Many aspects of glass forming liquids, including the existence and nature of a thermodynamic glass transition, continue to be the subject of considerable scientific investigation. In particular, much recent work has been based on the inherent structure approach developed by Stillinger and co-workers. Within the inherent structure framework, Stillinger formulated an argument with the conclusion that a finite temperature ideal glass transition of the type associated with the Kauzmann paradox cannot occur for substances with limited molecular weight and with conventional intermolecular interactions. The argument, which relies on considerations concerning local defects that may occur in amorphous inherent structures, is tested numerically by generating inherent structures for a model liquid. The results concerning defects in inherent structures conform to Stillinger's description. The implications of these results are briefly discussed.