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A few months after their (2014) target article with comments from de Reuse, Dryer and me were published in the “Perspectives” section of Language, Henry Davis, Carrie Gillon and Lisa Matthewson have published their response (DGM 2015). Their original claim was that a UG-oriented approach is better suited to the discovery of linguistic diversity, in contrast to some of the claims made by Levinson &#38; Evans (2010). In particular, they stressed the need for systematic hypothesis-testing, which turned out to be uncontroversial.In my commentary (Haspelmath 2014b), I noted that the main difference between two types of approaches is not between “C-linguists” and “D-linguists” (a strange distinction that they adopt from Levinson &#38; Evans and continue to use in their response), but between linguists whose main goal is the discovery of UG (i.e. continuing the Chomskyan tradition) and linguists who want to chart all the existing diversity and eventually explain it in whatever way may be appropriate (i.e. continuing the Boasian and Greenbergian traditions).DGM (2015) explain that they continue to disagree with the Boasian/Greenbergian linguists (even though they acknowledge the more conciliatory tone of the replies by de Reuse, Dryer and Haspelmath). But I was very happy to note that with respect to my own commentary, they at least agree on the nature of the disagreements. This is a first step toward resolving the disagreements, so I’d like to comment on these points a bit further.A large number of theoretical linguists talk about “linguistic theory” as if there were only one way of doing it, so in my recent overview chapter on comparative syntax (Haspelmath 2014a) I contrasted two starkly different approaches: the restrictivist approach and the non-aprioristic approach. The former assumes that the features and categories of grammar are part of the innate UG, so that language description and language comparison are part of the same enterprise. This explains that in the original target article, DGM make no distinction between cross-linguistic comparison (as in the World Atlas of Language Structures, which they criticize) and language-specific generalizations, as discovered in original fieldwork. And in their response, they now confirm this: “there is no principled difference between descriptive and comparative fieldwork ... for us, as for generative linguists generally, fieldwork is certainly part of a cross-linguistic investigation” (p. e135-e136).In the non-aprioristic approach, as I described it, description is language-specific (using descriptive categories which may be unique to a language), while comparison makes use of special comparative concepts which may not be relevant to individual languages (see also Haspelmath 2010).The crucial argument that DGM (2015) are making in the response is that while they adopt categories from another language when doing fieldwork (or even categories postulated as universal), these categories are not adopted “as analyses about other languages, but only as initial hypotheses, which are often disproven” (p. e135)The mistake here is that categories cannot be disproven. The target article mentions a number of cases where claims about universals have been disproven by their work (e.g. the fact that Condition C of the binding theory is not always observed), but there is no way in which a category that is assumed as universal can be disproven. One can perhaps fail to find evidence in favour of a category (e.g. evidence in favour of a VP, or evidence in favour of binary branching), but if one assumes that all languages have binary branching and a VP, there is no problem. The resulting analysis may not be fully motivated by the language-specific phenomena, but this has never been stated as a requirement in generative linguistics.Non-apriorists, by contrast, are often uncomfortable with analyses that seem to be motivated primarily by comparison with some other, better-known language – for example, the idea that a language like Latin has subject agreement with a null subject pronoun in a sentence like venit ‘he is coming’ strikes me as eurocentric (cf. Haspelmath 2013). The null pronoun is not motivated by anything in Latin, only by the comparison with English and German (which are VERY unusual in requiring both a pronoun and a person marker on the verb). Since categories cannot be disproven, one cannot show that it is wrong to say that Latin has a null pronoun, but this is what Levinson &#38; Evans mean when they say that generative linguists take “off-the-shelf categories arising from specific grammatical traditions”, thus doing “procrustean violence” to the languages.Another example of this is the claim that Pacific Northwest languages have a noun-verb distinction just like English (§4.1 of the target article), despite earlier claims by Swadesh and others. Of course, one CAN describe these languages in this way, just as one CAN describe Latin with null pronouns and Hungarian with a VP. But since we are talking about categories, one can never disprove such analyses – they just do not look pretty to a non-apriorist. Perhaps Swadesh was too much focused on the amazing and exotic predicate-argument flexibility of these languages that he failed to see the subtle ways in which subclasses can be established within the unitary verb-noun category of these languages. And if these subclasses are semantically close to the English verbs and nouns, the temptation is great to say that the Pacific Northwest languages have verbs and nouns in the same way (similarly, Sandra Chung succumbed to the temptation of saying that Chamorro has verbs and nouns like English, as discussed elsewhere). Now it is certainly interesting that these subclasses have been found, and that they match the English classes, but since the class-defining properties are quite different in the two types of languages, one cannot really say that one has discovered the same categories. This is somewhat like saying that Germany has representatives of the universal Hindu-Muslim distinction just because there are two different religions with a tradition of fighting against each other (and where one religion emphasizes scripture and lacks pictures in its mosques, while the other religion worships a whole range of male and female deities with various attributes in its temples). Such a claim cannot be disproven, and it might not even be wrong, who knows.The larger moral of the basic point that categories cannot be disproven is that we should  focus more on claims that CAN be disproven, e.g. universals of the Greenbergian type (some of which have been disproven, cf. Dryer 1988). One such universal is Condition C, and DGM (2014) nicely showed that it does not hold exceptionlessly (though it may still hold with overwhelmingly greater than chance frequency). But in order to formulate testable universals, one needs categories that uncontroversially apply to all languages – i.e., categories such as VP or null pronouns cannot be part of testable claims. We thus need special comparative concepts, and this has been for me one of the main methodological lessons of the WALS and APiCS enterprises.ReferencesDavis, Henry, Carrie Gillon &#38; Lisa Matthewson. 2014. How to investigate linguistic diversity: Lessons from the Pacific Northwest. Language 90(4). e180–e226.Davis, Henry, Carrie Gillon &#38; Lisa Matthewson. 2015. Diversity driven but cognitively constrained: Boas meets Chomsky (Response to commentators). Language 91(3). e127–e143.Dryer, Matthew S. 1988. Object-verb order and adjective-noun order: Dispelling a myth. Lingua 74(2-3). 185–217.Haspelmath, Martin. 2010. Comparative concepts and descriptive categories in crosslinguistic studies. Language 86(3). 663–687.Haspelmath, Martin. 2013. Argument indexing: A conceptual framework for the syntax of bound person forms. In Dik Bakker &#38; Martin Haspelmath (eds.), Languages across boundaries: Studies in memory of Anna Siewierska, 197–226. Berlin: De Gruyter Mouton.Haspelmath, Martin. 2014. Comparative syntax. In Andrew Carnie, Yosuke Sato &#38; Dan Siddiqi (eds.), The Routledge handbook of syntax, 490–508. London: Routledge.Haspelmath, Martin. 2014b. Descriptive hypothesis testing is distinct from comparative hypothesis testing: Commentary on Davis, Gillon, and Matthewson. Language 90(4). e250–e257.Levinson, Stephen C. &#38; Nicholas Evans. 2010. Time for a sea-change in linguistics: Response to comments on “The myth of language universals.” Lingua 120(12). 2733–2758.