Mathematics

by "Rev. James V. Schall, SJ" - December 31, 2006

Reprinted with permission.

In his Verona address on October 19, 2006, Pope Benedict XVI returned to a theme he broached in his Regensburg lecture, namely, the relation between modern science, with its "mathematical" foundation, and the existing things of nature. In the Regensburg lecture, the pope related this mathematical background to Plato and Descartes. What is at issue here might seem, at first glance, to be relatively esoteric and hardly a matter of revelation. Yet this issue touches the very credibility of faith and its relation to reason.

Mathematics, while being its own discipline, rooted in quantity, and hence related to things that can be measured by norms reducible to mathematics, is something we are all supposed to study early in our training. We learn mathematics before we learn philosophy, as Plato wisely taught us. Mathematics has a certain fascination because of its clarity. We are all aware that many ethical and political problems can only be resolved "for the most part." Mathematics seems to give the mind that rare form of experience, that is, clearly established certitude. We are tempted to want all of our problems to be solved with the same clarity.

The pope, of course, had something else in mind. He wanted to acknowledge the place of mathematics both in itself and in its relation to nature. Contrary perhaps to Descartes, the pope did not want to have to prove the existence of God before he could relate his mental idea of things to existing things themselves. "Mathematics, as such," Benedict observed, "is a creation of our intelligence: [There exists] a correspondence between its structures and the real structures of the universe." Mathematics understood as such—as a systematic, conscious exposition of itself—exists only in the mind. But there is something curious about this existence in the mind, since it obviously has some relation to "real structures of the universe."

Modern science and technology, Benedict continues, "presupposes" this correspondence. He refers approvingly to Galileo's famous formula: "The book of nature is written in mathematical language." What Benedict is concerned with here, however, is what he calls the "self-limitation" of science. This self-limitation is designed to restrict science from talking about anything that is not mathematical in structure. Yet no one can simply let this relationship between mathematics and the existing world sit there, unattended, in his mind. In fact, it leads to what the pope calls "a big question."

What is this question? The relation implies that "the universe itself is structured in an intelligent manner, such that a profound correspondence exists between our subjective reason and the objective reason in nature." Many will try to avoid what comes next, but it is in the logic of the argument. It becomes "inevitable to ask oneself if there might not be a single original intelligence that is the common font of them both." One naturally wonders whether an order exists that includes both the mind and the world, since, however delicately, some correspondence between the two is already found in existence.

The pope, of course, here seeks to formulate the truth found in science over against the notion that there are other uses of intelligence that are not strictly mathematical. He does not deny that the mathematical is itself a legitimate and welcome use in its right area, but not all being is quantity.

The human mind, looking at the universe, notices that the mathematics that it formulates has a basis in reality that this mind did not itself make. The question arises, why is there mind? Why is there universe? It is neither unreasonable nor unscientific to wonder if they have a common source that might already include the origins of both universe and mind.

Fr. James V. Schall, S. J., teaches political science at Georgetown University. His latest book, The Mind That Is Catholic, is published by Catholic University of America Press.