Knowledge And The Philosophy Of Number
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Knowledge And The Philosophy Of Number
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Author : Keith Hossack
language : en
Publisher: Bloomsbury Publishing
Release Date : 2020-02-20
Knowledge And The Philosophy Of Number written by Keith Hossack and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-20 with Mathematics categories.
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
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Author : David Nirenberg
language : en
Publisher: University of Chicago Press
Release Date : 2021-10-20
Uncountable written by David Nirenberg and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-20 with History categories.
"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"--
Philosophy Of Mathematics
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Author : John Francis
language : en
Publisher: Global Vision Pub House
Release Date : 2008-08
Philosophy Of Mathematics written by John Francis and has been published by Global Vision Pub House this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08 with Mathematics categories.
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
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Author : L. Dow Balliett
language : en
Publisher: CreateSpace
Release Date : 2015-06-25
The Philosophy Of Numbers written by L. Dow Balliett and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-25 with categories.
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]
Mathematics And The Mind
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Author : Hassan Tahiri
language : en
Publisher: Springer
Release Date : 2015-11-18
Mathematics And The Mind written by Hassan Tahiri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-18 with Philosophy categories.
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.
Philosophy Of Mathematics
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Author :
language : en
Publisher: Elsevier
Release Date : 2009-07-08
Philosophy Of Mathematics written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-08 with Philosophy categories.
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
Philosophy Of Numbers Their To
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Author : L Dow Mrs Balliett, B Ed
language : en
Publisher: Wentworth Press
Release Date : 2016-08-28
Philosophy Of Numbers Their To written by L Dow Mrs Balliett, B Ed and has been published by Wentworth Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-28 with History categories.
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.
Mathematical Intuition
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Author : R.L. Tieszen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Intuition written by R.L. Tieszen 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 2012-12-06 with Philosophy categories.
"Intuition" has perhaps been the least understood and the most abused term in philosophy. It is often the term used when one has no plausible explanation for the source of a given belief or opinion. According to some sceptics, it is understood only in terms of what it is not, and it is not any of the better understood means for acquiring knowledge. In mathematics the term has also unfortunately been used in this way. Thus, intuition is sometimes portrayed as if it were the Third Eye, something only mathematical "mystics", like Ramanujan, possess. In mathematics the notion has also been used in a host of other senses: by "intuitive" one might mean informal, or non-rigourous, or visual, or holistic, or incomplete, or perhaps even convincing in spite of lack of proof. My aim in this book is to sweep all of this aside, to argue that there is a perfectly coherent, philosophically respectable notion of mathematical intuition according to which intuition is a condition necessary for mathemati cal knowledge. I shall argue that mathematical intuition is not any special or mysterious kind of faculty, and that it is possible to make progress in the philosophical analysis of this notion. This kind of undertaking has a precedent in the philosophy of Kant. While I shall be mostly developing ideas about intuition due to Edmund Husser! there will be a kind of Kantian argument underlying the entire book.
The Philosophy Of Numbers
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Author : Mrs L Dow Balliett
language : en
Publisher: CreateSpace
Release Date : 2013-12
The Philosophy Of Numbers written by Mrs L Dow Balliett and has been published by CreateSpace this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12 with categories.
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.
The Philosophy Of Numbers Their Tone And Colors
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Author : Sarah Joanna Balliett
language : en
Publisher: Legare Street Press
Release Date : 2022-10-27
The Philosophy Of Numbers Their Tone And Colors written by Sarah Joanna Balliett and has been published by Legare Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-27 with categories.
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. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.