For example, the convention "Table" is not empty of "table" in TsongKhapa's system, but instead, it is empty of "inherent Table." One is then left with a table--which somehow exists or bears ontological meaning.
I'm wading out of my comfort zone here, but conebeckham's presentation is in fact accurate from the Gelug side. When the Gelugpas negate inherent existence, we do not negate the existence of the table, which we assert must be maintained to prevent the extreme of nihilism by over-negation. Unfortunately, I do not have access to my texts to back up my point. My best response as to what remains after negating inherent existence is dependently arising mere existence (something that non-Gelugpas have a big problem with). That is to say, when ordinary people perceive phenomena, we do not see the way in which they actually exist, because our mind's ignorance obscures that reality by positing at an inherent existence. Once we remove that ignorance from our mind, then we see the way those phenomena truly exist, merely labelled dependent arisings. Non-Gelugpas say that once the ignorance is removed, there are no further phenomena to be perceived.
When Gelugpas negate inherent existence, the true existence of the object is
negated. The problem is that you appear to be considering this "dependently arising mere existence" to have true existence. "Dependent arising" is not something that exists from its own side; it is also empty of inherent existence and does not have true existence. In other words, this "dependent arising" is not something that, in turn, needs to be negated; it is understood to be something whose true existence is already negated.
Perhaps this passage from my paper ( http://kenneth-chan.com/physics/direct- ... mechanics/
) may help give a correct sense of what I mean:
What “illusion-like” means is that our reality is what would be suggested by the phrase “an interplay between the elements,” only that we need to also remove the term “the elements” from the phrase. In other words, there is just the “interplay” without any inherently existing elements. To most people, this would be a revolutionary way of thinking, but Madhyamika philosophy is meant to revolutionise our way of thinking, in the same way that quantum mechanics also requires a revolution in our way of thinking.
We normally think of “an interplay” as being an interaction between inherently existing entities, but in Madhyamika philosophy, these interacting entities themselves are also empty of inherent existence. There is thus just the interplay between elements that are themselves also not existing on their own right. That is one sense of the phrase “like an illusion.” It is important to understand Madhyamika philosophy in this manner. (end of quote)
I should also add here that the "interplay" itself is empty of inherent existence, lacks true existence, and does not exist from its own side.