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Secondly, in the PM-Lisp it doesn't necessarily prove that theorem a proves b, it just shows that b can be a successor of the formulas in a


Hi Ethn!

Existence of the [Gödel 1931] proposition I'mUnprovable is inconsistent with the following theorem to the effect that theorems can be used in proofs:

      ⊢∀[Proposition Ψ] (⊢Ψ)⇒Ψ


Axioms can be used in proofs, and they are not provable.

If a proposition is not provable, yet raises no issues if regarded as true, then it can be added as an axiom and used in theorems.


It turns out that for powerful theories of Computer Science,

there must exist infinitely many propositions that are

inferentially undecidable, that is, can be neither proved nor disproved.

However, the propositions cannot be specified constructively

and so are not very interesting.

Currently, there seem to be no propositions interesting to

practical Computer Science that are provably inferentially

undecidable.


For a statement so short it would be easy to avoid using jargon...


The following theorem says that every theorem can be used in another proof:

         ⊢∀[Proposition Ψ] (⊢Ψ)⇒Ψ
The above theorem is completely standard mathematical notation.


What character set or input method is used in creating this mathmatical characters?


Just to be clear

      ⊢∀[Proposition Ψ] (⊢Ψ)⇒Ψ
is not jargon. Instead, it is standard mathematics.


It absolutely is jargon. The fact that you explained it by saying it's "mathematics" instead of "English" suggests as much. Jargon means that it's technical language specific to a field and not used in everyday vernacular. What you wrote can't even be typed on a standard keyboard. It's jargon.

I'm pointing it out because its use is not so innocent. Jargon is often used to obfuscate meaning, especially when it means something that would otherwise be easy to say plainly.




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