It seems to me that Gibbs' Paradox (that the entropy of a classical ideal gas, calculated by phase-space volume, is not extensive) can be resolved without assuming that particles are indistinguishable. Suppose instead the opposite: that particles are distinguishable, meaning that each one can in principle be identified- imagine a minuscule serial number stamped on every molecule. Now this should apply not only to the system under consideration, but to the universe as a whole- the serial numbers run from one to A, where A is the total number of molecules (of a particular type) in the universe. This immediately implies that specifying the position and momentum of each of the N particles in our box does not fully determine the microstate of the system! We must also specify which, out of the A molecules in existence, are in fact the N ones in the box. The total number of microstates should include all such possibilities. This means multiplying the phase-space volume by "A choose N", that is, A!/(N!(A-N)!). Since A>>N, the factor A!/(A-N)! tends to AN. Thus we are left with the desired factor of 1/N!, giving the standard (extensive) entropy, plus a constant contribution N log(A) that is also extensive and (I think) has no observable effects.