“The world is totally connected. Whatever explanation we invent at any moment is a partial connection, and its richness derives from the richness of such connections as we are able to make. ...mathematics suffer from the same partiality. Gödel, Turing, and Tarski all proved this. Gödel proved that you cannot have a complete axiomatization of the whole of mathematics, that every system which you devise is partial and suffers from one great shortcoming. If it is consistent, there are theorems which are true that cannot be proved in it. And Turing showed that every machine that we can devise is like a formal system, and that therefore no machine can do all of mathematics. And Tarski put it even more boldly when he said that no universal language for all of science can exist in all cases without paradox.<!--pp. 96-97-->”
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