The Buddhist World
According to the Buddhist emptiness teachings, the world is made up only of things that are "selfless" or empty. Even non-existents are empty. Non-existents would include round squares, the hairs of a turtle, etc., and inherent existence. Existents are divided into two classes, compounded things and non-compounded things.
Compounded things are said to disintegrate moment-to-moment, in a way analogous to aging. They are impermanent in this sense. Compounded things have pieces or parts and are produced from combinations of other factors. Compounded things include physical objects, colors, shapes, powers, sensations, thoughts, intentions, feelings, persons, collections, and states of being. These various things fall under the categories of Form (colors, shapes and powers), Consciousness (the sensory modalities and thinking processes), and Compositional Factors (collections and states of being).
Non-compounded things include do not disintegrate moment-to-moment. In this sense, they are said to be "permanent." There are two kinds of "permanent" existent. There are "occasional permanents," which come into existence and go out of existence. These include, for example, the space inside the cup and the emptiness of the cup. Even though the cup is compounded and consists of parts (such as the rim, the handle, the walls, etc.), the space inside the cup and the emptiness of the cup are not compounded and do not consist of parts. Also, the emptiness of the cup and the space inside the cup stop existing when the cup stops existing. There are also "Non-occasional permanents," such as emptiness in general and space in general. These are the referents of general concepts, and exist as long as any objects or relations exist.
For the student of emptiness, it is not important to remember or utilize this scheme or employ these categories in one's day-to-day use. What is important is to learn the lessons taught by this scheme:
According to the Buddhist world-view, everything that exists is said to be empty. For each thing, there is also the corresponding emptiness of that thing, because to exist is to be empty. Inherent existence falls under the category of non-existent things.
This last point is especially important when it comes to meditating on emptiness. When you meditate on emptiness, what you actually look for is inherent existence. Instead of finding inherent existence, you will find the lack of inherent existence. This lack itself is emptiness.
Emptiness and Dependent Arising
According to the Mahayana paths of Buddhism that emphasize the notion, emptiness is what the early Buddhist sutras were pointing to when they presented the notion of pratītyasamutpāda (Sanskrit) or paticcasamuppāda (Pali), namely "dependent arising":
There is the case where a disciple of the noble ones notices:
When this is, that is.
From the arising of this comes the arising of that.
When this isn't, that isn't.
From the cessation of this comes the cessation of that.
(Anguttara Nikaya X.92; Vera Sutta)
Centuries later, Nagarjuna (2nd century C. E.) became the preeminent expositor of emptiness teachings. His Mūlamadhyamakakārikā (Treatise on the Middle Way) is today considered the most profound and sophisticated exposition of emptiness in Buddhism. The text provides scores of arguments for the conclusion that to propose any kind of inherent existence or metaphysical essence involves the proponent in logical contradictions and incoherence. Chapter 24 actually contains two specific verses that characterize the notion of emptiness itself:
Whatever is dependently co-arisen,
That is explained to be emptiness.
That, being a dependent designation,
Is itself the middle way. (Treatise, 24.18)
Something that is not dependently arisen,
Such a thing does not exist.
Therefore a nonempty thing
Does not exist. (Treatise, 24.19)
In verse 18, Nagarjuna sets up a three-way equivalence:
emptiness : dependent arising : verbal convention
and identifies this equivalence with the Middle Way. The Middle Way is a form of nonduality that is free from the dualistic opposites of essentialism and nihilism. Even emptiness itself is characterized as being empty. It is empty because, instead of having the inherent nature of being dependent arising, it is merely "explained to be" dependent arising.
In verse 19, Nagarjuna states that whatever exists, is in some sense dependently arisen, that is, empty. If something is not dependently arisen, then it is not empty. If it is not empty, then it does not exist. And of course even things we would normally consider as non-existent, such as unicorns and round squares, are also empty.