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Martin Haspelmath: Edith, we have a long history of interacting, starting with the first course on universals that I attended at the University of Vienna (back in 1982, as I noted here). So I’m really glad that you took an interest in some of my recent work on singulative marking (Haspelmath &#38; Karjus 2017).Edith Moravcsik: I was reminded of it by the recent LINGTYP discussion about singulatives. I re-read the your 2017 paper on the topic (Haspelmath &#38; Karjus) and also your relevant 2018 blogpost on countabilities, and I wanted to share some thoughts with you. First of all, I would say that in some languages, the singulative is really an individualizer. This is the case if the noun with the singular affix can also be pluralized. An example is Welsh ‘feather” as cited in your paper (2017: 1221); also Russian gorox, goroš-ina, goroš-iny mentioned by Östen Dahl in the Lingtyp thread. If the marker does not occur in the plural form of the noun, it is a true singulative.Martin: Yes, this is a point about terminology that I understand. But as we say in that passage of the 2017 paper: We disregard the difference between individualizers that create new “lexemes” (and can thus have their own plural forms) and individualizers that can be easily thought of as singular-inflected forms (we call them all singulative markers). We want to focus on the commonalities and on the explanation of the patterns, and our idea is that the underlying causes are the same. Moreover, we don’t think that one can systematically distinguish between "inflected" forms and "derived forms". Linguists sometimes say that plural forms in some language are really derived forms, but they do not use consistent criteria. The difference betwen inflected forms and derived lexemes is irrelevant to the efficiency theory of asymmetric coding.Edith: The second point is the similarity between singulatives and classifiers (which was also mentioned in the Lingtyp discussion, by David Gil. This is borne out by Hungarian data. In Hungarian, certain nouns, when unmarked, are mass nouns or numerically-unspecified ones. When a particular quantity needs to be mentioned, classifiers are used.(a) víz ‘water,*egy víz  (egy ‘one’)egy csepp víz ‘a drop of water’ (csepp ‘drop’)(b) szőlő ‘grape’*egy szőlőegy szem szőlő ‘a grape’ (szem ‘eye’)(c) buza ‘wheat’*egy buzaegy szem buza ‘one grain of wheat’(d) káposzta ‘cabbage’*egy káposzta ‘one head of cabbage’egy fej káposzta ‘one head of cabbage’ (fej ‘head’)(e) haj ‘hair’*egy haj   egy szál haj ‘one hair’ (szál ‘thread’)As shown below, the classifier is optional if the objects are larger, such as cherries and plums, and it is ungrammatical if the objects are very large, such as a melon.(f) cseresznye ‘cherry’egy cseresznye ‘a cherry’egy szem cseresznye ‘a cherry’ (szem ‘eye’)(g) szilva ‘plum’egy szilva ‘a plum’egy szem szilva ‘a plum’(h) dinnye ‘melon’egy dinnye ‘a melon’*egy szem dinnyeMartin: Many thanks for sharing these observations on Hungarian. Yes, such measure nouns are interestingly similar to singulative markers and to individualizers more generally. There is a long tradition of treating such nouns as individualizing, and your examples show very nicely that the size of the granular element plays a role in the distribution of such nouns in Hungarian. This is expected if smaller-size elements occur more frequently as aggregates than larger-size elements. This is entirely plausible, of course. (Anna Wierzbicka had a beautiful 1985 paper on oats vs. wheat, where she focused on the semantics, but there is also an important frequency element here.)Edith: What is interesting is that the syntactic construction may in some cases alternate with a morphological one: classifiers may be compounded with the noun. Here, the syntactic classifier becomes a morphological individualizer. This is so if the nouns refer to very small units of a substance, such as a drop or a grain or a thread but not if the units are larger such as a cherry.(i) egy vízcsepp ‘a drop of water’egy szölöszem ‘a grape’egy buzaszem ‘a grain of wheat’egy hajszál ‘a hair’*egy cseresznyeszem ‘a cherry’*egy szilvaszem ‘a plum’Martin: Yes – so again, the exact morphosyntactic status does not really matter – what matters is that some extra marking is used for uniplex referents with nouns denoting aggregates like grapes, wheat or hair.Edith: Now some thoughts about cross-linguistic generalizations. The generalization that you and Karjus propose (your (14) on page 1228) is the following:“Universal frequency asymmetries (resulting in predictability asymmetries) explain universal form asymmetries, via universal diachronic tendencies.”Here I would like to make three points. First, it is important to note that in the hypothesis, frequencies are assumed to be universal not only across the languages of today but also historically. This is plausible perhaps but not certain and it needs to be stated. It is of course more difficult to test the historically uniform frequency claim since large corpora from five hundred or a thousand years ago – when the number-marking system of a language first solidified – may not be available.Martin: Yes, that is true. In general, my theory of universal asymmetric coding assumes that the frequency asymmetries are universal as well. And this means universal across families and continents, as well as universal across time. This may seem like an extraordinarily strong claim, but there are a fair number of grammatical phenomena where it is fairly clear that cultural differences are irrelevant to the frequencies. This applies not only to singular/plural, but also to present/future, to 2nd/3rd person, to allative/ablative, affirmative/negative, declarative/interrogative, and others. Linguists rarely talk about these very basic contrasts, but once you think about them, it should not be so astonishing that they are independent of cultures and asymmetric in the same way everwhere and at all times.Edith:  My second point: You say that frequency/meaning is sufficient for predicting asymmetries. Is it also necessary? Or, equivalently, can coding asymmetries in turn predict frequency/meaning asymmetries? If you find a noun mostly used in the plural, your generalization predicts that it will have a singulative. Does this also work in reverse? That is, if you find that a noun has a singulative, can you infer from this that it is mostly used in the plural?Martin: Yes, absolutely – in probabilistic terms. The predictions do not work at the level of individual words, but are meant to account for general tendencies. Of course, in most cases they will also be true for individual words, but the existence of exceptions is expected. What is predicted is that there should be a quantitative trend, in both directions.Edith: OK, so let us get to my third point, the most important one: Your generalization (14) covers languages like Welsh, but is contradicted by English and languages like it. For example, ‘feather’ in Welsh has a singulative due to the fact that it is a multiplex noun. But ‘feather’ in English does not have a singulative even though it is assumed to have the same meaning/frequency as the Welsh word. Thus, I cannot see that (14) can be said to have explanatory force. In order for a generalization to be an explanation, only true facts should follow from it (either in an absolute sense or probabilistically) and no incorrect ones. But this is not the case here: the predicted facts for English are incorrect. So it seems to me that the data on singulatives only allow for crosslinguistic statements of the existential kind but not for absolute universal ones. You can say this:“There are languages where in some instances, frequency is correlated with coding asymmetries and there are languages where this is not the case.”This observation is interesting; but it is not a language universal.Martin: Well, it’s an implicational universal: “IF a language has subclass-conditioned asymmetric coding, THEN it will be in the predicted direction.” Maybe the paper did not make this clear enough, but it’s a general feature of universals of asymmetric coding: Languages need not have subclass-conditioned coding – they may have plural marking throughout their noun lexicons, following the pattern of the numerically larger class (= singular-plurative nouns). As you have discussed in your own work (e.g. Moravcsik 2007; 2012), this is how implicational universals work: If the antecedent of the implication is true, then the consequent is true as well. So your restatement in existential terms is too weak: It would allow languages where asymmetric coding goes in the opposite direction. But we never find such languages. Languages are either uniform (with longer plural markers and shorter, or zero, marking of singular), or they are asymmetric in such a way that the aggregate nouns have overt singulars (singulatives) and zero plurals.Edith: OK, you are right: the existential statement is too weak since it allows for a correlation that is the reverse of what is found. Instead, as you said, an implicational universal is called for. You formulated it like this:“IF a language has subclass-conditioned asymmetric coding, THEN it will be in the predicted direction.”I had earlier thought about the following formulation:“If in a language, some nouns have a singulative marker, these nouns are more frequent in the plural than in the singular.”But since you say that marking and frequency are bidirectionally predictive, it should really say this:“If in a language, some nouns have a singulative marker, these nouns are more frequent in the plural than in the singular; and if in a language some nouns have a singulative marker and some nouns are more frequent in the plural, these will be the nouns that are marked for the singulative.”Martin: Yes, I agree. As we’re talking about probabilistic generalizations, I would put it like this:“In all languages, multiplex-prominent nouns (= those occurring more often in the plural than average) are more likely to have a singulative marker, and in all languages, singulative-marked nouns (=those that have a singulative marker when occurring in the singular) are more likely to occur more often in the plural in the plural than average (= to be multiplex-prominent).”Edith: I think this is indeed a very interesting generalization. What I am uncomfortable with is considering it to be explanatory, as you and Karjus suggest. If a generalization is to be taken as an explanation of certain facts, it would have to be the case that all known true facts follow from it and no untrue facts do. As you say on page 5 of the blogpost, individual languages that are exceptional would not invalidate the proposal nor would individual nouns that do not follow the prediction. If so, the question is: What would invalidate the claim? In other words, how is it an empirically testable proposal?Martin: To show that the claim is wrong, one would have to present a (reasonably representative) sample of the world’s languages in which the generalization does not hold. One may say that this is too difficult, but it is perfectly doable if one had the resources to get the relevant data for the languages. No further analytical steps are needed, so I feel that this sort of generalization is more testable than claims which can in principle be tested by a single language, but where one may always reanalyze recalcitrant data (as in generative linguistics with all its moving parts).Edith: Finally, about markedness: Your paper also discusses the difference between markedness theory and the frequency explanation (2017: 1218). But I don’t really see a contradiction between the two. In both approaches, the correlation of markedness symptoms (syntagmatic simplicity, paradigmatic complexity, frequency) is acknowledged. The difference is that while in the basic markedness approach, the three types of symptoms are viewed as on a par, in your approach, frequency is elevated to being a cause for the other symptoms. This is an important innovation but it does not really create a conflict between the two. There would be a conflict only if the basic markedness theory denied the causal role of frequency.Martin: Yes, if one sees “markedness theory” like this (what you call the “basic markedness approach”, Greenberg 1966), then there is no contradiction. You coedited a 1986 book on markedness (Moravcsik et al. 1986) that I learned a lot from, and in particular your opening chapter influenced my thinking a lot (and Bernard Comrie’s chapter in that old book provided the inspiration for a recent paper of mine on differential place marking). But on the one hand, “markedness theory” as just described by you makes a stronger claim: That “unmarked” values should be paradigmatically more complex. I do not know if this is generally true (though the examples in Greenberg 1966 are very suggestive). The claim has never been tested properly. And on the other hand, “markedness” is almost never treated in this way. “Markedness” is no longer a fashionable topic, but when people invoke it, they almost always suggest that the semantic asymmetry somehow causes the formal asymmetry (e.g. recently in work by Kiparsky and Dixon, as discussed here). And this is what I have been arguing against.&#160;