As discussed in the previous post, numbers seem to be at the bottom of everything in physics. As Stephen Hawking noted, "a physical theory is a mathematical model."
Father Stanley Jaki has been arguing for years that Kurt Gödel's famous mathematical theorem says something very important about such physical theories, and their ability to provide a complete explanation of reality.
By complete, I mean one that says there is nothing more, and what is has to be here and behave in a fixed, deterministic manner. And that because it is necessarily this way, it is not contingent upon God.
"It should also be obvious," notes Jaki in an important essay entitled "A Late Awakening to Gödel in Physics," "that the more advanced is a physical theory the more mathematics it contains and the more advanced is the mathematics. From this the ground for connecting Gödel's theorem with physics readily follows.
"For insofar as Gödel's theorem states that no non-trivial system of arithmetic propositions can have its proof of consistency within itself, all systems of mathematics fall under this restriction, because all embody higher mathematics that ultimately rests on plain arithmetic. Then it follows that there can be no final physical theory which would necessarily be true at least in its mathematic part."
You may have a physical theory, but because it is based upon mathematics, you cannot know that it is final, and you can never show that the universe is a certain way "necessarily."
The essay goes on to bemoan the fact that many prominent physicists have not picked up on this little inconvenience to their search for a final answer to the universe.
Particularly ironic, as Jaki notes, the close relationship between Einstein - who searched for a unified field theory -- and Gödel, whose work showed he'd fail.
As Jaki notes in another essay entitled "Reflection on Einstein's Theories," "the application of Gödel's theorem to cosmology shows that a disproof of the contingency of the universe is impossible. The mental road to the extracosmic Absolute remains therefore fully open."
Interesting to ponder.
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