The original sense of this word is far richer and more nuanced than its common usage. This point can be demonstrated from the two times the word is used in Tanach. Based on its appearance in Mishlei 11:2, where tzniut is associated with wisdom, it must relate to the intellect; but it also must be associated with values, since in Micah 6:8 it is juxtaposed with justice and a love of kindness. In both of these cases, interpreting the word as modesty would make nonsense of the rest of the verse.
A more fitting translation, offered by Jonah Gerondi, Abravanel, and Malbim, is intellectual submission, or the acceptance of our mental limits. Using this interpretation, the verses make far more sense. With such acceptance, one can attain wisdom, since one who acknowledges the limits of his or her knowledge is more receptive to new ideas. At the same time, this interpretation is more consistent with values or attitudes, since this type of humility is how a person orients themselves to the world. And although intellectual humility and demureness may share conceptual similarities, the differences between them are vast. For one thing, intellectual humility cannot be forced upon an individual by someone else. It is done internally, through reflection. For another, you cannot measure it with a ruler.