1. Refutation by the observation of the opposite

Two opposite predicates cannot simultaneously be attached to the same subject. In other words, if an individual says something and one can see and show that the opposite is true, what the first speaker has said is rejected. This is a clear application of the principle of non-contradiction, two opposites cannot simultaneously exist in the same subject. This topic, as trivial as it is effective, is consistent with the view the facts are the best argument: “You say this, but I can see the opposite.” Example:

1. 1. Claim: Peter has white hair.
   2. Actual observed reality: Peter has black hair
   3. Rule of opposites: “white” and “black” are opposite properties (here of contrary opposite, they cannot be simultaneously true but can be simultaneously false, for example, if Peter has red hair).
   4. Conclusion Peter has white hair is false and must be rejected.

This argument has very broad scope when it comes to the refutation of factual assertions; it is actually the standard rebuttal scheme. If we are able to call upon a case in which an opposite property can be predicated of the same subject, the opponent’s claim in refuted.

The refutation predicates an opposite term of the subject, so we will use the singular, “refutation by (the predication of an) opposite”. In the quite different case of the topic of the opposites, the word is used in the plural. S. Opposites.

The condition of belonging to the same family of opposites is necessary: « Marie has a cat” (claim) is not refuted by stating, “Marie has a rabbit”.

The same procedure works for contrary and contradictory opposites. In the traditional system of genres, the claim “Mary is a man” is denied by the observed contradictory fact that Mary is a woman. Similarly, if two terms are in a relationship of possession / deprivation, (another form of opposites). If I am accused of having ripped off someone’s ear, I can refute the accusation by asking that person to come to court and show that he still has both his ears.

2. Facts against theories

The scheme applies to predictive discourse, somebody predicts that event E should happen, but, in due time, anybody can see that not-E, as is often the case in practical discourse.

In science, the scheme is involved in the Popperian concept of experimental refutation (Popper, 1963). When the predictions made by the theory are clearly false, the theory should be rejected or seriously revised. But at least in the humanities, the finding of the opposite is much less conclusive than it appears to be in the previous examples. The theory asserts, directly or indirectly P. Yet, common sense urges rather to notice and report Q, excluding P. How can we solve the dilemma? Several solutions are available:

— Rejecting the theory, a costly and painful solution.

— Minimizing and marginalizing the inconvenient fact, by opposing the mass of facts explained by the theory, that support, confirm the theory.

— Reform the intuition, and decide that the theory is brilliant, precisely because it makes us see things “differently”, so richer and deeper, and that in fact P is a kind of deep structure underlying the elementary intuition expressed by Q. The refutation can be resisted by choosing to reform the internal hypotheses (the theory) or the external hypotheses (what counts for a fact).

3. Refutation by the impossibility of the opposite

Refutation by the impossibility of the opposite rejects a judgment about a person, arguing that it is not possible for this person to be the subject of contrary opinion: “To be praised for his sobriety, he must have the opportunity to be intemperate”; it is ironic to praise poor people for their sobriety.

This is the topic “he cannot say otherwise”, so what you say makes no sense. Suppose that the Proponent says of Peter that “he is kind”. This quality has an opposite, “to be mean”. In order that the statement makes sense, the quality can be attributed to the individual only if, in another state of the world, the attribution of the opposite quality to this same individual would also make sense:

L1: — Peter acted in a friendly manner (so you have to be grateful to him)
L2: — To say that, still he would have to have the possibility of not being friendly (i.e. of being mean), I definitely owe him nothing

For a statement to contribute real information in a given situation, it is necessary that the opposite information be meaningful, “everyone agrees, how not to agree”.

In Le Figaro today the CEO of EDF asserts that the French nuclear park is in a very good state; well, it is difficult to see how he could have said the contrary. (France Culture Radio News, 04-18-2011; the CEO of EDF is in charge of the French nuclear park)