I’m not sure I buy the whole ‘subverbal’ thing—it seems to me that misleading phrasing is a big part of the problem. If asked to find the “rule” which “governs” a sequence of three numbers, I’d (incorrectly …) assume that the questioner was thinking of some simple rule that can be used to generate all of the valid sequences. Given the examples, I’d guess it was something like ‘x x+2 x+4’ or ‘2x 2(x+1) 2(x+2).’ Now, after I started typing this I realized that you could map all ascending 3 integer sequences to the whole numbers, so there is a “rule” that could be used to generate the solution, but nobody would look at the solution in these terms naturally—instead, we think of the solution as the set of sequences with the “property” of being in ascending order. If the questioner said that he was thinking of “a property which sequences of 3 numbers either have or lack,” rather than a “rule” which “governs” the sequences, I suspect more folks would discover the correct solution.
I’m not sure I buy the whole ‘subverbal’ thing—it seems to me that misleading phrasing is a big part of the problem. If asked to find the “rule” which “governs” a sequence of three numbers, I’d (incorrectly …) assume that the questioner was thinking of some simple rule that can be used to generate all of the valid sequences. Given the examples, I’d guess it was something like ‘x x+2 x+4’ or ‘2x 2(x+1) 2(x+2).’ Now, after I started typing this I realized that you could map all ascending 3 integer sequences to the whole numbers, so there is a “rule” that could be used to generate the solution, but nobody would look at the solution in these terms naturally—instead, we think of the solution as the set of sequences with the “property” of being in ascending order. If the questioner said that he was thinking of “a property which sequences of 3 numbers either have or lack,” rather than a “rule” which “governs” the sequences, I suspect more folks would discover the correct solution.