The Incompleteness of Deductive Logic: And Its Consequences for Epistemic Engineering - Couverture souple

Kuczynski, John-Michael M

Couverture souple

ISBN 10 : 1968752056 ISBN 13 : 9781968752057

Editeur : Zhi Systems, 2026

Synopsis

This book proves a new theorem in recursion theory with major consequences for logic, philosophy, AI, and epistemic engineering. The main result is that the class of all recursive, truth-preserving deductive logics is not recursively enumerable-no algorithm can list all possible formal systems. This strengthens Gödel: incompleteness does not just block any single system from capturing all truths; it prevents recursion itself from surveying the space of formal systems. The core philosophical payoff is overturning the long-standing but false assumption that rationality = recursivity. Rational thought includes both recursive rule-following and non-recursive pattern-recognition capacities, and neither can be reduced to the other. This insight dissolves classical problems (induction, rule-following, foundationalism), explains why GOFAI failed, clarifies why neural networks succeed, and reframes mathematical and linguistic understanding as non-recursive pattern-based cognition. As a result, epistemic engineering-the design of systems that expand, stabilize, and operationalize human knowledge-must integrate non-recursive rational mechanisms rather than treating rationality as algorithmic.

Détails de l'édition

• Éditeur: Zhi Systems
• Date d'édition: 2026
• Langue: anglais
• ISBN 10: 1968752056
• ISBN 13: 9781968752057
• Reliure: Paperback
• Nombre de pages: 90
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible