This work presents two theoretical challenges to Conceptual Metaphor Theory (CMT). The first argument shows CMT’s foundational _Conceptual Claim—_that abstract concepts are necessarily structured by concrete concepts—entails the blurring of the literal–figurative distinction, which calls into question the legitimacy of standard methods of metaphor identification used in CMT. The second argument aims at the _Linguistic Claim—_that conceptual metaphors are necessary for metaphorical language—by showing that conceptual metaphors are neither necessary nor sufficient for linguistic metaphors and that, therefore, the existence of (...) conceptual metaphors cannot be validly inferred from the presence of their linguistic counterparts. In light of the arguments put forward, the CMT theorist is forced to accept one of four options: (A) hold on to both the Conceptual Claim and Linguistic Claim, by adequately addressing problems presented here, (B) discard the Conceptual Claim and give up the theory, (C) discard both claims and give up the theory, or (D) accept the Conceptual Claim but reject the Linguistic Claim and abandon the methods of discovering conceptual metaphors through analysis of figurative language. I argue that the only tenable option is D. (shrink)