On the other hand my claim is proven analytically.promethean75 wrote: ↑Thu Apr 27, 2023 11:45 pm "argumentum ad verecundiam is not a fallacy within inductive inference, yet it must be a qualified authority."
indeed peter.
skepdick wasted no time reminding me of the fact that just becuz i might think of wtf as a person who by his mathematical knowledge would be an authority on the matter, it doesn't mean that he would be right.
"That a broad consensus of physicians agree on a medical opinion provides strong evidence (yet zero proof) that the opinion is correct."
indeed peter.
just becuz a couple or more people consistently disagree with skepdick, I'd not be justified in claiming that it's more likely that he's wrong therefore.
When G asserts its own unprovability in F the proof of G in F requires a
sequence of inference steps in F that prove that they themselves do not exist.
The standard definition of mathematical incompleteness:
Incomplete(T) ↔ ∃φ ∈ F((T ⊬ φ) ∧ (T ⊬ ¬φ))
requires formal systems to do the logically impossible:
to prove self-contradictory expressions of language.
So formal systems are "incomplete" in the same sense that we determine
that a baker that cannot bake a proper angel food cake using ordinary
red house bricks as the only ingredient lacks sufficient baking skill.