We argue that the pictorial nature of certain constructions in signs and in gestures explains surprising properties of their syntax. In several sign languages, the standard word order (e.g. SVO) gets turned into SOV (with preverbal arguments) when the predicate is a classifier predicate, a distinguished construction with highly iconic properties (e.g. Pavlič 2016). In silent gestures, subjects also prefer an SOV order in extensional constructions, irrespective of the word order of the language they speak (Goldin-Meadow et al. 2008). But in silent gestures and in Brazilian Sign Language (Libras), intensional constructions can override these SOV preferences, yielding SVO instead (Schouwstra and de Swart 2014, Napoli et al. 2017. This distinction was argued to be due to iconicity: arguments are expressed before the verb if they correspond to entities that are present before the action, otherwise they follow the verb. While agreeing with this intuition, we propose that the extensional/intensional distinction is neither empirically nor theoretically appropriate. In new data from American Sign Language (ASL), we replicate the distinction among extensional classifier predicates: for x ate up the ball, the ball is typically seen before the eating and a preposed object is preferred; but for x spit out the ball, the ball is typically seen after the spitting and a postposed object is preferred, although both eat up and spit out are used extensionally. We extend this finding to data involving pro-speech (= speech-replacing) gestures embedded in French sentences. We argue for a Visibility Generalization according to which arguments appear before the verb if their denotations are typically visible before the action, and we develop a new formal account within a pictorial semantics for visual animations (inspired by Greenberg and Abusch). It derives the observed word order preferences, it explains how the semantics of classifier predicates combines iconic and conventional properties, and it makes a more general point: sign language semantics combines logical semantics with pictorial semantics.