Abstract. We distill Penrose’s argument against the “artificial intelligence premiss”, and analyze its logical alternatives. We then clarify the different positions one can take in answer to the question raised by the argument, skirting the issue of introspection per se. 1 The Argument It follows that there are four sons: one wise; and one wicked; one simple; and who knows not how to ask. —Mekhilta of R. Ishmael (c. 300) Artificial Intelligence (AI) is the endeavor to endow mechanical artifacts with human-like intellectual capacities. The “strong” AI hypothesis (as propounded in [7], for example, and critiqued in [18]) avows that “an appropriately programmed computer really is a mind” [18]. The Computational Hypothesis asserts that the human mind is in reality some kind of physical symbol-manipulation system. The “weak” version of the hypothesis (“A physical symbol system has the necessary and sufficient means for intelligent action.” [13]) allows for the pos...