In introducing microcanonical ensemble of classical statistical mechanics one pretty much starts by postulating that entropy of the system has the form
$S(V,E) = k \log \Gamma(V,E)$,
where $\Gamma$ is appropariate measure of available volume in phase space, with a few possible choices. I am not spelling out the details because I assume these are known, but I remark that I use the definitions given in the classical book "Statistical mechanics" by K. Huang. To justify identification of this quantity with thermodynamical entropy one, among other things, shows that it is extensive. Now again this proof is probably well known and can be found in any book in stat. mech. so I don't quote it. The problem is as follows: after introducing all this Huang uses this definition to calculate entropy of ideal gas. He discusses that there is some problem in that this expression cannot be true due to the Gibbs paradox and then introduces the so called correct Boltzmann counting. Now physical origin of this (as classical limit of bosonic/fermionic statistics) is clear. However what bothers me is that entropy obtained before introducing the correct Boltzmann counting is not extensive (it is after the correction). I remind that necessity of Boltzmann counting was not taken into account in the proof of extensiveness of entropy. Therefore it seems that there was some mistake in the proof. It seems that this is a counterexample! This bothers me because it is a foundational concept which seems to break down in the simplest possible case. Is there some problem in my reasoning?