  Abridged. We use COSMOS to study in a self-consistent way the change in the
number densities of quenched early-type galaxies (Q-ETGs) of a given size over
the interval 0.2 < z < 1.0 to study the claimed size evolution of these
galaxies. At 10^10.5<Mgalaxy<10^11 Msun, we see no change in the number density
of compact Q-ETGs, while at >10^11 Msun we find a decrease by 30%. In both mass
bins, the increase of the median sizes of Q-ETGs with time is primarily caused
by the addition to the size function of larger and more diffuse Q-ETGs. At all
masses, compact Q-ETGs become systematically redder towards later epochs, with
a (U-V) difference consistent with passive evolution of their stellar
populations, indicating that they are a population that does not appreciably
evolve in size. At all epochs, the larger Q-ETGs (at least in the lower mass
bin) have average rest-frame colors systematically bluer than those of the more
compact Q-ETGs, suggesting that the former are younger than the latter. The
idea that new, large, Q-ETGs are responsible for the observed growth in the
median size of the population at a given mass is supported by the sizes and
number of the star-forming galaxies that are expected to be progenitors of the
new Q-ETGs over the same period. In the low mass bin, the new Q-ETG have 30%
smaller sizes than their star-forming progenitors. This is likely due to the
fading of their disks after they cease star-formation. Comparison with higher z
shows that the median size of newly-quenched galaxies roughly scales, at
constant mass, as (1+z)^-1. The dominant cause of the size evolution seen in
the Q-ETG population is thus that the average sizes of individual Q-ETGs scale
with the average density of the Universe at the time when they were quenched,
with subsequent size changes in individual objects through eg merging of
secondary importance, especially at masses <10^11 Msun.
