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Objectivity over Objects: Gödel’s Late Platonism and Phenomenology

30. Juni 2011 von Gianluca Ustori

Until the 50s Gödel’s Platonism is centered in the belief in the independent existence of mathematical concepts and objects. From the 60s on, Gödel writes on the contrary that the existence of mathematical objects is not necessary, and that it suffices to believe in the objectivity of mathematics. Hauser interprets the evolution of Gödel’s thought from Platonism to objectivism as a result of the discovery of Husserl’s phenomenology (Gödel started to read Husserl in 1959, and became soon very sympathetic with his philosophy). In my opinion, Hauser’s thesis is wrong, and is due to the fact that Hauser follows the analytical interpretation of phenomenology given by Føllesdal and his disciples. I suggest that the origin of Gödel’s turn to objectivism could be in his conversations with Kreisel: the oft cited Kreisel’s dictum says that “the problem is the objectivity of mathematics, not the existence of mathematical objects”. Dummett considers Kreisel’s dictum as expressing semantic realism, i.e. realism about truth, opposed to metaphysical realism, concerning existence. Also in physics we can find a move from a metaphysical to a verifiable realism, with Einstein’s realism of properties, opposed to the classical realism of objects: this shift is very near to Gödel’s one from Platonism to objectivism. Gödel shares Einstein’s realistic convictions about quantum mechanics, and believes that undecidability in mathematics is due to the fact that we have only a partial knowledge of mathematical reality. What we need, in Gödel’s/Einstein’s opinion, is to expand set theory/quantum mechanics to a complete theory, providing a complete description of the respective states of affairs. I believe that Husserl’s mature phenomenology is nearer to Dummett’s and Bohr’s approach, underlining that mathematical and physical entities are constituted in an open process from the vagueness of the life-world, and are not to be considered as an independent existing and totally determinate reality.

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