link does not work for me, and my book is not divided into chapters, except within some of the “mansions”. The sections on each “mansion” which do have chapters do not have further numbered subdivisions, so I would need more direction to the passages you have in mind.
If you mean the part in the First Mansion that speaks of self-knowledge as the fruit of humility. For progress in mental prayer and the spiritual journey Teresa emphasizes the importance of humility over and over. I believe her point at the end of the first mansion is that self-knowledge, that is honest appraisal of one’s spiritual condition and perfect contrition for sin, is not obtained by introspection, by looking inward at oneself, by comparing one’s spiritual condition to that of others, by seeking the good opinion of others, or by anything that leads to pride and vanity. She seems to be saying that self-knowledge can come authentically only when we are completely focused on God, not upon ourselves.
Teresa says that we confuse true self-knowledge with self-evaluation or self-congratulation when we constantly focus on ourselves, the quality of our prayer and good deeds, trying to assess our own progress, and that the devil tempts us to do this because it removes our attention from God to our own vanity. We forget that it is God who will reveal our true self, that we cannot know ourselves apart from him. Any spiritual activity which turns attention to myself, my feelings, my progress, and away from God, away from worship and praise of God, away from contemplation of God, is a temptation to pride, the enemy of humility. Without humility there can be no self-knowledge, because without humility we try to assess ourselves. With humility, we allow God to judge, and to tell us what we need to know about ourselves.