Aristotle, through Frege to Gödel

Butterfly Weed

 Logic. There are three stages of this deep, unlikable terror. I say terror because if a system is complete, then everything that matters has already been decided, written down, and indexed. The future is just a deterministic loop, a closed machine.

 Of the three stages, stage one can be called Aristotle. That Ancient Greek wanted something stronger, more reliable than the slipperyness of Mythos, or stories, in which to anchor his thoughts. "The evidence must hold under its own weight, not just because the king says so." Hence the syllogism, the Law of Non-Contradiction and the therefore. "All Humans are Mortal." "Socrates is a human." "Therefore Socrates is Mortal."

Two thousand years later, Frege was a whole different fish. Language was unreliable, far too wishy-washy. His inspiration was Predicate Logic, he got rid of language as words and gave us shivering inadequate mortals Modern Symbolic Logic. Instead of words like Human or Mortal, he replaced words with symbols. Without Frege’s symbolic logic, computer science could not exist. Every line of code, every microchip, and every digital network running the modern world is a descendant of Frege’s chilling attempt to turn human thought into a flawless mathematical machine.

The Austrian Kurt Gödel, who died in 1978, and this requires careful reading, proved that in any "consistent mathematical system large enough to do basic arithmetic, there will always be statements that are true, but cannot be proven using the rules of that system." What this means is that Gödel didn't destroy logic; he gave it its deepest, most glorious nuances. He proved, using Frege's symbolic Logic that truth is a larger category than proof. He showed the West that even its most perfect, sterile, logical systems are fundamentally porous. Stuff gets in and once in it behaves poorly, therefore and hence logical systems can never be completely closed, finished, or self-contained.

 As me alter ego Bobby has suggested when logic proves its own incompleteness, it acts like a hand turning a key in a lock we thought was rusted shut. It guarantees that the universe remains an un-collapsed wave function and we life forms in all our speciation remain free.

 So go ahead, infer and predicate that untul you change color.