Double negatives, and split infinitives for that matter, did not make sense in classical Latin. The more scholarly people in times gone all learnt Latin and therefore tried to be 'better' than the 'ordinary' people by not using such devices. There is no reason at all to not add extra negatives, or split infinitives, in standard English.

By making sure we don't not lapse into that there furrin tripe we can all boldy go where no language has gone before..;-)

Cheers

DtG