Is it possible for Nothing to exist in Something ? e.g. if something is the whole set can nothing be an element of it ?

If you take Nothing from something something remains. If nothing cannot exist in something. how can you take nothing from something.

In set Theory null set means an empty set a collection of 0 elements. But it doesn't mean nothing.the abstract collection still exists though it has no elements inside it.

So does Nothing exist even ? and If exists another question arises Where ?

  • 2
    Is there any chance you can develop your concern here a bit more? I would also encourage you to share a little bit about the context and motivations behind the question (what might you be reading or studying that has made this concern an important or urgent one for you? What might you have found out so far? And so on)
    – Joseph Weissman
    May 30 '12 at 20:23
  • This remembered me the axiom of the empty set from set theory.
    – Red Banana
    May 31 '12 at 5:54
  • Can't understand the reason of Downvoting !!
    – Neel Basu
    May 31 '12 at 10:32
  • @NeelBasu: I didn't downvote myself, but I suspect that the downvotes are because the question is poorly framed, and seems to be based on trivial language games ("if nothing cannot exist in something, how can you take nothing from something?") May 31 '12 at 15:09
  • This reminds me of a question in math. There is a unique function from the empty set to the empty set (namely that which takes nothing to nothing). The question is: is it constant? This is also almost a linguistic question. May 31 '12 at 16:47

I believe the question here makes assumptions which invalidate the endeavor. You assume that "nothing" is something which exists; without getting into the philosophical and formal approaches to the concept of "nothingness," this is patently contradictory.

Taking from the discussion here, one may propose that "nothing" can be defined as "not anything," or in a very rough sense, the negation of all that there is (minus the contradictory negating of course; refer to the history of modern set theories and formal logic to see what I mean).

So, in the strictest sense, it is not possible to subtract not anything from any set as subtraction is a binary operation; i.e., what you are asking is equivalent to asking, for example, "58 - ". Doesn't hold, does it?

At any rate, I hope I've addressed your concern here.

  • in set Theory null set meant an empty set. and empty set doesn't meant nothing. Its just a collection of 0 elements.
    – Neel Basu
    May 31 '12 at 5:29
  • Yes, that is true. May 31 '12 at 15:55
  • But the question asks whether Nothing exists or not.
    – Neel Basu
    May 31 '12 at 15:59
  • "Nothing" is the state (if you will) of complete non-existence. This is a very rough description. The notion of "nothing" is very subtle and abstract, and perhaps even counter-intuitive. Let us for a moment try to imagine what nothing means. Certainly, starting with "empty" space is a valid enough starting point. Then, let's imagine this space doesn't exist anymore, and we may envision that there is now a "void" of sorts. Well, let's take that out too. What are we now left with? Nothing? Not quite. If you examine the situation closely, you will find that we are still imagining the... May 31 '12 at 16:16
  • non-existence of the void. We must stop that too. And, if successfully done, we should've now stopped imagining altogether and "returned to reality." So, to put it in a make-do fashion, and in a strict sense, "nothing" cannot be said to exist, for if it did, it would be something instead of the lack of it. Do you see what I'm trying to drive at? May 31 '12 at 16:19

Although "nothing" is a noun, it is not a singular term. That is, it does not stand for any element of the domain of quantification. This distinguishes "nothing" from "Aristotle" (which stands for Aristotle). Both are names, but only the latter is a singular term.

Suppose we formalize "Aristotle is here" thus: Ha -- where "H" stands for the property of being here, and "a" stands for Aristotle. Now, since Frege it is widely accepted that the right way to formalize "Nothing is here" is not Hn (where n would be a singular term that stands for nothingness, or some such). The right way to formalize it is: ~ Ex (Hx) -- there is not anything such that it is here (the E should be looking backwards, but oh well).

The idea would be, then, that "is it possible for Nothing to exist in something?" only means the following: could it be that there is something such that nothing exists in it? Which could be formalized thus (introducing the notation Iab for "a is in b"). The question above asks for the possibility of the following state of affairs:

Ex ~ (Ey (Iyx))

I guess that boxes which are forever empty are possible, which means that the answer to your question is yes. There is nothing very deep about nothing possibly being in something.


In set theory (a branch of mathematics) the empty set is a subset of any other set except itself. wikipedia entry for the empty set

  • He seems to know that.
    – Red Banana
    May 31 '12 at 5:55
  • 1
    After he edited his post an hour ago he now seems to know that, yes.
    – ingenious
    May 31 '12 at 6:52

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