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Can there be no nonrecursive functions?

Published online by Cambridge University Press:  12 March 2014

Joan Rand Moschovakis
Joan Rand Moschovakis*
Affiliation:
Occidental College, Los Angeles, California 90041
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Extract

In 1936 Alonzo Church proposed the following thesis: Every effectively computable number-theoretic function is general recursive. The classical mathematician can easily give examples of nonrecursive functions, e.g. by diagonalizing a list of all general recursive functions. But since no such function has been found which is effectively computable, there is as yet no classical evidence against Church's Thesis.

The intuitionistic mathematician, following Brouwer, recognizes at least two notions of function: the free-choice sequence (or ordinary number-theoretic function, thought of as the ever-finite but ever-extendable sequence of its values) and the sharp arrow (or effectively definable function, all of whose values can be specified in advance).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 36 , Issue 2 , June 1971 , pp. 309 - 315
Copyright
Copyright © Association for Symbolic Logic 1971

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References

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