Hey, a little help?

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kerflux
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Hey, a little help?

Postby kerflux » Fri Jan 13, 2012 8:26 pm

Can anyone clarify this for me? I was going over one of the guides here on conditional reasoning, and came across this.

Unless Mac drops the ball, we will win the game.

My mental process went "the only way we will not win the game is if mac drops the ball"

I wrote this as
Mac drops ball -> ~win the game
win the game -> ~mac dropped ball

The answer key goes more like
~Win the game -> Mac dropped ball
And ~Mac dropped ball -> Win the game

Where is my error?

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ConfidenceMan2
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Re: Hey, a little help?

Postby ConfidenceMan2 » Fri Jan 13, 2012 8:43 pm

Unless Sam eats ham, he will die.

Now think... what follows from Sam not eating ham? Death to poor Sam.

What follows from Sam eating ham? Not dying? Not necessarily. Maybe he eats some ham but gets struck by lightning later in the day. (ETA: Same thing with Mac dropping the ball. Maybe if Mac doesn't drop the ball, then we win the game NECESSARILY, but if he does drop the ball, then we only win POSSIBLY. Maybe the only rule of the game is that one team tries to make Mac drop the ball, and then throw it in his face while the other team tries to prevent it. See? Mac dropped the ball, so we MIGHT lose now... but only if they manage to throw it in his face. The game's not over yet!!!!)

All we know is that if Sam doesn't eat some damn ham, he's certainly a dead man. And if he by some great miracle shows up tomorrow alive, you know that he ate some ham (thank God I mean how hard is it to eat ham)
~H -> D, and thus ~D -> H

You know this stuff already, I do believe. Hope this helps though.

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MachineLemon
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Re: Hey, a little help?

Postby MachineLemon » Fri Jan 13, 2012 8:55 pm

ConfidenceMan2 wrote:Unless Sam eats ham, he will die.

Now think... what follows from Sam not eating ham? Death to poor Sam.

What follows from Sam eating ham? Not dying? Not necessarily. Maybe he eats some ham but gets struck by lightning later in the day. (ETA: Same thing with Mac dropping the ball. Maybe if Mac doesn't drop the ball, then we win the game NECESSARILY, but if he does drop the ball, then we only win POSSIBLY. Maybe the only rule of the game is that one team tries to make Mac drop the ball, and then throw it in his face while the other team tries to prevent it. See? Mac dropped the ball, so we MIGHT lose now... but only if they manage to throw it in his face. The game's not over yet!!!!)

All we know is that if Sam doesn't eat some damn ham, he's certainly a dead man. And if he by some great miracle shows up tomorrow alive, you know that he ate some ham (thank God I mean how hard is it to eat ham)
~H -> D, and thus ~D -> H

You know this stuff already, I do believe. Hope this helps though.


+1 for logic, +1 for 'tar

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kerflux
Posts: 196
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Re: Hey, a little help?

Postby kerflux » Fri Jan 13, 2012 9:00 pm

A little fuzzy, but thanks, the edit actually cleared it up a lot! So if mac drops the ball, we MAY not win the game, but if Mac does not drop the ball, we definitely will win the game?

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ConfidenceMan2
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Re: Hey, a little help?

Postby ConfidenceMan2 » Fri Jan 13, 2012 9:07 pm

kerflux wrote:A little fuzzy, but thanks, the edit actually cleared it up a lot! So if mac drops the ball, we MAY not win the game, but if Mac does not drop the ball, we definitely will win the game?


Correct! Sorry it was fuzzy. Hard to follow someone else's thinking sometimes.

Here's the simple trick: when you see "unless" in a conditional statement like that, just replace it with "~"

So it's just ~D -> W (and thus also ~W -> D), where W = Winning the game and D = Mac dropping the ball

In my other, more rambling post, I tried to show why this is the case (through my own train of thought), but you really don't have to follow that. Just replace "unless" with "~" and boom, profit.

notaznguy
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Re: Hey, a little help?

Postby notaznguy » Sat Jan 14, 2012 2:28 am

Short answer:

If you see the words, "the only" instead of "only," then it is a sufficient condition.

i.e. The only fruits are apples

Fruits --> Apples

vs.

i.e. Only fruits are apples

Apples --> Fruit

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kerflux
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Re: Hey, a little help?

Postby kerflux » Sat Jan 14, 2012 1:35 pm

I appreciate the breakdown. And the ~ makes sense, because unless roughly equates to if not?

SanDiegoJake
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Re: Hey, a little help?

Postby SanDiegoJake » Thu Jan 19, 2012 6:10 pm

The way I understand, and diagram, anything using the word "unless" is the following.

There's an action after the word "unless". Begin your thought process by asking yourself, "What if that action does NOT happen?". Then, it should make sense both in your head and on your diagram.

In this case, the sentence is: "Unless Mac drops the ball, we will win the game."

So I begin by saying, "What if Mac does NOT drop the ball?" Well, says my brain, then we will win the game.
I diagram that ~Drop --> Win. Then I diagram the contrapositive. ~Win --> Mac must've dropped the ball. That's all you know and exactly what you know.

If mac drops the ball, you might still win the game. But if he doesn't drop it, you definitely win.

Your mistake was not in your thought process. It's true that the only way we don't win is if Mac drops it. Your mistake is in the diagramming of this thought. Just because it's the only way it CAN happen, doesn't mean that it DOES happen. So you can't say that if he drops the ball then we don't win. It's the word "only" that is screwing you up. "If" and "Only if" don't mean the same thing at all. You thought "we won't win only if Mac drops the ball", but you diagrammed "we won't win if Mac drops the ball."

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LexLeon
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Re: Hey, a little help?

Postby LexLeon » Thu Jan 19, 2012 6:57 pm

Try thinking of the word "unless" as the phrase "if not". These two are (always?) interchangeable in the context of informal reasoning within the LSAT.

So:
"Unless Mac drops the ball, we will win the game."

Would become:
If not Mac drops the ball, we will win the game.

And that's logically equivalent to:
~M --> W ; and
~W --> M

Because the "If" above indicates a sufficient condition, you find that Mac's not dropping the ball is sufficient to bring about victory, to make victory necessarily the case.

Unless can be a tricky work; see if "If not" makes things easier for you.

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kerflux
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Re: Hey, a little help?

Postby kerflux » Thu Jan 19, 2012 7:23 pm

Thanks for your insight guys - yeah, it definitely clarifies the situation for me when I swap "unless" for "if not". Also, if I follow, I was throwing in that only unnecessarily




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