The handsome bust above is of Heraclitus, a Greek philosopher who lived before Plato's time. I put it here because I want people to think it's Plato and be favorably disposed to him, at least for a moment. The guy (Plato) is out of favor now and needs every help he can get.
A while back I talked about Coursera, an internet school which offers free lectures and courses (graded or ungraded) on liberal arts subjects. Well, one of Coursera's latest offerings is a class on three of the dialogues of Plato. I'm not a Platonist but I grudgingly like the man because...Aaargh!... it's hard to finish that sentense. Plato's not a logician like Aristotle. What he has to offer is more subtle, more difficult to articulate. I'll give it a shot here, but I'm not confident that what I say will stand up to scrutiny.
Plato (that's him above) wants to be useful to real people in real situations. He believes in logic but he accepts the fact that real people are bound to culture and tradition and have a kind of in-built romantic bias. In order to reconcile all that he's willing to entertain ideas that are somewhat contradictory, something that Aristotle would never do.
If you were to tell Aristotle that you don't believe in ghosts but would be scared to spend a night in a haunted house, Aristotle might turn his back on you in disgust. Plato, on the other hand would be sympathetic, but...he might require you to at least try to find a unifying principal.
Plato's aware that accepting contradictions can lead to chaos so he emphasizes the need for character and thoughtfulness. A philosopher should study mathematics so he has a good ground in logic, but he should also sharpen his intuition and be self-critical and pious. Most people aren't capable of this kind of self-discipline, which is why Plato didn't believe in democracy. Neither did his hero, Socrates (above). I do believe in democracy, but it's possible to enjoy Plato without agreeing with him.