The Incompleteness of Deductive Logic (Paperback)
Language: English
Published by Zhi Systems, 2026
- Softcover
- New
Seller: AussieBookSeller, Truganina, VIC, AustraliaAussieBookSeller
AbeBooks seller since June 22, 2007
Condition: New
£ 17.28
Quantity: 1 available
Add to basketItem description from seller
Paperback. 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 Goedel: 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. A new theorem in recursion theory showing that formal systems cannot be recursively enumerated, with major consequences for logic, AI, and epistemology. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. …
Seller Inventory # 9781968752057
- Title
- The Incompleteness of Deductive Logic (Paperback)
- Author
- John-Michael M. Kuczynski
- Publisher
- Zhi Systems
- Publication year
- 2026
- Condition
- new
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1968752056
- ISBN 13
- 9781968752057
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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AussieBookSeller
Truganina, VIC, Australia
AbeBooks seller since June 22, 2007
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| Item | 25 to 45 business days | 8 to 14 business days |
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