Re: Undecidability based on epistemological antinomies V2 --Mendelson--

On 2024-04-26 15:28:08 +0000, olcott said:

On 4/26/2024 3:42 AM, Mikko wrote:

On 2024-04-25 14:27:23 +0000, olcott said:
 

On 4/25/2024 3:26 AM, Mikko wrote:

epistemological antinomy

 It <is> part of the current (thus incorrect) definition
of undecidability because expressions of language that
are neither true nor false (epistemological antinomies)
do prove undecidability even though these expressions
are not truth bearers thus not propositions.

 That a definition is current does not mean that is incorrect.
 

 ...14 Every epistemological antinomy can likewise be used for a similar
undecidability proof...(Gödel 1931:43-44)
 

An epistemological antinomy can only be an undecidable sentence
if it can be a sentence. What epistemological antinomies you
can find that can be expressed in, say, first order goup theory
or first order arithmetic or first order set tehory?
 

 It only matters that they can be expressed in some formal system.
If they cannot be expressed in any formal system then Gödel is
wrong for a different reason.

How is it relevant to the incompleteness of a theory whether an
epistemological antińomy can be expressed in some other formal
system?
--
Mikko