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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Structures and Algorithms - Mathematics and the Nature of Knowledge (Hardcover, 1st ed. 2018)
Loot Price: R3,435
Discovery Miles 34 350
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Structures and Algorithms - Mathematics and the Nature of Knowledge (Hardcover, 1st ed. 2018)
Series: Logic, Argumentation & Reasoning, 15
Expected to ship within 12 - 19 working days
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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.
General
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