Can anything be described by describing what it is not? For example, a dog can be described as all that is not a dog. "All crows are black": all things that are not black are not a crow but not all things that are black are crows.

  • A male human being is a human being that is not female. – Philip Klöcking Jul 16 '16 at 6:21
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    @PhilipKlöcking: You first described the thing ("human") which greatly restricts what it might be. But if you say "not an animal and not female" - could be a diamond ring, or a jam sandwich, and so on. – gnasher729 Jul 16 '16 at 8:00
  • @gnasher729: That's quite the point. While in the definiens the differentia specifica might by expressed negatively, the genus proximum cannot. – Philip Klöcking Jul 16 '16 at 8:49
  • IFF you assume a Universe where every descriptive question has been answered, then theoretically, "Yes". However, as Ares pointed out, there are computational limitations to such a position. – Samuel S. Mandal Jul 16 '16 at 16:59
  • @Philip But we need not use an Aristotelian definition. Apophatic theology describes God exclusively as what he is not en.wikipedia.org/wiki/Apophatic_theology, and any axiomatic definition may involve negatively predicated axioms only. There is that Spinoza's passage that Hegel loved so much, "determination therefore does not pertain to the thing in regard to its being; on the contrary, it is its non-being", omni determinatio est negatio philosophy.stackexchange.com/questions/26837/… – Conifold Jul 19 '16 at 4:05

From a different mathematical point of view, for any given thing, there are more things it is not than there are sentences to describe them.

Not every real number can actually be described in language, there are more of them than there are formulas or sentences. From there, we certainly can't describe all of the real numbers that are not his specific one, much less all the things other than real numbers...

So, you may be able to select a item from a set, and then negate that selection. But you surely can't build up any kind of real description of an item by stating what it is not.

Basically, negation seems simple and applicable to all cases, but it has all kinds of problems, starting with the one addressed here: https://philosophy.stackexchange.com/a/36294/9166

Pairs of contrasting things can be identified, especially if you have identified the whole that they together make up. But that is not identifying either one of them in terms of 'what it is not'. It is, in fact, without a surrounding positive frame of reference, impossible to identify anything by what it is not.


In mathematics (specifically discrete ~) we have the concept of the set complement. Given a set, it basically means "whatever is not on your set."

Your supposition leads to a strange paradox. What is the set complement of everything? You would probably say nothing. Does that mean that nothing is not in everything? How does that make sense? If everything is everything then how can nothing not be inside of it? If nothing isn't the complement of everything, then what's its complement?

You could go in circles forever. It's tautological.

So, I don't think so, no.

  • This post seems a bit confused. If we would have a set of everything E, then the set complement is E \ E = Ø, i.e. the empty set. That does not mean however that Ø ∉ E. There is a difference between member-of and subset-of. – Keelan Jul 18 '16 at 9:04

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