What did Plato mean by the divided line?
What Plato meant by the divided line is explained by Socrates in the Republic:
Now take a line which has been cut into two unequal parts and divide each of them again in the same proportion, and suppose the two main divisions to answer, one to the visible and the other to the intelligible, and then compare the subdivisions in respect of their clearness and want of clearness, and you will find that the first section in the sphere of the visible consists of images. And by images I mean, in the first place, shadows, and in the second place, reflections in water and in solid, smooth and polished bodies and the like: Do you understand?
What Socrates hoped his listeners would understand was that what they saw through sight was less clear and further from the truth than what they were able to "see" in their "mind's eye" or understanding.
Did Plato change his philosophy as he grew older?
Plato became more conservative in his outlook and more attentive to existing social values and traditions as he aged. The city of the Republic would have required a revolution to set up. In the later Laws, Plato becomes less revolutionary and describes a "second-best" city in which there are traditional families and rulers are elected, rather than specially bred.
In the Parmenides Plato offers a series of criticisms to his earlier theory of forms, which he is apparently unable to answer and which are later taken up by Aristotle. The most famous of these is the "third man argument." Suppose we discover a form that accounts for what makes similar things similar. For example, every cat is different, but all cats share the same catness because they participate in the cat form. Now, if we compare this form with any one thing that participates in it—in this case, compare your cat with the cat form—the form and the participating thing will have similarities that make it necessary to posit a second form. If we then make comparisons of the cat to the second form, a third form will need to be posited, and on and on and on to an infinite regress. That is, Plato was aware of the theoretical problems with his theory of forms.
Did Plato change his philosophical theory of forms?
In the Philebus, one of his later works, instead of equating the good life with contemplation of the forms, Plato acknowledges that pleasure seems to be an important component of what is good. He then explains how goodness consists of proportion, beauty, and truth, and argues that intelligence is better than pleasure because it is closer to those three. This was a new, more down-to-earth theory of the good life for Plato because it suggested that the best life for a human being was a life of enjoyment of what seemed to be real, rather than a life dedicated to contemplating the forms.
What was Plato's view of love?
Plato had two theories on love: one "Platonic" and the other not. In the Phadreus he describes the development of passion between a mature man and a beautiful boy. The man's love for the particular beautiful person grows into a love of beauty in general. That general love of beautiful things becomes a love of the beauty in laws, and its final form is a love of beauty in thought, or the form of beauty. (It should be remembered that the ancient Greeks prized what we would call homosexual [and possibly pederastic] relationships between beautiful youths and wiser older men. The older man was the lover, the youth the beloved.) In Plato's version of such unions, their highest form was thus chastity, or what came to be called "Platonic love."
In Plato's Symposium, Socrates credits Diotima with what he knows about love. Diotima has told him that love or Eros is a spirit, the child of Need and Resource (or Lack and Plenty), who was conceived at Aphrodite's (the goddess of beauty) birth:
So love was born to love the beautiful.... As the son of Resource and Need, it has been his fate to be always in need; nor is he delicate and lovely as most of us believe, but harsh and arid, barefoot and homeless, sleeping on the naked earth, in doorways, or in the very streets beneath the stars of heaven, and always partaking of his mother's poverty. But, secondly, he brings his father's resourcefulness to his designs upon the beautiful and the good, for he is gallant, impetuous, and energetic, a mighty hunter, and a master of device and artifice—at once desirous and full of wisdom, a lifelong seeker after truth, an adept in sorcery, enchantment, and seduction.
The playwright Aristophanes is present at this discussion, and he gives an account of why love is so important to human beings. In the beginning, humans had three types that were each composed of two people conjoined in a spherical shape: female and female; male and male; male and female. These creatures were very strong and tried to storm Heaven itself. The gods did not want to destroy them, but something had to be done. Zeus' solution was to weaken them by cutting each of the beings in half. The result is that every human being is in search of their missing half. Men and women who were conjoined as hermaphrodites seek each other, Lesbians seek other women to complete themselves, and men who were joined to men are attracted to other men. Both Diotima and Aristophanes' explanations of love clearly involve sexual consummation and are not "Platonic."