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I was thinking about the question "Why is there something rather than nothing?" , and have read about some theories that **existence is the case because non-existence is logically impossible**

So, I devised a logical proof that shows nothingness is impossible, but only if we can formally denote nothingness by : **"There exists x, so that for all y , y is not identical to x"**.

**(∃x)(∀y)(y≠x)**

Which violates the law of identity, therefore : nothingness is logically impossible. (there is no x that is not identical to all y)

**My question : are there any references that try to denote "nothingness" in formal terms?**

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– Philip Klöcking – 2019-09-10T02:08:59.4201Not that I know of. It seems to be an idea that takes us out of the system. To say 'Nothing exists' might be okay if we assume an x may be real and not-exist (not stand-out) but to say 'Nothing is real' is to say there is no x and logic collapses. This would be connected with Bradley's comment that subject-predicate language, while necessary, is unsuitable for metaphysics. . . – None – 2019-09-14T13:24:41.057

@PeterJ agree, or put another way, if nothing exists then there is no proposition that denotes nothing exists, because if there is a true proposition that meabs nothing exists, then it would follow that the proposition is wrong since there is something which is a true proposition thank you – SmootQ – 2019-09-16T11:15:13.207