In mathematics, a totally indescribable cardinal is a certain kind of large cardinal number.

Formally, a cardinal number κ is called totally indescribable iff for every natural number n, proposition φ, and set A ⊆ V_κ with (V_κ+n, ∈, A) ⊧ φ there exists an α < κ with (V_α+n, ∈, A ∩ V_α) ⊧ φ.

More generally, a cardinal number κ is called Π^m_n-indescribable if for every Π_n proposition φ, and set A ⊆ V_κ with (V_κ+m, ∈, A) ⊧ φ there exists an α < κ with (V_α+m, ∈, A ∩ V_α) ⊧ φ.