Tuesday, September 30, 2014

Finishing your vegies may still not get you dessert

Wish I had captured this on video. It is absolutely priceless!
Mother: Jeff, if you don't finish your food you won't go with us. [pause] Jeff Anderson! Did you hear what I said?!

My 4-yr old nephew finally takes his eyes off of the TV and turns toward his mom: Yes mommy. If I don't finish my food I can't go with you. If I finish my food I can go.
Classic logical fallacy from the mouth of babes! And let's not pat ourselves on the back because we all make this mistake just about every time.

A = you don't do 100 push-ups
B = you won't be allowed to take your meal

The drill sergeant yells, If A then B. Does it follow then that if not A then not B? That if you complete the number of push-ups you'll finally be able to fill your empty belly?

No, of course not. To say so would be to commit the fallacy of inversion.

Here's Deborah Bennett in her Logic Made Easy giving an example which played right before my eyes this morning. Talk about textbook case! :)
As a part of natural language and conversation, 'if p then q' conditional statements that are promises and threats commonly invite the inference, 'if not p then not q.' Take, for example, the promise, 'If you eat your dinner, you may have dessert.' We would probably agree that this promise invites the threat of the inverse, 'If you don't eat your dinner, you won't have dessert.' But the statement says no such thing.... It is curious that even though the common interpretation of this parental warning has no basis in logic, both the parent and the child (and probably all of us) understand the intention of the statement.

I love the example given by Jonathan Baron [who the heck is he?!]. Presented with the threat, 'If you don't shut us I'll scream,' we would all be surprised if the speaker screamed anyway after you shut up. The speaker probably intends that your interpretation of this conditional to include its inverse, 'If you don't shut up, I'll scream and if you do shut up, I won't scream.'" This interpretation may be illogical but it isn't unreasonable; it makes perfect sense. In ordinary discourse, we make practical assumptions about what a person likely means.


Bennett, Deborah J.. Logic Made Easy: How to Know When Language Deceives You. New York: W.W. Norton & Co., 2004. p.115-116