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I originally thought of 0 for this question. 0 is used to represent nothing withing mathematics. However, I thought that by defining nothing as 0 which (at some level is something) does it no longer make nothing nothing and rather nothing something?

I followed on with the idea of the word. By using the word nothing we are defining nothing as something. So does this mean nothing is no longer nothing?

I finished this thought with what you could call a hypothesis stating that if you define nothing with something (i.e. a word) does it cease being nothing and become something, therefore, meaning nothing is undefinable?

Mauro ALLEGRANZA
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Joshua Killen
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    It is a sort of playing with words... we can "define" non-existent things (like the well-known unicorn) and this does not "trun" them into existence. – Mauro ALLEGRANZA Oct 04 '17 at 14:11
  • We define a concept and we may have concepts that do not "apply" to any existent object: the round square or the concept "not being equal to itself" (the "standard" property used to define the empty set). – Mauro ALLEGRANZA Oct 04 '17 at 14:13
  • In math the empty set exists but it is not "nothing": it is a set and is empty. I.e. nothing belongs to it. – Mauro ALLEGRANZA Oct 04 '17 at 14:13
  • We can define unicorns in terms of broader categories, but what I find interesting about the question is whether *nothing* can be defined in a non-circular way. Or, what would such a definition have to presuppose to give it meaning? –  Oct 04 '17 at 14:15
  • See also [Nothingness](https://plato.stanford.edu/entries/nothingness/) for discussion. – Mauro ALLEGRANZA Oct 04 '17 at 14:18
  • [See also](https://philosophy.stackexchange.com/q/40774/28067) for an existential view – ttnphns Oct 04 '17 at 17:19
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    Possible duplicate of [What is and how far extends existence?](https://philosophy.stackexchange.com/questions/46293/what-is-and-how-far-extends-existence) – Conifold Oct 04 '17 at 21:43
  • A defined 'nothing' would seem to be 'something', as you say. Zero is a number and form. Lao Tsu would say that the world begins before number and form. Thus the something-nothing problem is avoided in his ontology. –  Oct 05 '17 at 15:22

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There's a distinction between language and reality. Language consists of verbal behaviors and concepts which may or may not have a correspondence to reality. So having a word doesn't mean that there's a corresponding object. Previous posters have mentioned classic examples like unicorns or even the obviously logical contradiction of square circles.

But there's something else here that you touch upon which I think has some validity. Is nothing really the complete absence of anything? We can see many examples which seem to contradict this, all of which revolve around the fact that these nothings seem to do some real work.

For instance, you bring up 0. 0 is supposed to be nothing, no quantity, yet its role in math is significant, and some consider it one of the most important developments in mathematics, possibly being the thing that made positional notation practical and with it, the relative ease of calculation that we have today. It's hard to imagine something not existing (having unreality) while simultaneously having this very real effect.

Or take the more mundane example of the space inside a cup. A cup is hollow inside, hence most people would think there's nothing there. Yet, it's this nothing that allows the cup to hold fluid, and which gives it its use. Without this nothing -- with a "filled cup" we'd have a useless chunk of matter.

So really, maybe nothing isn't nothing? If something exists in some level -- even as a contradictory idea -- it can have some impact on reality. Unicorns don't exist, but the idea of them has caused paintings, shows, etc... to feature them. That's certainly something. Square circles don't exist, yet we write about them, discuss them, and their analogies involve our discourse on contradictions. That's certainly something.

So we use nothing in a relative sense, not in an absolute sense.

R. Barzell
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  • So, is that "working nothing" a potentiality? Is it that "crack" on the solid body of reality (being) which isolates isles of it as things having _meaning_, i.e. entities wanting something or needing something (= necessary for something)? https://philosophy.stackexchange.com/a/45193/28067 – ttnphns Oct 04 '17 at 18:40
  • And, doesn't that "nothing in a relative sense" mean that the nothing cannot precede being, that it is secondary, like a blow up or a cracking of being (giving the being its "vividness" and "facets")? – ttnphns Oct 04 '17 at 18:50
  • The only things that don't exist are things that have no impact and that we're not aware of. The moment we think of anything, it exists, even if only mentally. Therefore, being is a vacuous term and thus leads to confusion and incoherence. Saying "nothing cannot precede being" is thus nonsensical for nothing belongs in the category of nothing. Examples of nothing are like examples of square circles. We can talk about them in the abstract, but can't give examples. Just because a word can participate in syntax doesn't mean it forms a meaningful statement. – R. Barzell Oct 05 '17 at 04:09
  • The use of 0 in mathematics is more subtle than "0 represents nothing". For example: In coordinate geometry, a horizontal line has a slope. That slope is 0. For a vertical line the word "slope" is not defined and "the slope of a vertical line" does not exist (is not defined). – Jim H Oct 05 '17 at 12:27
  • @JimH well, one way to think about it is that the slope is the measurement of the incline of a line and a horizontal line has no incline, hence the slope is 0. This is perfectly consistent with saying "0 represents nothing". Of course I'm using intuitive interpretations for mathematical terms and that is fraught with danger :). However, that's not really a big deal either way. I was keeping my response short and building on the example the OP used. – R. Barzell Oct 05 '17 at 15:33