1 + 1 = 2: But Can You Prove It?
John C. Rankin
(April 4, 2014)
We all make assumptions, from the macro to the micro, and they affect our lives profoundly. The question is to what extent these assumptions are true or false. And, how well do we test our assumptions?
Kurt Gӧdel is the most eminent mathematician in the twentieth century, and colleague of Albert Einstein. In mathematics, Gödel (in his Incompleteness Theorems) demonstrates that within its closed system it cannot be proven that 1 + 1 = 2 (e.g., decimally). It must first be assumed (from outside and prior to the system), and then all mathematics works beautifully. Namely, unless this simplicity is first assumed, then mathematical equations, by definition, are not possible. When the assumption of 1 + 1 = 2 is in place, physics, engineering, architecture, music, art and other cognate sciences become possible. Mathematics is thus objective and utterly consistent in all means of human measurement.
In the expanding cosmos, the existence and properties of gravity have to be assumed, and accordingly all astrophysics work beautifully. In cultural anthropology, unwritten assumptions are the key to the core of the given (and usually ancient and extinct) social order.
Yet, there is the greatest assumption to consider, stated only in the opening words of Genesis: “In the beginning God created.” From there comes a series of cognate assumptions in the biblical order of creation, the sum of which is the finest basis for a genuine liberal arts education in pursuit of all good knowledge.