Can you summon a monster in face up defense mode?

Under normal circumstances, a Normal Summon will be in face-up attack mode, and a Set will be in face-down defence mode.

Some cards can change this, such as Light of Intervention, which prevents monsters from being set, but allows them to be Normal Summoned in face-up defence mode.

Special summons are different - the default is face-up attack or face-up defence position. Again though sometimes individual card effects can 'special set' the card, or restrict it to a specific mode.