I suspect most native English speakers never realize that the prefix un- is actually two unrelated prefixes, both of which sometimes get attached to the same word. Consider these two sentences:
(1) I tried to carry out all the tasks on my list, but some remained undone.
(2) As soon as the new leader took office, he quickly saw to it that the previous leader’s excesses were undone.
The un- in (1) means ‘not,’ while the un- in (2) adds the sense ‘reversed, counteracted.’ Granted, there’s some semantic overlap, because to reverse an action is in some sense to negate it, to leave it not being as it was. In fact that partial semantic overlap has influenced the development of one of the prefixes and may account for the fact that so many native speakers conflate the two.
The un- that means ‘not’ traces back to the Indo-European negative *ne, which also gave rise to the negative Latin prefix in– (with assimilating variants im-, il-, and ir-). The counteracting un- arose from the Indo-European root *ant-, whose senses were ‘front’ and ‘forehead.’ It’s surprising to realize what that root gave rise to in Latin: the prefix anti-, which meant ‘against.’ The semantics must have been that when you confront something you figuratively push your head forward into it and therefore go against it. In any case, Spanish and English have many words that incorporate the prefix anti-.
© 2016 Steven Schwartzman