On 9/13/23, mailbombbin <mailbombbin@gmail.com> wrote:
<blockquote>'''First Incompleteness Theorem''': "Any consistent formal system {{mvar|F}} within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of {{mvar|F}} which can neither be proved nor disproved in {{mvar|F}}." (Raatikainen 2020)<!-- this is a direct quote from (Raatikainen 2020) --></blockquote>
So, this is indeed a formal statement that contradictions with a proving system exist, Maybe that’s something for me to think about some. Godel’s first theorem claims there are statements in every formal system that are neither provable nor unprovable. If I am to accept that this is because one can describe proving in the formal system, and then write an expression that a provable statement is unprovable, or such, i might then wonder about defining a third form of proving that provides for identifying such contradictions.