Something and nothing and logic.

I stumbled upon a quasi-philosophical account about nothing being something which disgusted me. The vague argument mixed with bad points and unnecessary references was something along the lines of

1.       Nothing is the negation of something.   Premise

2.       The idea of nothing is something.           Premise

3.       Nothing is something.                               Conclusion

And from here on the anonymous author took off and concluded all sorts of things: ultimate infinity, a deity, etc. I wish to use the argument above as an example of absurdity, with simple formal logic allowing us to clear the fog.

What the argument does is present two different claims in the first two premises, and then mixes them in a logically invalid way in the conclusion. To clear the air using some proper logical terms: Call something S. The negation of something, namely nothing, is then not S. In logic, the symbol for “not” is usually a line or a squiggle, like so: (⌐S) This simply means not something. In this sense, nothing is not really a proper concept, but simply the negation of another concept. Nothing is the negation of something.

Moving on to the idea of nothing, which is indeed a proper concept. Call this (I). Why is this a proper concept, and not simply a negation? To answer this, it is important to be precise at this moment: nothing and the idea of nothing are not identical. A thing is not identical to its idea. For example: A shirt and the idea of a shirt are not identical. This is easily seen if we express it logically: (⌐S) ≠ (I) Meaning: (not Something) is not identical to (the Idea of nothing). What would be correct is (I) = (I) and (⌐S) = (⌐S).

Now for the conclusion: what the argument does is to take the two definitions of two different things, namely nothing and the idea of nothing, and mix them so that the result is that nothing becomes something. It tries to say that it is both the case that nothing is (⌐S) & (I) at the same time. Logically, this is not impossible. A shirt for example can be both blue and not green at the same time. The problem arises due to the nature of the objects in question: things. The object is so general that claiming that “nothing” both is “something” and at the same time the negation of “something” is absurd. The idea of nothing is in fact a thing, but that is an idea, separate from “nothing”. Actual nothing is not an idea. Thus, what the argument truly says is: Nothing = (S) & (⌐S). Translated: nothing is both (something) and (not something). And here we expose the absurdity: a thing cannot both be and not be. A shirt cannot both be green and not green.

If you wish to go further into logic (the logic above is what’s known as propositional logic), I propose Harry Gensler’s Introduction to Logic which can easily be found online.