On the other hand, precise statements that are somewhere in the vicinity of the truth can be dangerous, because people tend to mistake precision for accuracy, and because modes of reasoning (e.g., formal logic) adapted to precise statements tend to be brittle—one can deduce very wrong conclusions from slightly wrong premises.
A charitable reading of Smullyan would be that when a precise statement is made, he likes to examine it as closely as its precision allows, to avoid such dangers; and that a vague statement, so far as it’s vague, is not worth the trouble of criticizing.
(For the avoidance of doubt: I think such a reading would probably be too charitable, and I upvoted Eliezer’s comment.)
I do not agree with all interpretations of the quote but primed by:
That’s not right. It’s not even wrong.
—Wolfgang Pauli
I interpreted it charitably with “critical” loosely implying “worth thinking about” in contrast to vague ideas that are not even wrong.
Furthermore, from thefreedictionary.com definition of critical, “1. Inclined to judge severely and find fault.”, vague statements may be considered useless and so judged severely but much of the time they are also slippery in that they must be broken down into precise disjoint “meaning sets” where faults can be found. So vague ideas cannot necessarily be criticized directly in the fault finding sense. (Wide concepts that have useful delimitations in contrast to arbitrary ill-formed vague ones can be useful and are a powerful tool in generalization. In informal contexts these two meanings of vague overlap).
Surely, to label a statement “vague” is a higher order of insult than to call it “wrong”. Newton was wrong but at least he was not vague.
On the other hand, precise statements that are somewhere in the vicinity of the truth can be dangerous, because people tend to mistake precision for accuracy, and because modes of reasoning (e.g., formal logic) adapted to precise statements tend to be brittle—one can deduce very wrong conclusions from slightly wrong premises.
A charitable reading of Smullyan would be that when a precise statement is made, he likes to examine it as closely as its precision allows, to avoid such dangers; and that a vague statement, so far as it’s vague, is not worth the trouble of criticizing.
(For the avoidance of doubt: I think such a reading would probably be too charitable, and I upvoted Eliezer’s comment.)
I do not agree with all interpretations of the quote but primed by:
I interpreted it charitably with “critical” loosely implying “worth thinking about” in contrast to vague ideas that are not even wrong. Furthermore, from thefreedictionary.com definition of critical, “1. Inclined to judge severely and find fault.”, vague statements may be considered useless and so judged severely but much of the time they are also slippery in that they must be broken down into precise disjoint “meaning sets” where faults can be found. So vague ideas cannot necessarily be criticized directly in the fault finding sense. (Wide concepts that have useful delimitations in contrast to arbitrary ill-formed vague ones can be useful and are a powerful tool in generalization. In informal contexts these two meanings of vague overlap).
Given what I’ve read of The Tao is Silent, I’m inclined to take a more literal (and less agreeable) interpretation of his quote here.