This paper offers two reasons why students frequently struggle to read Venn diagrams and discusses the semantic knowledge requisite for the appropriate perceptual experience of them. The first reason students struggle is that Venn diagrams require one to intentionally effect a certain figure-background organization that runs counter to the tendency of perceptual organization which attends to similarity in line over similarity in form. The second reason is that, while Venn diagrams rely on Boolean truth conditions to determine shading patterns, Venn (...) diagrams are not capable of literally representing Boolean truth conditions. It is therefore not something within the diagram that tells us what to attend to perceptually, but rather knowledge of the semantic relation between Boolean truth conditions and Venn diagrams. After explaining the semantics of each of these and the discrepancy between them, the author argues that Venn diagrams are nevertheless capable of metaphorically representing Boolean truth conditions. This metaphorical representation is addressed in detail and the author concludes that this form of representation does not tell against teaching Venn diagrams as a method for testing validity, especially since their legibility is greatly increased with the semantic knowledge expounded here. (shrink)