Lisp's Grandfather Paradox

Computing Machinery and Intelligence. The article discusses the concept of recursion, particularly primitive recursion, and its historical context in mathematics and computer science. It highlights the contributions of key figures such as Skolem, Dedekind, and McCarthy, who laid the groundwork for understanding recursion in programming languages like Lisp. The piece emphasizes the importance of experiential learning through programming to grasp the principles of recursion, contrasting it with traditional mathematical approaches. It explains the foundational functions of primitive recursion, including the zero function, successor function, and projection function, and illustrates how these can be used to define arithmetic operations like addition, multiplication, and factorial. The article also touches on the limitations of primitive recursion, noting that while all primitive recursive functions are computable, not all computable functions are primitive recursive, as demonstrated by the Ackermann function. The discussion extends to the implications of recursion in programming languages, particularly in relation to Turing completeness and the distinction between bounded and unbounded loops. The author reflects on the philosophical connections between recursion, logic, and the origins of Lisp, suggesting that Lisp's design allows for a rich exploration of these concepts. The narrative concludes with an invitation for further engagement on the topic, hinting at potential future writings.