Resolved means what it sounds like: it's a deliberate, committed disposition.
As a 19-year old in the mid-1700s, Jonathan Edwards became serious about the direction of his life. He began to understand the nature of God, and what he discovered was both delightful and disturbing. The more he investigated the infinite tributaries of God's nature, the more he unearthed his own sinfulness. From then on, the weight of God's glory became the gravity of his life. He was compelled to respond.
So he sat down with a quill and paper and wrote out a series of commitments. These were simple statements, conclusions, and commitments forged in the immensity of God and the trauma of His holiness. All of them began with the same word—"Resolved".