Charles and Miller (1989) attempt to answer this question. They propose two possible answers to this question, one of which they go on to study in greater detail. Their two hypotheses are called the co-occurrence hypothesis and the substitutability hypothesis, and they are quoted below:
Co-occurrence: Two adjectives are learned as direct antonyms because they are heard together and are spoken together in the same sentences more often than chance would allow..Substitutability: Two adjectives are learned as direct antonyms because they are interchangeable in most contexts, i.e., because any noun phrase that can be modified by one member of the pair can also be modified by the other (Charles and Miller 1989, 360)
Charles and Miller say that the co-occurrence hypothesis is simpler, but that there is an independent need for the substitutability hypothesis, for example, to explain other facts of word association and to explain how people learn which part of speech a word belongs to, so they decided to test the substitutability hypothesis first to see if it can explain how people learn antonyms.
This was their basic procedure. First, they chose a set of four adjectives to study. The set was made up of a pair of antonyms, strong and weak, and two synonyms of these antonyms, namely powerful and faint. The synonyms were used so that they could compare the results found with the antonym pair strong/weak to the results found with the indirect antonym (near-opposite) pairs strong/faint and powerful/weak. For each adjective, they found 25 sentences containing the adjective in the Brown corpus. Then they typed each sentence on a separate card, leaving a blank in place of the target word, as in this example: "Third, there were those, notably Patrice Lumumba, who favored a Unified Congo with a very ______ central government." Subjects were asked to sort the cards, placing all the cards which were missing the same word together; then they were asked to fill in the missing word. Charles and Miller predicted that if the substitutability hypothesis were correct, subjects would confuse the contexts for the direct antonyms, but not for the indirect pairs. That is, they would be likely to infer that the missing word was weak when in fact it was strong and vice versa, but they would not infer that the missing word was faint when in fact it was strong or weak when it was powerful.
The results seemed to argue against the substitutability hypothesis: Subjects rarely confused the contexts of the antonyms. For example, when subjects were asked to sort out the sentences which contained strong and weak, strong was guessed correctly in 179 responses out of 200 (200 responses = 25 sentences filled in by eight different subjects), and weak was substituted for strong only 4 times. (The other 17 responses were other adjectives, e.g., ardent, great, etc.) Similarly, weak was guessed correctly in 164 responses out of 200, and strong was substituted for weak in only 13 out of 200 responses. Subjects did not substitute the indirect antonyms for each other either. When the contexts for strong and faint were sorted, for example, the subjects correctly identified strong in 113 cases out of 200 and only substituted weak for strong in one case; they correctly identified faint only 46 out of 200 times, and substituted faint for strong only 23 out of 200 times. Overall, subjects had a harder time identifying faint and powerful from the context than they did strong and weak.
Charles and Miller repeated the experiment with four other adjectives, the antonyms public and private and their synonyms open and secret. The results were similar to those in the first experiment. Private and public were easier to identify from the context than secret and open, but they were rarely substituted for each. Charles and Miller say that these results argue against the substitutability hypothesis, since they show that the sentential contexts of direct antonyms are not interchangeable. However, they say, "It may still be true, however, that a noun phrase that can incorporate one adjective can also incorporate its antonym. Disambiguation may be based on the rest of the sentence." Therefore, they did another experiment, this time cutting down the amount of context to just the noun phrase. They gave these examples of the types of noun phrase contexts that were used:
(3)a very _____ central government
________, sickly, little things
the ________ eye
many _______ sources
In this experiment, the noun contexts for four adjectives were compared: strong, weak, public and private (that is, this experiment had no indirect antonyms), and the subjects were told what the adjectives were. Again, they were told to sort the cards so that the cards in each stack could be filled in with the same missing word. This time, subjects substituted antonyms for each other more often than in the previous experiment, but they substituted the unrelated adjectives too. For example, the context of strong was correctly identified in 132 out of 200 cases, but in 29 examples, weak was chosen instead, in 27 cases public was chosen, and 12 cases private was chosen. Therefore, it seems that the contexts of antonyms are not interchangeable.
Charles and Miller say that even within a noun phrase, there is enough disambiguating evidence that the correct adjective can often be identified. In the example " _______, sickly, little things" the other adjectives sickly and little help the subject to choose weak. They admit that some of the noun phrases form collocations that are "almost compound nouns." But, they say:
The point, however, is that it is simply not true that any noun phrase that can take one adjective can equally well take its direct antonym. Hence, even though substitutability might provide an important cue for learning which contrasting adjectives to pair as direct antonyms, it is still not an attractive hypothesis. (Charles and Miller 1988, 372)
Since Charles and Miller believe that the results of this study show that antonyms are not learned through substitution, they turn to the co-occurrence hypothesis as a more likely explanation. That is, they suggest that speakers learn that strong and weak are antonyms (but strong and faint are not) because they encounter strong and weak (but not strong and faint) used together in the same sentence fairly often. The Brown corpus is too small to accurately measure co-occurrence, but they note that they found five examples in which strong and weak occurred in the same sentence, but no sentences with strong and faint, weak and powerful, or faint and powerful.
Other adjectives occur more frequently in the Brown corpus and so provide might a better test of the co-occurrence hypothesis; this is the case with big, little, large and small,1 a set which Charles and Miller find particularly interesting because big and large are similar in meaning and therefore, according to the WordNet model, associated with the same concept; small and little are likewise associated with the same concept. Considering the fact that large is usually paired with small rather than little and big is usually paired with little rather than small, Charles and Miller say, "If co-occurrence in the Brown Corpus could be shown for these adjective pairs [large/small and big/little], it should serve to discount any proposal that antonymous pairing reflects some kind of conceptual or semantic generalizations" (Charles and Miller 1988).
Counting all the co-occurrences in the corpus, they find that big/little and large/small co-occur more often in the same sentence than chance would predict and three times more often than either big/small or large/little. Charles and Miller say that given these findings,
[I]t seems reasonable to suppose that the antonymous pairings--the "clang" association between direct antonyms--is a consequence of frequently perceiving and using these words together in the same syntactic structures. (Charles and Miller 1988, 374)2
Thus according to Charles and Miller, the results of this study help to answer one of the biggest questions raised by Deese"s research, the question of how antonyms come to be associated in the mind. They say that the substitution hypothesis does not seem plausible and that co-occurrence can probably explain how antonyms become associated. Charles and Miller believe that this in turn supports the characterization of antonymy as a lexical rather than conceptual relation--if antonyms are linked as a result of co-occurrence, there appears to be no need to rely on word meanings to explain their association. However, there are many researchers who do not accept this characterization of antonymy, and as will be shown in the next sections, they interpret Charles and Millers findings in very different ways.
Murphy and Andrew start by discussing Charles and Miller's suggestion that co-occurrence alone can explain how two words come to be associated. They begin by pointing out, "There are a number of other words that co-occur but are not even near-antonyms: dentist/teeth, food/eat, sick/tired, and a variety of idioms and phrasal expressions" (Murphy and Andrew 1992, 3). How do word learners know that some kinds of co-occurring words are antonyms, but others are not?3
Their second criticism is even more to the point. They say:
[A]n explanation is needed for why antonyms co-occur. If it is because they are associated in semantic memory, then we have formed a completely circular explanation in which co-occurrence is caused by the relation, and the relation is caused by co-occurrence. (Murphy and Andrew 1992, 3-4)
This also occurred to me the first time I read Charles and Miller (1989). It seems that the only way out of this circularity is to take the meanings of the words into account. After all, when people speak, they choose words to express their ideas; if people are choosing to use antonyms together in the same sentence, it is because they intend to convey a contrast in meaning and they are choosing words which effectively convey that contrast. As Murphy and Andrew put it, "If antonymy is just a kind of lexical association, then the semantic component would be superfluous, whereas in fact it seems to be the crucial element" (Murphy and Andrew 1992, 4).
Murphy and Andrew's final criticism is that an increasing amount of the research done on word meanings suggests that "[S]emantic relations should be definable in terms of conceptual relations," but in the WordNet model, antonymy is a lexical association that is not based on conceptual relations.
Murphy and Andrew believe that word meanings are mentally represented as concepts and that semantic relations, including antonymy, can be "computed" by a language user as necessary. To test whether this in fact is true of antonymy, they conducted a few simple experiments making use of research on conceptual combination which shows that the meaning of an adjective depends to some extent on the noun it is modifying. As an example, they point out that the meaning of fresh is somewhat different in the phrases fresh shirt, fresh idea and fresh fish. If, as Gross, Fischer and Miller claim, antonymy is a relationship between word forms and not concepts, Murphy and Andrew say that fresh should have a single antonym, and this antonym should be the same regardless of the context in which fresh occurs. If, on the other hand, antonymy is a relation between concepts, then an adjective would be expected to have different antonyms in different contexts because the same adjective evokes different concepts (each with its own antonym) in different contexts.
Murphy and Andrew test this prediction by giving subjects two lists, one of adjectives in isolation and one of the same adjectives modifying nouns. They then asked the subjects to give the antonym of the adjective. For example, they were asked in the first part of the test to produce antonyms for fresh, cold, dry and so on, and in the second part, they were asked to give the antonym of the adjective in phrases such as fresh fish, fresh shirt, cold water, cold facts, etc. In the second part, each adjective occurred in two noun phrases, one which Murphy and Andrew felt would have the same antonym as the adjective in isolation and one which would probably be different. For example, they expected hot to be given as the antonym of cold in isolation, and they also expected hot to be given as the antonym of cold in the phrase cold water but not in the phrase cold facts.
The results matched their expectations quite well. They found that subjects generally did not give the same antonym for the same adjective in all three cases. They report, "Only half the time did subjects give the same opposite to an adjective when it was alone as when it was in a phrase" (Murphy and Andrew 1992, 12). They feel that this is lower than would be expected by the account of antonymy as a relation between word forms; since the same word form is used in all cases, that account would predict a match rate of close to 100%, much higher than the actual rate found by Murphy and Andrew.
Murphy and Andrew found similar rates of matching in another experiment in which the subjects were asked to give synonyms of adjectives alone and in context. They argue that these results show that antonymy and synonymy are similar types of relations and are not structurally different as in the WordNet model.
In their discussion, Murphy and Andrew say that although some synonyms and antonyms may be "pre-stored" in the mental lexicon as a result of associations that arise from frequent co-occurrence, the relations of synonymy and antonymy are basically conceptual in nature and so they can also be figured out when necessary. They say:
Synonyms can be computed via conceptual similarity--they do not have to be pre-stored. Antonyms for a given word can likewise be produced by searching the space of semantically related words...they can be generated by choosing words with similar meanings and searching for one that differs only in one dimension...(Murphy and Andrew 1992, 18)
The significance of Murphy and Andrew's study for my research is that it offers good reasons to reject the claim of Miller and his colleagues that antonymy is simply an association between particular word forms, and it encourages us to look for a semantically based explanation for the question of why speakers choose to use two particular words together so often.
Although Justeson and Katz conclude that antonymy involves a link between two specific words, just as Miller and his colleagues claimed, they also say that a semantic component is necessary to antonymy:
We conclude that antonyms are those semantically opposed words that are conjoined and often opposed to one another at relatively high rates in sentences by substitution for one another in otherwise essentially identical (or parallel) phrases (italics mine). (Justeson and Katz 1992)
Justeson and Katz reached these conclusions after investigating the co-occurrence patterns of many pairs of antonyms, first in the Brown corpus (useful because it was tagged) and then in a larger, untagged corpus of 25,000,000 words. The larger corpus was used to check patterns seen in the smaller corpus but which were not statistically significant because some of the adjectives did not occur very frequently.
They began by looking at at the occurrences of the antonyms studied by Deese (listed in (4) above). Of the 35 pairs they looked at,5 30 pairs occurred together in the Brown corpus in the same sentence at least once; if the co-occurrence was simply random, Justeson and Katz argue, they would have expected only about 9 pairs to co-occur.6 They say that a more stable and relevant measure of the strength of the association between the antonyms is in terms of rate, defined as "the conditional probability that the more frequent of the antonyms occurs in a sentence given that the less frequent does so."7 On average, the antonym pairs from Deese's list occurred together at a rate of once in every 14.7 opportunities.
Next, Justeson and Katz measured the co-occurrences of antonyms on a new list of 22 frequently occurring adjectives, which included pairs such as absent/present, ancient/modern and beautiful/ugly.8 Again, they found that as a group, these antonyms co-occurred much more frequently than expected by chance. Out of the 22 pairs, 14 occurred at least once in the Brown corpus, and the overall rate of co-occurrence was once every 18.2 opportunities.
Even though most of the adjective pairs Justeson and Katz examined were found to co-occur in the Brown corpus, there were several that did not, presumably because of the small size of the corpus. For example, the pair deep/shallow did not co-occur, but deep occurred 84 times and shallow only 14 times, so there were in fact only 14 possible opportunities for the two to co-occur. Therefore Justeson and Katz checked for co-occurrence in a larger untagged corpus of 25 million words. In the larger corpus, they found that all of the antonym pairs on both lists co-occurred at relatively high rates, e.g. shallow and deep co-occurred at a rate of one out of every 26.5 sentences.
Using the large corpus, Justeson and Katz also examined the co-occurrence patterns of 346 antonym pairs in which one of the words was morphologically derived from the other, e.g., rational/irrational and contributory and non-contributory. They say that overall, the adjectives in these pairs occurred so infrequently that it was not possible to compare the actual and predicted co-occurrence rates of individual pairs, but they were able to measure the co-occurrence rates for the class as a whole. They report, "[T]he seventy-four observed co-occurrences represent a highly significant excess over the 2.1 expected by chance, yielding an overall co-occurrence rate of once every 18.2 opportunities."
Justeson and Katz say that the co-occurrence rates of the frequent antonyms are high enough to create a "training effect" which causes the antonyms to be associated in the mind; in other words, they believe that the clang effect, the strong association described by Deese and later by Miller and his associates, comes about because people learn from experience which antonyms are used together. This training effect is strengthened by the fact that when the antonyms co-occur, they usually do so in a syntactic frame that highlights the contrast in meaning. For example, of the 237 cases of co-occurrences of antonyms from Deese's list, 58 cases are of the form adjective-conjunction-adjective, as in this example: That was one reason she did not look forward to Cathy's visit, short or long. In another 49 cases, the antonyms occur in noun phrases that are identical except for the adjective, e.g., Under normal circumstances, he had a certain bright-eyed all-American charm, with great appeal for young ladies, old ladies and dogs.
Justeson and Katz also believe that the training effect of co-occurrence can explain why speakers have a hard time deciding whether a particular pair of words are antonyms or not. They say:
[I]t is our experience that all uncertain cases involve a rather clear semantic contrast; accordingly, the variation in strength of antonymy must be ascribed mainly to the lexical criterion [that is, to the association of word forms]. We suggest that such cases typically involve too little co-occurrence via phrasal substitution, at least in the experience of the person who is unsure about antonymy judgments. (Justeson and Katz 1992)
In other words, speakers have strong intuitions about antonym pairs that they frequently encounter, but when they are asked to judge whether two less frequently occurring words are antonyms or not, they do not have such strong intuitions. Justeson and Katz give the example of sick/well. These two words show a clear contrast in meaning, but sick also contrasts with healthy and well also contrasts with ill, so semantic criteria alone are not enough to determine an antonym. If a speaker has enough exposure to sick occurring in the same sentence with well, she will quickly identify them as antonyms, but if not, she may not be able to make a judgment about them. If Justeson and Katz are right in this regard, then it seems that co-occurrence goes a long way toward explaining why antonymy seems to be a "gradient phenomenon" (their words), but unfortunately, no one seems to have yet tested this hypothesis by checking the co-occurrence rates of pairs such as sick/well to see if they are really significantly lower than the co-occurrence rates for more easily recognized antonym pairs.
In an earlier paper describing some of the same research, Justeson and Katz (1991) say that the lexical association learned through co-occurrence is enough to define antonymy, but in this paper, they step back from that claim and admit that some kind of semantic criteria is required too. They point out (as Murphy and Andrew 1992 also did) that antonyms are not the only kinds of words which regularly co-occur. They give several examples of other sets of co-occurring words, including the pair mental and physical and the triplet social, political and economic. Justeson and Katz suggest that the difference between these types of co-occurring words and antonyms is that, "Whereas antonyms oppose extreme values of a single dimension, these adjectives designate dimensions, and it is the dimensions themselves that stand in opposition." A semantic criteria must therefore be involved in antonymy in order for language users to be able to distinguish antonymic opposition from other kinds of semantic contrasts.
To summarize, like Charles and Miller, Justeson and Katz believe that co-occurrence in the same sentence leads language learners to associate antonyms in semantic memory. Unlike Charles and Miller, however, they believe that co-occurrence alone is not enough to explain the association; in particular, they pay attention to the syntactic frames in which the antonyms often occur, speculating that these frames draw attention to the antonyms and thus aid the association. Finally, they say that semantics must also be involved to some extent because speakers can distinguish antonyms from other kinds of contrasting words which also co-occur frequently. However, as always, there are some unanswered questions. As was shown earlier, Charles and Miller do not explain why speakers chose to use antonyms together so often in the same sentences. Justeson and Katz provide a clue in their observation of the commonly used syntactic frames, but they do not follow it up, so I am left wondering what is so special about these syntactic frames and why speakers use them. Fellbaum (1995) considers this question and comes up with some reasonable explanations which are discussed in the next section.
[D]oes the associative effect of antonymy transcend the borders of syntactic categories? If so, then there is nothing special about antonymous adjectives, other than that antonymy is more pervasive among adjectives; rather, there is something special about antonymous concepts, no matter in what form these concepts are lexicalized. (Fellbaum 1995)
In other words, she suggests, co-occurrence may not be limited to adjectives and antonymy may in fact reflect an association between antonymous concepts rather than an association between words forms.
Fellbaum began to investigate this by testing co-occurrences among verbs and nouns in the Brown corpus. (Like many others, she finds although the Brown corpus is smaller than she would like, the fact that it is tagged makes it convenient). She chose three pairs of concepts to study, lose/gain, start/finish, and increase/decrease. Each of these concepts can be expressed as either verbs or nouns.9 Counting up the actual co-occurrences she found that although the overall number was small, it was still higher than would be expected by chance.10
Fellbaum then expanded the study to include several more concept pairs; this time, she focused on concepts that were expressed by adjectives and/or adverbs in addition to nouns and verbs, e.g., the concept pair dark and light, expressed by dark, darken, darkness, light (adj), light (v) and light (n). She found many examples of co-occurrences across syntactic class boundaries. For example, the adjective dark co-occurred not only with the adjective light, but also with the verb and the noun forms.
Fellbaum says that the results of her study argue strongly against the view of antonym learning proposed by Justeson and Katz, that antonyms are learned through a "training effect" which results from exposure to frequent co-occurrence of words in a particular syntactic frame. Fellbaum shows that co-occurrence is not limited to adjectives, and that words of one syntactic class often co-occur with semantically contrasting words from other syntactic classes. For example, she found that the adjective wet occurred with the verb dry as well as with the adjective dry. 11 When the co-occurrences cross word class boundaries in this way, they do not occur in the kinds of syntactic frames that Justeson and Katz described. Therefore, she says, the question remains, "In the face of the demonstrated absence of syntactic clues, how does the child recognize semantically opposed words?" Fellbaum does not have an answer, but she believes that however children learn semantic relations such as antonymy, co-occurrence is not enough to explain it.
Fellbaum then goes on to consider the question of why speakers frequently refer to two opposed concepts in the same sentence, making some suggestions for future study. She notes that many of the semantic frames in which antonyms occur can accommodate nouns and verbs as well as adjectives; these include the ones listed below in (4).
(4) Some common syntactic frames of co-occurring antonymsFellbaum points out,
- (Both) x and y x as well as y
- x and y alike Neither x or y
- (Either) x or y now x, now y
- from x, to y
When antonyms occur in these frames, they usually constitute the most salient points at either end of a continuous scale, which expresses an attribute. Referring to the salient antonymic values of that attribute can have the effect of denoting the entire range of values, even if the antonyms may not be endpoints of the scale. (Fellbaum 1995, 295)
Thus Fellbaum is arguing that speakers use antonyms together in a sentence in order to achieve a particular rhetorical effect, that of efficiently indicating a range of possible values.
Fellbaum mentions other rhetorical effects that can be achieved by using antonyms together. One is emphasis through redundancy, using phrases such as "not x but y", "instead of x, y" and "y, not x". Humor can also be effectively achieved through using antonyms together. As she says, "Strong effects can be achieved by juxtaposing complementaries, which are incompatible," as in this example from the Brown Corpus: How easily he could hate the lovable Irish (Fellbaum 1995, 296).
Finally, Fellbaum notes that it is natural to use antonyms together when describing actions and events that involve a change of state. These kinds of actions and events are very common in people's experiences and so are also common topics of communication. She says,
This is reflected in the lexicon, which contains many concepts denoting physical, temporal, emotional, and other changes.12 Explicit reference to one state sometimes implies the opposite or reverse state; for example, opening something presupposes that it was closed; drying something implies that it is wet. Such presuppositions are frequently overtly expressed, resulting in the co-occurrence of semantically opposed words. Other sentences explicitly refer to a change from state A to state B (Fellbaum 1995, 297).
Fellbaum gives several examples of this from the Brown corpus, including the two below.
(5)After being closed for seven months, the Garden of the Gods club will have its gala summer opening Saturday, June 3.
Pass the iron rations please, and light another candle because it's getting dark down here...
By looking at the meanings of the syntactic frames in which antonyms frequently occur together, I think Fellbaum provides a very likely explanation for the co-occurrence of opposites. People are not using opposites together as a kind of reflex simply because they have heard other people use them together--they use them together because they are a very effective way of conveying a meaning or creating a rhetorical effect.
Mettinger (1994) provides further support. He identifies several frequently occurring syntactic frames and discusses their function in texts, providing many examples from a corpus of modern novels.13 For example, he says that the syntactic frame X and Y has two main functions; one is to indicate "the simultaneous validity of X, Y" in phrases such as Johnson was always well up in arrivals and departures and ...life and death are the affair of the good God. A second function is to indicate "confrontation" in phrases such as the old wife and the new wife (Mettinger 1994, 47).
17Big occurs 316 times, little 273 times, large 347 times and small 504 times.
1Big and little occur together in 12 sentences, but would be expect to occur together in 1.6 if they were occurring independently. Large and small occur together in 26 sentences (3.2 expected by chance), large and little occur together in only 3 sentences (1.7 expected expected by chance), and big and small occur together in only 4 sentences (2.9 expected by chance). Charles and Miller do not discuss the fact that some English speakers do in fact pair big with small as antonyms, and that big/small sounds much better than large/little, even though neither of these pairs co-occur very often in the Brown corpus.
2In sections 1.5.3 and 1.5.4 below, a partial explanation will be discussed: when antonyms occur together in the same sentence, they usually are found in one of a set of particular syntactic frames that emphasize the contrast in meaning. Noun-verb pairs such as food/eat and noun-noun pairs such as dentist/teeth do not occur in these frames.
3This paper summarizes and extends earlier work described in Justeson and and Katz (1991).
4Four of the original pairs on Deese's list were eliminated from the study because one or both of the members were not tagged as adjectives in the Brown corpus. The four pairs are; alone/together, few/many, first/last and married/single.
5Justeson and Katz give actual and predicted co-occurrence rates for each individual pair, but for some of the pairs, the actual and predicted frequencies are so low that no conclusions can be drawn. For example, the pair heavy/light would be predicted by chance to co-occur in the Brown corpus 0.11929 times, but it actually occurs once. Since it is impossible for something to occur 0.1 times, it is hard to interpret this figure. However, for other individual pairs, the figures are more meaningful. For example, new and old were predicted to occur 10.40936 times by chance and actually co-occurred 28 times.
6For example, large occurs 347 times in the Brown corpus and small occurs 504 times, so there are potentially 347 opportunities for large and small to occur in the same sentence (assuming that large does not occur in any sentence twice.) They actually occur together in 26 sentences, so the rate is one out of every 13.3 opportunities.
7In the previous study, Justeson and Katz (1991) described how they came up with this list. First, they made a list of all the adjectives that occurred frequently in the Brown corpus but were not on Deese's list. Then they asked a lexicographer, a linguist, and an elementary school teacher to form pairs of antonyms from these adjectives.
8In the case of lose, the noun takes a slightly different shape, loss, but in the other cases the morphological shape of noun and verb are the same.
9For example, lose and gain(v) occurred together in 5 sentences when only 0.384 would be expected by chance, and loss and gain (n) occurred 4 times, with only 0.14 expected.
10She says that "the adjective wet occurs as often with the verb dry as with its antonymous adjective dry," but since there were only two examples of each in the Brown corpus, "as often" seems a little strong to me. Here is one of the two examples: She leaned unconcerned against the broken porch fence, brushing and drying her wet, gilded hair in the sun.
11She has a reference here to: Miller, G.A. and C. Fellbaum. 1991. Semantic networks of English. Cognition 41: 187-229.
12Mettinger's study of antonymy is quite interesting, but he does not deal much with the issues that concern me in this dissertation. His main purpose is to examine the various types of dimensions (e.g. scalar, the type of dimension found with gradable antonyms, and digital, the type found with complementary opposites) using a large number of pairs of opposites.