I think that one of the strongest examples of a philosophical approach employed in Edwards' sermon is the construction of the divine as a force of anger. Edwards borrows from the time period of the Great Awakening in the belief that God is angry. This notion of the divine places the divine in the philosophical paradigm of a wrathful and rather vengeful notion. In this, Edwards hopes to control the ethical conduct of the listener or the reader in aligning their own actions towards the anger of God. This is philosophical in its approach to constructing the nature of reality as one in which individuals cannot escape the wrath and anger of God. The relationship that individuals must carry with their divine is one of immediate subservience to the anger of God, caused by the actions of the individual. Edwards seeks to ensure that the philosophical rendering of the divine is one in which individuals recognize that their own actions represent the reason that God is angry and that they continue to carry themselves in the light that ensures individual compliance with the will of the divine. The use of Biblical passages to illuminate this brings out the idea that individuals lack hope without understanding the construction of God as one filled with anger at the transgressions of individuals.
Jonathan Edwards' sermon is based on Puritan dcotrine, which in turn is based on John Calvin's theology (the kind of philosophy deal with religion), and that in turn is based on the philosophy of St Thomas Aquinas. The starting point is: because of the sin of Adam and Eve (in Genisis) the human race is "fallen," is corrupt by nature. All humans are born with the stain of Original Sin (the sin of Adam and Eve's disobedience). Edwards preaches that we all deserve eternal damnation, eternity in Hell, because our nature is inseparable from sin.
God knows all things and we can do nothing to save ourselves. We are worms beneath the feet of Almighty God. Despite this, God takes a few of us, His Elect, into Heaven. God has known since the beginning of time who would be saved and who would be damned; therefore our lives, our actions, are Predestined. We have no free will. That is another part of Edwards' philosophy. Whether we believe in Christ, Whether we live holy lives--these things have been determined for us by God since the beginning of time.
No one may question God's "justice" and no one may "earn" God's Grace. We are unworthy.