Seeing means the ability to observe. It means having a more accurate perception and interpretation. Seeing is the ability to employ spiritual reasoning through prayerful thought and conversation with Christ, ongoing questions, and paying attention to God’s answers and counter-questions that he may impress on you.
It is important to note that most of the "random" thoughts that cross your mind are the false self - constant chatter from a source that attempts to know it all and run constant commentary. It is like having the tuner on your radio turned to talk radio all day: the chatter and commercials never shut up.
On the other hand, most of what we willfully give thought to is to our true self. When we actively choose our thoughts and line of reasoning, we are far less likely to be operating from our false self. Inviting God into the course of conversation with our hearts, and listening for him speaking, completes the picture. This is the engaged practice of seeing with the eyes of our heart.
An excerpt from The Heart of a Warrior Journal Workbook.