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It's an interesting question. I'd like to hear sketched answers from both ravi and Carrol.
My own answer is mixed. Whenever I read Plato's works, I can't believe they were written two thousand five hundred years ago. There is something really pristine about much of them. I've only been through the Republic, Symposium, Phaedrus, Ion, Timaeus and here and there. I've never systematically read him.
What's funny thinking on it now is Shane Mage's complaint of my characterization of Plato in an old (Strauss) thread. I agreed him! And yet I didn't. It was great to hear that Socrates was reputed to be a stone mason or from a stone mason family. There is a deep logic to the construction of a building that is very difficult to explain to someone who has never been on a crew who built a building or a sculpture, which is very much like the same thing. And this logic is not a fixed art. You can show that medieval cathedrals are a patchwork of itinerant tradesmen who were trained in slightly different traditions when the concepts of stone construction were changing. It's a bloody miracle more of these things didn't just fall over after the mason scaffolds were taken down. If you think about that, then for example the scaffolds explain the flying buttress construction of Chartes, Notre Dome,... just build a permanent scaffold. Make it a feature and not a bug!
Well, I guess buildings that fall down are like the squirrels who can't climb trees. They are all dead, so we never see them. The funny thing is I have squirrels in my apartment backyard and I always watch for the losers. Sure enough I see them make disastrous leaps and crash, chattering and flicking their tails. Watching the bad judgment of squirrels is a very fun sport.
I've got Heath's translations of Euclid and his study of Greek mathematics. I can pick an idea and go look it up in these books and always learn something new and interesting.
At first impression Plato and Euclid seem extremely remote from common, mundane, the gritty realism of the bad judgment squirrels. And yet they are not at all that way. Euclid arises directly out of the building trades and trade craft of stone, wood, metal, etc. Euclidean geometry was in practice and developed as a skill in Mesopotamia, Egypt, and the Indus long before the scholars in Alexandria wrote this knowledge down and long before Euclid collected these works and tried to but them into systematic order.
Plato called his works Dialogs. So they arise from the all too human world of conversation and political argument, from law and human conflict as seen in the poets and playwrights and after dinner conversation. Isn't that what the Symposium is, a banquet, conference, and standing around the posters in the lobby, going to the bar to have it out? Why not include a gang fight in the parking lot, gun shots fired, sirens and helicopters, news media arriving to the mayhem, suspects frog marched to the black mariahs? Well, and off to be grilled, tortured, dungeon bound, and then cast away into darkness.
So my approach to these works is to try to ground them in the world from which they arose.
CG