Image by John Flaxman (1879)
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Starting with the story of Daedalus and Icarus, the plot unfolds to give hope that duo of father and son can somehow make an escape from their captivity on the island of Crete. However, due to the emergence of Icarus' euphoria of his new wings, he becomes overzealous and flies too close to the sun. He then falls to his death in the sea.
In the context of the time and culture that this story is told in, I would think that the significance of the death of Icarus would be to be thankful for freedom but avoid "drowning" yourself in the sensation.
(Here's a link to the story)
The poem then moves on to visit the instance of Philemon and Baucis: they're an old couple that have lived in poverty most of their lives, yet have remained very in love with each other and faithful to the gods. Jupiter and Mercury, in disguise as mortal passerbys, visit the marsh town that Philemon and Baucis reside in to test the strength of the spiritual belief of the town. The two gods are disappointed when all the doors to all houses in the village remain shut for them. However, Philemon and Baucis let the two disguised gods in, and trouble themselves with serving them dinner, despite their old age and lack of resources. Jupiter and Mercury reveal themselves and make the elderly couple the keepers of their temple for the end of their days, so that they need not suffer the pains of poverty ever again. They do this until their deaths: they pass at the same time, so that one doesn't live without the other, and they have two fruitful trees growing over their graves in their honor.
This tale points to a very traditional way to use the instance of death: even in old age, you should be content and true with yourself during the spiritual journey that you have taken in your life.
(Here's a link to the story)
The next story is that of Erysichthion, a man scornful of the gods, who most notably struck down the most sacred tree in Ceres' woods. The reason he does so is not clear, but perhaps it is purely his sense of irreverence for the gods. In any case, Erysichthion takes an axe and a squad of servants to Ceres' woods and begins to cut down this great oak. This tree is a symbol of worship to the Nymphs, an Earthly manifestation of Ceres herself. The Dryads live by it, using it as a way to channel the divine commune they have with the Goddess. Upon receiving the sound chops from the axe head, the tree begins to fall and a Nymph cries out to Erysichthion, begging him to stop. But the proud man does not cease; he continues until the tree is felled. As a result, in the next story in the unit, a chain of events is set off that turns out to be Erysichthion's undoing.
This story uses the death of the oak for a specific lessen: revere all that the gods have created, including manifestation, if only to see past your own selfish whims.
(Here's a link to the story)
The death of Hercules is an oddly gruesome one: the shirt of Nessus the centaur possesses a poison that slowly boils the blood and peels the skin off its host's musculature. Despite his great strength and courage, Hercules cannot bring himself to overcome the poison that has been inflicted on him. As death begins to take him, he laments his glory and life's journeys. After a long time of mad wandering, Hercules finds his end in a funeral pyre. The people whom Hercules was known to come from far and wide to grieve for the hero, and their cries do not go unnoticed. Zeus, upon judgement of Hercules' efforts in life to establish justice and good in the world, grants the hero the gift of immortality. This allows Hercules to shed his mortal body, and join his Olympian family in the celestial regions of their home.
I think the conditions of Hercules' death are very unusual: he is given the shirt of Nessus by his wife, who suspected him of having an affair with another woman. His wife, not knowing that the shirt was lined with poison, give it to Hercules as a sign of faithfulness to him. This background leads me to think that the lesson in the death of Hercules is that: no good deed will go unpunished, but when all is said and done, the gods are the ones who pass final judgement.
(Here's a link to the story)
(Here's a link to the unit)