O Sapientia, quae ex ore Altissimi prodiisti, attingens a fine usque ad finem fortiter, suaviterque disponens omnia: veni ad docendum nos viam prudentiae.
O Wisdom, who hast proceeded from the mouth of the Most High, who reaches from end to end mightily and orders all things sweetly, come to teach us the way of prudence” (cf. Ws 8:1).
But how can this be put into practice? Can all of human knowledge be ordered?
In the first half of the last century, one school of philosophy, called the Analytic Movement, thought the answer might be “yes.” Thinkers like Bertrand Russell and Alfred North Whitehead sought to create a logical system in which every “verifiable” statement could be included. (Anything not verifiable, they said, was not worth consideration.) Using the language of symbolic logic, they undertook the ambitious task of systematizing all knowledge in that purest and most certain of fields—mathematics. They began with primitive propositions, such as “Zero is a number,” and developed rules for deriving true statements, or theorems, from these first principles. Their three-volume work, Principia Mathematica, remains influential even now, a century later.
In 1931, however, Austrian-born mathematician Kurt Gödel found a gaping hole in this system. He devised a rule of assigning a unique number to each symbol in the language, as well as to each statement that could be formed or proof that could be argued. For example, the proposition, “You can add one to any number to get another number” would be represented by the number 626,262,636,333,262,163,636,262,163,111,123,262; and more advanced statements would be mapped to even larger numbers. By effectively turning theorems into numbers and the rules of proof into mathematical relations, Gödel showed that statements about arithmetic could be expressed within arithmetic.
Using these rules, and in this language, Gödel was able to construct the sentence, ”This statement is unprovable within the system.” This presents a quandary: if you can prove it to be true, it becomes false, and vice versa. Just as with the recent popular song lyric, “You don’t know you’re beautiful, and that’s what makes you beautiful,” the sentence is true, but there is no way to know it with logical certainty. This idea, known as Gödel’s First Incompleteness Theorem, showed that Russell and Whitehead’s project had failed. In any logical system large enough to contain the rules of arithmetic, there are some statements that are intelligible and true, but not verifiable.
This principle extends beyond mathematics to other areas of thought. For example, one can understand what is meant by the statements, “There exists a unique God in three Persons,” and, “The Word became flesh and dwelt among us”; and Christians know these propositions to be true by the divine light of faith. Yet, they cannot be proven within the system of human reason. Even Aristotle himself could not have come up with them. These sentences, known as articles of faith, can only be known as given from a source of knowledge outside our natural reason—they must be revealed by God. St. Thomas Aquinas attests to this at the very beginning of his Summa Theologiae, as he embarks on his project to order the knowledge of God, man, and the universe: “It was necessary for the salvation of man that certain truths which exceed human reason should be made known to him by divine revelation.” St. Thomas continues,
Sacred doctrine essentially treats of God as viewed as the highest cause—not only so far as He can be known through creatures, just as philosophers knew Him . . . but also as far as He is known to Himself and revealed to others. Hence sacred doctrine is especially called wisdom.
The gift of faith is what shows us the truth that lies beyond our limited power of reason. It perfects reason and brings us to a more complete wisdom. As we prepare for the coming of Jesus during this Year of Faith, let us ask Him to increase our faith, that we may know Him more closely, and know all things as ordered to Him:
To us the path of knowledge show,
And teach us in her ways to go.