Beyond the obvious technical difficulties, human attempts to communicate with hypothetical Extra-Terrestrial Intelligences also present a number of philosophical puzzles. After all, an alien intelligence is likely the closest thing to a Wittgensteinian lion humanity could ever encounter. In this paper I advance a new challenge for the feasibility of communication with extra-terrestrials. The problem I raise is a practical problem that falls out of the history and philosophy of mathematics and the implementation of METI projects—specifically, the semiprime self-decryption schema (...) of the Drake Pictures message strategy. The Drake Pictures strategy presumes that aliens share the concept ‘prime number’ with us, as understanding that concept is necessary to decrypt our message. However, if the concept ‘prime number’ exhibited open texture at any point in its history, it could have developed in a different direction than it did in our history. If that is so, an alien could have the concept ‘prime number’ and still not be capable of decrypting our messages. I argue that this new problem is more trenchant than previous arguments in both the philosophy and SETI literature, such as applications of the aforementioned Lion argument and other concerns about the possibility of long-range communication without the assumption of shared concepts. (shrink)