Antonyms and mutually exclusive words

Solution 1:

A good question, but not an easy answer.

Antonymy comes in several flavours:

• Simple antonyms that are binary pairs - dead/alive, hit/miss, pass/fail etc. One is the absence of the other. Dead = not alive.

• Gradable antonyms - hot (warm, tepid, cool)cold. One is not necessarily the negative of the other. It is not hot, not cold, but somewhere in between.

• Reverses - one is the reverse of the other. Push/pull, right/left, north/south.

• Converses - these are almost paraphrases and depend on view point. Above/below, own/belong, employer/employee - the library is above the shop and the shop is below the library.

• Taxonomic sisters - this is where mutual exclusivity comes in. Red and blue are members of the same taxonomy of colours, and something that is red cannot be blue - they are mutually exclusive.

Your north-south is clearly an antonym, a reverse. Your other non-North directions could be antonyms by being taxonomic sisters, if you view south-east as excluding north or and south or any other direction; or gradable antonyms if you view south-east as including some 'south' in it.

Simple answer - they are all antonyms but of different kinds.

Solution 2:

Wikipedia states that one "[...] usage (particularly that of the influential Lyons 1968, 1977) defines the term antonym as referring to only gradable opposites (the long : short type) while the other types are referred to with different terms. Therefore, as Crystal (2003) warns, the terms antonymy and antonym should be regarded with care. In this [the Wikipedia-] article, the usage of Lyons (1963, 1977) and Cruse (1986, 2004) will be followed where antonym is restricted to gradable opposites and opposite is used as the general term referring to any of the subtypes [...]" [emphasis mine]