Academic journal article Perspectives on Science and Christian Faith

The Matter of Mathematics

Academic journal article Perspectives on Science and Christian Faith

The Matter of Mathematics

Article excerpt

Does faith matter in mathematics? Not according to the Swiss theologian Emil Brunner. In 1937 he suggested a way to view the relationship between various disciplines and the Christian faith. Calling it the "Law of Closeness of Relation," he commented,

   The nearer anything lies to the center
   of existence where we are concerned
   with the whole, that is, with man's
   relation to God and the being of the
   person, the greater is the disturbance of
   rational knowledge by sin; the further
   anything lies from the center, the less
   the disturbance is felt, and the less
   difference there is between knowing
   as a believer or as an unbeliever. This
   disturbance reaches its maximum in
   theology and its minimum in the exact
   sciences and zero in the sphere of the
   formal. Hence it is meaningless to
   speak of a "Christian mathematics." (1)

Thus, Brunner holds a nuanced version of the doctrine of noetic depravity: sin affects the reasoning ability of humans, but does so in varying degrees depending on how "close" the object of reasoning is to their relationship with God. Mathematics, being a purely formal discipline, is beyond the reach of any adverse noetic effects. Christians and non-Christians will therefore come to the same mathematical conclusions, so that, for Brunner, the phrase Christian mathematics is an oxymoron.

Of course, on one level Brunner is correct. If one agrees to play the game of mathematics, then one implicitly agrees to follow the rules of the game. Different people following these rules will--Christian or not--agree with the conclusions obtained in the same way that different people will agree that, at a particular stage in a game of chess, white can force checkmate in two moves. In this sense mathematical practice is "world-viewishly" neutral. Moreover, the paradigm for mathematical practice has remained relatively unchanged since Euclid published his masterpiece, The Elements, in 300 BC. That paradigm is to derive results in the context of an axiomatic system. (2)

It would be a mistake, however, to apply Brunner's dictum to all areas of mathematical inquiry. One can be committed to the mathematical game, but also participate in analyzing it (and even criticizing it) from a metalevel. In doing so, faith perspectives will surely influence the conclusions one comes to on important questions about mathematics. (3) But is the investigation of such questions really a legitimate part of the mathematical enterprise? At least two reasons can be given for an affirmative answer: (1) such questions are actually taken up at every annual joint meeting of the American Mathematical Society and the Mathematical Association of America; (2) historically, such questions have always been investigated by the mathematical community. Indeed, David Hilbert, one of the greatest mathematicians of the twentieth century, chose two topics for discussion in conjunction with the oral defense of his doctoral degree. The first related to electromagnetic resistance. The second was to defend an intriguing proposition: "That the objections to Kant's a priori nature of arithmetical judgments are unfounded." (4) Hilbert is credited as being a founder of the school of formalism, which insists that axiomatic procedures in mathematics be followed to the letter. It is thus interesting that even those who held a strict view of mathematical practice and meaning saw the investigation of important metaquestions relating to mathematics as a legitimate undertaking by mathematicians.

Is there a helpful classification for metalevel questions that Christian mathematicians might pursue as they attempt to explore the interaction between their discipline and faith? Arthur Holmes suggests four categories of faith-integration in his well-known book The Idea of a Christian College: the foundational, worldview, ethical, and attitudinal. (5) The remainder of this article will look at some developments in mathematics that lead naturally to questions in those categories. …

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