In another post here, I asked whether the analytic/synthetic distinction could be grounded in/reframed as an erotetic distinction. So assuming that grounding/reframing in the background as 'given' (if only for the sake of argument), I now would like to ask whether any of the following cases involves analytic knowledge a posteriori. Their template is the idea of "self-answering questions," i.e. wh-questions whose predominant wh-term is "solved for" by the entire question being "fed back into" the original erotetic function. (Historical precedents/precursors with which I am familiar include Smullyman's What Is the Name of This Book?, Quine's, "Yields falsehood when preceded by its own quotation," and (though by conceptual happenstance) the, "Speak, friend, and enter," riddle from The Fellowship of the Ring.)
- Imagine there is an artificially sentient door that has been programmed to open only if it is asked a specific question. So there is a natural inquiry along the lines of, "What question, when asked, opens this door?" or, poetically, "What is the key to this door?" Suppose, then, that some question like this (perhaps in a different language or even arbitrarily many languages) is what the door was programmed to respond to by opening itself. In that event, the question is its own answer, and the very act of asking the question in front of the door will unwittingly open it. So is "What is the key to this door?" is the key to this door known analytically a posteriori?
- ?Mμɑϝ ᴉƨ ϝμԍ dnԍƨϝᴉou ϝμɑϝ λon ɑʁԍ ʁԍɑqᴉuმ ʁᴉმμϝ uoʍ nbƨᴉqԍ-qoʍu ᴉu ɑ wᴉʁʁoʁƾ Chances are, if you've taken the time to resolve this one, you're standing in front of a mirror with a phone or a tablet or a laptop in hand, held upside-down. Or you're a lexical virtuoso who can flip and fold the alphabet in your head. Does that mean that the question, when it is its own correct answer, is only contingently so? But then, if this is also a matter of analytic aposteriority, have we uncovered a contingent analytic truth? (Or: when read via mental flipping and folding, is the question then apprehended a priori, to the further effect that it is not only contingent whether the question is its own answer, but whether its answer is known a priori? For when mentally reconfigured, the question is no longer its own answer, although there might be another question, "What is the question that you just reconfigured in your visual imagination?" that serves our earlier purpose, here... Or what about: "What is the question that you are reading in a mirror right now OR that you just flipped and folded in your head?")