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
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
Yes: Automata can think »Yes: Automata can think
Natural phenomena best understood via mechanism »Natural phenomena best understood via mechanism
Gödel refutes the philosophy of mechanism
Gödel doesn't solve constructivity problem »Gödel doesn't solve constructivity problem
Strong mechanism refuted: weak mechanism safe »Strong mechanism refuted: weak mechanism safe
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