To Jonathan Edwards, all people deserve to be damned. They are so evil that all are abhorrent to God. However, he believes that people can do something to save themselves from eternal damnation.
What he says is that Jesus is calling out to all people, inviting them to the Kingdom of God. All they really have to do is accept his invitation and embrace him. They are to renounce their sinful ways and come to God.
If they will accept this invitation, then they will have a chance to be saved.
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Edwards spends a great deal of the sermon making people appear unworthy of God's mercy because all people are sinners. He also states that life is unpredictable and that Hell awaits all sinners. He goes into great detail describing the fires of Hell, and how Man avoids it only because of God. After Edwards makes the parishioners feel as though they are doomed for eternal damnation, he offers hope--salvation through God's grace. He then goes into detail to describe repentance as a turning away from sin and turning toward God. It entails one admitting that one lived life incorrectly and would seek a better way through God and his Son, Jesus Christ. The contrast between damnation and salvation is quite stark in Edwards's sermon and is meant to get a reaction from the attendees. The sermon was very popular and widely printed, so one can imagine that Edwards's message convinced many of the error of their ways.