I'm reading Plato's symposium and I had a question about the section 199b - 201c where Socrates responds to Agathon. This comes after Agathon's speech, but before Socrates tells the tale of Diotima.
In 199d, Socrates gets Agathon to agree that love is "of" something like a father is of a child. Agathon agrees that it is in the essential nature of love that it is of a particular thing. In 200a, Socrates then gets Agathon to agree that love is "of" that which it desires. Furthermore he convinces Agathon in 200b that whatever love desires it necessarily cannot be in possession of. Socrates then reminds Agathon in 201a that in his speech, he said that the Gods' interests were established by the love of beauty.
Socrates then uses these premises to conclude that love can neither be beautiful nor good. Since the love in question is love of beauty, and love cannot possess that which it desires, love cannot be beautiful. And since what is good is beautiful, and love does not possess beauty, then love cannot be good either.
It seems to me however that Socrates is not right to conclude that love cannot be beautiful. In 199d, when Agathon agrees that love is "of" something, it seems like Agathon really meant that a man's love, or a god's love is of something rather than love itself. Agathon's speech was in reference to the God love, and not the particular love of a person. Socrates gets Agathon to agree as if he were speaking of a particular love, and then based on this concludes that the God love is not beautiful. It appears that Socrates tricked Agathon into claiming something that lacked specificity, and then used that lack of specificity to equivocate on the term love.
It's pretty essential to the rest of this dialogue that Socrates is able to successfully conclude that the God love is neither good nor beautiful. Diotima's argument that love is a spirit is wholly based on the principle that love, being neither good nor beautiful cannot be a god. Since all gods are both good and beautiful, if love were neither of these things, love could not be a god, but it really seems to me that Socrates has done an insufficient job establishing this, and I was hoping for some clarification before I accuse Plato of making an error.