I’ve been having trouble with this one…looked through all kinds of forums, literature, articles, thought about it for hours on end, and still I cannot come up with an answer.
How are abstract thoughts possible? How can they exist apart from reality? Nothing can exist that does not follow the laws of reality, but thoughts don’t have to…why? What constitutes “thought”? Since thoughts exist, they must have some sort of physical identity…but if they did, then they would be subject to reality and volition would be eliminated. 
I’m probably missing a very obvious premise…so please help!
You really believe that thoughts don’t have to follow the laws of reality? How? When you reach a problem like this, the first thing is to concretize it. What thought have you ever had that did not follow the laws of existence and identity?
Perhaps you mean that a man can imagine a block floating in mid-air with no support, but that this is not possible in reality. You need to remember that there is a distinction between what is in your mind, and what is in reality. This distinction is grasped by each baby the day he wants his mother and his mother does not magically appear. What is in your mind is the imagination of a block floating in mid-air, what is in reality is something else. This imagination in your mind is subject to a different set of laws from the block. Imagination involves the combination of material derived originally from the senses.
Without the neccessary materials (previous awareness of something similar to a block, something similar to floating), there can be no imagination. Also, imagination requires either a conscious focusing on the materials, or a subconscious process that is performed automatically based on previous, related, conscious processes. These are both instances of the law of identity.
So, you were missing a very obvious distinction indeed, the distinction between existence and consciousness.
As for volition being an exemption from the law of identity, see Leonard Peikoff’s “Objectivism: the Philosophy of Ayn Rand”, chapter 2. In the meantime, why don’t you “will” yourself into turning into an orange, or tell the person you love the most that you can’t see them any more because for all you know, you might be “willed” to stab them to death tomorrow.