Feferman (1960) demonstrated that the choice of provability predicate is conventional, since differently defined but extensionally equivalent predicates yield divergent unprovability results.

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Divergent(describing how these three confirmation measures give conflicting results): Moving in different directions; disagreeing or coming to different conclusions.
Feferman(as a historical figure in logic and philosophy of mathematics): Solomon Feferman (1928–2016), a logician and philosopher who studied the foundations of mathematics and how different formal systems relate to each other.
Provability predicate(mathematical logic): A mathematical tool that checks whether a statement can be proven true within a formal system, like a built-in function that answers 'yes' or 'no' to 'can this be proven?'
Unprovability results(as the divergent outcomes produced by different provability predicates): The conclusions you reach when you demonstrate that certain statements cannot be proven true within a logical system—basically, proof of what can't be proven.
conventional(social ontology): In ordinary usage, 'conventional' may mean merely that a phenomenon is social, or that something about it is arbitrary or a matter of choice. In social ontology, however, 'conventional' is understood more precisely, following variants of David Lewis's 1969 analysis or analyses that challenge Lewis's approach.
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

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