The Continuum Hypothesis seems to be a counterexample to David Chalmers’s A Priori Scrutability thesis, according to which there is a compact class of truths (the scrutability base) from which all truths are a priori scrutable. Chalmers’s three-part answer to this problem (which I call the “Chalmers trilemma”) runs as follows: either the Continuum Hypothesis is indeterminate; or adding a new axiom will settle the issue; or, if these two options do not work, we should add the Continuum Hypothesis (or its negation) to the scrutability base. I argue that Chalmers’s answer is unsatisfactory: the first horn of the trilemma can be interpreted in several ways, and either it departs from common mathematical practice and rests on weak analogies, or it shares the same problems with two other horns; the second horn does not provide good reasons to believe that from a fixed system of axioms all truths about our world are scrutable; the third horn of the trilemma renders Chalmers’s project empty.

Barz (2018) contends that there is no specification of the phenomenon of first-person authority that avoids falsity or triviality. This paper offers one. When a subject self-ascribes a current conscious mental state in speech, there is a presumption that what she says is true. To defeat this presumption, one must be able to explain how she has been led astray.