Even though many studies in linguistics rely heavily on introspective insights, it is sometimes claimed that such first-person methods lack what Bert Peeters calls “neurocognitive depth” and, more generally, that they are inherently unscientific. While Peeters admits that introspection is a valuable source of data, he also suggests that the real measure a linguistic theory is the extent to which the data inform or are compatible with neurological theories. However, there are at least two serious challenges that every neurological theory of mental phenomena will inevitably face: the so-called hard problem of consciousness as defined by David Chalmers and the multiple realizability thesis proposed originally by Hilary Putnam.I will argue that unless the hard problem of consciousness and the multiple realizability thesis are confronted and dealt with (at least provisionally), every neurolinguistic theory of this sort is bound to be incomplete and impoverished. In other words, unless the two challenges are overcome, third-person methods will have to be supplemented by first-person methods in order to provide a complete picture of a linguistic phenomenon under investigation. A case study examined in the article is a research program developed by George Lakoff as the Neural Theory of Metaphor, which I consider a paradigmatic attempt to relate the data from introspection to neuroscientific findings.