Restricted deducibility and deferential understanding
Dave Chalmers kindly explained his views on deducibility to me. He thinks that anything one could reasonably call non-deferential understanding of the fundamental truths would suffice for being able in principle to deduce macrophysical facts, provided that these fundamental truths, unlike my P, contain phenomenal facts and laws of nature. He also notes that I shouldn't have called these restrictions (to non-deferential understanding and the rich content of fundamental truths) assumptions, since they are really just restrictions. I'm still not sure if any kind of non-deferential understanding would suffice, but with the restrictions in place it's not as easy to come up with counterexamples as I thought.
Brian Weatherson posted a nice example of how one can understand a sentence (non-deferentially) and yet not be able to derive all its deductive consequences: Knowledge of the introduction and elimination rules for 
might suffice for understanding (pq)p, but it doesn't suffice for deriving p from it.
Actually, my response to this wouldn't be to conclude that Peirce's law isn't a priori, but that you haven't really grasped the meaning of just by knowing the introduction and elimination rules. Rather, you would speak an impoverished ideolect in which the sentence ((pq)p)p, that looks to us like Peirce's law, isn't logically true (nor a priori). I don't think that more substantial knowledge is required. What's missing is deferential knowledge: You have to believe that what other people in your linguistic community think about is relevant to its meaning. If someone doesn't believe this it will be impossible to convince him that Peirce's law is true:
- Look at the truth table!
- Why should I accept the validity of truth tables here?
- Because
- No it's not. It's defined by the introduction and elimination rules.
and so on. It doesn't seem crazy to interpret this as a clash of ideolects.
If in this manner deferential components are always required for understanding concepts of public language, the Chalmers-Jackson restriction to non-deferential understanding might turn out to be rather severe. Not too severe perhaps, if non-deferential understanding -- private language -- is at least possible, as I believe it is.