Chapter 5 analyses the body-decoration inference about Neanderthal language. This inference includes the following three inferential steps, depicted by the arrows: Blocks of manganese dioxide yielding black pigment were associated with Neanderthal ocupants of sites S1,…,Sn → This pigment was used by these Neanderthals to decorate their bodies → These body decorations had a symbolic function for these Neanderthals → These Neanderthals had language. [Sites S1,…,Sn include Pech d l'Aze I and Pech de l'Aze IV in southern France.] Chapter 5 goes into doubts about the first inferential step of this inference. The main one is that it has not been excluded that the Neanderthals concerned used black pigment for an utilitarian instead of a symbolic function. Black pigment is known to have been used ethnographically and prehistorically for many utilitarian functions. And, importantly, there is experimental evidence that the Neanderthals at Pech de l'Aze I used manganese dioxide for fire-making. Until seccessfully challenged, this finding represents a good reason for doubting the soundness of the second inferential step. This leaves the second and third inferential steps ungrounded.