Genre and place in the book. An extended argument against DOGMAposthumous fame (ὑστεροφημία) — the longest fragment in the series on the vanity of repute. A double assault: (1) the fame will be extinguished anyway; (2) even were it eternal, it is nothing to you.
The extinction of memory. Those who remember will die, then their successors, until the whole memory is quenched, "passing through men who are kindled and are quenched" (διὰ ἁπτομένων καὶ σβεννυμένων): the generations are like lamps, lit and put out, handing the memory on. This is the temporal EXERCISEview from above: even long fame is nothing on the scale of time (cf. 03-10; Med. 4.33 — the antiquation of names; 4.35 — "everything is for a day, both the rememberer and the remembered").
"What is that to you?" The second move is the stronger: ὑπόθου — suppose the memory eternal. And then? τί πρὸς σέ; — to the dead fame is nothing (he is not), and to the living praise is merely "household business" (οἰκονομία): not a good, but at most a means. Fame is an indifferent, not a genuine good (cf. DOGMAvirtue-is-sufficient); cf. 02-12: reputation rests on the judgements of people who do not know what is good.
A textual note. The last sentence (πάρες… τὴν φυσικὴν δόσιν… ἄλλου τινὸς ἐχομένην λόγου λοιπόν) is difficult and apparently corrupt: Long breaks off at "the utility of praise," while Rogovin renders it as "give up now the concern for this vain gift, which depends only on human talk."
The disciplines. The principal one is desire: not to crave fame (neither in life nor after death). The secondary is assent: the judgement that fame in itself is nothing — only a name in others' mouths.
Parallels. The oblivion of fame — Med. 4.35; 4.33; 03-10; cf. EXERCISEview-from-above. The absurdity of craving the praise of posterity — Med. 6.18; 8.44. Fame is no good, resting on others' opinion — cf. DOGMAvirtue-is-sufficient; 02-12.