>>12459720Fun fact: even asking such an apparently simple question as "whether an algorithm X halts" is not a meaningful question. For any axiomatic system containing arithmetic, there will always be an algorithm whose halting status is unprovable. Also you can attach different axioms to get consistent axiomatizations of arithmetic which give you different answers to halting questions. The platonist fanatics claim that some of these correspond to "nonstandard" arithmetic, a patently absurd notion because there is no evidence that a "standard" arithmetic even exist. There is no real way to determine which axioms about arithmetic to accept and which to reject. Any notion of the "actual completed set of naturals" is a wishy-wash unsupported by any evidence or reason. There are as many "actual sets of naturals" as there heads on the planet, i.e. it's fiction. The completed infinite is complete nonsense.
Of course when you appeal to the reality of complete nonsense (definiteness of halting) you get a completely nonsensical constant which cannot be represented. The real question here is: who cares?
