Sunday, August 27, 2017

Logical Consistency/Objectivity

This week's Sunday reflection taken from Michael Guillen's “Bridges To Infinity” (1983):
“…the world of today’s mathematician is one not only in which truth is not synonymous with logical proof but also in which merely trusting in the validity of a logical proof is itself a matter of faith. This is because Gödel not only showed that any logical system is unable to prove all the mathematical statements that are actually true, but also that any system of logic is unable to prove its own logical consistency. Believing in logic, in other words, is no less subjective a frame of mind than believing in, say, a secular or mystical principle of faith, because even logic itself cannot be verified logically or objectively.”

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