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#6015·Michael Briffa, 2 days ago·AI-assistedThanks. 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.
As a rule of thumb, please try making your writing less verbose. For example: ‘unknowability implies existence.’
Brevity helps not just your readers but yourself: the longer your text, the more vulnerable it becomes to criticism.
If your readers need more info, they can ask.