John-Michael Kuczynski

The Incompleteness of Deductive Logic (eBook, ePUB)

And Its Consequences for Epistemic Engineering

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Zhi Systems
• Seitenzahl: 101
• Erscheinungstermin: 19. November 2025
• Englisch
• ISBN-13: 9781968752040
• Artikelnr.: 75942199