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If north is the antonym of south, then what is the relationship between north and all other non-north directions such as east, west, south, south-east, south-west, etc.?

Similarly, if male is the antonym of female, then what is the relationship between male and the other non-male genders such as transgender variants, female, etc.?

Perhaps I can illustrate my question as:

        antonym
 north<--------->south

          ?
north<--------->everything non-north

They are perhaps mutually exclusive. But I expect that there's a semantic term that better describes this relationship. If there's no straightforward technical term available, I'd appreciate non-technical alternatives as well.

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sibling? tilde-X? peer? –  Kris Oct 11 '12 at 9:19
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4 Answers

up vote 3 down vote accepted

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.

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The general understanding is that an antonym refers to a member and not to a class. In order to have an antonym, we begin with a class of two and only two members. Father-Mother, Yes-No ... When there are more than two members in a class, each being the antonym of all other members cannot be seen as logical by the common folk. If taxonomic sisters are to considered antonyms, the defined antonyms we already learned may need to be unlearned (er... I'm afraid, so actually). :) –  Kris Oct 11 '12 at 9:54
    
No... the antonyms you learned are still antonyms, but now you can intimidate colleagues by calling them simple antonyms. The antonym, that is. Not the colleagues. –  Roaring Fish Oct 11 '12 at 10:42
    
+1 Thank you. This is very interesting! I see that converse antonyms are (also) known as relational opposites. I also see complementary pairs used to possibly describe binary pairs. Could you please link your definitions to appropriate sources? Standard terminology will make this answer even more useful. –  coleopterist Oct 11 '12 at 16:32
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@coleopterist~ terminology is 'in flux'... My terminology follows John Saeed (Semantics chapter 3), but both Lyons and Cruze have differing terminology. Online, there is a ppt lecture here (staff.um.edu.mt/albert.gatt/teaching/dl/semLecture7.pptx) that uses the same definitions that I do. –  Roaring Fish Oct 13 '12 at 9:25
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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]

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'Antonym' may or may not be the correct term. The question is, what is the correct term. –  Kris Oct 11 '12 at 9:56
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Sorry, you are right, in its current form it's a non-answer (pun intended). I will consider reworking it shortly or posting it as a comment. –  Alexander Kosubek Oct 11 '12 at 9:59
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You could say hyponym. According to Wikipedia,

In linguistics, a hyponym is a word or phrase whose semantic field is included within that of another word, its hypernym. In simpler terms, a hyponym shares a type-of relationship with its hypernym. For example, scarlet, vermilion, carmine, and crimson are all hyponyms of red (their hypernym), which is, in turn, a hyponym of colour.

So, in your examples, north, east, southwest, etc. are all hyponyms of direction, while male, female, and transgendered could be considered hyponyms of gender.

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That would be the relation to the hypernym direction, not to the other directions themselves. –  Kris Oct 11 '12 at 9:20
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@Kris: You're correct, of course. (I was aware that it's not an exact fit for what the O.P. requested, but the O.P. asked for a "semantic term," and that's the closest one I could think of or find. There may be a better one, but I figured it wouldn't hurt to get the ball rolling with hyponym.) Thanks for pointing that out, though; it's a valid point. –  J.R. Oct 11 '12 at 9:34
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Not quite what you were looking for, but I often use hear and use the word orthogonal to describe points along conceptually different axes or dimensions.

East and west are orthogonal to north; south, no.

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