What Integration is and isn’t Russell W. Howell Westmont College Some Approaches William Hasker – “Faith-learning integration may be briefly described as a scholarly project whose goal is to ascertain and to develop integral relationships which exist between the Christian faith and human knowledge, particularly as expressed in the various academic disciplines.” Karl Barth – “Where confession is serious and clear, it must be fundamentally translatable.” Some Approaches Arthur Holmes – The Idea of a Christian College: Four approaches – Attitudinal (Augustine, Trueblood) Ethical (“Middle level” concepts and fact-value relationships) Foundational (Philosophical perspectives) Worldview (Pluralistic; open-ended) In retrospect, Holmes thinks “contribution” may have been a better choice of words than “integration” when used in the phrase integration of faith and learning. Some Implications Integration is not – – – Integration is more than – – Indoctrination A defensive apologetic A trivialized mixing of discipline with faith Prayer or devotionals before class An articulated position on a particular issue Integration is – – A living dialogue between faith and discipline An infusion of faith into all areas of life David Hilbert, Early Career Ph.D. (Königsberg) on February 7, 1885 Topics for defense against “opponents” • The method of determining absolute electromagnet resistance by experiment • The a priori nature of arithmetic Immanuel Kant (1724 – 1804): Proposed the “synthetic a priori” nature of space and number David Hilbert, 1886 Kant and the Synthetic A Priori Analytic truths – – Synthetic truths – – Those whose predicate is not contained in the subject. E.g., “Sacramento is the capital of California.” A priori truths – – Those whose predicate is contained in the subject. E.g., “A bachelor is an unmarried male.” Those that are known independently of experience E.g., “If it’s either raining or snowing and it’s not raining, then it’s snowing.” A posteriori truths – – Those that are known on the basis of experience. E.g., “All men are mortal.” Putting the Terms Together Analytic A p r i o r i A p o s t e r i o r i A bachelor is an unmarried male The morning star is the evening star (Kripke) (A necessary truth—Venus is necessarily identical to itself—rather than an analytic truth) Synthetic 2+3 = 5 (or, 2+3 have one sum) Sacramento is the capital of California Early Mathematical Triumphs The Solution to “Gordan’s Problem” • Every subset of the polynomial ring k[z1, z2, …, zk] has a finite ideal basis • Hilbert’s proof was one of existence, not one of construction Gordan’s Reaction: “Das ist nicht Mathematik. Das ist Theologie!” David Hilbert, 1890 Georg Cantor Cantor’s 1874 Result: The irrationals are uncountable Hilbert on Cantor’s work: “...the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity.” Leopold Kronecker “God created the integers, all else is the work of man.” Hilbert: “No one will drive us out of this paradise that Cantor has created for us!” Lutzen Brouwer Published in topology Founder of intuitionism • Troubled by set theory paradoxes • Insisted on strict constructions • Denied the validity of the excluded middle principle Interaction during a Göttingen lecture: Student: “You say that we can’t know whether in the decimal representation of ten 9’s occur in succession. Maybe we can’t know—but God knows!” Brouwer: “I do not have a pipeline to God.” Expanding Disciplinary Boundaries Possibilities for discussion Does God know whether the continuum hypothesis is true or false? Yes: Mathematical realism No: Mathematics as a human construction P ≠ NP, could God create a polynomial-time algorithm for the traveling salesman? Are the truths of mathematics eternal and necessary? If Faith-Learning and Collateral Reading Elementary Calculus – Berkeley’s The Analyst Multivariable Calculus, Linear Algebra –Edwin Abbott’sOR, Flatland THEAbbott ANALYST; A DISCOURSE Addressed to an Infidel MATHEMATICIAN. –Michio Kaku’s HyperspaceWHEREIN It is examined whether the Object, Principles, and Inferences of the modern Analysis are –James Gleick’s Chaos more distinctly conceived, or more evidently deduced, than Probability and Statisticsand Points of Faith. Religious Mysteries –Plantinga’s An Evolutionary Argument Against Naturalism Real Analysis –Hardy’s A Mathematician’s Apology –Kanigel’s The Man Who Knew Infinity Faith-Learning and Collateral Reading Artificial Intelligence – – – Automata and Formal Languages – – Rudy Rucker’s Infinity and the Mind Hofstadter’s Gödel, Escher, Bach: An Eternal Golden Braid Introductory Programming – – Kurtzweil’s The Age Of Spiritual Machines Dreyfus’ What Computers Can’t Do Really, too many to mention Weizenbaum’s Computer Power and Human Reason Gene Chase’s article, What does a Computer Program Mean? See also http://www.messiah.edu/acdept/depthome/mathsci/acms/bibliog.htm Analogical Opportunities for Faith Discussions in Mathematics/CS Level’s of infinity Density of rationals, irrationals vs. inability to put them in a 1 – 1 correspondence Halting Problem Das ist nicht Mathematik. Das ist Theologie!