# Are axioms non-empty?

In Buddhism the concept of inherent existence plays a very important role:

an object is "empty" is synonymous with saying that it is dependently originated.

So I was looking for non-empty things. Abstracts things, like mathematical proofs for example. But I found that they maybe boiled down to mathematical axioms, premises so evident as to be accepted as true without controversy.

So, are axioms non-empty?

• To help my understanding, can you tell me if the empty set of ZF is dependently originated? Commented May 12, 2014 at 20:06
• @user4894 I would say it isn't, but that's my question... Commented May 12, 2014 at 20:12
• Yes, axioms are non-empty in the sense that their acceptance is independent of our acceptance of other theorems. Commented May 12, 2014 at 23:54
• @rostomyan what about the possibilty to choose from a set of axioms? Commented May 13, 2014 at 10:37
• @draks... That axiom isn't independent, as it's formulated for [particular] set theory, to be cornerstone in that theory. You can also deny any axiom and try to build another theory (example is Lobachevskian geometry constructed on rejection of "obvious" Playfair's axiom), or try to build another [better] set of (definitions of) axioms. Yes, axioms are used for construction of theorems, but still axioms are constructed too to be useful parts for later construction. Commented May 15, 2014 at 10:16

## 1 Answer

1. The fact that you can't apply concept of emptiness to the object doesn't make object non-empty. It could be just irrelevant to the concept.

2. This is weird treatment of concept of emptiness either. Emptiness (in the most general definition) is the absence of (usually false) knowledge in the true knowledge. And in particular, absence of atman in the dharmas (skandhas, etc).

One of justifications of some dharmas being empty is that they are dependently originated. But some other dharmas are still empty without being dependently originated, like nirodha or tathata.

3. So one supposedly non-empty thing is atman, but it doesn't exists, as it's false concept.

• Thanks. Can you provide some explanations for atman, nirodha and tathata? Commented May 15, 2014 at 7:54
• @draks... Atman is delusional concept of Self, nirodha is cessation of suffering (nirvana), and tathata is true reality. Commented May 15, 2014 at 7:58