Chapter 4 elucidates various inferences about Neanderthal language drawn from so-called cave art attributed to Neanderthals. Skeletally, these inferences look as follows, arrows depicting inferential steps: The markings M1,…,Mn are found on the walls of the Iberian caves C1,…,Cn → These markings represent art made by Neanderthal occupants of the caves → This art had a symbolic function for these Neanderthals → These Neanderthals had language. The markings include a hashtag engraving, red disks and hand stencils, a red ladder-shaped sign and red painted mineral deposits. Serious concerns have been expressed about the soundness of these inferences. Two are fundamental. First, the empirical grounding of some are suspect: the dating of the markings is claimed to be inaccurate. This means that some markings may have been made by a modern human rather than a Neanderthal. Second, it has been pointed out, the meanings of the markings are a mystery. This implies that it is unwarranted to infer that these markings were symbols. They could have had a non-symbolic function, which would make the third inferential step ungrounded. Chapter 4 discusses these and other doubts at length.