Necessary Wisdom draws on one of the simplest ways to get at what makes such new understanding new: such thinking successfully "bridges" polarities. It draws an encompassing circle around the either/ors of conventional thought-political left and political right, might and body, masculine and feminine, alley and enemy, or matter and energy. Besides applying the concept of bridging to issues such as those above, it draws on Creative Systems Theory to help tease apart how our thinking can stop short of the needed conceptual maturity.

Creative Systems Theory identifies three kinds of polar traps, what it calls Unity Fallacies, Separation Fallacies, and Compromise Fallacies. Each issue-focused chapters ends with a listing of ways we can fall for each of these kinds of fallacies in attempting to address those particular concerns.