{ "item_title" : "The Incompleteness of Deductive Logic", "item_author" : [" John-Michael M. Kuczynski "], "item_description" : "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.", "item_img_path" : "https://covers2.booksamillion.com/covers/bam/1/96/875/205/1968752056_b.jpg", "price_data" : { "retail_price" : "19.95", "online_price" : "19.95", "our_price" : "19.95", "club_price" : "19.95", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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