| olcott <NoOne@NoWhere.com>: Oct 17 09:58AM -0500 On 10/17/2020 8:33 AM, André G. Isaak wrote: >> in theory T. > You don't "stipulate" a proposition to be undecidable. It either is or > it isn't. This: (T ⊬ φ) and (T ⊬ ¬φ) is stipulated to define the concept of undecidable proposition. Symbols only have meanings when meanings have been assigned to them. > concerned, we've only identified a tiny fraction of the undecidable > propositions. Because there is no general method for deciding whether a > proposition is decidable, most will never be identified. When we determine that every single undecidable proposition known or unknown proven or unproven is only undecidable because it is incorrect then we have covered ALL of them with NONE left out. When we do this then every single proof of incompleteness that depends on undecidable propositions utterly fails. For the same reason that we cannot decide that a medical doctor is "incompetent" in the basis of their inability to restore health to the cremated** we cannot decide that a formal system is "incomplete" on the basis of it inability to prove or disprove incorrect expressions of language. ** Even Christ never did that. > still leaves you with all of the unknown examples of undecidable > propositions, which means the system remains incomplete. > André When we rename the whole category of "undecidable proposition" to "incorrect proposition" then there are zero undecidable propositions left to prove incompleteness. -- Copyright 2020 Pete Olcott |
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