Daisy’s Reviews > Incompleteness: The Proof and Paradox of Kurt Gödel > Status Update
Daisy
is on page 106 of 296
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.
— Jul 05, 2026 12:00PM
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Daisy
is on page 140 of 296
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.
— Jul 06, 2026 10:30PM
Daisy
is on page 25 of 296
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.
— Jul 01, 2026 07:13AM
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Jul 05, 2026 12:04PM
“I once wanted to give a few words in the foreword which now actually are not in it, which, however, I’ll write to you now because they might be a key for you: I wanted to write that my work consists of two parts: of the one which is here, and of everything I have not written. And precisely this second part is the important one. For the Ethical is delimited from within, as it were, by my book; and I’m convinced that strictly speaking it can ONLY be delimited in this way. In brief, I think: All of that which many are babbling today, I have defined in my book by remaining silent about it.”
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Yet, if one pushes beyond the metamathematical irreconcilabilities separating Wittgenstein and Gödel, one comes upon a surprising commonality, at least between the early Wittgenstein and the logician, masked by the positivist interpretation of Wittgenstein. In a sense, the early Wittgenstein put forth an incompleteness thesis of his own in his final proposition of the Tractatus. Just as Gödel demonstrated that our formal systems cannot exhaust all that there is to mathematical reality, so the early Wittgenstein argued that our linguistic systems cannot exhaust all that there is to nonmathematical reality. ( pp 190)
For Gödel, for each formal system there will be truths expressible in that system that will not be provable; and one of the most important truths about the system, that it is consistent, will not be provable within the system. So both Gödel and the early Wittgenstein are united against the positivists’ reiteration of the ancient Sophist’s slogan that man is the measure of all things. Both men assert a fundamental incompleteness that takes the measure of man. Wittgenstein’s is, by far, the more radical statement of incompleteness. For Gödel’s there is expressible knowledge which cannot be formalized. The limits of formalization, of our attempt to reduce all mathematical knowledge to the specified rules of a system, are not congruent with the limits of our knowledge. Our mathematical knowledge exceeds our systems. For early Wittgenstein there is no expressible knowledge that escapes the limits he delineates. On the other side of meaningfulness lies all the most important subjects: ethics and aesthetics and the meaning of life itself.( pp 191)