On 20/04/2026 16:31, olcott wrote:The result of undecidability proves that the currentOn 4/20/2026 3:49 AM, Mikko wrote:It is not useful to define new terms for comcepts that already haveOn 19/04/2026 20:21, olcott wrote:>On 4/19/2026 3:59 AM, Mikko wrote:>On 18/04/2026 15:58, olcott wrote:>>>
Unknown truths are not elements of the body of
knowledge is a semantic tautology. Did you think
that things that are unknown are known?
No, but that measn that for some sentences X True(X) is unknown and there
is no method to find out.
>
I don't know about philosophers but mathematicians and logicians don't
find it interesting if all you can say that all knowledge is knowable
and everything else is not.
Ross Finlayson, seemed to endlessly hedge on whether
or not the truth value of the Goldbach conjecture was
known. He seemed to think that there are alternative
analytical frameworks that make the question of whether
or not its truth value is known an ambiguous question.
>
I needed to refer to unknown truth values specifically
because all "undecidability" when construed correctly
falls into one of two categories.
(a) Semantic incoherence
(b) Unknown truth values.
A centence can be said to be undecidable when it is known that neither
the sentence nor its negation is a theorem.
When we skip model theory and and define True and False
as the existence of a back chained sequence of inference
steps of expressions x or ~x reaching axioms
good terms.
foundations are incoherent in the same way that
Russell's paradox proved that naive set theory had
a glitch.
If the sequence of inference steps is restricted toout-of-scope of the body of knowledge.
valid inferences the term "True" as defined above then "sentence is
true" is just another way to say "sentence is a theorem".
then it is a yes or no question that has no correct yesEven if a question has no answer within a formal theory of natural
or no answer within the formal system.
numbers it may have an answer in the natural numbers themselves.
My system is based on simple type theory and formalizedHow does your system handle questions that are not known to have a
natural language.
>
This makes it a yes or no question that has no
correct yes or no answer at all anywhere, thus
an incorrect polar question.
yes or no answer but k´nor known to lack such answer, either, e.g. Goldbach's conjecture ?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
--
Copyright 2026 Olcott
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
The complete structure of this system is now defined.
This required establishing a new foundation
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