From DeWitt's "Summum Bonum Fallacy" (December 1950). DeWitt is not using precisely the reasoning we are discussing in this thread, but I think his observations are helpful regardless of the "greatest" question, because what woul arguably support "life is greatest" would also support "life is everything."
The rest of this post is a quote from the article:
Recognition of life as "the greatest good" is on record in Vatican Collection 42: "The same span of time embraces both beginning and end of the greatest good." The meaning of this is not obscure. It marks life as limited by birth and death. It denies both pre-existence and survival of the soul, and is a contradiction of Plato, who sponsored both these doctrines. Editors, however, misled by the summum bonum fallacy, feel bound that "the greatest good" shall be pleasure, and consequently emend the text, producing a sentence genuinely obscure, which need not concern us.
Other confirmatory passages are citable. The "desirability of life" is mentioned as a reason for placing a higher value upon old age as against youth,' contrary to a prevailing opinion. The same feeling motivates the scorn expressed for a dictum of Theognis : "A good thing it is never to have been born or, being born, to have passed with all speed through the gates of Hades." The supreme value placed upon life determines also the attitude toward suicide (Vatican Collection 38) : "Small is the man from every point of view who discovers many plausible reasons for taking leave of life."
This doctrine of Epicurus furnished philosophy with a perennial topic. He thought of life as a voyage14 or a journey'5 in which the wise man should always find a balance of pleasure over pain.'6 Suicide in his opinion was not a dereliction of duty, but the abandonment of an opportunity to enjoy happiness to the fullest degree.
In the second of his books On Lives he is reported as saying: "But even if deprived of his sight, [the wise man] will not turn aside from the journey of life." It is from this point that Cicero discusses the topic, and that too with specific mention of Epicurus, in the Tusculan Disputations,' where he extends it to include loss of hearing.
Once the ball had been started to roll the temptation presented itself to go on through the list of deprivations, as in the sorites syllogism, and this is exactly what happened. Life being the greatest good, the question takes the shape, At what stage of deprivation would it lose all value? The answer came from Maecenas:
debilem facito manu, debilem pede coxo,
tuber adstrue gibberum, lubricos quate dentes,
vita dum superest, bene est; hanc mihi vel acuta
si sedeam cruce, sustine.
The beginning of the poem is lacking; only the lines that horrified Seneca are quoted. It may be assumed that Maecenas ran through the list of deprivations, working his way up to a climax.