The unreasonable effectiveness of mathematics in the natural sciences is an astonishing phenomenon that almost no one fails to recognize. (1) But regarding the harmony of faith and reason in the search for truth, does mathematics play any role at all? Here are some insightful observations on mathematics and the interplay between faith and reason in the search for truth.
In an encounter with the youth of Rome in Saint Peter Square, Pope Benedict XVI was asked to explain how the deposit of revelation and scientific theory can converge in the search for truth. In his answer, the Roman Pontiff invited the students to reflect first on the nature of mathematics.
Benedict XVI described mathematical tools as an invention of the human intellect. As such, he said, mathematical tools are key to understanding nature because nature is truly structured in a mathematical way.
We can work with nature, we can put nature at our service, and we can use nature, thanks to this invention of human intelligence. Mathematics gives us access to nature and allows us to see that the structure of the universe and the inventions of the human mind coincide in an incredible way.
In the world, there is man, the human being, an intelligent being, and there is also an intelligible material universe. That these two intelligibilities coincide is seen most clearly in the effectiveness of mathematics for scientific research.
At a higher level, the intelligibility of the acting person conceives the mathematical tools to work with and, at a lower level, the intelligibility of reality provides confirmation and support for mathematical conceptualization.
These two intelligibilities are identical, the Pope affirms, in the sense that the ability to speculate proper to the human intellect is matched by the intelligibility of the real world. This coincidence he identifies as a great enigma and a great challenge because in the final analysis this coincidence paves the way to ascend to an even superior level, the level of metaphysics, where the conclusion is that a supreme Intelligence links them both.
Our ability to speculate could not discover the intelligent structure of nature were there not an identical antecedent project for both.
Yet, even though the reliable and intelligent structure of the material world is a wise presupposition to start with, this conception of the world is not free from challenges. There is the alternative of the theories of chaos.
The theories of chaos, the Pope affirms, are limited. It seems more appropriate to say that mathematics is reliable and, because mathematics is reliable, technology is reliable too.
As a point of departure, our way of knowing the universe presupposes, on the side of the object of knowledge, the rational structure of matter. And thus we see again that man, a thinking subject, has access to an objectified intelligibility present in the external world. Chaos, on the other hand, seems to make technology impossible.
If reality is conceived as devoid of rational order because it is the result of chaos and chance, reason nevertheless cannot do other than to handle this irrationality (chaos and chance) according to its own standards, that is, according to the standards of reason. Even when pushed to go in that direction, reason ends up conceiving reality as not devoid of a rational ordering.
The phenomena of chaos and chance have received considerable attention. They have become the basis of certain philosophical positions. But where do these philosophical schools fall when the methodology of sound philosophy - the philosophy of the perennially valid metaphysical principles of the real - is applied?
The project of seeking the origin of reason in the irrational, for example, fails because, true to itself, reason reintroduces the priority of the rational over the irrational, which is precisely what is being denied. Reason cannot help but find its match in the external world.
The Pope returns to the two intelligibilities accessible to the human mind to wrap up the argument with the following statement:
"Of course, no one can now prove - as is proven in an experiment, in technical laws - that they both really originated in a single intelligence, but it seems to me that this unity of intelligence, behind the two intelligibilities, really appears in our world.
"In the end, to reach the definitive question, I would say: God exists or He does not exist. There are only two options.
"Either one recognizes the priority of reason, of creative Reason that is at the beginning of all things and is the principle of all, or one holds the priority of the irrational, inasmuch as everything that functions on our earth and in our lives would be only accidental, marginal, an irrational result. Reason would be a product of irrationality.
"One cannot ultimately 'prove' either project, but the great option is the option for rationality and for the priority of reason. This seems to me to be an excellent option." (2)
Later, in a related context, the Pope further clarified:
"Does the primacy belong to unreason or to reason?
"As believers we answer, with the creation account and with Saint John, that in the beginning is reason. Reason is there at the beginning: creative, divine Reason.
"Hence we can and must place ourselves on the side of reason, freedom and love - on the side of God who loves us so much.
"Yes, we believe in God, the Creator of heaven and earth. [He has] definitively established that reason is stronger than unreason, truth stronger than lies, love stronger than death." (3)
In conclusion, by examining the relationship that exists between (a) the mathematical tools available to human reason, (b) the intelligibility of the material world, and (c) the existence of God, Benedict XVI has extended our understanding of and called our attention to how faith and reason converge in the search for truth.
Notes
(1) See Eugene P. Wigner, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," in "Symmetries and Reflections," M.I.T. Press, Cambridge, MA, 1970, pp. 222-237.
(2) Pope Benedict XVI, "Encounter with Youth of Rome and the Lazio Region", 6 April 2006, in "Acta Apostolicae Sedis," 2006, vol. 98, pp. 356-357. See English translation in "L'Osservatore Romano English Weekly Edition," 12 April 2006, p. 6.
(3) Benedict XVI, "Homily," Rome, Easter Vigil Mass, 23 April 2011.