Mill agrees that mathematical statements are synthetic and he believes that all knowledge about the world is a posteriori, not a priori. Unlike rationalists, something that is inconceivable is still possible. He believes that 7 + 5 = 11 is possible even if it is inconceivable. If you can't conceive something, then it is analytic, which is not falsifiable. If it is true, then it can be conceived as false.
He believes that inconceivability and certainty are feelings and states of emotion and conviction that arise in us in the face of a posteriori evidence.
When there is more evidence, there is higher certainty. As a posteriori evidence increase, our beliefs become stronger.
He believes certainty is simply a feeling of conviction based on a posteriori evidence, and that feelings should not be used to say what is or what isn't true.