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  1. Metamathematics and the philosophy of mind.Judson Webb - 1968 - Philosophy of Science 35 (June):156-78.
    The metamathematical theorems of Gödel and Church are frequently applied to the philosophy of mind, typically as rational evidence against mechanism. Using methods of Post and Smullyan, these results are presented as purely mathematical theorems and various such applications are discussed critically. In particular, J. Lucas's use of Gödel's theorem to distinguish between conscious and unconscious beings is refuted, while more generally, attempts to extract philosophy from metamathematics are shown to involve only dramatizations of the constructivity problem in foundations. More (...)
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  • Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems.Rod J. L. Adams & Roman Murawski - 1999 - Dordrecht, Netherland: Springer Verlag.
    Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
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  • On the Anti-Mechanist Arguments Based on Gödel’s Theorem.Stanisław Krajewski - 2020 - Studia Semiotyczne 34 (1):9-56.
    The alleged proof of the non-mechanical, or non-computational, character of the human mind based on Gödel’s incompleteness theorem is revisited. Its history is reviewed. The proof, also known as the Lucas argument and the Penrose argument, is refuted. It is claimed, following Gödel himself and other leading logicians, that antimechanism is not implied by Gödel’s theorems alone. The present paper sets out this refutation in its strongest form, demonstrating general theorems implying the inconsistency of Lucas’s arithmetic and the semantic inadequacy (...)
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