"- try pondering this one. Why does 2 + 2 come out the same way each time? Never mind the question of why the laws of physics are stable - why is logic stable? Of course I can't imagine it being any other way, but that's not an explanation."

I have recently had a thought relevant to the topic; an operation that is not stable.

In certain contexts, the operation d is used, where XdY means "take a set of X fair dice, each die having Y sides (numbered 1 to Y), and throw them; add together the numbers on the uppermost faces". Using this definition, 2d2 has value '2' 25% of the time, value '3' 50% of the time, and value '4' 25% of the time. The procedure is always identical, and so there's nothing in the process which makes any reference to time, but the result can differ (though note that 'time' is still not a parameter in that result). If the operation '+' is replaced by the operation 'd' - well, then that is one other way that can be imagined.

Edited to add: It has been pointed out that XdY is a constant probability distribution. The unstable operation to which I refer is the operation of taking a single random integer sample, in a fair manner, from that distribution.