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“Gödel (and indeed the whole mathematical community) failed to realise that all valid mathematical axioms must be tautological, i.e. must be shown to have a common root, of which they are equivalent expressions. Any mathematical axioms that are not tautologous automatically fall foul of Cartesian substance dualism, i.e. they imply different ontologies and epistemologies – different and incompatible versions of mathematics – hence cannot be complete and consistent with regard to each other. In other words, Gödel simply came up with an ingenious way of showing that existence must be predicated on monism, and not on dualism or pluralism.” — Mike Hockney
Gödel (and indeed the whole mathematical community) failed to realise that all valid mathematical axioms must be tautological, i.e. must be shown to have a common root, of which they are equivalent
expressions. Any mathematical axioms that are not tautologous automatically fall foul of Cartesian substance dualism, i.e. they imply different ontologies and epistemologies – different and incompatible
versions of mathematics – hence cannot be complete and consistent with regard to each other. In other words, Gödel simply came up with an ingenious way of showing that existence must be predicated on monism, and not on dualism or pluralism.