Known, Unknown and Unknowable
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With an account, you can revise, criticize, and comment on ideas.By definition, there is nothing in the unknowable, since it can't be known. One can rationally and with confidence move on and not even entertain anything that claims to be 'beyond human understanding.'
By definition, there is nothing in the unknowable, since it can't be known.
This isn’t true. There are unknowable things. Look up uncomputable functions, see eg
- https://en.wikipedia.org/wiki/Computable_function#Uncomputable_functions_and_unsolvable_problems
- https://www.reddit.com/r/compsci/comments/2s2wgy/what_is_an_uncomputable_function/.
So there are things that computers like our brains can never access – there are fundamental, natural limitations.
In this context, I think of mysticism as restricting criticism and preventing error correction, ie creating a man-made barrier for reason. That’s different.
It is unclear to me why uncomputable should mean unknowable. The halting problem shows that no algorithm can correctly decide, for every program and input, whether the program will halt. Yet we can understand why such an algorithm is impossible, and we can determine the answer in particular cases. Are you equating the impossibility of a universal computational procedure with the impossibility of knowledge? What exactly is being claimed to be unknowable here?
Hi Michael, welcome to V.
The halting problem shows that no algorithm can correctly decide, for every program and input, whether the program will halt. Yet we can understand why such an algorithm is impossible, and we can determine the answer in particular cases.
Yes, we can, but note the switch from knowing such an impossible algorithm to understanding why such an algorithm is impossible. Those are two different things.
What exactly is being claimed to be unknowable here?
A universal halting algorithm.
Thanks. I agree that knowing an algorithm and understanding why it is impossible are different things. The theorem says there is no universal halting algorithm to know.
The contradiction arises when we assume that an algorithm satisfying those requirements exists. The conclusion is that no algorithm meets those requirements. Describing such an algorithm as “unknowable” seems to treat it as something that exists but is inaccessible to us, when its existence is precisely what the theorem rules out.
Consider an exact circle made from finitely many straight line segments. We will never discover what such a figure looks like because no figure satisfies those requirements. Calling its appearance “unknowable” seems to turn the nonexistence of an object into a limitation on our knowledge of it.
In the same way, “we will never know a universal halting algorithm” amounts to saying that we will never discover an algorithm that does not exist, based on our current theories. If that is all you mean by “unknowable,” I think the only thing we would not agree about is the definition of “unknowable” itself.