XPost: comp.theory, sci.math   
   From: mikko.levanto@iki.fi   
      
   olcott kirjoitti 5.12.2025 klo 19.31:   
   > On 12/5/2025 3:03 AM, Mikko wrote:   
   >> olcott kirjoitti 4.12.2025 klo 16.18:   
   >>> On 12/4/2025 3:29 AM, Mikko wrote:   
   >>>> olcott kirjoitti 3.12.2025 klo 18.13:   
   >>>>> On 12/3/2025 5:17 AM, Mikko wrote:   
   >>>>>> olcott kirjoitti 2.12.2025 klo 16.07:   
   >>>>>>> On 12/2/2025 3:56 AM, Mikko wrote:   
   >>>>>>>> olcott kirjoitti 1.12.2025 klo 14.19:   
   >>>>>>>>> On 12/1/2025 4:31 AM, Mikko wrote:   
   >>>>>>>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:   
   >>>>>>>>>>> [ Followup-To: set ]   
   >>>>>>>>>>>   
   >>>>>>>>>>> In comp.theory olcott  wrote:   
   >>>>>>>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:   
   >>>>>>>>>>>   
   >>>>>>>>>>>>> In comp.theory olcott  wrote:   
   >>>>>>>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:   
   >>>>>>>>>>>>>>> dart200  wrote:   
   >>>>>>>>>>>   
   >>>>>>>>>>> [ .... ]   
   >>>>>>>>>>>   
   >>>>>>>>>>>>>> *Within A new foundation for correct reasoning*   
   >>>>>>>>>>>   
   >>>>>>>>>>>>>> (a) Every element of the body of knowledge that can   
   >>>>>>>>>>>>>>       be expressed in language is entirely composed of   
   >>>>>>>>>>>>>>     (1) A finite set of atomic facts   
   >>>>>>>>>>>>>>     (2) Every expression of language that is semantically   
   >>>>>>>>>>>>>>         entailed by (1)   
   >>>>>>>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning   
   >>>>>>>>>>>>>>       Postulates combined with The Kurt Gödel definition   
   >>>>>>>>>>>>>>       of the "theory of simple types"   
   >>>>>>>>>>>>>>       https://en.wikipedia.org/wiki/   
   >>>>>>>>>>>>>> History_of_type_theory#G%C3%B6del_1944   
   >>>>>>>>>>>>>>       Where every semantic meaning is fully encoded   
   >>>>>>>>>>>>>> syntactically   
   >>>>>>>>>>>>>>       as one fully integrated whole not needing model   
   theory   
   >>>>>>>>>>>   
   >>>>>>>>>>>>>> We have now totally overcome Gödel Incompleteness   
   >>>>>>>>>>>>>> and Tarski Undefinability for the entire body if   
   >>>>>>>>>>>>>> knowledge that can be expressed in language. It   
   >>>>>>>>>>>>>> is now a giant semantic tautology.   
   >>>>>>>>>>>   
   >>>>>>>>>>>>> You can't "overcome" these theorems, since they're not   
   >>>>>>>>>>>>> obstacles.   
   >>>>>>>>>>>>> They're fundamental truths.   
   >>>>>>>>>>>   
   >>>>>>>>>>>> I just showed the detailed steps making both of   
   >>>>>>>>>>>> them impossible in the system that I just specified.   
   >>>>>>>>>>>> A counter-example is categorically impossible.   
   >>>>>>>>>>>   
   >>>>>>>>>>> Your construction is impossible, as proven by Gödel's   
   >>>>>>>>>>> Incompleteness   
   >>>>>>>>>>> Theorem.   
   >>>>>>>>>>   
   >>>>>>>>>> Doesn't a theory that has no theorems satisfy all above stated   
   >>>>>>>>>> requriements?   
   >>>>>>>>>   
   >>>>>>>>> Every element of the body of knowledge   
   >>>>>>>>> is not such a formal system.   
   >>>>>>>>   
   >>>>>>>> That's right, the body of knowledge is irrelevant here.   
   >>>>>>>   
   >>>>>>> If we are not talking about elements of the body   
   >>>>>>> of knowledge that are missing or unknown truths   
   >>>>>>> then there is no notion of actual incompleteness   
   >>>>>>> that remains.   
   >>>>>>   
   >>>>>> The body of knowledge includes that certain quesstions have answers   
   >>>>>> but doesn't include now what those answers are.   
   >>>>>   
   >>>>> Unknowns are outside of the body of knowledge.   
   >>>>>   
   >>>>>> For example, we   
   >>>>>> know that North Sentinel Island is population but we don't know   
   >>>>>> what language is spoken there. This and other examples show that   
   >>>>>> the body of knowledge is incomplete.   
   >>>>>   
   >>>>> If anyone anywhere knows then it is in the body of general knowledge.   
   >>>>   
   >>>> It is not general knowledge as it is not known to anybody outside   
   >>>> North Sentinel Island.   
   >>>>   
   >>>> I know the color of my bedroom wall. Is that general knowledge?   
   >>   
   >>> To simply things the body of general knowledge   
   >>> can be everything written down in any published   
   >>> book or published paper. Also anything that can   
   >>> be deduced from these sources.   
   >>   
   >> General knowledge also includes that there are claims that might be   
   >> deducible from published knowledge or might be not, and it is not   
   >> yet known whether or how. Examples of such claims can be found in   
   >> published sources.   
      
   > Yes this is correct.   
      
   Therefore it is not correct to say that all claims decucible from   
   general knowledge are in general knoledge. The claims that are   
   deducible from general knoledge but neither known to be deducible from   
   the common knowledge nor ottherwise knwon are not in general knowledge.   
   This is an incompleteness in general knowledge.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)