Question: Can fallen man do anything to please God? Can the natural man make choices all the time for things that are good and evil?
Response: All fallen, unregenerate human beings are endowed with many of God's common graces. God has blessed all men with a conscience and the capacity to promote virtue and civil righteousness. It is abundantly clear that many beautiful aspects of the world we live in have been brought forth by those which are unredeemed by God's regenerative grace. God has gifted natural men and women with the skill to create beautiful music, make profound works of art, to invent intricate machines and do countless things that are productive, excellent and praiseworthy. But even these "good things" are not done purely to glorify God. i.e. the source of natural man's affections and motives for doing things come from a polluted well.
Fallen man's many good works, even though in accord with God's commands, are not well pleasing to God when weighed against His ultimate criteria and standard of perfection. The love of God and His law is not the unbelievers' deepest animating motive and principle (nor is it his motive at all), so it does not earn him the right to redemptive blessings from a holy God. The Scripture clearly implies this when it states "...without faith it is impossible to please Him." (Hebrews 11:6a, NASB) and "whatever is not from faith is sin." (Romans 14:23)
So then even his "virtue" is considered evil in the sight of God. His purpose for doing good works are not from a heart that loves God. Being unspiritual, that is, without the Holy Spirit, "... men do not rise above themselves" (Calvin) But now through our justification and regeneration in Christ, we are enabled, for the first time, to be pleasing to God on the basis of Christ's work.
"Those who are in the flesh cannot please God." - Romans 8:7
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Quiz: If "Those who are in the flesh cannot PLEASE God" as Romans 8:7 declares, and "And without faith it is impossible to PLEASE God." (Heb.11:6) then how can those in the flesh have the faith necessary to PLEASE God? (Answer: 1 Cor 2:14, 1 Cor 2:12 & John 6:63, 65)