Amazing Truths: How Science and the Bible Agree by Guillen Michael

Author:Guillen, Michael [Guillen, Michael]
Language: eng
Format: azw3, epub
Publisher: Zondervan
Published: 2016-02-09T05:00:00+00:00

All dogs have four legs

Fido is a dog

Therefore, Fido has four legs

Euclid was the first to utilize the rules of Aristotelian logic in a spectacular way. Starting with only ten assumptions — for example, if two things are equal to the same thing then they themselves are equal — Euclid deduced the whole of plane geometry. He proved for all time the scores of theorems students in high schools everywhere learn today.

At the end of the nineteenth century, German logician Gottlob Frege set about to logically deduce the whole of arithmetic in the same way that Euclid had done with geometry. It took him ten years, but he did it.

Or so it seemed.

In 1902, just as Frege was preparing to publish the last part of his great achievement — his Grundgesetze der Arithmetik (Fundamental Laws of Arithmetic) — mathematician Bertrand Russell spotted a problem. Not a mistake by Frege, but a basic defect in logic itself — serious enough to spell the end of not only Frege’s ambitious enterprise, but eventually our entire centuries-long honeymoon with logic as well.

Russell’s devastating insight, which concerned the logical study of classes of objects, would take me several pages to explain.6 Instead, I can easily illustrate the point by asking you to consider this seemingly simple declaration:

“This statement is not true.”

Do you see the problem? If the assertion is true, then it is not true. If it is not true, then it is true. It is a paradox, one of logic’s many shortcomings.

“A scientist can hardly meet with anything more undesirable than to have the foundation give way just as the work is finished,” Frege lamented. “In this position I was put by a letter from Mr. Bertrand Russell as the work was nearly through the press.”7

Logic’s suddenly diminished stature was further and permanently sealed three decades later by the landmark discovery of a twenty-five-year-old named Kurt Gödel, arguably the most perspicacious logician who ever lived, after Aristotle himself. In 1931 the young Austrian proved that when it comes to systems at least as complicated as arithmetic, logic crashes — like an overloaded supercomputer — and proof isn’t always possible. Stated in plain language, Gödel’s so-called incompleteness theorem means this: There will always be objective truths that we can’t prove using logic. Ever.

In 1956, after a long and illustrious career, Russell reflected back on the irrevocable damage Gödel and he himself had inflicted on the once vaunted reputation of logic and proof. “I wanted certainty in the kind of way in which people want religious faith. I thought that certainty is more likely to be found in mathematics than elsewhere.” But, he concluded, “after some twenty years of arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.”8

Truth is bigger than proof.

In one way or another, this same loss of certainty has occurred in the other two classes of science as well — the hard and soft sciences. The only difference is they didn’t have as far to fall.

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