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. William S. Veatch is a practicing attorney, living in San Francisco, California.  He obtained his B.A. degree in History at the University of Winnipeg, Winnipeg, Manitoba, Canada (1985), where he also studied Mathematics and Philosophy; his LL.B. law degree at the University of Manitoba, Winnipeg, Canada (1985); and his J.D. law degree from the University of California, Hastings College of the Law, San Francisco, California (1987).Bill has extensive transactional experience in the fields of banking, equipment leasing, venture lending and leasing, cross-border leasing, vendor finance, and receivables finance and securitization. He devotes a substantial portion of his practice to advising financial institutions and company clients on the structuring of global equipment and software vendor programs, including the sale and securitization of receivables. In addition to his debt, equipment leasing, and receivables finance / securitization practice, he works with the technology innovation team at the global law firm of Reed Smith LLP. He wrote Math Without Numbers -- Vol. 1. Foundations (2016), describing a new mathematics of ideas; Propositional Logic as a Boolean Algebra -- A New Perspective, Vol. 1 (2017), describing a new "logic of lattices"; and The New Logic of the Law -- Building a Foundation for Artificial Intelligence in the Law (2018). Examples of the application of artificial intelligence will be posted on Bill's webpage from time to time. Bill welcomes anyone interested in the application of artificial intelligence to the law, and legal tech and innovation generally, to contact him by email. Bill is a member of the American Bar Association and the San Francisco Bar Association. He is also a former member of the Uniform Commercial Code Committee of the State Bar of California and a former member of the Legal Committee of the Equipment Leasing Association.