By analyzing an N-body simulation of a bulge formed simply via a bar instability mechanism operating on a kinematically cold stellar disk, and by comparing the results of this analysis with the structural and kinematic properties of the main stellar populations of the Milky Way bulge, we conclude that the bulge of our Galaxy is not a pure stellar bar formed from a pre-existing thin stellar disk, as some studies have recently suggested. On the basis of several arguments emphasized in this paper, we propose that the bulge population that, in the Milky Way, is observed to not be part of the peanut structure corresponds to the old Galactic thick disk, thus implying that the Milky Way is a pure thin+thick disk galaxy, with only a possible limited contribution by a classical bulge.