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Church-Turing Thesis
The Church-Turing thesis, properly understood, is a thesis about the semantic relationship between a group of linguistic expressions. It is a thesis for which there can be no mathematical proof, but it is generally considered to be beyond reasonable doubt and is almost universally accepted by mathematicians and philosophers of mathematics. The thesis is that a certain many-membered set of precisely defined mathematical expressions, which are coextensive with each other, are coextensive with the nonmathematical expression effectively computable, as that expression is used by mathematicians. The fact that there are many members of the set of precisely defined mathematical expressions is of utmost importance. To enable readers to understand what the thesis, as stated, means, the purpose of this entry is to enable them ...
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