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Gödel Versus Wittgenstein

Book by Mike Hockney · 3 quotes · Godel, Incompleteness, Mathematics

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Gödel Versus Wittgenstein Quotes

“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.”

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“Gödel’s scheme has nothing to do with mathematics in and of itself. It concerns false approaches (i.e. non-ontological approaches) to the definition of what math is. The incompleteness theorems proved that such approaches are doomed to failure. Gödel didn’t prove a single thing about what math is. What he proved is what’s it’s not. He proved that it definitely isn’t manmade.”

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