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A Case against Stephen Kleene’s Incomputability

Edgar Graham Daylight

Philosophy and Realistic Reflection · 103–125 · 10.55121/prr.v3i1.658

In Mathematical Logic (1967), Stephen Kleene addresses a central activity of software engineering through his introduction of tally-based Turing machines. Yet in doing so, he inadvertently builds a subtle form of impredicativity into his theory: he implicitly defines the semantics of Turing computability by appealing to the very