Truth Proof And Infinity
DOWNLOAD
Download Truth Proof And Infinity PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Truth Proof And Infinity book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Truth Proof And Infinity
DOWNLOAD
Author : P. Fletcher
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Truth Proof And Infinity written by P. Fletcher and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Philosophy categories.
Constructive mathematics is based on the thesis that the meaning of a mathematical formula is given, not by its truth-conditions, but in terms of what constructions count as a proof of it. However, the meaning of the terms `construction' and `proof' has never been adequately explained (although Kriesel, Goodman and Martin-Löf have attempted axiomatisations). This monograph develops precise (though not wholly formal) definitions of construction and proof, and describes the algorithmic substructure underlying intuitionistic logic. Interpretations of Heyting arithmetic and constructive analysis are given. The philosophical basis of constructivism is explored thoroughly in Part I. The author seeks to answer objections from platonists and to reconcile his position with the central insights of Hilbert's formalism and logic. Audience: Philosophers of mathematics and logicians, both academic and graduate students, particularly those interested in Brouwer and Hilbert; theoretical computer scientists interested in the foundations of functional programming languages and program correctness calculi.
Roads To Infinity
DOWNLOAD
Author : John Stillwell
language : en
Publisher: CRC Press
Release Date : 2010-07-13
Roads To Infinity written by John Stillwell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-13 with Mathematics categories.
Winner of a CHOICE Outstanding Academic Title Award for 2011!This book offers an introduction to modern ideas about infinity and their implications for mathematics. It unifies ideas from set theory and mathematical logic, and traces their effects on mainstream mathematical topics of today, such as number theory and combinatorics. The treatment is h
Infinity And Truth
DOWNLOAD
Author : Chitat Chong
language : en
Publisher: World Scientific
Release Date : 2013-11-28
Infinity And Truth written by Chitat Chong and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-28 with Mathematics categories.
This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters cover topics in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo–Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progress in foundational studies. The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of interest to students, researchers and mathematicians concerned with issues in the foundations of mathematics. Contents:Invited Lectures:Absoluteness, Truth, and Quotients (Ilijas Farah)A Multiverse Perspective on the Axiom of Constructiblity (Joel David Hamkins)Hilbert, Bourbaki and the Scorning of Logic (A R D Mathias)Toward Objectivity in Mathematics (Stephen G Simpson)Sort Logic and Foundations of Mathematics (Jouko Väänänen)Reasoning about Constructive Concepts (Nik Weaver)Perfect Infinites and Finite Approximation (Boris Zilber)Special Session:An Objective Justification for Actual Infinity? (Stephen G Simpson)Oracle Questions (Theodore A Slaman and W Hugh Woodin) Readership: Mathematicians, philosophers, scientists, graduate students, academic institutions, and research organizations interested in logic and the philosophy of mathematics. Keywords:Mathematical Logic;Foundations of Mathematics;Philosophy of Mathematics;Mathematical Truth;Infinity;Set Theory;Proof Theory;MultiverseKey Features:All the contributors are world-renownedThe final chapter is written by Theodore A Slaman and W Hugh Woodin, who are two of the leading logicians in the world. They are also the volume editors
Truth Proof
DOWNLOAD
Author : Paul Sinclair
language : en
Publisher:
Release Date : 2016
Truth Proof written by Paul Sinclair and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Infinity And The Proofs For The Existence Of God
DOWNLOAD
Author : Glenn F. Chesnut
language : en
Publisher: iUniverse
Release Date : 2019-03-15
Infinity And The Proofs For The Existence Of God written by Glenn F. Chesnut and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-15 with Philosophy categories.
This book is more than just a set of logical proofs. It shows us who and what God is, and explains how our universe exploded into existence in the Big Bang, some 13.799 billion years ago, in such a way that all other Being in the universe derives its existence and nature — and its capacities for growth, power, moral character, change, and novelty — from God as the Ground of Being. This is a book for people who are interested in philosophy. It begins with a discussion of some of the fallacies into which the concept of infinity has led careless thinkers over the centuries. In particular, Chesnut demonstrates how often the modern defenses of atheism have been based on what are no more than pseudo-infinite regresses. This includes in particular self-delusive attempts to get rid of God by constructing what would be no more than imaginary universe-sized perpetual motion machines. The last half of the book then has as its central focus the set of Five Proofs for the Existence of God formulated by the great medieval thinker St. Thomas Aquinas, where Chesnut begins by showing how each of the proofs was interpreted in the middle ages. But the development of modern science requires that the Five Proofs be reworked for today, so he shows, for example, how the Proof from Motion can be reworded as an Argument from Energy, subject to the laws of thermodynamics, and how the Proof from Gradations in Truth and Value forces us to decide whether we will accept that at least some moral values are real, or instead will become what modern psychologists call psychopaths. This present book, combined with the work Chesnut authored nine years ago — God and Spirituality: Philosophical Essays — sets out an architectonic philosophical system for the twenty-first century, grounded on one side in the classics of the ancient Greco-Roman world and the medieval period, but on the other hand taking seriously the revolutionary changes in western thought produced by the development of twentieth-century science, including relativity, quantum theory, the uncertainty principle, and Gödel’s proof.
Truth Objects Infinity
DOWNLOAD
Author : Fabrice Pataut
language : en
Publisher: Springer
Release Date : 2017-01-27
Truth Objects Infinity written by Fabrice Pataut and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-27 with Philosophy categories.
This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status of numbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics. Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.
Reference Truth And Conceptual Schemes
DOWNLOAD
Author : G. Forrai
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Reference Truth And Conceptual Schemes written by G. Forrai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Philosophy categories.
1. HISTORICAL BACKGROUND The purpose of the book is to develop internal realism, the metaphysical-episte mological doctrine initiated by Hilary Putnam (Reason, Truth and History, "Introduction", Many Faces). In doing so I shall rely - sometimes quite heavily - on the notion of conceptual scheme. I shall use the notion in a somewhat idiosyncratic way, which, however, has some affinities with the ways the notion has been used during its history. So I shall start by sketching the history of the notion. This will provide some background, and it will also give opportunity to raise some of the most important problems I will have to solve in the later chapters. The story starts with Kant. Kant thought that the world as we know it, the world of tables, chairs and hippopotami, is constituted in part by the human mind. His cen tral argument relied on an analysis of space and time, and presupposed his famous doctrine that knowledge cannot extend beyond all possible experience. It is a central property of experience - he claimed - that it is structured spatially and temporally. However, for various reasons, space and time cannot be features of the world, as it is independently of our experience. So he concluded that they must be the forms of human sensibility, i. e. necessary ingredients of the way things appear to our senses.
Logic Truth And The Modalities
DOWNLOAD
Author : J.N. Mohanty
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Logic Truth And The Modalities written by J.N. Mohanty and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Philosophy categories.
This volume is a collection of my essays on philosophy of logic from a phenomenological perspective. They deal with the four kinds of logic I have been concerned with: formal logic, transcendental logic, speculative logic and hermeneutic logic. Of these, only one, the essay on Hegel, touches upon 'speculative logic', and two, those on Heidegger and Konig, are concerned with hermeneutic logic. The rest have to do with Husser! and Kant. I have not tried to show that the four logics are compatible. I believe, they are--once they are given a phenomenological underpinning. The original plan of writing an Introduction in which the issues would have to be formulated, developed and brought together, was abandoned in favor of writing an Introductory Essay on the 'origin'- in the phenomenological sense -of logic. J.N.M. Philadelphia INTRODUCTION: THE ORIGIN OF LOGIC The question of the origin of logic may pertain to historical origin (When did it all begin? Who founded the science of logic?), psychological origin (When, in the course of its mental development, does the child learn logical operations?), cultural origin (What cultural - theological, metaphysical and linguisti- conditions make such a discipline as logic possible?), or transcendental constitutive origin (What sorts of acts and/or practices make logic possible?).
Mathematical Intuitionism And Intersubjectivity
DOWNLOAD
Author : Tomasz Placek
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Mathematical Intuitionism And Intersubjectivity written by Tomasz Placek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
In 1907 Luitzen Egbertus Jan Brouwer defended his doctoral dissertation on the foundations of mathematics and with this event the modem version of mathematical intuitionism came into being. Brouwer attacked the main currents of the philosophy of mathematics: the formalists and the Platonists. In tum, both these schools began viewing intuitionism as the most harmful party among all known philosophies of mathematics. That was the origin of the now-90-year-old debate over intuitionism. As both sides have appealed in their arguments to philosophical propositions, the discussions have attracted the attention of philosophers as well. One might ask here what role a philosopher can play in controversies over mathematical intuitionism. Can he reasonably enter into disputes among mathematicians? I believe that these disputes call for intervention by a philo sopher. The three best-known arguments for intuitionism, those of Brouwer, Heyting and Dummett, are based on ontological and epistemological claims, or appeal to theses that properly belong to a theory of meaning. Those lines of argument should be investigated in order to find what their assumptions are, whether intuitionistic consequences really follow from those assumptions, and finally, whether the premises are sound and not absurd. The intention of this book is thus to consider seriously the arguments of mathematicians, even if philosophy was not their main field of interest. There is little sense in disputing whether what mathematicians said about the objectivity and reality of mathematical facts belongs to philosophy, or not.
Herald Of Truth
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 1835
Herald Of Truth written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1835 with Universalism categories.