Establishing a Foundation For the Mathematics of Ideas Based on Set Theory and Logic - Couverture souple

Veatch, William S.

Couverture souple

ISBN 10 : 1520577540 ISBN 13 : 9781520577548

Editeur : Independently published, 2017

Synopsis

This article starts from a classical logic approach to extension (objects) and in-tension (attributes), and develops a foundation for the mathematics of ideas based on set theory and logic. Beginning with an assumption that idea-atoms exist, i.e., ideas that are not capable of further subdivision, the article shows that all other ideas are compound ideas that we can map to elements of the power set of such atoms. From there, the article demonstrates how we can form chains of ideas ordered by inclusion, and partitions of ideas into subsets that by defini-tion form an exhaustive partition and are pairwise disjoint. Using the principles of Boolean algebras and Boolean lattices to create “partition equations,” the ar-ticle develops a new technique for drawing “nested partition lattices” that re-flect the relevant relationships among ideas. By constructing a firm philosoph-ical foundation for the Mathematics of Ideas using set theory and logic, we open the door to applying the tools and techniques of Math Without Numbers (MWN) more broadly to any subject area, whether part of mathematics, physical sciences, social sciences, humanities, or virtually any other field of study. This article summarizes the principal ideas and arguments presented in the book: Veatch, William S.: Math Without Numbers – The Mathematics of Ideas, Vol. 1 Foundations, CreateSpace (2016).

Détails de l'édition

• Éditeur: Independently published
• Date d'édition: 2017
• Langue: anglais
• ISBN 10: 1520577540
• ISBN 13: 9781520577548
• Reliure: Broché
• Nombre de pages: 25
• Coordonnées du fabricant: Manufactured by Amazon on behalf of the author; https://www.amazon.fr/hz/contact-us; ; c/o Amazon Media EU S.à.r.l., 38 Avenue John F. Kennedy; Luxembourg; L-1855; Luxembourg