Moderator's note: the first few posts in this thread were split from another thread What you did in your example was show that mathematics' rules are consistent with the model you proposed. This is a plus point for mathematics, and the model. It doesn't prove that (-1)*(-1)=1. Whether or not such a view of mathematics as divorced from what it is modelling is a good thing is a whole other philosophical kettle of fish. They each have their flaws - yours because it presupposes physical intuition, and the acceptance of signed quantities in the first place.