Among other things, Cardinal Kasper calls attention to what he refers to as the "multicultural world" and claims that Pope Francis himself refers to "polyhedral reality" (page 20).
According to Kasper, "The pope names two fundamental challenges of plurality [to the emergence of a new Christian presence in Europe and elsewhere]: 'The challenge of multipolarity and the challenge of transversality.' With the concept of multipolarity, he pleads for a Europe of unity in diversity, which excludes hegemonic supremacy and respects the cultural diversity of peoples and of religions. Again he harks back to the image of the polyhedron, in which the unity of the whole preserves the distinctiveness of the different parts. Transversal communication means an open, respectful, and enriching exchange between generations, between people and groups of disparate ancestry and different ethnic, linguistic, and religious traditions in a spiritual of mutual understanding and mutual respect. In this transversal communication, Christianity today can find its place anew [in Europe]" (pages 85-86).
In a lengthy discussion note, Kasper further explains the concept of transversality:
"The concept of transversality, which derives from mathematics and geology is found nowadays also in economics (the theory of exchange rates), sociology, political science, and psychology as well as in the aesthetics and theory of modern media. In philosophy the concept of transversality has become fundamental in view of the ineluctable plurality of our globalized world. It stands for a theory of rational communication and creative interaction between different ethnic, cultural, religious, and other kinds of groups. In the process, it seeks to avoid the relativism and the mutual indifference of a postmodern anything goes attitude as well as the neocolonial, Eurocentric exclusiveness and one-sided normativity of Western modernity. It has to do with a transmodern concept of reason, which creatively links identity and plurality and thus enables a creative coexistence and cooperation, in which the identity of each respective culture and religion is cherished and, in the encounter with other cultures and religions, is simultaneously enriched. In Latin America, this way of thinking is found above all in Enrique Dussel, who comes from Argentina [as does Pope Francis]" (page 116).
Your guess is as good as mine as to whether or not the American Catholic theocons that Damon Linker writes about in his book THE THEOCONS: SECULAR AMERICA UNDER SIEGE (2006) will endorse this concept of transversality.
In connection with the concept of transversality, I now want to discuss Ong's thought about print culture in Western culture and about contemporary secondary oral culture.
First, let's review.
For Ong, as mentioned above, print culture in Western culture emerged after the emergence of the Gutenberg printing press in the 1450s. From the time of ancient Greek philosophy exemplified in Plato and Aristotle, formal education in Western culture accentuated visual cognitive processing -- before the Gutenberg printing press emerged in the 1450s. After the Gutenberg printing press emerged in Western culture, formal education continued to accentuate visual cognitive processing and formal education expanded to a much larger percentage of the population -- indeed, an unprecedented percentage -- in Europe and European colonies, including the American colonies.
For Ong, secondary oral culture emerged in Western culture as the result of the cultural conditioning of communications media that accentuate sound. By, say, 1960, the communications media that accentuate sound had reached a critical mass, which has not yet receded to this day.
Now, in a wide-ranging review essay in STUDIES IN ENGLISH LITERATURE, volume 4 (1964): pages 163-194, Ong describes ancient and medieval chirographic culture (before the emergence of the Gutenberg printing press in the 1450s) and print culture as involving "the detribalization of man and the reconstitution of the collective unconscious through the successive shifts in communication media" (page 193).
I associate the term collective unconscious with the thought of C. G. Jung, M.D. (1875-1961), the Swiss psychiatrist and psychological theorist.
No doubt the collective unconscious has been undergoing a further reconstitution under the influence of the cultural conditioning of communications media that accentuate sound.
So I consider the concept of transversality as Kasper outlines it to be connected with our contemporary cultural conditioning by communications media that accentuate sound.
Now, we Americans should not consider certain distinctively American principles to be universal. Or if we hypothesize that certain American principles may be universal, we would probably be well advised to take a go-slow approach to promoting them in non-Western cultures around the world today. After all, our American experiment in democratic government is a historical development in Western culture. It took Western culture many centuries to get to 1776 and the Declaration of Independence -- a long cultural build up that somehow worked out reasonably well in American culture historically, but not so well in France after the revolution there in 1789.