Exist, v. i. [imp. & p. p. Existed; p. pr. & vb. n. Existing.] — Webster enters it under “exist”
Etymology: [L. existere, exsistere, to step out or forth, emerge, appear, exist; ex out + sistere to cause to stand, to set, put, place, stand still, fr. stare to stand: cf. F. exister. See Stand.]
1. To be as a fact and not as a mode; to have an actual or real being, whether material or spiritual. Who now, alas! no more is missed Than if he never did exist. Swift. To conceive the world . . . to have existed from eternity. South.
2. To be manifest in any manner; to continue to be; as, great evils existed in his reign.
3. To live; to have life or the functions of vitality; as, men can not exist water, nor fishes on land.
Syn. -- See Be.
Shades of meaning
Fernald has no entry of its own for existing; he lists it under alive.
Where he writes about it:
Alive applies to all degrees of life, from that which shows one to be barely existing or existent as a living thing, as when we say he is just alive, to that which implies the very utmost of vitality and power, as in the words "he is all alive," "thoroughly alive." So the word quick, which began by signifying "having life," is now mostly applied to energy of life as shown in swiftness of action. — from alive