What used to be an annoyance to me has grown into a concern. Some who are hostile to Christianity invoke science not as the fruit of our gift of intelligence, but as something superior to faith or even incompatible with it. Yet we Christians have known for millennia that the two are fully compatible and that in reality they purify one another.
I would like to tell the stories of two very accomplished Catholic scholars in history who would like to reassure you and me that anybody who claims that exact science is the exclusive route to truth is simply wrong.
Wittgenstein on Language and Logic
The first is a quirky but brilliant man named Ludwig Wittgenstein from a prominent Catholic family in Austria just before First World War. He was intrigued by mathematics and logic, and wondered how they are capable of arriving at truth. He did not want to know how to do math or logic—he already knew that. Wittgenstein wanted to understand what it was about these languages that made them trustworthy guides to truth, and to understand better the kinds of truth they facilitated.
In 1922, Wittgenstein published the results of his investigations in a very important book, Tractatus Logico Philosophicus in which he claimed that he had definitively solved the problem. However, Wittgenstein quickly added that in so doing, he had shown more importantly “how little is achieved when these problems are solved.” Doesn’t it strike you as odd that a man like this would demean his own most important finding?
Hardly anyone knew in 1922 what he meant by that statement. A strong suggestion is made by Wittgenstein’s biographer Ray Monk who illustrated the possible meaning of this statement with the following story.  The Vienna Circle—a very influential group of leading, world class philosophers and scientists—were so impressed by Wittgenstein’s accomplishment that they invited him to speak at their meetings. Now, Wittgenstein as I said was an eccentric man; he seemed at times oblivious to established social rules. Yet even with his social awkwardness being well known, it was unsettling when on more than one occasion, the elite members of the Vienna Circle seated themselves for a formal lecture on the logic of scientific inference, only to find that “Wittgenstein would turn his back on them and read poetry . . . as if to emphasize to them . . . that what he had not said in the Tractatus was more important than what he had.” (p. 243)
Wittgenstein seemed to know he had defined science in such a way as to illuminate by contrast the rest of human life, the spiritual dimension, things that cannot be said scientifically but are rather contemplated as mystery. The song of Wisdom begins precisely at the boundary where scientific language ends. Wittgenstein ended up saying that he merely showed that “what can be said, can be said clearly, and everything else must be left unspoken.” Scientific questions alone are solved decisively by proof and demonstration.
There are two ways to take this. One is to say that everything outside of exact science is mere emotion, to be dismissed or merely endured. This is a widely held view among materialists. Consider, for example, A.J. Ayer’s highly influential Language, Truth and Logic. As the Vienna Circle incident suggests, however, Wittgenstein did not see it that way. He seemed to believe that metaphor, intuition, common sense, art, music, and mysticism are complementary to science as ways to know what science is incompetent to discover.
In short, we credit Wittgenstein with the suggestion that the symbolism of math and logic rests on solid ground, and guarantee a certain kind of exact truth. But these powerful systems are like strong dogs on a very short leash. They are effective only within a very small radius of empirical facts. We, their masters, understand and value not only their strength, but also life outside the radius where we answer questions about moral truth, goodness, and beauty.
Michael Polanyi on Science and Personal Knowledge
Michael Polanyi is the second figure I would like to introduce you to. Born in Budapest at the turn of the 20th century, he was trained as a physician but later earned a doctorate in Chemistry and pursued an academic career. A child of a Jewish family who was baptized Catholic and considered himself a Christian, he fled to England when the Nazis rose to power and he spent his life teaching science and philosophy at Oxford. Two of his students, together with his son John, went on to become Nobel Prize winning Chemists, so he must have been not only a brilliant scientist, but an inspiring teacher and father as well. He was invited to give the Gifford Lectures in Aberdeen in 1951-52, an honor extended to a small number of influential scholars in history, and his lectures are published under the title of Personal Knowledge.
What attracted my attention to his work is his ability to depict precisely how the limits of scientific language that we’re talking about manifest themselves. He shows us how to articulate the interface between science and faith—the boundary where science ends and the spiritual aspirations of a human person with a rational soul begin. He does so with the concept of tacit knowledge—knowledge that only the human person at home in the world can possess. Science as understood in the contemporary mind does not account for this aspect of knowing.
In the book Meaning, with Harry Prosch, Polanyi shows the necessity of tacit knowledge by playing devil’s advocate and framing the following question.  What if the materialists are right? What if the optimistic vision of science—the Laplacean ideal—were true? The Laplacean ideal is a criterion for what would constitute the triumph of empirical science. According to this criterion, if the universe were a strictly material system with no other content whatsoever, then it should be possible—at least in principle—to predict the future using measurements from the present. All that is required is that we know the positions and velocities of all the particles in the universe at this moment, plus the magnitudes of all forces acting on them; then we could use the equations of physics to compute the state of the universe at any arbitrary time, past or future.
What if science were to make these quantitative calculations? What exactly would come into our possession?
The answer is a very large swarm of numbers.
But the numbers interpret themselves and show us the nature of things well into the future, right?
In a real laboratory experiment, here and now, the numbers refer to readings on laboratory equipment, beakers, gauges, clocks, etc. that the scientist recognizes as the human person who has used them, who owns them and knows what they feel like.
But suppose in contrast, says Polanyi, you had the data from the future, and wanted to know if the primroses in your garden will bloom next spring. Presumably one would sift through the mass of numbers to find out how they fared. How do the numbers tell you whether your primroses blossomed? They don’t. The primroses themselves have no constancy, no identity in the system of quantitative measurements, nor does your garden. Their “whatness,” their quiddity, derives from the human person with a rational soul. They don’t come and tap you on the shoulder saying, ”Here I am, your primroses.” Nothing about the results of this Laplacean exercise tells you anything about what the world would look like to you as a person at a later point in time.
The topography would be factual as far as the numbers go, but you would lack the capacity to interpret the numbers. Such an experiment would tell you literally nothing that you are actually interested in.
In short, the results of exact science deliver a map of the world, but the map cannot interpret itself. The human person qua person, a spiritual element, is required in order to interpret the map by connecting it to his personal knowledge.
For some, science is said to have solved all of the riddles of the world, including the mystery of good and evil. For others like Wittgenstein and Polanyi, the world is a mystery that we are given to understand by means of our personal experience, the trustworthy guidance of exact science, and adherence to the Christian faith.
I want to close by offering my thanks to another great scholar of a more recent time, my friend Professor Stacy Trasancos, whose book Science was born of Christianity immersed me once again in these important topics after a long absence.  My reading of her work in recent months provided the inspiration for this essay. Professor Trasancos’ masterful articulation of the idea of exact science is the exemplar of how these conversations must go forward, and what we must teach our children.
 Monk, R. (1990). Ludwig Wittgenstein: the Duty of Genius. New York: Penguin.
 Polanyi, M. & Prosch, H. (1975). Meaning. Chicago: University of Chicago Press.
 Trasancos, S. (2013). Science was born of Christianity: The Teaching of Fr. Stanley L. Jaki.