My title is a mash-up of the titles of two well-known philosophy papers: Gregory Kavka’s “The Toxin Puzzle,” which I discussed earlier today here, and Saul Kripke’s “A Puzzle about Belief.” But my topic is all Kavka: extending Kavka’s Toxin Puzzle, which is about intentions, in a way that some remarks of Kavka’s at the end of his paper suggest: to cover beliefs. 

So, suppose that, in accordance with an agreement you made earlier with
him, our eccentric billionaire will pay you $10 million if you are able
to form a belief of the billionaire’s choosing. Oh, and we should work
some toxin into the example, so, if you fail to have the relevant
belief, you will have to drink the vial of toxin that will make you ill
for a day. It will work like this: You will meet at the billionaire’s
lair, he will tell you what belief you are to have, give you one minute
to get your thoughts together, and then you will step into his
belief-o-meter, which, as you fully realize, will harmlessly and
accurately (never mind how) determine whether you really believe the
item in question. If you do, the $10 million is yours; if not, you
drink the toxin and have a miserable day.

Let’s suppose you clearly recall eating several things yesterday. For
instance, you not only remember eating lunch, but you remember whom you
had lunch with, what you ordered, and how good you thought it was when you ate it. And
suppose that when you get to the billionaire’s lair, he tells you that
what you must believe to get the money and avoid the toxin is that you
didn’t eat a single thing all day yesterday. Can you do it?

It seems pretty clear to me that I could not.  This seems even clearer than that I couldn’t form the relevant intention in the original Toxin Puzzle.  But what do you think?

And let’s consider a couple of quick variants of this puzzle, which will be relevant to points I hope to consider later.

First, let’s try a different belief.  Suppose Mary works at the same place you do, and parks in the same parking lot that you do.  There are 5 rows of parking places in this lot, and in your experience, Mary has no favorite row, and seems to park in each of the different rows about equally as often: some days her car is in row 1, some days in row 2, etc., etc., etc.  You didn’t go to work yesterday, so you didn’t see where Mary parked.  You think she probably went to work and parked in one of those five rows — she almost always does on work days — but you have no idea which row she parked in.  Now, suppose what the billionaire tells you that you must believe to get the money and avoid the toxin is that Mary parked in row 4 yesterday.  Can you do it?  Is this any easier than believing that you didn’t eat anything yesterday?  After all, in this case, the billionaire is asking you to believe something that, given your evidence, may well be true (though it probably isn’t).

Next, unpleasant as it is, I have reason to consider this variation.  In fact, this case is most important to my purposes.  Go back to the case where you are trying to believe that you didn’t eat anything yesterday, but let’s now change the stakes.  Now suppose you are dealing with a very evil billionaire, who is torturing and killing your loved ones right in front of you.  He will stop — and you somehow know this to be so — and let you and all your loved ones who haven’t yet been killed go free with no further harm if and only if you really believe that you didn’t eat anything yesterday when you enter his belief-o-meter in one minute.  You are of course deeply traumatized by what’s happening in front of you.  Can you form the belief?

Finally, combine our two variations: Suppose all you have to believe to stop the torturing and killings is that Mary parked in row 4 yesterday.  Can you?

For now, these are just questions to consider.  I hope to later relate them to belief in hell.