Knowledge And The Philosophy Of Number

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Knowledge and the Philosophy of Number

Keith Hossack
Knowledge and the Philosophy of Number Book PDF

Author : Keith Hossack
Publisher : Bloomsbury Publishing
Page : 216 pages
File Size : 47,6 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9781350102910

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Knowledge and the Philosophy of Number by Keith Hossack Pdf

If numbers were objects, how could there be human knowledge of number? Numbers are not physical objects: must we conclude that we have a mysterious power of perceiving the abstract realm? Or should we instead conclude that numbers are fictions? This book argues that numbers are not objects: they are magnitude properties. Properties are not fictions and we certainly have scientific knowledge of them. Much is already known about magnitude properties such as inertial mass and electric charge, and much continues to be discovered. The book says the same is true of numbers. In the theory of magnitudes, the categorial distinction between quantity and individual is of central importance, for magnitudes are properties of quantities, not properties of individuals. Quantity entails divisibility, so the logic of quantity needs mereology, the a priori logic of part and whole. The three species of quantity are pluralities, continua and series, and the book presents three variants of mereology, one for each species of quantity. Given Euclid's axioms of equality, it is possible without the use of set theory to deduce the axioms of the natural, real and ordinal numbers from the respective mereologies of pluralities, continua and series. Knowledge and the Philosophy of Number carries out these deductions, arriving at a metaphysics of number that makes room for our a priori knowledge of mathematical reality.

Uncountable

David Nirenberg,Ricardo L. Nirenberg
Uncountable Book PDF

Author : David Nirenberg,Ricardo L. Nirenberg
Publisher : University of Chicago Press
Page : 429 pages
File Size : 49,9 Mb
Release : 2024-05-09
Category : History
ISBN : 9780226828367

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Uncountable by David Nirenberg,Ricardo L. Nirenberg Pdf

Ranging from math to literature to philosophy, Uncountable explains how numbers triumphed as the basis of knowledge—and compromise our sense of humanity. Our knowledge of mathematics has structured much of what we think we know about ourselves as individuals and communities, shaping our psychologies, sociologies, and economies. In pursuit of a more predictable and more controllable cosmos, we have extended mathematical insights and methods to more and more aspects of the world. Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity. Yet, in the process, are we losing sight of the human? When we apply mathematics so broadly, what do we gain and what do we lose, and at what risk to humanity? These are the questions that David and Ricardo L. Nirenberg ask in Uncountable, a provocative account of how numerical relations became the cornerstone of human claims to knowledge, truth, and certainty. There is a limit to these number-based claims, they argue, which they set out to explore. The Nirenbergs, father and son, bring together their backgrounds in math, history, literature, religion, and philosophy, interweaving scientific experiments with readings of poems, setting crises in mathematics alongside world wars, and putting medieval Muslim and Buddhist philosophers in conversation with Einstein, Schrödinger, and other giants of modern physics. The result is a powerful lesson in what counts as knowledge and its deepest implications for how we live our lives.

Uncountable

David Nirenberg,Ricardo L. Nirenberg
Uncountable Book PDF

Author : David Nirenberg,Ricardo L. Nirenberg
Publisher : University of Chicago Press
Page : 429 pages
File Size : 53,5 Mb
Release : 2021-10-20
Category : History
ISBN : 9780226646985

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Uncountable by David Nirenberg,Ricardo L. Nirenberg Pdf

"From the time of Pythagoras, we have been tempted to treat numbers as the ultimate or only truth. This book tells the history of that habit of thought. But more, it argues that the logic of counting sacrifices much of what makes us human, and that we have a responsibility to match the objects of our attention to the forms of knowledge that do them justice. Humans have extended the insights and methods of number and mathematics to more and more aspects of the world, even to their gods and their religions.Today those powers are greater than ever, as computation is applied to virtually every aspect of human activity.But the rules of mathematics do not strictly apply to many things-from elementary particles to people-in the world.By subjecting such things to the laws of logic and mathematics, we gain some kinds of knowledge, but we also lose others. How do our choices about what parts of the world to subject to the logics of mathematics affect how we live and how we die?This question is rarely asked, but it is urgent, because the sciences built upon those laws now govern so much of our knowledge, from physics to psychology.Number and Knowledge sets out to ask it. In chapters proceeding chronologically from Ancient Greek philosophy and the rise of monotheistic religions to the emergence of modern physics and economics, the book traces how ideals, practices, and habits of thought formed over millennia have turned number into the foundation-stone of human claims to knowledge and certainty.But the book is also a philosophical and poetic exhortation to take responsibility for that history, for the knowledge it has produced, and for the many aspects of the world and of humanity that it ignores or endangers.To understand what can be counted and what can't is to embrace the ethics of purposeful knowing"--

The Philosophy of Numbers

L. Dow Balliett
The Philosophy of Numbers Book PDF

Author : L. Dow Balliett
Publisher : CreateSpace
Page : 170 pages
File Size : 50,6 Mb
Release : 2015-06-25
Category : Electronic
ISBN : 1514704420

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The Philosophy of Numbers by L. Dow Balliett Pdf

This book has been written in response to the requests of those who are interested in the study of number vibrations. The requests have come from all parts of the world, asking for more of the simplified knowledge founded upon the one principle of unity,-that all things have but one source-and express in different forms the unity of the whole. The hidden strength or weakness of names, states, etc., as shown by the vowels, have been evolved through the philosophy of numbers. From this source many unwritten laws can be made plain. Pythagoras said: "The heavens and earth vibrate to the single numbers, or digits of numbers. Each single number, from 1 to 9, are digits. To find your own numbers, divide the alphabet into nine parts. To get a scientific cause for the expression of life, and to understand what has been taught us by Pythagoras, Plato, Aristotle, and Socrates, we must realize that these philosophers were mystics. A mystic at that time, as at present, believed in the Oneness of All, that everything came from one source, that every separate thing was entirely dependent upon every other separate thing, yet all the separate things were joined in the Great Universal Chain of Infinite Lives. As many persons want to know how the vibration of numbers can be understood and used, we would recommend this book, and "The Ancient Science of Numbers," to such enquirers. Chapter XXIII explains the vibrations of numbers to States, and it is rather interesting, after having found one's own name vibration, to know what States will harmonize with such vibration, so that a person can make a successful selection of locality to live in. It is an interesting book of 147 pages, and no doubt will receive a hearty reception. -The Phrenological Journal and Science of Health [1908]

Philosophy of Mathematics

Anonim
Philosophy of Mathematics Book PDF

Author : Anonim
Publisher : Elsevier
Page : 735 pages
File Size : 49,8 Mb
Release : 2009-07-08
Category : Philosophy
ISBN : 9780080930589

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Philosophy of Mathematics by Anonim Pdf

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics. -Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included

Introduction to Mathematical Philosophy

Bertrand Russell
Introduction to Mathematical Philosophy Book PDF

Author : Bertrand Russell
Publisher : Courier Corporation
Page : 230 pages
File Size : 42,5 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 0486277240

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Introduction to Mathematical Philosophy by Bertrand Russell Pdf

In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet — a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.

Naturalizing Logico-Mathematical Knowledge

Sorin Bangu
Naturalizing Logico Mathematical Knowledge Book PDF

Author : Sorin Bangu
Publisher : Routledge
Page : 319 pages
File Size : 43,9 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9781351998444

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Naturalizing Logico-Mathematical Knowledge by Sorin Bangu Pdf

This book is meant as a part of the larger contemporary philosophical project of naturalizing logico-mathematical knowledge, and addresses the key question that motivates most of the work in this field: What is philosophically relevant about the nature of logico-mathematical knowledge in recent research in psychology and cognitive science? The question about this distinctive kind of knowledge is rooted in Plato’s dialogues, and virtually all major philosophers have expressed interest in it. The essays in this collection tackle this important philosophical query from the perspective of the modern sciences of cognition, namely cognitive psychology and neuroscience. Naturalizing Logico-Mathematical Knowledge contributes to consolidating a new, emerging direction in the philosophy of mathematics, which, while keeping the traditional concerns of this sub-discipline in sight, aims to engage with them in a scientifically-informed manner. A subsequent aim is to signal the philosophers’ willingness to enter into a fruitful dialogue with the community of cognitive scientists and psychologists by examining their methods and interpretive strategies.

Philosophy Of Mathematics

John Francis
Philosophy Of Mathematics Book PDF

Author : John Francis
Publisher : Global Vision Pub House
Page : 164 pages
File Size : 50,7 Mb
Release : 2008-08
Category : Mathematics
ISBN : 8182202671

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Philosophy Of Mathematics by John Francis Pdf

This Book Provides Introductory Knowledge Of The Philosophical Analysis And Historical Development Of All Important Aspects Of Mathematical Philosophy. The Book Is Intended For Laymen, But None Of The Essence Of The Philosophy Of Mathematics Has Been Omitted; It Is Not A Simple Book, But It Is Rewarding.

The Philosophy of Numbers

Mrs L Dow Balliett
The Philosophy of Numbers Book PDF

Author : Mrs L Dow Balliett
Publisher : CreateSpace
Page : 170 pages
File Size : 53,6 Mb
Release : 2013-12
Category : Electronic
ISBN : 1494797208

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The Philosophy of Numbers by Mrs L Dow Balliett Pdf

A review from The Phrenological Journal and Science of Health, Volume 121: THIS book has been written in response to the requests of those who are interested in the study of number vibrations. The requests have come from all parts of the world, asking for more of the simplified knowledge founded upon the one principle of unity, - that all things have but one source-and express in different forms the unity of the whole. The hidden strength or weakness of names, states, etc., as shown by the vowels, have been evolved through the philosophy of numbers. From this source many unwritten laws can be made plain. Pythagoras said: "The heavens and earth vibrate to the single numbers, or digits of numbers. Each single number, from 1 to 9, are digits. To find your own numbers, divide the alphabet into nine parts. To get a scientific cause for the expression of life, and to understand what has been taught us by Pythagoras, Plato, Aristotle, and Socrates, we must realize that these philosophers were mystics. A mystic at that time, as at present, believed in the Oneness of All, that everything came from one source, that every separate thing was entirely dependent upon every other separate thing, yet all the separate things were joined in the Great Universal Chain of Infinite Lives. As many persons want to know how the vibration of numbers can be understood and used, we would recommend this book, and "The Ancient Science of Numbers," to such enquirers. Chapter XXIII explains the vibrations of numbers to States, and it is rather interesting, after having found one's own name vibration, to know what States will harmonize with such vibration, so that a person can make a successful selection of locality to live in. It is an interesting book of 168 pages, and no doubt will receive a hearty reception.

Knowledge in a Nutshell: Classical Philosophy

Michael Moore
Knowledge in a Nutshell Classical Philosophy Book PDF

Author : Michael Moore
Publisher : Arcturus Publishing
Page : 196 pages
File Size : 54,9 Mb
Release : 2019-01-15
Category : Philosophy
ISBN : 9781789504293

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Knowledge in a Nutshell: Classical Philosophy by Michael Moore Pdf

From Socrates' fascinating discussions of morality and virtue to Pythagoras' attempts to understand the arrangement of the cosmos, the thinkers of the ancient world provided us with an astonishing array of ideas that has helped to shape the modern world. Ranging across Ancient Greek and Roman philosophy from Anaximander to Plotinus, Classical Philosophy in a Nutshell explains important ideas such as Plato's Theory of Forms, Zeno's Paradox, and the Stoicism of Marcus Aurelius. Filled with helpful diagrams and simple summaries of complex theories, this essential introduction brings the great ideas of antiquity to everyone.

The Social Life of Numbers

Gary Urton,Primitivo Nina Llanos
The Social Life of Numbers Book PDF

Author : Gary Urton,Primitivo Nina Llanos
Publisher : University of Texas Press
Page : 294 pages
File Size : 44,5 Mb
Release : 2010-07-05
Category : Social Science
ISBN : 9780292786844

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The Social Life of Numbers by Gary Urton,Primitivo Nina Llanos Pdf

Unraveling all the mysteries of the khipu--the knotted string device used by the Inka to record both statistical data and narrative accounts of myths, histories, and genealogies--will require an understanding of how number values and relations may have been used to encode information on social, familial, and political relationships and structures. This is the problem Gary Urton tackles in his pathfinding study of the origin, meaning, and significance of numbers and the philosophical principles underlying the practice of arithmetic among Quechua-speaking peoples of the Andes. Based on fieldwork in communities around Sucre, in south-central Bolivia, Urton argues that the origin and meaning of numbers were and are conceived of by Quechua-speaking peoples in ways similar to their ideas about, and formulations of, gender, age, and social relations. He also demonstrates that their practice of arithmetic is based on a well-articulated body of philosophical principles and values that reflects a continuous attempt to maintain balance, harmony, and equilibrium in the material, social, and moral spheres of community life.

PHILOSOPHY OF NUMBERS THEIR TO

L Dow Mrs Balliett, B Ed
PHILOSOPHY OF NUMBERS THEIR TO Book PDF

Author : L Dow Mrs Balliett, B Ed
Publisher : Wentworth Press
Page : 164 pages
File Size : 41,6 Mb
Release : 2016-08-28
Category : History
ISBN : 1372247157

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PHILOSOPHY OF NUMBERS THEIR TO by L Dow Mrs Balliett, B Ed Pdf

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.

The Essence of Numbers

Frédéric Patras
The Essence of Numbers Book PDF

Author : Frédéric Patras
Publisher : Springer Nature
Page : 180 pages
File Size : 47,6 Mb
Release : 2020-10-06
Category : Mathematics
ISBN : 9783030567002

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The Essence of Numbers by Frédéric Patras Pdf

This book considers the manifold possible approaches, past and present, to our understanding of the natural numbers. They are treated as epistemic objects: mathematical objects that have been subject to epistemological inquiry and attention throughout their history and whose conception has evolved accordingly. Although they are the simplest and most common mathematical objects, as this book reveals, they have a very complex nature whose study illuminates subtle features of the functioning of our thought. Using jointly history, mathematics and philosophy to grasp the essence of numbers, the reader is led through their various interpretations, presenting the ways they have been involved in major theoretical projects from Thales onward. Some pertain primarily to philosophy (as in the works of Plato, Aristotle, Kant, Wittgenstein...), others to general mathematics (Euclid's Elements, Cartesian algebraic geometry, Cantorian infinities, set theory...). Also serving as an introduction to the works and thought of major mathematicians and philosophers, from Plato and Aristotle to Cantor, Dedekind, Frege, Husserl and Weyl, this book will be of interest to a wide variety of readers, from scholars with a general interest in the philosophy or mathematics to philosophers and mathematicians themselves.

Mathematics and the Mind

Hassan Tahiri
Mathematics and the Mind Book PDF

Author : Hassan Tahiri
Publisher : Springer
Page : 76 pages
File Size : 43,7 Mb
Release : 2015-11-18
Category : Philosophy
ISBN : 9783319252384

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Mathematics and the Mind by Hassan Tahiri Pdf

This book examines how epistemology was reinvented by Ibn Sīnā, an influential philosopher-scientist of the classical Islamic world who was known to the West by the Latinised name Avicenna. It explains his theory of knowledge in which intentionality acts as an interaction between the mind and the world. This, in turn, led Ibn Sīnā to distinguish an operation of intentionality specific to the generation of numbers. The author argues that Ibn Sīnā’s transformation of philosophy is one of the major stages in the de-hellinisation movement of the Greek heritage that was set off by the advent of the Arabic-Islamic civilisation. Readers first learn about Ibn Sīnā’s unprecedented investigation into the concept of the number and his criticism of such Greek thought as Plato’s realism, Pythagoreans’ empiricism, and Ari stotle’s conception of existence. Next, coverage sets out the basics of Ibn Sīnā’s theory of knowledge needed for the construction of numbers. It describes how intentionality turns out to be key in showing the ontological dependence of numbers as well as even more critical to their construction. In describing the various mental operations that make mathematical objects intentional entities, Ibn Sīnā developed powerful arguments and subtle analyses to show us the extent our mental life depends on intentionality. This monograph thoroughly explores the epistemic dimension of this concept, which, the author believes, can also explain the actual genesis and evolution of mathematics by the human mind.

Somewhere Between the One and the Zero-- : the Philosophy of Number

Kevin P. Cerveny
Somewhere Between the One and the Zero the Philosophy of Number Book PDF

Author : Kevin P. Cerveny
Publisher : Trafford Publishing
Page : 126 pages
File Size : 53,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9781412035125

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Somewhere Between the One and the Zero-- : the Philosophy of Number by Kevin P. Cerveny Pdf

Somewhere Between the One and the Zero is a book about the philosophy of numbers. The book is dedicated to exploring the meaning found in numbers and the evidence that they provide for the existence of the "infinite." A detailed look into "what" it is that makes up infinity is pursued with the hope that a focused study will help to demystify what is most often a misrepresented concept. The purpose of this venture is to better understand our place in the universe. The hope of the book is for all to understand the infinite value of all things. The messages that are displayed out in number provide all of the evidence required to permit both purpose and hope to be achieved.