I scanned the sermon briefly and it’s more or less a very condensed version of what he says in his treatise on Religious Affections. In that somewhat famous treatise he does a lot of arguing around what are ‘real’ and what are ‘counterfeit’ strong emotions.
His basic premise is something along the line of: true affections from God are in love with the things themselves, the eternal excellencies of God and bring about true admiration and praise of God, true love of God, and therefore all the good attitudes that we find in the beatitudes in the sermon on the mount. Also the fruit of the spirit: love, joy, peace, gentleness, etc. And that these affections that are real are all ‘gospel based’, recognizing our own constant sinfulness and God‘s free justification and imputation of his righteousness, apart from our works, that is a righteousness apart from our subsequent experience of sanctification, as the sole foundation of our faith and gratitude to God.
Edward‘s emphasis in all his writings, is not just, ’do what the Bible says and don‘t just think about it.’ That is as potentially similar to the Pharisees line of thinking, than it is a Christian’s, although one can say that in a true sense for sure. To some extent it is what we find in James in a practical way of denying the existence of a faith that sits all by itself, all alone, without the fruit of the spirit or compassion on the poor, including action in genuine care, not just sending good thoughts to them. What Edwards is here describing is more than just practice what you preach but describes it as a lack of having strong genuine gracious affections. In other words, Edwards is more concerned about a genuine heart and having mercy. He is more like: have a genuine experience, from genuine faith and then give your life over to God sincerely and freely. Devote your whole heart to appreciating and apprehending God’s grace because the only contribution you make to your salvation is your own sin. In doing this we are also willing to bear the cross of the sufferings that he has designed for us, cheerfully, even while the more righteous persecute us, as the slave child persecuted the free child (Gal 4:23) or as the holy Pharisees persecuted Christ.
The Devils can all have ‘terror under the Law’ and ‘fear Christ as Lord‘. They feared him as the Lord, asking what he would do with them, even before the disciples knew he was the Christ, the Son of God. The Devils children can also know what is the most important command and even tested Jesus with the known answer (Matt 22:34). But the Devils can‘t ‘rely on his grace’ and by faith and gratitude for their salvation; ‘love God truly’ because of that faith in his grace and constant awareness of their own sin forgiven.
Edwards in that sermon, furthermore says that, every one who is not born again is a child of the Devil. So any experience that an unbeliever can have, also is no sure evidence of grace in the heart. We know the Pharisees could work very hard to make a convert, be extra diligent in good works, look down on the disciples as loose and carefree and irreverent with respect to righteousness and zeal, and yet they were all essentially devils too, seeking attention from men. Their experiences are meaningless and demonic even as zealots for God.
The wicked devilish men, can pray about Gods grace but betray it by judging others. Grace makes us humble in our sin, not way above others who we consider sinful:
The Pharisee stood by himself and prayed: ‘God, I thank you [for your grace] that I am not like other people—robbers, evildoers,
adulterers—or even like this tax collector. I fast twice a week and
give a tenth of all I get.’ Luke 18:11-12 (words in [brackets] are mine)
Here are a few quotations from the sermon that give you an idea (from The works of Jonathan Edwards Vol. 2, Banner of Trust, 1974):
Devils and damned men have a strong and most affecting sense of the
awful greatness and majesty of God. (p. 46)
Devils and damned men have some kind of conviction and sense of all
attributes of God, both natural and moral, that is strong and very
affecting. (ibid p. 46)
This is the foundation of every thing else that is distinguishing in
true Christian experience. This is the foundation of the faith of
God’s elect. This gives the mind a saving belief of the truth of
divine things. It is a view of the excellency of the gospel, or sense
of the divine beauty and amiableness of the scheme of doctrine there
exhibited, that savingly convinces the mind that it is indeed divine
or of God (ibid p. 48)
This sight of the beauty of divine things will excite true desires and
longings of soul after those things: not like the longings of devils,
but natural free desires; the desires of appetite, the thirstings of a
new nature, as a new-born babe desires the mother’s breast; and as a
hungry man longs for some pleasant food he thinks of; or as the
thirsty hart pants after the cool and clear stream. This sense of
divine beauty is the first thing in the actual change made in the soul
in true conversion, and is the foundation of every thing else
belonging to that change (ibid p. 49)