(KWOD-li-bet) 
noun
1. A subtle argument, especially on a theological or philosophical issue.
2. A musical medley: a whimsical combination of popular tunes.
Etymology
From Latin quodlibetum, from Latin quod (what) + libet (it pleases), meaning "whatever pleases". Earlier the term referred to a mock exercise in discussion. Sense 2 arose from its use in German to refer to a gallimaufry of light-hearted musical compositions
Usage
"Someone was sending me a signal. If words are unimportant, punctuation is something even more lowly. Why worry about such quodlibets? When was the last time anyone even noticed?" — Charles R. Larson; Its Academic, Or Is It?; Newsweek (New York); Nov 6, 1995.
"The swirling mist of sound [pianist Joanna MacGregor] made of the end of the penultimate quodlibet was almost shocking." — Rian Evans; Joanna MacGregor: St George's, Bristol; The Guardian (London, UK); Feb 5, 2005.