Incompatibility

The sense relation which is analogous to the relation between classes with no members in common is incompatibility. Two lexical items X and Y are incompatlbles if a sense of the form A is f(X) can be found which entails a parallel sentence on the form A is not f(Y).

It’s a cat entails It’s not a dog.

It’s a carnation entails It’s not a rose.

John is the one who is walking entails John is not the one who is running.

John is near the building entails John is not in the building.

There are certain parallels between incompatibility and compatibility. Like ‘mere’ compatibility, mere incompatibility is of relatively little interest: the fact that affix and volcano are incompatibles is not specially informative. However, a special significance attaches to sets of incompatibles (as well as to compatibles) which fall under a single superordinate: animal: cat, dog, lion, elephant, etc.

Declarative sentences identical except for different incompatible terms in parallel syntactic positions (besides those used in the test) are frequently in a contrary relationship: if I cycled to work is true, then I walked to work is false, but if I cycled to work is false, then I walked to work may be either true or false. However, the relationship between incompatibility and contrariety in natural sentences, like the relationship between hyponymy and entailment, is by no means straightforward, and the expected contrariety does not always appear. For instance, the truth of I met Mary today does not entail the falsity of I met Mary yesterday, although yesterday and today are incompatibles. However, if both are true, they obviously refer to different occasions of meeting Mary — a single occasion of meeting cannot be both yesterday and today. The contrary relation will therefore show up in a sentential context that specifies, or at least implies, that a single event is being referred to, such as I only met Mary once, and that was today / yesterday or (somewhat less convincingly) It was today / yesterday that I met Mary. Another example is I bought some apples, which does not stand in a contrary relationship with I bought some pears. In this case, both sentences can be true without their necessarily referring to separate events: one may purchase apples and pears simultaneously. Contrariety will only appear here if it is specified that apples (or pears) constituted the whole of the purchase: All I bought were some apples / pears. Colour terms present a particular problem. Most speakers would agree, I think, that Mary wore a red dress and Mary wore a blue dress were contraries (assuming, of course, that they refer to the same occasion, and that Mary, as would be normal, wore only one dress at a time); the colour terms refer to the predominant colour of the dress, and there can be only one predominant colour. But colour terms frequently qualify only part of the object their head noun denotes; furthermore, different colour terms may typically apply to different parts, so that, for instance, Mary’s eyes are blue and Mary’s eyes are red are not contraries (N.B. there’s no lexical ambiguity in these sentences). Clearly, to yield contrary sentences, a pair of colour terms must refer to the same area of uniform colour; but it is far from obvious how to devise linguistic contexts which will guarantee this.

Like hyponymy, incompatibility features as a typical syntagmatic relation between constituent lexical items of certain common locutions. To give one example, items in a coordinated list are typically incompatibles, and gross deviations from this lead to abnormality:

I like mangoes and bananas.

? I like fruit and bananas.

However, and this is another parallel with hyponymy, strict incompatibility is not necessary, so there is no basis for a definition of incompatibility along these lines. It is perfectly normal, for instance, to say You meet all kinds of people here — students, bank managers... even though Arthur is a student does not entail Arthur is not a bank manager.