Gödel, Turing, and Church independently arrived at extensionally equivalent formalizations, and this invariance across disparate formalisms gives the thesis a quasi-definitional status rather than a contingent one.
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Quasi-definitional status(describing how the Church-Turing thesis is treated as essentially true rather than just a hypothesis)
Having a status that is almost like a definition—accepted as a fundamental truth rather than something that needs to be proven.
Turing
# Turing
Alan Turing was a British mathematician and scientist (1912-1954) who is considered the father of computer science and artificial intelligence. He invented the "Turing Machine," a theoretical device that helped define what computers could and couldn't do, and created the "Turing Test," a famous challenge to determine whether a machine can exhibit intelligent behavior indistinguishable from a human. His groundbreaking work during World War II on code-breaking, combined with his pioneering ideas about thinking machines, made him one of the most influential thinkers of the 20th century.
contingent(De Interpretatione 12–13)
Equated with 'possible'; on the two-sided interpretation, contingency excludes necessity (possibility implies non-necessity).
extensionally equivalent(Applied to Church's thesis and Turing's thesis regarding functions of positive integers)
Two theses are extensionally equivalent when they are about one and the same class of functions
invariance(Woodward's criterion within the manipulability account of causation)
A measure of the extent to which a relationship between two variables satisfying the manipulation condition remains stable or unchanged as various other changes are made in the background of that relationship