You come home one day to find your very angry roommate pointing at an empty space on the kitchen table. "Look at this table!" he says. You look. "Do you see a pie on this table?" You don't. "WHAT DID YOU DO WITH MY PIE?" he screams.
You gulp, guiltily. There's only two of you living in the apartment. You don't remember eating your roommate's pie, but you suspect you may have done it during one of your hungry sleep-walking adventures. And if it wasn't you, who else could it have been?
At just that moment, your roommate's dog Fluffy ambles happily into the kitchen and rubs against your leg. A brainwave strikes you. "Maybe it was Fluffy?" you say innocently.
"IT COULDN'T BE FLUFFY BECAUSE FLUFFY CAN'T GET UP TO THE TABLE!", your roommate screams. "He can barely jump up to the chair."
Your face falls. You look down at Fluffy, wagging his innocent tail. You look over at the chair, then at the dresser, then at the table...
"Hang on!," you say. "If Fluffy can jump from the floor to the chair then he can jump from the chair to the dresser. And if he can jump from the chair to the dresser then he can jump from the dresser to the table. So Fluffy could have eaten your pie, after all!"
The argument you're making here is a plausibility argument. You're in no way trying to prove that Fluffy did eat the pie, and not even that he's the most likely eater of the pie, but simply that it's possible that he ate the pie – that we shouldn't discount that hypothesis completely, that if someone were to claim "it's impossible that Fluffy ate the pie" then that person would be wrong.
In different situations there are different levels of argument that might be appropriate or useful:
In mathematics, the arguments used are often a matter of absolute proof: you can show that something must be true, with no room for dispute.
In politics and business and everyday life, arguments are often a matter of "the balance of probabilities" or "weighing pros against cons": you're often trying to convince someone that a certain policy is the right one, on balance, despite our uncertain world and despite the drawbacks each possible policy has.
But there are also many situations in business and politics and everyday life where simply showing that something is plausible is a large contribution in itself. If you're having a debate with someone and they say "I just can't understand how anyone could believe in X/Y/Z, you'd have to be evil to believe that!" then – even if you yourself think X/Y/Z is wrong on balance – simply showing why it's plausible seems like an important exercise in empathy and understanding the world. Or if you're trying to make some kind of security system perfectly safe and someone notices a flaw in your system then – even if that person can't show exactly how the flaw would be exploited – you should probably take the plausibility of a flaw quite seriously.
And, of course, if you're trying to get off the hook for eating your roommate's pie then simply having a plausibility argument for an alternative culprit is a pretty useful thing. Especially when poor Fluffy can't talk back and discredit you.
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