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lukeprog comments on Rationality Quotes April 2014 - Less Wrong
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Comments (656)
Clifford Truesdell
This is beautiful: I can't turn it into equations. Does that refute it or support it?
Did you try? Each sentence in the quote could easily be expressed in some formal system like predicate calculus or something.
There are symbol-juxtapositions which are syntactically or semantically disconnected from any model set in ZFC. There are no sets in ZFC which are similarly separated from statements in a suitable language.
This looks like the sort of thing that I usually find enlightening, but I don't understand it. Could you repeat it in baby-speak?
You can write nonsense formulas on paper which don't correspond to theorems about anything. You can't construct nonsense universes which aren't described by theorems anywhere.
Words only mean anything because we interpret them to correspond to the real world. In the absence of words, the real world continues existing.
I don't see why an equation can't be nonsensical. Perhaps the nonsense is easier to spot when expressed in symbols, or then again perhaps not.
Equations can be nonsensical, but it's harder to write a nonsense equation than a nonsense sentence (like the old joke: it's easy to lie with statistics, but it's easier to lie without them). In a way this was the unpleasant surprise of Godel's incompleteness theorem; before that we'd hoped that every well-formed proposition was true or false and could be proven to be so.