In a sense this is a followup to my earlier question Does the (1-)topos structure on simplicial sets have any homotopy-theoretic significance?.

In the topos of simplicial sets, the subobject classifier $\Omega$ is injective, hence it is a contractible Kan complex.

So we can view $\Omega$ as an $\infty$-connected $\infty$-groupoid, in particular its two objects $\mathbf{true},\mathbf{false}:1\to\Omega$ are isomorphic.

Does this fact have any significance for the internal logic of simplicial sets? For a logician it must look somehow disconcerting...