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

By John-Michael M Kuczynski

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 G del: 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.

• Format: Paperback
• Language: English
• ISBN: 1968752056
• ISBN13: 9781968752057
• Release Date: April 2026
• Publisher: Zhi Systems
• Length: 90 Pages
• Weight: 0.51 lbs.
• Dimensions: 0.2" x 8.5" x 11.0"