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84), thought that it was Turing’s analysis that captured the concept of computability in the most adequate way.He claimed that it is “absolutely impossible that anybody who understands the question and knows Turing’s definition should decide for a different concept” (Wang Gödel wrote that “the correct definition of mechanical computability was established beyond any doubts by Turing”.On this understanding the two theses differ significantly in many aspects.
Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses as .
This move opens up the possibility that both accounts could be adequate, albeit in their own different ways.
A way out of a possible philosophical standoff would be to view Turing’s and Church’s theses not as competing conceptual analyses, but rather as explications— While there can be only one adequate conceptual analysis of a given concept, there may be several equally fruitful explications of the same pre-systematic concept.
In consequence, one can defend both attempts—Church’s and Turing’s—as good explications of effective computability, and there is no need to argue for one to the disadvantage of the other.
Church’s thesis, formulated in 1936, identifies the pre-systematic concept of “effectively computable” or “calculable” with the property of “being generally recursive” defined for functions on natural numbers.
Turing’s thesis, formulated in the same year, translates this pre-systematic concept into “being computable by a Turing machine”.
In consequence, claims Rescorla, Turing’s thesis fails to be an analysis of computability at all.
Rescorla refers to the well known problem, sometimes called “the semantical Halting problem”, according to which if there were no “external” constraints on the choice of such a semantics—for instance, constraints on possible denotation functions that can be used for mapping from numerals to numbers—a Turing machine would compute—under some “deviant semantics”—non-computable functions on natural numbers (Shapiro Disagreements about the proper analysis of important concepts tend to linger on indefinitely, as witnessed by many similar debates in the history of philosophy.
explanation, account - a statement that makes something comprehensible by describing the relevant structure or operation or circumstances etc.; "the explanation was very simple"; "I expected a brief account" sur le developpement des relations entre le Soudan et la Turquie et sur les relations soudano-allemandes et a affirme l'importance de realiser un partenariat entre le Soudan et la Turquie ainsi que l'echange des expertises entre les deux pays.