  The Euler characteristic, thought of as a function that assigns a numerical
value to every finite simplicial complex, is locally determined in both a
combinatorial sense and a geometric sense. In this note we show that not every
function that assigns a numerical value to every finite simplicial complex via
a linear combination of the numbers of simplices in each dimension is locally
determined in either sense. In particular, the Charney-Davis quantity $\lambda
(L)$ is not locally determined in either sense if it is defined on a set of
simplicial complexes that includes all flag spheres of a given odd dimension.
