Wikipedia on a priori: Relations of ideas, according to Hume, are "discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe".

This points out clearly the problem that I have with "a priori". It is a fundamentally Cartesian-dualist notion. The "mere operation of thought" takes place INSIDE THE UNIVERSE, as opposed to anywhere else.

To observe your own thoughts is a kind of evidence, if the spikings of your neurons be entangled with the object of your inquiry (relative to your current state of uncertainty about both). If, for example, I do not know what will happen with two earplugs and two earplugs on the nightstand, I can visualize two apples plus two apples to find out. All of this takes place in the same, unified, physical universe, with no ontological border between the atoms in my skull and the atoms outside my skull. That's why the trick works. It would work just as well if I used a pocket calculator. Is the output of a pocket calculator an a priori truth? Why not call the earplugs themselves a priori truths, then? But if neither of these are a priori, why should I treat the outputs of my neurons as "a priori"? It's all the same universe.

It appears to me that "a priori" is a semantic stopsign; its only visible meaning is "Don't ask!"

Vassar: It sure seems to me that our evolution and culture constructed ethical attitudes are entangled with the world.

They're causal products of the world, and yes, if I was ignorant about some evolution-related factual question, I might be able to use my ethical attitudes as evidence about conditions obtaining in my ancestral environment. That's not the same as my stating an external truth-condition for it being wrong to slaughter the first-born male children of the subjects of an unelected Pharaoh. It is perfectly acceptable for me to say, "I can think of no encounterable situation that would transform the terminal value of this event from negative to positive."

Spear: The test of any religion is whether cultures believing it tend to thrive and improve the quality of their lives or not.

Ah, yes, the old theory that there are reasons to believe2 in an assertion-of-fact besides its being true.

Lee: If he proclaims "two and two makes three," then he must be talking about something other than the integers. You cannot be mistaken about the integers, you can only misunderstand them.

Just to be clear, when I say "be convinced that 2 + 2 = 3", I mean being convinced that the system of Peano axioms with standard deductive logic and:

\a.(a + 0 = a) \ab.(a + Sb = S(a + b))

does not have as a theorem

SS0 + SS0 = SSSS0

but does have as a theorem

SS0 + SS0 = SSS0

and is consistent. Just as I currently believe that PA is consistent and has a theorem SS0+SS0=SSSS0 but not SS0+SS0=SSS0. So yes, this blog post is about what it would take to convince me that 2 + 2 actually equalled 3. I am not supposed to be convinced of this, if I am sane, and if it is not true. But at the same time, my belief in it should not be unconditional or nonevidential, because there are particular evidences which convinced me that 2 + 2 = 4 in the first place.

I also note that if you do not believe that there is a finite positive integer which encodes a proof of Godel's Statement, then you clearly are not using Peano Arithmetic to define what you mean by the word "integer".