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Author: Bonnie Gold
Publisher: MAA
Published: 2008
Total Pages: 392
ISBN-13: 9780883855676
DOWNLOAD EBOOK →Sixteen original essays exploring recent developments in the philosophy of mathematics, written in a way mathematicians will understand.
Author: Keith R Leatham
Publisher: Springer Science & Business Media
Published: 2014-07-08
Total Pages: 212
ISBN-13: 1461469775
DOWNLOAD EBOOK →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.
Author: Marcel Danesi
Publisher: Springer Nature
Published: 2019-09-14
Total Pages: 344
ISBN-13: 3030225372
DOWNLOAD EBOOK →This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Author: Gianluigi Oliveri
Publisher: Springer Nature
Published: 2022-03-08
Total Pages: 365
ISBN-13: 3030847063
DOWNLOAD EBOOK →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.
Author: Øystein Linnebo
Publisher: Oxford University Press
Published: 2018-05-24
Total Pages: 288
ISBN-13: 0192558773
DOWNLOAD EBOOK →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.
Author: Elizabeth G. Price
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2024-04-22
Total Pages: 464
ISBN-13: 3111027201
DOWNLOAD EBOOK →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.
Author: Cesare Cozzo
Publisher: Cambridge Scholars Publishing
Published: 2014-07-03
Total Pages: 295
ISBN-13: 1443863351
DOWNLOAD EBOOK →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.
Author: Allyn Richert
Publisher: Page Publishing Inc
Published: 2023-05-12
Total Pages: 366
ISBN-13: 1662476264
DOWNLOAD EBOOK →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.
Author: Neil Tennant
Publisher: Oxford University Press
Published: 2022-02-10
Total Pages: 320
ISBN-13: 0192661981
DOWNLOAD EBOOK →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.
Author: Jens Erik Fenstad
Publisher: Springer
Published: 2018-03-10
Total Pages: 134
ISBN-13: 3319729748
DOWNLOAD EBOOK →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.
