“Inscrutable”, related to the meta-rationality sphere, is a word that gets used a lot these days. On the fun side, set theory has a perfectly scrutable definition of indescribability. Very roughly: the trick is to divide your language in stages, so that stage n+1 is strictly more powerful than stage n. You can then say that a concept (a cardinal) k is n-indescribable if every n-sentence true in a world where k is true, is also true in a world where a lower concept (a lower cardinal) is true. In such a way, no true n-sentence can distinguish a world where k is true from a world where something less than k is true. Then you can say that k is totally indescribable if the above property is true for every finite n.
Total indescribability is not even such a strong property, in the grand scheme of large cardinals.
“Inscrutable”, related to the meta-rationality sphere, is a word that gets used a lot these days. On the fun side, set theory has a perfectly scrutable definition of indescribability.
Very roughly: the trick is to divide your language in stages, so that stage n+1 is strictly more powerful than stage n. You can then say that a concept (a cardinal) k is n-indescribable if every n-sentence true in a world where k is true, is also true in a world where a lower concept (a lower cardinal) is true. In such a way, no true n-sentence can distinguish a world where k is true from a world where something less than k is true.
Then you can say that k is totally indescribable if the above property is true for every finite n.
Total indescribability is not even such a strong property, in the grand scheme of large cardinals.