Further points about incompatibility

The relation of antonymy, exhibits the same pattern of entailment: there are entailments from affirmative sentences to negative sentences containing the antonym, but not from negative sentences to the corresponding affirmatives. For example, long and short are antonyms. Notice the way that the following entailments that these two words give us fit the larger pattern shown in (3.9d, e): a long ladder is not short and a short ladder is not long. However, a ladder that is not long is not necessarily short; it could just be middling in length. And a ladder that is not short is not necessarily long; it could be somewhere between long and short. Antonymy holds between many pairs of adjectives (and adverbs, for example quickly and slowly). It would be correct to say that long and short are incompatible, but, as most semanticists use the special term antonymy for incompatibility between pairs of adjectives (or adverbs), it is easier to keep with tradition. When adjectives occur in larger sets than pairs – as with {black, purple, blue, brown, green, yellow, orange, red, pink, white, grey} – then the appropriate term for the relation holding within the set is incompatibility.

Synonyms, yield an exception to the generalization that hyponyms of a given superordinate are incompatible with each other. The following are all hyponyms of seat: chair, bench, stool, sofa, settee. The relation of incompatibility holds between most of them: for example, if we know that Hazel is sitting on a chair, then we know that she is not (at that moment) sitting on a bench, stool, sofa or settee. If she is on a bench, then she is not (at that moment) on a chair, stool, sofa or settee; and so on. However sofa and settee, because they are synonyms, are not incompatible with each other. If Hazel is sitting on a sofa, then she is sitting on a settee, and vice versa.

(Non-synonymous) hyponyms of a word immediately superordinate to them are not only incompatible with each other but are also incompatible with hyponyms of their higher-level superordinates. The lists in (3.10) can be used to illustrate this.

A tea cup is not only not a coffee cup or any other kind of cup. It is also not a glass or a mug, nor any of the hyponyms of glass or mug. It might seem that this is boringly obvious: no given thing can be something else. That is not true, however. A cup can be a present, a possession, a piece of crockery and various other things.

Incompatibility is not pure unconstrained difference. Incompatibility is difference against a background of similarity. Remember that hyponyms of any superordinate have as their meaning the meaning of the superordinate plus some modification, for instance a tumbler is a ‘glass without a stem’ and a glass is a ‘drinking vessel made of glass’. In the meaning given here for tumbler, the modifier ‘without a stem’ records the difference between a tumbler and other glasses, and ‘glass’ represents the similarity that the meaning of tumbler has with the meanings of all the other kinds of glasses.