These are the frequently received complaints against the proof of non-existence of a universal discussed in the previous few posts:
- You bastard! You set up into a situation it cannot handle: Yes. All I did was point out one situation cannot be correct about. There may be other more embarrasing scenarios won’t work on. Therefore, an ideal is impossible.
- What if I write an that looks into to see if contains self contradicting predicaments?: And do what? Return “undecidable” or “not a number”? If bites the bullet and says it can’t predict if the will halt or not, then it just confirms the proof that it is impossible to have a perfect that can predict whether any algorithm can halt or not.
- If there can be no way to predict whether “any” algorithm will halt or not, how do we predict things about the output of algorithms: We bite the bullet and play the undecidable card if we can’t decide the nature of output of the algorithm.
- Can’t I make arguments similar to the one against the existence of to any algorithm that makes a boolean decision about the output of an algorithm? Yes. All algorithms that makes a boolean decision about the nature of output, or classifies the output of all algorithms to one of 2 arbitrary sets based on an arbitrary criteria, can potentially be made to contradict itself by making a analogue that creates the opposite effect.
This means there is no way to predict anything about the output of all processes, because there will always be an undecidable scenario. There is however the enginneer’s solution i.e. make something that is correct almost all of the time.
What does all this mean?
- There are no short cuts to the future (a.k.a output) than to actually go there. Sometimes there is no future to go to. Things get so unpredictable. Heisenberg’s Uncertainty Principle is not just the property of the physics of this universe. Things will always be uncertain.
- Not all truths can be proved to be right or wrong with a fixed set of axioms. Somethings are accidentally true. Somethings are accidentally false. You may want to consider accepting those accidentally true things as axioms if it keeps becoming so all the time you verify it. And in case you were wondering: No. Modern religions are not just internally inconsistent, they do not even correspond with reality as we know it. BTW Any fool can make an infinite number of internally consistent world views e.g. String Theory.
Conclusion: Religions do not fall into same category as things that may be accidentally true like Goldbach’s Conjecture. Because as so far as we can verify Goldbach’s Conjecture hasn’t failed its prediction. On the other hand religions fail even the first few simple tests of correspondence with reality.