[FOM] Solution (?) to Mathematical Certainty Problem

[Robbie Lindauer]

M.J. Murphy wrote:

> Maybe the sun won't rise tomorrow; maybe tomorrow 2 + 2 will come out
> to be five.

To see the difference between these kinds of beliefs you just have to 
imagine the worlds in which they were false.  It's easy enough to do in 
the case of the sun not rising tomorrow - perhaps the Vogons will clear 
a space-trail for their intergalactic highway and it will run right 
through the middle of Sol or perhaps God will call an end to this 
Universe tonight.   Your betting behaviour will be similarly challenged 
in those contexts.  You wouldn't bet your eternal soul (assuming you 
had one...) that the sun will come up tomorrow when your bookie is God 
(assuming there is one), neither would you bet that they Vogons 
(assuming there could be some) couldn't bull-doze our star if they'd 
already offered to save you, your family & friends.

On the other hand, the worlds in which 2 + 2 = 4 are significantly less 
describable.  If 2 + 2 = 5, then 2 = 3 and black is green, true is 
false, up is down, war is peace, etc.  Your betting behaviour would 
therefore be contradictory no matter what you bet in those situations, 
and so it will also be best to bet and assume that 2 + 2 = 4 no matter 
what is at stake.

Robbie Lindauer