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presence 
1 attendance, being, companionship, company, existence, habitation, inhabitance, occupancy, residence 
2 closeness, immediate circle, nearness, neighbourhood, propinquity, proximity, vicinity 
3 air, appearance, aspect, aura, bearing, carriage, comportment, demeanour, ease, mien  (literary) personality, poise, self-assurance 
4 apparition, eidolon, ghost, manifestation, revenant, shade  (literary) spectre, spirit, supernatural being, wraith 
presence of mind  
alertness, aplomb, calmness, composure, cool  (slang) coolness, imperturbability, level-headedness, phlegm, quickness, sang-froid, self-assurance, self-command, self-possession, wits