Goedel's work is one of the cornerstones of computer science, specifically decidability. The branch of mathematics which covers what is decidable is recursive function theory, which is considerably beyond the scope of this forum. The relevance to this discussion has to do with the limits of rationality. What Goedel showed was that any formal system consisting of a finite set of axioms and rules of inference is condemned to be either incomplete or inconsistent. Since reality by definition is complete, any attempt to understand it rationally will result in inconsistency (i.e., paradox). This is not just theory, but has been experimentally verified many times and ways over the past 30 years. A google search on "quantum paradox" provides many illuminating references. My personal favorite is Frank Tipler's seminal paper Does Quantum Nonlocality Exist? Bell's Theorem and the Many-Worlds Interpretation (see xxx.lanl.gov for the full text)
In many ways, as you have observed, the most surprising aspect of Goedel's work is that logic can be used to prove its own limits.
As far as the Trinity goes, back in my catechism days we learned that the Trinity was a "mystery of faith", meaning that it was not something which could be ascertained by reason unaided by the light of faith and revelation. See, for example, catholic.org where we see "The mystery of the Trinity in itself is inaccessible to the human mind and is the object of faith only because it was revealed by Jesus Christ, the divine Son of the eternal Father".
Perhaps you adhere to a different doctrine on the subject, in which case please substitute whatever other example you prefer. |
