Sometimes the glass transition is described as a transition from "a hard, brittle, 'glassy' state" to a "molten or 'rubbery' state" (that one's from Wikipedia, but most sources say something similar).
The words "molten" and "rubbery" seem contradictory to me - in a rubbery material the elastic behavior should dominate over the viscous behavior, while in a molten material, the response should be primarily viscous. The classic examples seem to be similarly torn: balls bouncing at various heights depending on temperature, and silly putty flowing or not.
So then, is the glass transition a decrease in the Young's modulus of the elastic material, or a transition to a softer, plastically deforming phase, which therefore has no easily defined Young's modulus?