the principles of mathematics revisited

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The Principles Of Mathematics Revisited

Author : Jaakko Hintikka
ISBN : 0521624983
Genre : Mathematics
File Size : 72. 83 MB
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This book, written by one of philosophy's pre-eminent logicians, argues that many of the basic assumptions common to logic, philosophy of mathematics and metaphysics are in need of change. It is therefore a book of critical importance to logical theory. Jaakko Hintikka proposes a new basic first-order logic and uses it to explore the foundations of mathematics. This new logic enables logicians to express on the first-order level such concepts as equicardinality, infinity, and truth in the same language. The famous impossibility results by Gödel and Tarski that have dominated the field for the last sixty years turn out to be much less significant than has been thought. All of ordinary mathematics can in principle be done on this first-order level, thus dispensing with the existence of sets and other higher-order entities.

Newton S Principia Revisited

Author : Michael Schmiechen
ISBN : 9783837053074
Genre :
File Size : 68. 34 MB
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PROBLEM. The treatise is devoted to the reconstruction of our 'instinctive beliefs' in classical mechanics and to present them 'as much isolated and as free from irrelevant additions as possible'. The same motivation has driven many authors since the publication of Newton's Principia. IMPORTANCE. Classical mechanics will remain the basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of relativistic and quantum mechanics. But it can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made 'absolutely' clear. METHOD. Based on the 'instinctive belief' that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only 'outside', classical mechanics is 'understood' by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the 'language of dynamics'. Evidence is produced that available philosophical expositions are not adequate for the purpose at hand. Mechanics is treated as part of physics, not of mathematics. Not sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundation of mechanics in general is subject and purpose of the exercise. The goal is reached using axiomatic systems as models. SCOPE. Following an account of the unsatisfactory state of affairs the treatise covers the epistemological foundations, abstract proto-mechanics, i. e. the theories of time and space, meta-mechanics, i. e. the theories of state space models and of quantities proper, and, as an instance of the latter, abstract elementary mechanics, the theory of translational motions of 'small' solid bodies in three-dimensional Euclidean space, including classical general relativity. Subsequently the theory of classical kinematics is developed as basis for interpreted proto-mechanics and interpreted elementary mechanics. As an amus

Lingua Universalis Vs Calculus Ratiocinator

Author : Jaakko Hintikka
ISBN : 9789401586016
Genre : Philosophy
File Size : 33. 29 MB
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R. G. Collingwood saw one of the main tasks of philosophers and of historians of human thought in uncovering what he called the ultimate presuppositions of different thinkers, of different philosophical movements and of entire eras of intellectual history. He also noted that such ultimate presuppositions usually remain tacit at first, and are discovered only by subsequent reflection. Collingwood would have been delighted by the contrast that constitutes the overall theme of the essays collected in this volume. Not only has this dichotomy ofviews been one ofthe mostcrucial watersheds in the entire twentieth-century philosophical thought. Not only has it remained largely implicit in the writings of the philosophers for whom it mattered most. It is a truly Collingwoodian presupposition also in that it is not apremise assumed by different thinkers in their argumentation. It is the presupposition of a question, an assumption to the effect that a certain general question can be raised and answered. Its role is not belied by the fact that several philosophers who answered it one way or the other seem to be largely unaware that the other answer also makes sense - if it does. This Collingwoodian question can be formulated in a first rough approximation by asking whether language - our actual working language, Tarski's "colloquiallanguage" - is universal in the sense of being inescapable. This formulation needs all sorts of explanations, however.

Appraising Lakatos

Author : György Kampis
ISBN : 9789401707695
Genre : Science
File Size : 65. 72 MB
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Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed the cultural and societal elements within scientific practices. Recently there has been, above all, an increasing interest in Lakatos' philosophy of mathematics, which emphasises heuristics and mathematical practice over logical justification. But suitable modifications of his approach are called for in order to make it applicable to modern axiomatised theories. Pioneering historical research in England and Hungary has unearthed hitherto unknown facts about Lakatos' personal life, his wartime activities and his involvement in the political developments of post-war Europe. From a communist activist committed to Györgyi Lukács' thinking, Lakatos developed into a staunch anti-Marxist who found his intellectual background in Popper's critical rationalism. The volume also publishes for the first time a part of his Debrecen Ph.D. thesis and it is concluded by a bibliography of his Hungarian writings.

Russell Revisited

Author : Alan Schwerin under the auspices of the Bertrand Russell Society
ISBN : 9781443806893
Genre : Philosophy
File Size : 63. 41 MB
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Bertrand Russell has played a central role in the development of modern western philosophy, especially analytic philosophy. An appreciation of the main themes and arguments of the thinkers who contributed to this modern movement in philosophy must include references to and analyses of Russell’s important contributions. It would seem that many do recognize the significance of his thought and have shown this in a somewhat dramatic manner. Russell’s Google number, for instance, is about 2.35 million. If the number of entries listed in this search engine is any indication of the level of interest online in Russell, we can surely conclude that the thought and life of this aristocratic English philosopher, logician and humanist still captures the imagination of tens of thousands, if not millions around the globe – even some thirty-seven years after his death. How do we account for this abiding interest in Russell? In a word it is accessibility. Whether it is the complex epistemological issue of the veracity of sense-data, the conundrums associated with the possibility of non-existent objects, the intricacies of the debates on the nature of language or the interminable search of a clear understanding of happiness, Russell inevitably has something profound and clear to say on the matter. Readers of Russell Revisited: Critical Reflections on the Thought of Bertrand Russell will be reminded of this fact time and time again as they explore the analyses here. Representing some of the best of the most recent scholarship on Russell, the articles gathered in this collection serve as a testament to the value of Russell’s diverse contributions to a wide range of challenging philosophical issues.

Proceedings Of The Amsterdam Colloquium

Author :
ISBN : STANFORD:36105122315398
Genre : Linguistics
File Size : 77. 13 MB
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Quantification Transcending Beyond Frege S Boundaries

Author : Aleksy Molczanow
ISBN : 9789004224179
Genre : Philosophy
File Size : 88. 36 MB
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Drawing on the original conception of Kant’s synthetic a priori and the relevant related developments in philosophy, this book presents a reconstruction of the intellectual history of the conception of quantity and offers an entirely novel transcendental-metaphysical account of quantification.

The Proceedings Of The Twentieth World Congress Of Philosophy

Author : Akihiro Kanamori
ISBN : 1889680109
Genre : Philosophy
File Size : 58. 2 MB
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On Hintikka

Author : Daniel Kolak
ISBN : 053458389X
Genre : Biography & Autobiography
File Size : 80. 26 MB
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This brief text assists students in understanding Hintikka's philosophy and thinking so they can more fully engage in useful, intelligent class dialogue and improve their understanding of course content. Part of the Wadsworth Notes Series, (which will eventually consist of approximately 100 titles, each focusing on a single "thinker" from ancient times to the present), ON HINTIKKA is written by a philosopher deeply versed in the philosophy of this key thinker. Like other books in the series, this concise book offers sufficient insight into the thinking of a notable philosopher, better enabling students to engage in reading and to discuss the material in class and on paper.

Conservation Equations And Modeling Of Chemical And Biochemical Processes

Author : Said S.E.H. Elnashaie
ISBN : 0203911504
Genre : Science
File Size : 89. 45 MB
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Presenting strategies in control policies, this text uses a systems theory approach to predict, simulate and streamline plant operation, conserve fuel and resources, and increase workplace safety in the manufacturing, chemical, petrochemical, petroleum, biochemical and energy industries. Topics of discussion include system theory and chemical/biochemical engineering systems, steady state, unsteady state, and thermodynamic equilibrium, modeling of systems, fundamental laws governing the processes in terms of the state variables, different classifications of physical models, the story of chemical engineering in relation to system theory and mathematical modeling, overall heat balance with single and multiple chemical reactions and single and multiple reactions.

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