Abstract
The investigation of effective procedures used in mathematics led to a mathematical investigation of such procedures. The recursive functions were singled out from the totality of all functions (from natural numbers to natural numbers) as those that are effectively computable. This was done in the early thirties, not very long after the period in which the concept of an abstract, “arbitrary” function, possibly without any rule for determining its values, had been universally adopted. The need for a strict definition of computability emerged especially in view of the possibility that some interesting functions are not effectively calculable. Indeed, the logically interesting function, assigning to a sentence its smallest proof in a given formalized theory (if there is one, and, say, 0, if there is none), came out to be nonrecursive for appropriate theories (cf. “Decidability” §3.1).
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Krajewski, S. (1981). Recursive Functions. In: Marciszewski, W. (eds) Dictionary of Logic as Applied in the Study of Language. Nijhoff International Philosophy Series, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1253-8_57
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DOI: https://doi.org/10.1007/978-94-017-1253-8_57
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