/ɛpɪˈmiːθiəs/; Greek: Ἐπιμηθεύς, which means “hindsight” or “afterthought” was the brother of Prometheus, he is depicted as foolish compared to his brother Prometheus who is characterized as ingenious and clever.
The myth tells of the twin Titans, entrusted with distributing the traits amongst the creatures created now dwelling the Earth. Epimetheus gave a positive trait to every animal, but when it was mankind’s turn he had nothing left to give them.
Prometheus feeling sorry for man had taken it upon himself to give them the gift of fire and with that the tools in which to create using it. Unfortunately the Gods Athena and Hephaestus didn’t take this act of kindness too well and punished him.
“Epimetheus, the being in whom thought follows production, represents nature in the sense of materialism, according to which thought comes later than thoughtless bodies and their thoughtless motions.” – Plato
Epimetheus was the one who accepted the gift of Pandora from the gods, it was only inferred that they married. But in later myths, Pyrrha the daughter of Epimetheus and Pandora was married Deucalion, Prometheus descendant. They are the only two humans who survived the deluge.
David calls Walter “Brother” in the Engineer’s Cathedral, but what I find interesting is that in the extended scenes it is Walter that hands Daniels a lighter to light the fire. David in this case could also be seen as Epimetheus as he utilizes the accelerant to gift special traits to his creations. But Walter is also Epimetheus, Daniels and Oram ask Walter if David is dangerous, but he only tells them that he is Disturbing and confusing.
Epimetheus represents nature in the sense of materialism, according to which thought comes later than thoughtless bodies and their thoughtless motions. His duty to the crew and desire to help them achieve their mission doesn’t factor in how to go about doing it if someone like David were to try and stop him. His every action is a thoughtless motion much like his efforts in protecting Daniels from the Neomorph, telling David it was duty that propelled him and not love.