Gödel’s Proof and Science

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Kurt Gödel, the 20th century mathematician, proved that the axioms of mathematics cannot be finally and absolutely proved by the axioms of mathematics. Something, in other words, must be taken on faith: once an initial axiom is assumed, a consistent system can be built upon it, but Gödel’s theorem means that there is always room at the beginning for subjective creativity. How does this affect the classical claim of science that we can eventually understand, explain, and predict, everything about the universe, the claim that everything is determinable? According to the positivist view of science, a valid physical theory can be reduced to a mathematical model. But if there are mathematical statements that inherently cannot be proved (and this is what Gödel demonstrated), there are physical problems that simply can not be predicted. “Some people will be very disappointed if there is not an ultimate theory, that can be formulated as a finite number of principles.I used to belong to that camp, but I have changed my mind. I’m now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery.wIthout it, we would stagnate.” (Stephen Hawking, unedited transcript of a lecture, “Gödel and the End of Physics”, which can be found here: http://www.damtp.cam.ac.uk/strings02/dirac/hawking)