A GFCI does work properly in a circuit with no ground.
I can understand the fear of flipping a light switch while standing on a not perfectly dry floor and getting electrocuted. If the power feed to the light subcircuit was daisy chained through a receptacle outlet box upstream, you can put an ordinary GFCI receptacle in that outlet box and connect what continues beyond that point to the load terminals of the GFCI. (Or use a GFCI breaker as mentioned earlier to protect the entire circuit.)
This offers protection although not code compliance.
Originally Posted by jwhite
Also you do not have positive and negative wires, unless your home is wired in DC instead of AC.
I know the usage is incorrect but occasionally I have referred to the two legs of a regular 120/240 volt AC service as plus 120 and minus 120 respectively. (The neutral is zero.)