When Buddhists speak of a thing or person being 'empty' they really mean 'empty of inherent existence'.
So what is this`'inherent existence' that it is so important to refute?
I've been trying to get my empty head around what an inherently existing object would be like. Here's a few ideas:
(1) An inherently existing entity exists in splendid isolation without the need to reference any other entity. It is completely defined by its own nature.
(2) An inherently existing entity is uncaused.
(3) It is indestructible.
(4) It is eternal.
(5) It is unchanging when viewed externally.
(6) It cannot undergo any internal changes of state.
(7) It either has no constituent parts, or if it has parts those parts are inseparable.
(8) Consequently, nothing can be ejected or removed from it.
(9) Nothing can be added to it (this would change its definition).
(10) No change in external conditions (up to and including the destruction of the entire universe) can affect it.
The fact that an inherently existent object would be indestructible rules out anything composed of physical particles, because every subatomic particle is destructible when it meets its nemesis, in the form of its corresponding antiparticle.
Inherent existence of mathematics
I used to think that mathematics might be inherently existent, but from my limited knowledge of Goedel's theorem, I understand that no system of mathematics can be completely self-defined, and must always reference something external to itself.
Inherent existence of God
God might be another candidate for an inherently existing entity, but if he were truly inherently-existent he could never undergo a change of state in response to external conditions (eg become angry at sinners/infidels and send plagues, pestilences etc to destroy them). Neither would it matter to him whether he was worshipped or not, for no external factor could in the slightest degree affect him.
Also, if God is omnipotent, he has the power to destroy everything, including himself. So even God must be empty of inherent existence because his continued existence is contingent on his not committing suicide.
Invisibility of an inherently existent object
Returning to point (5), a physical, inherently existing object probably couldn't be viewed because the physics of viewing requires the electrons in the object to interact with the photons of light, which would require a rearrangement of the 'parts' of the object. Hence the object would be altered by external conditions.
Also, all physical objects are composed of particles of various sorts, and all particles are changed by being known (Heisenberg, dual wave/particle nature, entanglement etc). So no physical object could ever be inherently existent, as it is composed entirely of parts which are dependently-related to the knower ( and some very weird things happen when you try to find the 'true nature' of fundamental particles.)
Possibly a more abstract object could be known without viewing, in the same way that a mathematical entity such as 'Pi' can be known without being physically viewed.
Not that Pi or any other mathematical function is inherently existent. Pi depends upon the circumference and diameter of a circle. All mathematical entities are imperfect, incomplete and make Goedelian 'external references'.
For a more detailed explanation of this subject see BUDDHIST PHILOSOPHY
- Sean Robsville
Sunyata - the emptiness of all things
Existence, Impermanence and Emptiness in Buddhism
Essentialism in Physics, Chemistry and Biology
The Four Seals of Dharma
Quantum Buddhism - Buddhist Particle Physics