Proof And Other Dilemmas
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Proof And Other Dilemmas
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Author : Bonnie Gold
language : en
Publisher: MAA
Release Date : 2008
Proof And Other Dilemmas written by Bonnie Gold and has been published by MAA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Risk Dilemmas
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Author : M. Jablonowski
language : en
Publisher: Springer
Release Date : 2007-10-23
Risk Dilemmas written by M. Jablonowski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-23 with Business & Economics categories.
This book identifies the pitfalls of applying precautionary strategies to high-stakes risks that have already become entrenched. Precaution must be applied on a precautionary basis, considering alternative paths to progress that maintain natural risk levels. This requires a radical rethinking of the way we define and achieve progress.
Vital Directions For Mathematics Education Research
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Author : Keith R Leatham
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Vital Directions For Mathematics Education Research written by Keith R Leatham 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 2014-07-08 with Education categories.
This book provides a collection of chapters from prominent mathematics educators in which they each discuss vital issues in mathematics education and what they see as viable directions research in mathematics education could take to address these issues. All of these issues are related to learning and teaching mathematics. The book consists of nine chapters, seven from each of seven scholars who participated in an invited lecture series (Scholars in Mathematics Education) at Brigham Young University, and two chapters from two other scholars who are writing reaction papers that look across the first seven chapters. The recommendations take the form of broad, overarching principles and ideas that cut across the field. In this sense, this book differs from classical “research agenda projects,” which seek to outline specific research questions that the field should address around a central topic.
Objects Structures And Logics
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Author : Gianluigi Oliveri
language : en
Publisher: Springer Nature
Release Date : 2022-03-08
Objects Structures And Logics written by Gianluigi Oliveri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Science categories.
This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
The Bar Hima S Dilemma
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Author : Elizabeth G. Price
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-04-22
The Bar Hima S Dilemma written by Elizabeth G. Price and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Religion categories.
When debating the need for prophets, Muslim theologians frequently cited an objection from a group called the Barāhima – either a prophet conveys what is in accordance with reason, so they would be superfluous, or a prophet conveys what is contrary to reason, so they would be rejected. The Barāhima did not recognise prophecy or revelation, because they claimed that reason alone could guide them on the right path. But who were these Barāhima exactly? Were they Brahmans, as their title would suggest? And how did they become associated with this highly incisive objection to prophecy? This book traces the genealogy of the Barāhima and explores their profound impact on the evolution of Islamic theology. It also charts the pivotal role that the Kitāb al-Zumurrud played in disseminating the Barāhima’s critiques and in facilitating an epistemological turn in the wider discourse on prophecy (nubuwwa). When faced with the Barāhima, theologians were not only pressed to explain why rational agents required the input of revelation, but to also identify an epistemic gap that only a prophet could fill. A debate about whether humans required prophets thus evolved into a debate about what humans could and could not know by their own means.
The Logic Of Number
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Author : Neil Tennant
language : en
Publisher: Oxford University Press
Release Date : 2022-02-10
The Logic Of Number written by Neil Tennant and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Philosophy categories.
In The Logic of Number, Neil Tennant defines and develops his Natural Logicist account of the foundations of the natural, rational, and real numbers. Based on the logical system free Core Logic, the central method is to formulate rules of natural deduction governing variable-binding number-abstraction operators and other logico-mathematical expressions such as zero and successor. These enable 'single-barreled' abstraction, in contrast with the 'double-barreled' abstraction effected by principles such as Frege's Basic Law V, or Hume's Principle. Natural Logicism imposes upon its account of the numbers four conditions of adequacy: First, one must show how it is that the various kinds of number are applicable in our wider thought and talk about the world. This is achieved by deriving all instances of three respective schemas: Schema N for the naturals, Schema Q for the rationals, and Schema R for the reals. These provide truth-conditions for statements deploying terms referring to numbers of the kind in question. Second, one must show how it is that the naturals sit among the rationals as themselves again, and the rationals likewise among the reals. Third, one should reveal enough of the metaphysical nature of the numbers to be able to derive the mathematician's basic laws governing them. Fourth, one should be able to demonstrate that there are uncountably many reals. Natural Logicism is realistic about the limits of logicism when it comes to treating the real numbers, for which, Tennant argues, one needs recourse to geometric intuition for deeper starting-points, beyond which logic alone will then deliver the sought results, with absolute formal rigor. The resulting program enables one to delimit, in a principled way, those parts of number theory that are produced by the Kantian understanding alone, and those parts that depend on recourse to (very simple) a priori geometric intuitions.
From A Heuristic Point Of View
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Author : Cesare Cozzo
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2014-07-03
From A Heuristic Point Of View written by Cesare Cozzo and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-03 with Science categories.
How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.
God The Dimensional Revelation
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Author : Allyn Richert
language : en
Publisher: Page Publishing Inc
Release Date : 2023-05-12
God The Dimensional Revelation written by Allyn Richert and has been published by Page Publishing Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-12 with Philosophy categories.
What questions do you have about Your Life, Your Being, Your Soul, and Your Conscious Awareness? GOD--The Dimensional Revelation is a book revealing reality. Broadly stated, reality is defined as "all that exists." The study of reality is called "metaphysics." Metaphysics is the primary field of philosophy. Metaphysics is divided into two major fields of study. These are cosmology and ontology. GOD--The Dimensional Revelation reveals cosmological facts about our big bang. Our research reconciles relativity theory and quantum mechanics. Ontologically, This Teaching Reveals a clear theology about GOD and Your Relationship with GOD. Learn how to use the scientific method to prove that the Reality You and I Experience is a partial Fusion of our physical universe with our separate Spiritual Universe. This Teaching proves this in the context of 10 Dimensions of Reality, some of which are original to this book. These 10 Dimensions are clearly explained and verified. Dimensional Reasoning is offered as a tool anyone can use to answer all the great questions of Existence. The Source of Being is clearly identified, as well as the Destination of Individual Being. Reading and Participating in the Knowledge Shared in this book will increase your Confidence, Personal Power, and help You Grow Spiritually.
Thin Objects
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Author : Øystein Linnebo
language : en
Publisher: Oxford University Press
Release Date : 2018-05-24
Thin Objects written by Øystein Linnebo and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-24 with Philosophy categories.
Are there objects that are " in the sense that not very much is required for their existence? Frege famously thought so. He claimed that the equinumerosity of the knives and the forks suffices for there to be objects such as the number of knives and the number of forks, and for these objects to be identical. The idea of thin objects holds great philosophical promise but has proved hard to explicate. Øystein Linnebo aims to do so by drawing on some Fregean ideas. First, to be an object is to be a possible referent of a singular term. Second, singular reference can be achieved by providing a criterion of identity for the would-be referent. The second idea enables a form of easy reference and thus, via the first idea, also a form of easy being. Paradox is avoided by imposing a predicativity restriction on the criteria of identity. But the abstraction based on a criterion of identity may result in an expanded domain. By iterating such expansions, a powerful account of dynamic abstraction is developed. The result is a distinctive approach to ontology. Abstract objects such as numbers and sets are demystified and allowed to exist alongside more familiar physical objects. And Linnebo also offers a novel approach to set theory which takes seriously the idea that sets are " successively.
Structures And Algorithms
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Author : Jens Erik Fenstad
language : en
Publisher: Springer
Release Date : 2018-03-10
Structures And Algorithms written by Jens Erik Fenstad and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-10 with Philosophy categories.
This book explains exactly what human knowledge is. The key concepts in this book are structures and algorithms, i.e., what the readers “see” and how they make use of what they see. Thus in comparison with some other books on the philosophy (or methodology) of science, which employ a syntactic approach, the author’s approach is model theoretic or structural. Properly understood, it extends the current art and science of mathematical modeling to all fields of knowledge. The link between structure and algorithms is mathematics. But viewing “mathematics” as such a link is not exactly what readers most likely learned in school; thus, the task of this book is to explain what “mathematics” should actually mean. Chapter 1, an introductory essay, presents a general analysis of structures, algorithms and how they are to be linked. Several examples from the natural and social sciences, and from the history of knowledge, are provided in Chapters 2–6. In turn, Chapters 7 and 8 extend the analysis to include language and the mind. Structures are what the readers see. And, as abstract cultural objects, they can almost always be seen in many different ways. But certain structures, such as natural numbers and the basic theory of grammar, seem to have an absolute character. Any theory of knowledge grounded in human culture must explain how this is possible. The author’s analysis of this cultural invariance, combining insights from evolutionary theory and neuroscience, is presented in the book’s closing chapter. The book will be of interest to researchers, students and those outside academia who seek a deeper understanding of knowledge in our present-day society.