Clearly the character to start with in responding to this question is Ran, who is defined by her philosophical stance in life. Note the way that she believes "reason is man's only proper judge of values and his only proper guide to action." Her philosophical approach, that she calls "objectivism," is clearly linked to Greek philosphical thought and becomes an important theme of the novel as a whole.
You might also like to consider the character of Roark and how he demonstrates this "objectivism" in identifying what sustains his ego and thus preserves his life. This of course draws attention to another important philosophical concept, which is that of individualism, which he demonstrates through his determination to reject the attempts of others to change his vision or specify what success would look like.
This novel therefore presents us with key philosphical beliefs and practices that represent a continuation with Greek philosphical thought. Each of the characters seems to live out their own personal brand of philosphy that is a continuation to the thoughts of the Ancient Greeks regarding issues such as individuality and objectivity.