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Everybody knows that subject person indexing (“subject agreement”) derives from earlier personal pronouns which were reduced and came to be used alongside full nominals, which were originally in a special topic position (Givón 1976):(1) The boy, he came late. &#62; The boy he-came late.This explains two observations: (1) subject person indexes often have shapes that are very similar to the shapes of independent person pronouns, and (2) in many (in fact most) languages, subject person indexes can be used not only together with full nominals in subject position, but also on their own with anaphoric function. Thus, Italian allows not only (2a), which is like English, but also (2b), where the subject person index -e still seems to function like English he.(2a) Il ragazzo vien-e. [the boy come-3SG] ‘The boy comes.’(2b) Vien-e[come-3SG] ‘He comes.’This has often been cited as a prime example of grammaticalization (e.g. van Gelderen 2011, among many others).We also observe something very similar with object indexing, e.g. in Spanish, where the object person index sometimes cooccurs with an object nominal, as in (3a), but can also be used alone.(3a) Lo=vi a él.[3SG.M.OBJ=I.saw ACC him] ‘I saw HIM.’(3b) Lo=vi.[3SG.M.OBJ=I.saw] ‘I saw him.’Can this also be subsumed under grammaticalization? A very interesting recent paper by Haig (2018)  argues that things are not so simple. Subject person indexing and object person indexing work rather differently in the world’s languages. For one thing, languages are much more likely to show subject person indexing, and Moravcsik (1974: 27) had even claimed that a language with object indexing also has subject indexing. As shown by Siewierska’s (2005) WALS map, languages with only subject indexing (“person marking of the A argument”) are indeed much more common than languages with only object indexing, though she also documents quite a few of the latter type.More intriguingly, object indexing seems to tend to differ from subject indexing in two ways:First, object indexes seem to be pro-indexes (in complementary distribution with object nominals) in very many cases, rather than cross-indexes (cooccuring with object nominals, as in (3a)). Thus, a Persian object clitic cannot occur with an object nominal (Haig 2018: 795), unlike a subject suffix (which works like Italian).(4) ne-mibin-am=aš (*dočarxe) [NEG-see-1SG=3SG.OBJ] ‘I don’t see it / *I don’t see the bike.’(There is not a lot of research on the extent to which subject and object indexes can be cross-indexes or are only used as pro-indexes, but my sense is that Haig is right.)Second, object indexing is very often differential in the sense that it occurs only under specific conditions, e.g. only when the object is topical, or definite, or animate, or is a personal pronoun (as in (3a) from Spanish above), i.e. when it is high in referential prominence. This was also observed as early as in 1974 by Moravcsik (cf. her universals 4 and 5). Since Iemmolo (2011), some people have used the term differential object indexing for such situations. Subject indexing need not be uniform either (and is sometimes omitted when the subject is not high in referential prominence), but such partial subject indexing seems much less common than partial object indexing.Thus, it appears that object indexing tends to be more limited in two ways: In that it is often pro-indexing, and in that it is often differential.Now Haig (2018) points out that the idea of inexorable grammaticalization pathways that has come to be very prominent since the 1990s does not explain that object indexing is more limited than subject indexing. After all, the first part of the grammaticalization is widely found with objects as well: Full object pronouns get shortened and are bound to verbs, just as happens to subject pronouns. So it seems that object indexing “wants to be partial” – in other words, that partial object indexing is an “attractor state” (see also Bybee &#38; Beckner (2015) on “attractor dynamics”). This is a concept that has not been part of classical grammaticalization studies, which have emphasized the idea that grammaticalization is source-determined, or that there are a limited number of pathways (path-determined). The notion of an attractor state would seem to be more in line with the idea of functional adaptation (and result-determined or adaptive changes, as discussed in an earlier post).One very nice piece of confirmation for this idea is a set of diachronic changes from Middle Iranic to Modern Iranic languages, especially Central Kurdish: The Middle Iranic oblique clitics got used object clitics, but stayed pro-indexes, while when used as subject clitics (of transitive clauses in the past tense, in a kind of ergative pattern), these same forms became cross-indexes, thus apparently completing the grammaticalization. Now very intriguingly, the earlier object person suffixes (deriving from subject markers on a copula verb) became object clitics, and they changed from cross-indexes to pro-indexes in Central Kurdish – clearly a case of degrammaticalization! This would be very surprising, but the idea of an attractor state (meaning that object indexes don’t “want” to be like subject indexes, even if they started out as subject markers) makes us feel that we understand this curious development better.The “attractor state” story would be even nicer if we had a good explanation for why it would be better for object indexes to behave differently from subject indexes. Haig invokes the idea that while objects may differ in number and gender, they hardly ever differ in person – in most texts, 90% or more of all objects are third person. Thus, we can understand that person indexing is more useful for subjects.I did not find this explanation fully convincing, because object person indexing is very widespread (it is found in 57% of Siewierska’s languages, 217 out of 378) – if the explanation were correct, one would expect that objects are primarily reflected in number or gender marking on verbs, not in person marking.What we find instead, according to Haig (and I share his impressions), is that object person indexing tends to be partial – pro-indexing rather than cross-indexing, and often conditioned by referential prominence (“differential object indexing”). So what is different from subject indexing is primarily the way in which third-person objects are expressed. Maybe this can be explained by observing that objects are more diverse than subjects: Whereas subjects strongly tend to be definite, animate, and given (and thus rarely expressed by full nominals), objects are a more diverse bunch: they may be definite or indefinite, person-forms or full nominals, animate or inanimate. Thus, differential coding may be more useful for objects than for subjects. (Note also that the same is true for object flagging, which is very often differential.)ReferencesGivón, Talmy. 1976. Topic, pronoun and grammatical agreement. In Charles N. Li (ed.), Subject and topic. New York: Academic Press.Haig, Geoffrey. 2018. The grammaticalization of object pronouns: Why differential object indexing is an attractor state. Linguistics 56(4). 781–818. doi:10.1515/ling-2018-0011.Iemmolo, Giorgio. 2011. Towards a typological study of differential object marking and differential object indexation. University of Pavia PhD dissertation.Moravcsik, Edith A. 1974. Object-verb agreement. Working Papers in Language Universals 15. 25–140. doi:http://doi.org/10.5281/zenodo.1423196.Siewierska, Anna. 2005. Verbal person marking. In Martin Haspelmath, Matthew S. Dryer, David Gil &#38; Bernard Comrie (eds.), The world atlas of language structures. Oxford: Oxford University Press. (http://wals.info/feature/102A).van Gelderen, Elly . 2011. The grammaticalization of agreement. In Heiko Narrog &#38; Bernd Heine (eds.), The Oxford handbook of grammaticalization. Oxford: Oxford University Press. 10.1093/oxfordhb/9780199586783.013.0039