Gödel refutes the philosophy of mechanism
The existence of statements that are undecidable by formal systems—eg Gödel’s theorem—shows that mechanism can't provide a complete explanation of mathematical nature. So mechanism must be rejected as a universal theory of science.
Note:

Other Gödelian arguments against mechanism are spread throughout this map. See especially the "Is the Lucas argument dialectical?" arguments on this map.
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Artificial Intelligence »Artificial Intelligence
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Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
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Yes: Automata can think »Yes: Automata can think
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Natural phenomena best understood via mechanism »Natural phenomena best understood via mechanism
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Gödel refutes the philosophy of mechanism
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Gödel doesn't solve constructivity problem »Gödel doesn't solve constructivity problem
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Strong mechanism refuted: weak mechanism safe »Strong mechanism refuted: weak mechanism safe
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