Is there any exception that proves or suggests that the law of non-contradiction does not always apply?

I am thinking, because the law of non-contradiction is very similar to the law of excluded middle, that some of the examples that could be used are the same, but at the same time it seems like there are examples and exceptions that only apply to either one of them. So could you answer the question by taking that into account?


4 Answers 4


I depends on what you want your logic to model. You might want a logic that applies to some everyday process, like the laws, and not only to 'perfect' situations.

One way to look at this is in terms of types of modality. Modalities of obligation or of preference do not enforce non-contradiction. If you create a contradiction of obligations, there may be unavoidable loss, but the case is not impossible. if you create a contradiction of wishes you may feel guilty or torn, but life goes on. (Sorry to mention modals in every second post. I find this a productive unifying concept.)

Law is a modality of obligation, full of examples of contradictions that exist until they are resolved. So it is a good source of examples of violation of the law of non-contradiction.

Some of these contradictions are extremely explicit. The concept of common-law marriage is an example.

For a very long time in the U.S., into the 21st century in my own state of residence, (Illinois) an ongoing heterosexual relationship outside of marriage that also involved living in rental property rented in common was defined as unrelated co-habitation, and was illegal, as a form of fraud. (Even if you did not lie to the landlord.) But if you sustained such a relationship for seven years, you became married by common law, rendering the entire seven years worth of illegal behavior legal in retrospect.

This is a state of paraconsistency much like quantum superposition. Both the illegality of the situation and its potential future retroactive legality are real and opposite states that the current relationship is in.

Squatter's rights, considerations of easement, some kinds of custody, and other aspects of law have a similar status -- you sue someone to make existing illegal activity legal in retrospect and to place legal requirements upon the person whose rights you have officially been violating. And people cannot interfere just to prevent you from making this happen. If they want to maintain their rights, they have to be motivated by something genuine.

The law of the excluded middle also does not apply in this domain. You may enter a contract to provide some product, under the condition otherwise you must return some sum of money paid for it. And then your business might burn down, destroying that property and leaving you bankrupt. So you might do neither, while still not being considered to have violated the contract. We constantly make promises that one or the other thing will happen, which violate the law of the excluded middle in the case of our death or other extreme failures. It is not true that you either honor the agreement or violate it, leaving no other outcome.

The two are complements of one another, but they are not the same. In the language of constraint programming, they are opposite faults.

Contradiction happens when a situation is 'over-determined', when there are too many competing agendas involved to clean up the agreements ahead of time. Theoretically, then all outcomes are impossible. But there simply cannot be "no outcome" in real life. We just accept the one that happens and try to patch up history accordingly.

An excluded middle event happens when a situation is under-determined, when the objects involved are incomplete or imperfect by nature and their real behavior cannot be adequately foreseen. We just accept that none-of-the-above is sometimes forced upon us, and try to unwind the expectations in some balanced way.


See Dialetheism :

Probably the master argument used by modern dialetheists invokes the logical paradoxes of self-reference :

In its standard version, the Liar paradox arises by reasoning on the following sentence:

(1): (1) is false

where the number to the left is the name of the sentence to the right. As we can see, (1) refers to itself and tells us something about (1) itself. Its truth value? Let us reason by cases. Suppose (1) is true: then what it says is the case, so it is false. Then, suppose (1) is false: this is what it claims to be, so it is true. If we accept the aforementioned Law of Bivalence, that is, the principle according to which all sentences are either true or false, both alternatives lead to a contradiction: (1) is both true and false, that is, a dialetheia, contrary to the LNC.

Other Motivations for Dialetheism :

Dialetheias produced by the paradoxes of self-reference are confined to the abstract realm of notions such as set or to semantic concepts such as truth. However, the paradoxes of self-reference are not the only examples of dialetheias that have been mooted. Other cases involve contradictions affecting concrete objects and the empirical world, and include the following.

(1) Transition states: when I exit the room, I am inside the room at one time, and outside of it at another. Given the continuity of motion, there must be a precise instant in time at which I leave the room. [...]

(2) Some of Zeno’s paradoxes concerning a particular—though, perhaps, the most basic—kind of transition, that is, local motion.


If one thinks of the law of non-contradiction and the law of the excluded middle as two parts of a dichotomy, mutually exclusive and jointly exhaustive, it may be difficult to find examples that don't illustrate both at the same time.

What one needs is a class of propositions that one expects to be either true or false and so passes the jointly exhaustive part of a dichotomy, but which offers situations where one can't decide which is the case. That indecision would tempt one to deny the mutually exclusive part of a dichotomy.

Laurence R. Horn provides an example of what this might be. Consider the following dialogue:

—Were you pleased?
—Well, I was and I wasn't.

There is no desire to come up with a third possibility, perhaps "pleased-not-pleased". Rather the respondent to the question states, in violation to the law of non-contradiction, that he was both pleased and not pleased.

Horn, Laurence R., "Contradiction", The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/win2018/entries/contradiction/.


Is there any exception that proves or suggests that the law of non-contradiction does not always apply?

Abu Ali Sina (c. 980 – June 1037), perhaps better known as Avicenna, gave some thought to this...

Avicenna's commentary on Aristotle's Metaphysics illustrates the common view that the law of non-contradiction "and their like are among the things that do not require our elaboration." https://en.wikipedia.org/wiki/Law_of_noncontradiction

No "elaboration" then. But he had this advice in case of any problem:

Avicenna’s words for "the obdurate" are quite facetious: "he must be subjected to the conflagration of fire, since 'fire' and 'not fire' are one. Pain must be inflicted on him through beating, since 'pain' and 'no pain' are one. And he must be denied food and drink, since eating and drinking and the abstention from both are one [and the same]."

I guess this is not bad at all as an argument, though a few "obdurate" will still inevitably prefer to see the glass as both half-full and half-empty, which, come to think about it, it can indeed be.

In any case, it is not clear why anyone would want to change the rules of cricket as opposed to just start a new game with a different name.

Accepting the law of non-contradiction, I can remain consistent and dismiss any other position as just false. People refusing the law of non-contradiction will inevitably contradict themselves.

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