Premise 1: A "thing" is something that can be described with properties (this is just for clarification it includes everything there is)

Premise 2: There are no two "things" with the exact same properties (this makes sense since both would be the same otherwise)

Premise 3: One can find the opposite of every property there is. (This one is the part I'm a bit uncertain about. For example the opposite of cold would be hot but the opposite of red isn't that easy to establish. The question is if there are finite possible opposites for any given property. As long as that's the case it should be possible to establish opposites for any given "thing", even tho there would probably be A LOT of options for more complex "things")

If all the premises are true it would mean that it indeed is possible to find the opposite of any given "thing" as one could theoretically find all necessary properties of any given "thing" and find out the possible opposites of each property to get a list of possible opposites of said thing.

EDIT: I just thought about it again. This assumes that the opposite of a thing is the same as the opposites of it's properties which might not be the case but I'm not sure

  • Quite vague you use of "opposite": the opposite of white is not black; it is not-black. Commented May 29 at 13:58
  • Having said that, also if we can agree about Premise 3, from the fact that the opposite of mortal is not-mortal, it does not follows that there are immortal "things". There is no reason to assume that every conceivable property must be instantiated. Commented May 29 at 14:00
  • 2
    If the "length" property of a thing is "1 inch", what's the opposite property? "2 inches"? "1 mile"? "1 cm"? "0 inches"? Commented May 29 at 14:02
  • How hot is hot? The sun's surface? The interior? A supernova? The Big Bang? If there is only one hot thing, there can only be one cold thing. You've consigned existence to mediocrity!
    – Scott Rowe
    Commented May 29 at 20:50
  • Premise 1 is either trivial or vacuous. Without a characterization of allowed properties and a plausible argument that those are enough to distinguish things, it is hard to see how it says anything cogent. For any thing A, we can cook up a 'property' of "being A" and then, of course, A will be describable by this 'property'. And if this is allowed then the whole argument is circular, Premise 3 simply asserts what is concluded in different words.
    – Conifold
    Commented May 30 at 7:33

6 Answers 6


In addition to David Gudeman's answer which questions the validity of premise 3, I would also question the validity of premise 1.

Things in the real world (and in any reasonably interesting hypothetical world) aren't just tuples of property values. Properties are assigned labels, and as such they are not fully objective but very much subjective, and don't completely specify a thing but mostly serve to identify and distinguish different things. This means that the list of properties used to describe a thing is normally incomplete and depends on the context.


It isn't the case that every property has an opposite, and even if everything did have an opposite, that wouldn't guarantee that every object has a corresponding object with all properties opposite.

You gave one example of a property with no opposite in your question: redness does not have an opposite. Other examples include "sounding like a flute", and "tasting like lemon". It's hard to see how one could come up with an opposite for any property that can't be arranged on a linear scale.

Even if there is a theoretical opposite to a property, that doesn't mean that there is actually something that has that property. If we are talking about the natural numbers, then one property that all natural numbers have is "being even or odd". The opposite property would be "being neither even nor odd", and no natural number has that property.

  • Which property doesn't have an opposite? Why doesn't it guarantee that there is a theoretical "thing" that has the opposite properties of a different given "thing"?
    – M.B.
    Commented May 29 at 13:37
  • @M.B. I've updated my answer to answer this question. Commented May 29 at 14:28
  • Even many/most? linear scales don't have opposites. Examples from comments on the question include length and temperature. Commented May 29 at 21:52

Premisse 1 sounds more like a definition, not like a statement. But it doesn't make clear whether or not mathematical things, like numbers, are "things" too -- don't they have properties? Premisse 2 sounds like an axiom. If we restrict ourselves to physical objects, are you then saying that there is only one electron in the universe? Premisse 2 would only be true, I think, if "being in location x at time y" would also be seen as a property of the object - which seems a rather unusual use of the word "property". In premisse 3 it's not really clear to me what you mean by "opposite". Is the opposite of "(it is) red": "(it is) not red"? And an "opposite of thing x" would be a thing y that has none of the properties that x has? If so, you would usually be able to find an opposite of any thing x - but the problem would be, you'd have lots of totally different kinds of opposites. (Also, there is a hidden assumption here, that you can indeed enumerate all the properties of a thing x. It's not clear to me that we can.)

An unrestricted, totally generally use of "property" would also lead to Russell's paradox. A barber is someone who has the property that he shaves those men who don't shave themselve. Does the barber shave himself?


A property of is a measurable quality of a thing. Measurable qualities can be categorical (2 to N categories) or continuous (having infinitely gradated possible values).

The term 'opposite' implies a property of a thing that counterbalances or negates the same property on uniquely different thing. Thus, two people facing each other across a table have 'opposite' positions; blue is 'opposite' yellow on a color wheel, and 'opposite' red on the spectrum of human vision; a mountain top is 'opposite' a valley floor. 'Opposite' entails both separation and direction; something 'opposite' must be both away from and counter-facing its opposition.

The problem here is that the term opposite is both linear and relative. Something can only be 'opposite' along a specific dimension, given a specific frame of reference. The moment we begin joining properties together we create a multidimensional framework — with each property on its on axis — and the concept of being 'opposed' becomes complex. I mean, the thing we call a 'square' has several basic properties:

  • four sides
  • equal side length
  • equal angles of intersection
  • closure

and while we could imagine opposites for each or these measurable properties individually, within given frameworks, it's hard to imagine a framework that would uniquely specify opposites for all of the properties. In some frameworks, the opposite of a square will be a circle; in other frameworks, the opposite of a square will be a line or a cross… past one or two dimension. there's no easy or obvious point we can select to balance opposition


Although it is possible to take any term X and imagine its anti-term, just by prefixing "anti-" to X, this is not the same as having a distinct opposite of every term. For one, not only are "contradictory" and "contrary" already distinctive negations, so too are there multiple senses of "contrary," and so for example:

In particle physics, a truly neutral particle is a subatomic particle that is its own antiparticle. In other words, it remains itself under the charge conjugation, which replaces particles with their corresponding antiparticles. All charges of a truly neutral particle must be equal to zero. This requires particles to not only be electrically neutral, but also requires that all of their other charges (such as the colour charge) be neutral.

That is, the scheme of antiformation is something like, "A is the antiform of B if and only if A + B ↦ 0," and this trivially holds when A and B have a zero value of the requisite nature. But then A is self-contrary without having a substantial opposite.

Or, to use the same words but splitting the hairs at a little bit of a different angle, we will often be able to distinguish between saying, "A and B are on opposite ends of a spectrum," and, "A and B are on different spectra, and these spectra are what are the primary opposites in this case."🟥 For example, the phrase "necessary evil" notwithstanding, it is not as if, in a sequence of responsibilities, the positive responsibility with the highest priority is the good, and hence the anti-evil, such that the responsibility with the lowest priority has the property of being evil, or that the property of evil-in-itself appears as that lowest priority; but the positively obligated and the negatively forbidden are on separate lists/"schedules" (the former is always to be done at some time or other; the latter is never to be done at all). —Or consider that in category theory, there is all sorts of talk of self-duality, or a certain mapping to/from some C and its a priori Copcit. (see also here).

So the resolution of the question turns on whether we are careful in differentiating general contrariety from distinctive opposition, or even various senses of the word "opposition."

🟥For example, in a seven-color spectrum 🔴🟠🟡🟢🔵🟣1🟣2 (I couldn't find a light-purple emoji), red and violet are on opposite ends of the spectrum. However, combining them does not blank out all the coloration, is not an annihilation such as when matter and antimatter collide. So, "What is the opposite of red?" is ambiguous: it has a "good" possible answer when we mean "opposition as in spectral position" but perhaps not so much when we mean "opposition as in a propensity towards annihilation."

Or consider then the symmetry question for a single geometrical point. On the one hand, per the theory of n-spheres/balls, a point sometimes counts as a 0-ball, and a perfect n-sphere/ball is always the apex of (a certain sort of) symmetry in however many n dimensions. So we might say that a point is trivially (or even "degenerately") perfectly symmetrical (modulo the relevant sorts of symmetries). However, on another abstract level, the question should not as such even arise: a point doesn't have multiple sides to compare, and we might be better off using a description like "presymmetrical" rather than "asymmetrical" (and of course not "antisymmetrical"!) for it. And then insofar as all this microscopic geometry pertains to the logical cartography of alternation/negation and contrariety/opposition anyway, we have that there is a level (or stage) of general logical representation which does not involve the having of substantive opposites: there is neither intraspectral nor transpectral contrariety, here.

  • 1
    I love the mathematical use of the word 'degenerate', it's like running through the streets quoting from "The King's Speech" :-) I'm sure you would never be so unregenerate.
    – Scott Rowe
    Commented May 29 at 20:56

There is a problem with the premise 3.

Take for the example of the property (not containing an elephant) that is true of some room or house or instant of time. there is an infinite number of properties that contradict this property like the property of containing an elephant and the properties of containing two elephants,...etc. Talking about a "finite" number of contradictory properties seems nonsense to me.

  • 1
    Yes, this is a kind of reductio ad absurdum refutation.
    – Scott Rowe
    Commented May 29 at 20:52

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