 Coarse graining the probability distribution avoids Liouville's Theorem, and successive coarse grainings increase the coarse grained Gibbs entropy. The justification for coarse graining is usually attributed to our observations being insensitive to the fine grained structure of the original probability distribution p(X3N, P3N | i). The acceptability of this practice is one of the major problems for the Gibbs approach to statistical mechanics.