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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?

draks ...
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  • To help my understanding, can you tell me if the empty set of ZF is dependently originated? – user4894 May 12 '14 at 20:06
  • @user4894 I would say it isn't, but that's my question... – draks ... May 12 '14 at 20:12
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    Yes, axioms are non-empty in the sense that their acceptance is independent of our acceptance of other theorems. – Hunan Rostomyan May 12 '14 at 23:54
  • @rostomyan what about the possibilty to choose from a set of axioms? – draks ... May 13 '14 at 10:37
  • What about that possibility? – Hunan Rostomyan May 15 '14 at 08:01
  • Axioms are basically constructed for theorems. So they are still created things, and thus dependent. – catpnosis May 15 '14 at 08:05
  • @HunanRostomyan if you like to prove a theorem in a mathematical theory it depends on the axioms if and how to prove it. – draks ... May 15 '14 at 08:46
  • @catpnosis so the Axiom of extensionality "Given any set A and any set B, if for every set X, X is a member of A if and only if X is a member of B, then A is equal to B." is constructed? It looks pretty independant... – draks ... May 15 '14 at 08:50
  • Are you asking whether our choice of the axioms depends on other considerations? If yes, then you're equivocating between two uses of 'depends': one (1) where a theorem depends on axioms/rules of a particular system (in this sense axioms are independent), and the other is (2) where an axiom depends on someone's practical choice to include it among the axioms of the system instead of among the mere theorems of the system, and so on (in that sense, axioms are dependent). – Hunan Rostomyan May 15 '14 at 08:55
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    @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. – catpnosis May 15 '14 at 10:16
  • I'd suggest that the best way to look at this is to see how Buddhism conceptualised numbers, or thought about them. – Mozibur Ullah May 17 '14 at 04:21
  • @MoziburUllah where should I read on this topic? I just re-read your question Can there be Creation Ex Nihilo?, where you say that (physical) laws are of course not nothing. The only difference I see that axioms act on mathematical and physical laws on physical objects. But to me it looks that this makes a difference for you. What do you think? – draks ... Sep 30 '15 at 07:48
  • @draks: you're a year and a half too late; I moved on ... – Mozibur Ullah Sep 30 '15 at 07:50
  • @MoziburUllah in fact I asked back then right away. You didn't respond. So nowI deleted the old comment and re-asked. Sad that you moved... – draks ... Sep 30 '15 at 08:47

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  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.

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