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Complex spatial flags often consist of two or even three elements, of which typically one corresponds to the configuration (‘inside’, ‘on’, ‘under’, ‘next to’, etc.), and one to the direction (‘to’, ‘at’, ‘from’, ‘via’), as illustrated by English, Finnish and Lezgian below. These sorts of phenomena are the topic of an interesting typological paper by Lestrade, de Schepper and Zwarts (2011).(1) Englishfrom under the table(from = direction, under = configuration, table = locatum)(2) Finnishsien-ten pää-llemushroom-PL.GEN on-ALL‘onto the mushrooms’(3) Lezgianxürü-n win-elvillage-GEN above-SUPERESS‘(at) above the village’Lestrade et al. observe that the meaning can be described by the nested structure "[direction [ configuration [ground]]]", and that there are many cases where this is straightforwardly reflected in the formal structure of the complex spatial flag, such that the adposition expresses the configuration, and the adpositional case (allative in Finnish, superessive in Lezgian) expresses the direction outside of the adposition (following a postposition, or preceding a preposition, like from in English). There is also commonly a nominal case, i.e. the genitive on ‘mushrooms’ and ‘village’ in the above examples.Another frequent way of expressing spatial relations is by adpositions that collapse both meanings, such as bei ‘at, near’ in German, which is strictly limited to stationary (‘at’) uses (bei der Kirche ‘near the church’ can never be used with a goal or source meaning). In fact, in Lestrade et al.’s database of 35 languages, this is the most widespread pattern, found in almost all the languages.A rare type is represented by German (or rather Polish in their sample, but German works in the same way): With half a dozen prepositions, direction is expressed by the nominal case, rather than by a prepositional case:(4) Germanauf dem Tischon the.DAT table‘on the table’auf den Tischon the.ACC table‘onto the table’This pattern is puzzling for Lestrade et al., as it seems to go against the semantic structure, potentially violating the principle of compositionality. They seem to opt for an analysis in constructional terms, where a complex meaning is mapped to a complex form in a holistic way, rather than in the decompositional mode which the more straightforward patterns in (1)-(3) allow.But the fact that this way of linking form and meaning is possible (and has been widespread and robust in Slavic, Germanic, Latin and Greek) seems to indicate that its rarity is not due to any problem with compositionality. Conversely, the greater frequency of the Finnish pattern would not seem to be due to compositionality either (as Lestrade et al. propose). Compositionality is really an inviolable constraint, and one could at most have a preference for one-to-one matching of form elements and meaning elements. Instead, it seems that an alternative explanation is more likely: Finnish-type patterns are frequent because this is a very popular pathway for complex spatial flags to arise: Adpositions come from case-inflectable nouns which are combined with their possessed nouns in a standard way, as in other possessive constructions. Thus, Finnish sien-ten pää-lle in (2) originally meant ‘to the top of the mushrooms’. It seems that there is no need to invoke any kind of iconicity or one-to-one matching.As Lestrade et al. briefly note (citing Vincent 1999), the older Indo-European languages have a somewhat different pathway for complex spatial flags: These come from spatial adverbs in apposition to directional expressions. Thus, auf den Tisch ‘onto the table’ would originally have meant ‘upward, to the table’. If, as seems likely, this pathway is less commonly traveled, for whatever reason, then this might account for the rarity of the Indo-European pattern. (This shifts the explanation for the rarity further back, and it’s of course still possible that iconicity somehow has a role in disfavouring the rise of this pattern in other languages.)Be that as it may, perhaps the most important point of Lestrade et al.’s paper is that it is always configuration, but never direction, that is expressed by the adposition. We never find the opposite, i.e. direction expressed by an adposition, but configuration expressed by a case. Lestrade et al. attribute this to economy and grammaticalization, apparently equating grammaticalization with economy-induced shortening. It seems to me that they are right in linking this regularity to economy and frequency of use: Indeed, direction markers are more frequent than configuration markers, and are hence expected to be shorter, and thus to show up as “case affixes” rather than “adpositions”. However, I’m not so sure about “grammaticalization” – are short forms always short because they underwent a greater amount of shortening? It seems that more commonly, short forms are short because they were never lengthened, by renewal, replacement or accretion.Lestrade et al. limit their attention to “complex spatial PPs” which involve “case”, but it seems that their generalizations can be extended to complex flags of the type from under or on top of (as I already did above), because these behave quite analogously. Nothing really hinges on whether a short marker is a “case form” or an “adposition”. What matters is shortness of expression, as Lestrade et al. recognize.ReferencesLestrade, Sander, Kees de Schepper &#38; Joost Zwarts. 2011. The distribution of labor between adpositions and case within complex spatial PPs. STUF - Language Typology and Universals 64(3). 256–274. doi:10.1524/stuf.2011.0018.Vincent, Nigel. 1999. The evolution of c-structure: Prepositions and PPs from Indo-European to Romance. Linguistics 37(6). 1111–1153.