Ralph Erskine emphasizes that God's salvation of sinners is fundamentally for His own name's sake, rather than for any merit on the part of the sinners themselves. He explains that the glory of God's name is paramount in the act of salvation, as it showcases His mercy, justice, and power, even in the face of human sinfulness. Erskine illustrates this through the historical example of Israel's deliverance from Egypt, highlighting that God's grace is extended to the most grievous sinners, demonstrating His willingness to save despite their unworthiness. The sermon calls believers to recognize their dependence on God's grace and to glorify His name in their lives. Ultimately, Erskine reassures that God's saving work is rooted in His desire to magnify His name and attributes.