Responding to Aidan's concerns about imagination and modality, I'm going to spell out in greater detail how one comes to know the truth-value of subjunctive conditionals, and how one evaluates claims about necessary truths truth or falsity.
First, subjunctive conditionals, which have the form "if p were true, q". We imagine the closest world where p and then apply our whole set of beliefs to the facts of that world, to determine whether q in that world. So suppose I'm considering the subjunctive conditional, "If Gore had won the election, America wouldn't have invaded Iraq." I imagine the counterfactual situation, and extend my imagination into the future by applying my beliefs about Gore's intelligence, honesty, and rationality. My beliefs lead me to imagine a world where Gore doesn't invade Iraq and instead launches some kind of global antipoverty program after invading Afghanistan. So I accept the subjunctive conditional.
Now, claims about necessary truths. Let me just consider those which have the form "necessarily, if p then q". This actually seems simpler for the imagination account than the case of subjunctive conditionals does. "necessarily, if p then q" is false iff the following obtains in any one world: "p ^ ¬q". So we just try to imagine a world where p ^ ¬q obtains. If we can successfully imagine such a thing, the claim is false.
This, it seems to me, is exactly how I go about trying to think up counterexamples. Kant says, "If everyone made false promises all the time, then the institution of promising would necessarily collapse." He intends his claim to hold across all worlds, not just ones close to ours, so I'm licensed to imagine some pretty wacky worlds. I can imagine a world where everyone makes false promises all the time. Can I imagine the institution of promising flourishing there? Well, yes, if I imagine also that there's a psychoactive chemical in the water that causes everyone to forget all false promises, and gives them false memories according to which people have made great sacrifices to keep their promises. Since I can imagine (a world full of false promising) ^ ¬(the collapse of the institution of promising), Kant's claim is false.