12/14/2017 04:26:00 下午

 via here

[A]ny formal system S satisfying the following three conditions:
1. S is ω-consistent
2. S has a recursively definable set of axioms and rules of inference
3. Every recursive relation is definable in S
is incomplete, in the sense that there is a closed wff of S of the form ∀xFx such that neither $⊢_{s}$ ∀xFx nor $⊢_{s}$ ∼∀xFx, where on the intended interpretation F is assigned a recursively defined property of natural numbers.Hunter, G. (1973). Metalogic: An introduction to the metatheory of standard first order logic. University of California Press, pp. 256-257.
「ω-consistent」、「recursively definable」、「recursive relation」、「$⊢_{s}$ ∀xFx」都是數理邏輯的術語，看不懂的馬上便知自己看不懂。熟悉感消失，遐想煙消雲散，是有一點點可惜，但要人自知無知，總好過令人自以為知。