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The purpose of the present paper is to shed some light on the nature of logical thinking based on the career of mathematician Kurt Gödel (1906–1978), who demonstrated the incompleteness theorem, and conceived a spiritualist pantheon made of demons and angels. Our approach will be twofold: first, we try to individuate the impasses of Gödel’s “mysterious” philosophy and his universal logic, closer to the foundations of the scientific mind as well as paranoia. Secondly, based on Gödel’s unpublished philosophical papers, we attempt to grasp, in light of Lacanian theory, the subjective structural position of this mathematician through his creative thinking (scientific theory and marginal metaphysical productions). We postulate that his creative thinking could have had the effect of a “logical” sinthome, allowing him to maintain a subjective enunciation and avoiding decompensation (i.e., the coming apart of Borromean knots). Finally, the risk of imposture due to a misuse of the incompleteness concept will be approached.