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

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John-Michael M Kuczynski

The Incompleteness of Deductive Logic

Name: The Incompleteness of Deductive Logic
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ISBN: 9781968752057

And Its Consequences for Epistemic Engineering

John-Michael M Kuczynski

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English

Zhi Systems
03 April 2026

Philosophy: epistemology & theory of knowledge; Philosophy: logic; Mathematical logic

Summary
Details

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.

By: John-Michael M Kuczynski
Imprint: Zhi Systems
Dimensions: Height: 279mm, Width: 216mm, Spine: 5mm
Weight: 231g
ISBN: 9781968752057
ISBN 10: 1968752056
Pages: 90
Publication Date: 03 April 2026
Audience: General/trade , ELT Advanced
Format: Paperback
Publisher's Status: Active