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1 1 This chapter was written as part of the international research project MultiGender at the Centre for Advanced Study at the Norwegian Academy of Science and Letters in Oslo during the academic year 2019–2020, where both authors were fellows. We are grateful to an anonymous reviewer for very helpful comments on a previous version, and to Nicholas Allott for very detailed feedback. AL 554/8‐1 (Alexiadou) is also hereby acknowledged.

2 2 Chomsky (1965, 4) emphasizes the importance of developing explicit theories. In doing so, he contrasts generative grammar with traditional grammars. The latter provide a lot of structural information, but they do not offer mechanisms that can account for the “regular and productive syntactic processes.” Such mechanisms are implicit as these traditional grammars presuppose that speakers and listeners have such knowledge. That is, speakers know where to put the finite verb in a yes/no question, but an explicit theory should explain the rule that governs how the finite verb can in Can flying eagles swim? becomes the first constituent. Importantly, trying to be explicit also raises new questions, such as why Can eagles that fly swim? is a question about the swimming ability of flying eagles, not the other way around. Such new questions have continuously led to novel generalizations about languages and language in general.

3 3 Since then, two additional questions have also been put on the agenda (cf. Boeckx 2006):(i)How is that knowledge implemented in the brain?How did that knowledge emerge in the species?We will not discuss the first of these further here, but see Zaccarella and Trettenbein (Chapter 20 of this volume). We briefly discuss the latter in Section 3.5.

4 4 It is important to note that “knowledge” incorporated into mental systems need not be true. However, when it comes to each person's internal grammar, the question of truth does not really make sense. Furthermore, it is unclear whether knowledge needs to be believed. For sure, it does not have to be consciously available or integrated with general reasoning. Lastly, it does not have to be stored and retreivable (i.e. represented in the philosophers” sense): It may be simply embodied/instantiated by the workings of a particular system (here the I‐language). See Allott and Smith (Chapter 34 of this volume).

5 5 Note that in principle the linguistic theory should help explain any linguistic behavior, not just intuitions. See Gross (Chapter 35 of this volume) for further discussion.

6 6 It should be pointed out that Hankamer (1973) argued that the constraint in question was universal, but given cross‐linguistic variability in sluicing, that cannot be the case.

7 7 In the early stages of transformational grammar (Chomsky 1965), it was postulated that an evaluation metric helps the learner decide which grammar, amongst different ones which can all provide structural descriptions for the available primary linguistic data (PLD), is the optimal one. In terms of the evaluation metric, the core grammar is an optimal system.

8 8 This should not be taken to suggest that Fodor was committed to language being either a peripheral system or uninvestigable. Essentially, Fodor took for granted that the language faculty was essentially a database. See Allott and Smith (Chapter 34) for much discussion.

9 9 In GB, a fundamental difference is introduced between case and Case, where the latter denotes what is called abstract Case; a syntactic Case feature which is not phonologically realized. An example would be Sara and John in (i), Sara is assumed to have abstract nominative Case whereas John has abstract accusative Case – despite there being no morphological marking of case.Sara loves John.Abstract Case was first proposed by Vergnaud (1977) and further developed by Chomsky (1981). Note also that the literature typically distinguishes between Case assignment and Case checking, a difference we set aside here, but see Lasnik (2008, 24) for an overview and a historical perspective.

10 10 Evidence that this movement is necessary comes from facts about where adverbs and negation are placed. Semantically they modify the entire verb phrase, so they are inserted above the VP in the structure. Since the subject needs to precede the adverb, not follow it, as it would have if it did not move to SpecTP.(i)She often likes him.She does not like him.

11 11 Implementations differ in terms of how this is done technically. Chomsky (1993) proposed covert movement at LF, whereas others have argued that there is displacement overtly of the object, but that the verb moves even higher (so as to precede the object on the surface) (Postal 1974, Lasnik and Saito 1991, Koizumi 1995, and much later work).

12 12 Setting aside higher functional material such as tense, and also any internal projection involving they and cake.

13 13 Rothman (2009b, 156) defines a heritage language and a heritage speaker as follows:A language qualifies as a heritage language if it is a language spoken at home or otherwise readily available to young children, and crucially this language is not a dominant language of the larger (national) society. […] [A]n individual qualifies as a heritage speaker if and only if he or she has some command of the heritage language acquired naturalistically […] although it is equally expected that such competence will differ from that of the native monolinguals of comparable age.