(∃p ∈ P s.t. ¬(p ⊢ p ∈ C(halts)) ∧ ¬(p ⊢ p ∉ C(halts))) → ((p,s ⊢ p ∈ C(s)) → p is trivial)
Please supply a proof.
Note that it's quite true that
(∃p ∈ P s.t. ¬(p ⊢ p ∈ C(halts)) ∧ ¬(p ⊢ p ∉ C(halts))) → ((p,s ⊢ p ∈ C(s)) → *s* is trivial)
proved usually by reducing s to "halts" for any non-trivial s.
> Again, this is a logical error. Science is not a popularity contest, and in this specific context, straw polls resolve nothing.
I am not deciding it by poll. I am pointing out that there are objections to your reasoning that you have not addressed and persist in not addressing - despite them being made abundantly clear, repeatedly.
> I wonder if you know how to have a discussion like this, in which there are only ideas, no personalities, and no place for ad hominem arguments?
You're accusing me, as a person, of not understanding that a discussion like this has no place for accusations against a person? My complaint was not about you as a person, but about the form of your arguments in this discussion.
Let's be precise.
As I read the original statement, it was saying, I am not sure whether you read it differently.> As stated, it's a false claim.
You have said this repeatedly, but all you have done in support of it is point at the Halting problem. The Halting problem says:
You have claimed this eliminates the possibility of proving correct any non-trivial program:> [T]he Turing Halting problem (https://en.wikipedia.org/wiki/Halting_problem) demonstrates that one cannot establish that a non-trivial program is "provably correct."
I see no way to read that but as a claim that:
Please supply a proof.Note that it's quite true that
proved usually by reducing s to "halts" for any non-trivial s.> Again, this is a logical error. Science is not a popularity contest, and in this specific context, straw polls resolve nothing.
I am not deciding it by poll. I am pointing out that there are objections to your reasoning that you have not addressed and persist in not addressing - despite them being made abundantly clear, repeatedly.
> I wonder if you know how to have a discussion like this, in which there are only ideas, no personalities, and no place for ad hominem arguments?
You're accusing me, as a person, of not understanding that a discussion like this has no place for accusations against a person? My complaint was not about you as a person, but about the form of your arguments in this discussion.