Ask most any cognitive scientist working today if a digital computational system could develop aesthetic sensibility and you will likely receive the optimistic reply that this remains an open empirical question. However, I attempt to show, while drawing upon the later Wittgenstein, that the correct answer is in fact available. And it is a negative a priori. It would seem, for example, that recent computational successes in textual attribution, most notably those of Donald Foster (famed finder of Ted Kazinski a.k.a. “the Unibomber”) speak favorably of the digital model's capacity to overcome the “aspect blindness” handicap in this domain. I argue however that such results are only achievable when rigid input-to-output parameters are given, and that this element is precisely what is absent in standard examples of aesthetic judgment. I thus conclude that while the connectionist model anticipated by Turing may provide the best approach for the AI project, its capacity for meeting its own sufficiency requirements is necessarily crippled by its inability to share in what can be generally referred to as the collective engagements of human solidarity.