  The Kochen-Specker theorem has been discussed intensely ever since its
original proof in 1967. It is one of the central no-go theorems of quantum
theory, showing the non-existence of a certain kind of hidden states models. In
this paper, we first offer a new, non-combinatorial proof for quantum systems
with a type $I_{n}$ factor as algebra of observables, including $I_{\infty}$.
Afterwards, we give a proof of the Kochen-Specker theorem for an arbitrary von
Neumann algebra $\mathcal{R}$ without summands of types $I_{1}$ and $I_{2}$,
using a known result on two-valued measures on the projection lattice
$\mathcal{P(R)}$. Some connections with presheaf formulations as proposed by
Isham and Butterfield are made.
