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“ Here’s a basic example using the statement, “This true statement is not provable.” If it were provable, it would be false, making logic inconsistent. If it’s
by moi2388 1y ago
“ Here’s a basic example using the statement, “This true statement is not provable.” If it were provable, it would be false, making logic inconsistent. If it’s not provable, then it’s true, but that makes any system trying to prove it incomplete”
Only if you assume the law of the excluded middle, right?
Statements aren’t just true or false, they can also be malformed or undefined.
- cluckindan 1y agoThat example is particularly fishy. The truthiness of a statement is not part of the statement itself, so any explicitly stated truth value is not inconsistent with truthiness, rather it is meaningless. It’s like saying bool isTrue = true; bool isProvable = false; bool isTrueAndProvable = isTrue && isProvable; // false