  We first summarize the classical arguments that the vast majority of
glass-forming liquids require more than one "order" parameter for their
description. Critiques against this conventional wisdom are then presented, and
it is argued that the matter deserves to be reconsidered in light of recent
experimental developments. Out of the eight basic thermoviscoelastic
frequency-dependent response functions, there are generally three independent
functions. For stochastic dynamics we show that there are only two independent
response functions; for this case it is shown how analytic continuation may be
utilized to express the third response functions in terms of two others.
Operational criteria are presented for the linear thermoviscoelasticity being
described by a single "order" parameter, in which case there is just one
independent thermoviscoelastic response function. It is shown that a single
"order" parameter description applies to a good approximation whenever thermal
equilibrium fluctuations of fundamental variables like energy and pressure are
strongly correlated. Results from computer simulations showing that this is the
case for a number of simple glass-forming liquids, as well as a few exceptions,
are briefly presented. Finally, we discuss a new conjecture according to which
experiments at varying temperature and pressure follow the density-scaling
expression for the relaxation time, $\tau=F(\rho^x/T)$ ($\rho$ and $T$ are
density and temperature), if and only if the liquid is "strongly correlating,"
i.e., to a good approximation is described by a single "order" parameter.
