## Church-Turing Thesis

Church's notion of an effectively calculable function of positive integers should be identified with that of a recursive function, joined with Turing's idea that the identification of effectively calculable functions with functions whose values can be computed by a particular idealized computing device (a Turing machine). As the two mathematical notions are provably equivalent, the theses are "equivalent," and are jointly referred to as the Church-Turing thesis.

### Articles on KurzweilAI.net that refer to Church-Turing Thesis

The Paradigms and Paradoxes of Intelligence, Part 2: The Church-Turing Thesis By Ray KurzweilThe Age of Intelligent Machines, Chapter Three: Mathematical Roots By Ray Kurzweil

Chapter 6: Locked in His Chinese Room By Ray Kurzweil

The Age of Intelligent Machines, Chapter Four: The Formula for Intelligence By Ray Kurzweil

The Age of Intelligent Machines: Footnotes By Ray Kurzweil

The Age of Intelligent Machines: A NOR B--The Basis of Intelligence? By Ray Kurzweil

The Age of Intelligent Machines, Chapter Two: Philosophical Roots By Ray Kurzweil

Chapter 2: I Married a Computer By John Searle

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The Age of Intelligent Machines: Chronology By Ray Kurzweil

### Related Links

The Church-Turing ThesisChurch-Turing Thesis

Alan Turing