...I hear that in religious debates all the time, "Well I KNOW that MY religion is true because I just do."
Whenever I encounter someone who takes the attitude that something is true because their instinct or gut tells them that it is, I show them "The Monty Hall Paradox" (which Brian Dunning referred to in "S or F"), ask them what they would do (they ALWAYS say it doesn't matter) and then I tell them that they are better off switching and show them a simpe mathematical proof demonstrating why.
Most of them then tell me it's a math trick (like the supposed "Achilles vs the Tortise Paradox"), but then after I make them put money on it (suckers!), I show them another more convincing demonstration (the idea for which I got from quip Bob Novella made on a show a couple of years ago) using a lottery ticket metaphor that ALWAYS convinces them to switch.
On rare occasion, the result has been that the person who once put so much faith in their "hearts" on other things then think twice before they do so again.
BTW - I used this little trick last year to wager my boss into giving me the time off I needed to go to TAM7. He was soooo confident that it was a sure thing that he wouldn't even let me put anything on the table except to stop asking for time off. He is much wiser now...