The Case for the KRA

You have bought a ticket in a fair lottery with one million tickets and exactly one winner. The winning ticket has already been drawn, but the result has not been announced. I know that you own a ticket and I know that the odds against winning are massive. Upon meeting you, I assert that your ticket did not win the lottery. My assertion in this case is not a good one. The same goes for similar cases. Let a lottery proposition be any proposition of the form ‘ticket x does not win lottery l ’. When the only information one has about a given lottery concerns the odds against winning and when, for all one knows, those odds are non-zero, lottery propositions are not assertable. That is to say, if one does assert a lottery proposition, one’s assertion is bound not to be a good one. Why not? Champions of KRA have an explanation ready to hand. When the only information about a lottery we have is the probabilistic information about the odds of winning, we are not in a position to know lottery propositions. If so, we don’t know lottery propositions. If we assert a lottery proposition, we are bound to violate KRA. That’s why our assertion is bound not to be good.