Dig, Igor, Dig

The Answer...

The left grave.

Because we cannot determine whether the right inscription is true or false, Igor would be better off digging up the left grave.

The Question was...

Dr. Frankenstein has sent Igor out to find another body. In the cemetery are two graves. The inscription on the left tombstone says, "This grave is empty." The inscription on the right tombstone says, "This grave is full and only one of these inscriptions is correct." Where should Igor dig?