Mind Knowing Truth

Abstract

How is truth discovered and proved? One approach to answering this question begins by focusing the question more narrowly to ask whether new mathematics is invented or discovered. Opinions differ on the answer to this question, but everyone agrees that “new mathematics” must be expressed in the form of true mathematical statements. Are statements of mathematical truth discovered or invented? When the question is posed this way, it is clear that mathematical truth may be discovered, but never invented. This follows from the fact that true statements can be proved using deductive reasoning that leads from a statement already known to be true to the hypothesized mathematical truth which is to be proved. The key point about a sequence of deductive logical statements is that the conclusion is necessarily true if the premises of the argument are true. Mathematical truth, indeed all truth, must exist before it is discovered. It exists eternally and cannot be invented. In what does necessary eternal truth have its existence, in what does it subsist? The answer to this question has profound implications for the search for ultimate meaning. The misapprehension that new mathematics is invented derives from the impression of a creative event when new ideas arise in the mind of the mathematician by spontaneous insight. Spontaneous insight will be examined as the end-product of inductive reasoning. What philosophers, psychologists and neurobiologists have said about inductive reasoning will be explored at length in this chapter in an effort to answer the questions, “what is truth” and “how is it discovered and proved”.

I don’t know what I may seem to the world, but, as to myself, I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

Sir Isaac Newton in a letter written shortly before his death

“What is truth?^” (Question of Pontius Pilate at the trial of Jesus.)

Jn. 18:38

If you don’t care where you are going, any road will take you there (This is a common paraphrase of a longer passage from “Alice in Wonderland”: “Would you tell me, please, which way I ought to go from here? That depends a good deal on where you want to get to, said the Cat. I don’t much care where—said Alice. Then it doesn’t matter which way you go, said the Cat. —so long as I get SOMEWHERE, Alice added as an explanation. Oh, you’re sure to do that, said the Cat, if you only walk long enough.”)