Status Updates From Incompleteness: The Proof a...

Gödel’s first incompleteness theorem states the incompleteness of any formal system rich enough to express arithmetic. So Gödel’s conclusion, you might suspect, has something to say about the feasibility (or lack thereof) of eliminating all intuitions from mathematics.

Wittgenstein’s exasperation with his disciples even in his native Vienna, his insistence that although he might sound like a positivist he decidedly was not one, revolves around the meaning of the closing proposition of his Tractatus, numbered simply 7, the severely fulminating (so like a prophet of old): Wovon man nicht sprechen kann, darüber muss man schweigen, or: Of what we cannot speak we must remain silent.

Gödel’s theorems don’t demonstrate the limits of the human mind, but rather the limits of computational models of the human mind (basically, models that reduce all thinking to rule-following). They don’t leave us stranded in postmodern uncertainty but rather negate a particular reductive theory of the mind.

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