Interact Session 4 Flaws -Conditional Logic Flaw

[charlotte]

In the Examples of Flaws section of this session the following argument is presented: "The toddler won't be happy if he doesn't get candy. So if the babysitter gives him candy, the toddler will be happy". This makes sense to me and I cannot figure out what the flaw is.?

No candy - not happy
Happy - candy.

Many thanks.

[ohthatpatrick]

Here's how you correctly represented the conditional and the contrapositive:

"The toddler won't be happy if he doesn't get candy.:
No candy ---> not happy
Happy ---> candy

You're using "-" to represent the conditional arrow, and that might actually be contributing to your confusion. These statements have directionality: you have to read them from left to right.

If you tell me a toddler is happy, I can conclude the toddler was given candy.
If you tell me a toddler was not given candy, I can conclude the toddler is not happy.

But if you tell me the toddler was given candy, I can't conclude anything about his happiness.
and if you tell me the toddler is not happy, I can't conclude anything about whether he was given candy.

This argument concludes:
"So if the babysitter gives him candy, the toddler will be happy."

That's one of our illegal forms.

The problem is that in real life we feel this situation is a binary, bi-conditional idea.
Either you give the kid candy and he's happy
or you don't give the kid candy and he's not happy

That is NOT conditional logic. It's never an either/or. It's actually always a 3 out of 4.

Given the rule:
If you're in Los Angeles, you're in California

LA --> CA

There are four possible combos of that idea:
LA, CA (you are in LA and in CA)
LA, ~CA (you are in LA but not in CA)
~LA, ~CA (you are not in LA ... in fact you're not even in CA)
~LA, CA (you are not in LA, but you are in CA

The conditional rule only kills off one of those:
LA, ~CA (how could you be in LA but not be in California?)

The contrapositive kills the same scenario.
LA --> CA
~CA ---> ~LA

The idea of someone in Los Angeles, but not in California, contradicts the conditional rule by
triggering the left side [but] not delivering on the right side

(nerds will say "to disprove this conditional, we need something that IS the Sufficient condition but ISN'T the Necessary condition)

Anyhoo. Force yourself to think of conditional logic as a chronological thought:
1. IS the left side of the rule happening?

----- Yes, I know it is happening.
2. Then the right side must be true.

----- No, I know it is not happening.
2. Then the rule disappears and has no meaning. The right side could be true or false.

----- I don't know whether the left side is happening.
2. Okay, then we can't use this rule yet, but it still might be usable.

If you take a conditional like
LA --> CA
~CA --> ~LA
and mimic the example argument you're asking about, it should sound wonky.

"You are not in Los Angeles if you're not in California. So if you're in California, you're definitely in Los Angeles."

Another helpful way to break out of thinking through the toddler candy scenario as a binary is to think:
"If I don't give him candy, he's going to be mad."
but it's also possible that
"if I do give him candy, he's still going to be mad." After all, toddlers are cranky. Maybe you give him the wrong TYPE of candy from what he was really picturing, or maybe you unwrapped it for him but he wanted to unwrap it himself ... etc. #MyLife

[charlotte]

Thank you so much for your extensive and helpful reply.