical objects made famous by Willard Quine and Hilary Putnam. And Chihara presents a rationale for the nominalistic outlook that is quite different from those generally put forward, which he maintains have led to serious misunderstandings. A Structural Account of Mathematics will be required reading for anyone working in this field.
Barry Schein proposes combining a second-order treatment of plurals with Donald Davidson's suggestion that there are positions for reference to events in ordinary predicates in order to account for several of the more puzzling features of plurals without invoking plural objects, with its attendant metaphysics, and also provide an absolute truth-theoretic characterization of the semantics of sentences with plurals in them. How do we make sense of sentences with plural noun phrases in them? In Plurals and Events, Barry Schein proposes combining a second-order treatment of plurals with Donald Davidson's suggestion that there are positions for reference to events in ordinary predicates in order to account for several of the more puzzling features of plurals without invoking plural objects, with its attendant metaphysics, and also provide an absolute truth-theoretic characterization of the semantics of sentences with plurals in them. Schein's highly original argument should have significant impact on how natural-language semantics is done, with repercussions for philosophy and logic. The book opens with foundational arguments that the logical language should have four major features: reduction to singular predication via a Davidsonian logical form, amereology of events, a logical syntax that allows the constituents of a Davidsonian analysis to be predicated of distinct events and separated from one another by other logical elements, and descriptive anaphors that cross-refer to the events described by antecedent clauses. A semantics for plurality and quantification is developed in the remaining chapters, which address some of the empirical and formal questions raised by the variety of interpretations in which plurals and quantifiers participate.
Originally published in 1962. A clear and simple account of the growth and structure of Mathematical Logic, no earlier knowledge of logic being required. After outlining the four lines of thought that have been its roots - the logic of Aristotle, the idea of all the parts of mathematics as systems to be designed on the same sort of plan as that used by Euclid and his Elements, and the discoveries in algebra and geometry in 1800-1860 - the book goes on to give some of the main ideas and theories of the chief writers on Mathematical Logic: De Morgan, Boole, Jevons, Pierce, Frege, Peano, Whitehead, Russell, Post, Hilbert and Goebel. Written to assist readers who require a general picture of current logic, it will also be a guide for those who will later be going more deeply into the expert details of this field.
This book provides an overview of type theory. The first part of the book is historical, yet at the same time, places historical systems in the modern setting. The second part deals with modern type theory as it developed since the 1940s, and with the role of propositions as types (or proofs as terms. The third part proposes new systems that bring more advantages together.
Bertrand Russell (1872–1970) was renowned as one of the founding figures of "analytic" philosophy, and for his lasting contributions to the study of logic, philosophy of language, philosophy of mathematics and epistemology. He was also famous for his popular works, where his humanism, ethics and antipathy towards religion came through in books such as The Problems of Philosophy, Why I am Not A Christian, and The Conquest of Happiness. Beginning with an overview of Russell’s life and work, Gregory Landini carefully explains Russell’s philosophy, to show why he ranks as one of the giants of British and Twentieth century philosophy. He discusses Russell’s major early works in philosophy of mathematics, including The Principles of Mathematics, wherein Russell illuminated and developed the ideas of Gottlob Frege; and the monumental three volume work written with Alfred North Whitehead, Principia Mathematica, where the authors attempted to show that all mathematical theory is part of logic, understood as a science of structure. Landini discusses the second edition of Principia Mathematica, to show Russell’s intellectual relationship with Wittgenstein and Ramsey. He discusses Russell’s epistemology and neutral monism before concluding with a discussion on Russell’s ethics, and the relationship between science and religion. Featuring a chronology and a glossary of terms, as well as suggestions for further reading at the end of each chapter, Russell is essential reading for anyone studying philosophy, and is an ideal guidebook for those coming to Russell for the first time.
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