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by William S. Veatch (Author)
Math Without Numbers - The Mathematics of Ideas. Volume 1 - Foundations. This Volume 1 in the “Math Without Numbers” series explores the nature of Ideas, from both a practical and an abstract mathematical point of view. The book demonstrates that mathematics can explain “how” we think, but cannot tell us “what” to think or how to act. The author applies principles of Set Theory to Ideas, and illustrates how Ideas form structures that are well-known in the field of Mathematics, including Partitions/Equivalence Classes, Groups, Boolean Algebras, Rings, Lattices, and Topologies. The book touches on Logic, Argumentation, and Debate, which are topics that will be explored in detail in Volumes 2 and 3.
The discussion is original and accessible, and includes material appropriate for anyone with a background in basic high school math, as well as more advanced material for those looking for a challenge. The book begins at an introductory level, but proceeds to discuss more complex material for those interested in making language more precise and unambiguous.
Much of the focus is on Lattices and Boolean Algebras/Rings, as applied to Ideas rather than numbers. There are many similarities to the relatively new field of mathematics called Formal Concept Analysis, although Math Without Numbers focuses on building a foundation in Set Theory and Logic.
This book is intended for anyone interested in Set Theory, the Philosophy of Mathematics, the Philosophy of Language, Critical Thinking, Logic, and/or Artificial Intelligence. Those who like solving word puzzles will enjoy the Math Without Numbers series, which attempts to solve one of the greatest puzzles of all time: the Mathematics of Ideas.
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