The two comments made on my last post spurred me on to clarify Frame's position. I have no interest in defending him, just clarifying what he actually says. Many of the 'objections' to Frame will be cleared up, I think, with clarification.
First, the section I quoted comes as Frame is discussing the cultural mandate as it comes to Adam in Genesis 1:28. In this discussion, Frame traces the historical development of the cultural mandate. He reminds us that "The first human experience recorded in Scripture is the experience of hearing this command...It defines the purpose of human life". The section I quoted comes in this context - the context of prefall man. Consequently, when Frame speaks of using creation to 'serve their own purposes', it is still in the context of man in right relationship with God. He makes that explicit in the paragraph that follows the quote I provided. He writes, "God gave this command to Adam and Eve for the same reason, ultimately, that he does everything else: for his own glory... Adam was not to rule merely for himself, but for God, glorifying God in all he did."
Frame moves on from this discussion of the cultural mandate in the prefall context to discuss, briefly, what it means after the fall. As sinner, he asserts, we seek our own glory instead of God's. Here Frame chooses to talk more about what is still good in culture rather than what is bad, clearly righting against those who would reject culture as all bad. If he had chosen to write about what sin has done to man and their ability to fulfill the cultural mandate, he would, I think, say we are incredible failures. We have exploited. We have failed to master what we should (though I don't think he would say we need to develop every square inch of the world - I'm guessing he'd be opposed to a mini-mall in the Grand Canyon National Park - but I am only guessing). Nations have horded and are greedy, unjust and often cruel in how they use up resources. Yet, and this is where Frame focuses, even in sinful cultures common grace can be found. Even in evil cultures, there is some good.
Moving from a discussion of the fall and it's impact on culture, and God's common grace and it's impact on the same cultures, Frame moves to discuss God's special saving grace and asks "Does God's saving grace make an impact on culture?" Here I think a definition of culture (long overdue) will help. Basically, Frame distinguishes creation (what God does directly) from culture. Culture is everything man does (God does through man since God is ultimately sovereign in all things), including: what we make with our hands (tools, houses, cities, art), what we make with our minds (language, systems of thought, philosophy, science, politics), our institutions (families, churches, governments, corporations), as well as our values, customs, games, sports, music, literature, cuisine, etc. Obviously, his definition is comprehensive - he's not just speaking of high culture, or 'culchah' as he describes it. Going back to the question, Frame argue that God's saving grace certainly has an impact on culture. He writes, "When you believe in Jesus, your whole life changes direction: your thoughts, words, and deeds. Whether you eat, or drink, or whatever you do, you seek to do it for God' s glory... You'll fail, because you won't be perfect until glory. But you'll try. And sometimes trying can make a huge difference. You can influence your culture, as many Christians have." Frame actually sees the cultural mandate as not only coming from God's command to humanity through Adam (and Noah), but also coming specifically to Christians in the Great Commission. Again, I'll let Frame speak for himself, "The Great Commission tells us not only to tell people the gospel and get them baptized, but also to teach them to obey everything Jesus has commanded us. Everything. The gospel creates new people, who are committed to Christ in every area of their lives. People like these will change the world. They will plant churches and establish godly families, and they will also establish hospitals, schools, arts, and sciences. That is what has happened by God's grace. And this is what will continue to happen until Jesus comes."
I think there is still plenty to critique here, but just wanted to make sure I represented Frame's position well.