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Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 12:34 am
by JJDancer
I WILL GO TO THE MOVIES UNLESS IT RAINS

How to diagram this and its contrapositive?

Thanks

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 12:46 am
by Camron
Hmm, skimped over the actual formal logic section but are you just looking for the conditional reasoning diagram of this?

You basically take the term modified by unless to be the necessary, and negate the existing term and it becomes the sufficient condition:



No Movies -> Rain (if I do not go to the movies, then it is raining)
No Rain -> Movies (contrapositive) (if there is no rain, then I go to the movies

Hope this is correct.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 1:06 am
by JJDancer
The part after UNLESS becomes the necessary part and you negate the sufficient.
I thought that is how it was ^^

So,
Movies => -Rain
Rain => -Movies

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 1:46 am
by skip james
There are essentially two ways that I go about diagramming unless statements, and they vary on the 'placement' of the unless in the sentence.

For example:

1)Unless I go to the movies, then I will be bored.

2) I will be bored unless I go to the movies.

You should realize that these two statements are logically equivalent. So why, then would I use two different ways of diagramming unless?

Well it comes down to speed. If the 'unless' falls at the beginning of the sentence like in case 1, then I translate the 'unless' into an 'IF NOT'.

1)Unless I go to the movies, then I will be bored.

THEN...

1) IF NOT MOVIES ---> BORED

but if the 'unless' falls in the middle, then do a two step process: first, I NEGATE the part before it, THEN I turn the 'unless' into an arrow.

2) I will be bored unless I go to the movies.

THEN.

2) NOT BORED ---> MOVIES

as you can see, I end up with the contrapositive of the scenario in the first sentence, so I essentially end up with the 'same' conditional. Hope this helps.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 2:02 am
by iamtaw
here is my mindless way of doing it.

make sure the sentence is in the form A unless B. ( NOT "unless B, A.")

take either A OR B and negate it.

bring the negated part of the statement to the front of an if-then statement
eg: ~A -> B (~X= NOT X)
~B -> A

hope i did a good job of explaining this haha.
pm me if need be (~pm me -> ~need be) <- couldnt help it

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 2:15 am
by tomwatts
I do the "if not" thing regardless. How long does it really take to rephrase "I will go to the movies unless it rains" into "Unless it rains, I will go to the movies"? (Which I then mentally rephrase to, "If it doesn't rain, I will go to the movies," and I diagram that.)

Meh.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 2:22 am
by sirchristaylor
JJDancer wrote:I WILL GO TO THE MOVIES UNLESS IT RAINS

How to diagram this and its contrapositive?

Thanks
I always negate what "unless" refers to and call it the sufficient, and then the part not referred to by "unless" is the necessary. So:

-Rain --> Movies
-Movies --> Rain

With the way I do it, you're always starting with the contrapositive. It works most quickly for me this way.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 2:32 am
by Camron
JJDancer wrote:The part after UNLESS becomes the necessary part and you negate the sufficient.
I thought that is how it was ^^

So,
Movies => -Rain
Rain => -Movies
Hmm, you said the same thing as me but I don't think your diagram is right (sufficient -> necessary) since you negated the necessary and not the sufficient. An example could be to get a good mark in class (sufficient), you need to study (necessary). GM -> S But studying does not guarantee a good mark (i.e. S-> GM is not a correct inference), it is just a requirement to get a good mark.


Anyone please correct me if I am wrong.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 2:54 am
by sirchristaylor
Camron wrote:
JJDancer wrote:The part after UNLESS becomes the necessary part and you negate the sufficient.
I thought that is how it was ^^

So,
Movies => -Rain
Rain => -Movies


Hmm, you said the same thing as me but I don't think your diagram is right (sufficient -> necessary) since you negated the necessary and not the sufficient. An example could be to get a good mark in class (sufficient), you need to study (necessary). GM -> S But studying does not guarantee a good mark (i.e. S-> GM is not a correct inference), it is just a requirement to get a good mark.


Anyone please correct me if I am wrong.
You're right. The bolded above is incorrect.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 5:55 pm
by maks25
R > -M
M > -R

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 8:00 pm
by studylaw7
Camron wrote:
JJDancer wrote:The part after UNLESS becomes the necessary part and you negate the sufficient.
I thought that is how it was ^^

So,
Movies => -Rain
Rain => -Movies
Hmm, you said the same thing as me but I don't think your diagram is right (sufficient -> necessary) since you negated the necessary and not the sufficient. An example could be to get a good mark in class (sufficient), you need to study (necessary). GM -> S But studying does not guarantee a good mark (i.e. S-> GM is not a correct inference), it is just a requirement to get a good mark.


Anyone please correct me if I am wrong.

you're right. rain is the only cause for not going to the movies, therefore under any other circumstance I will still go to the movies...if it does not rain -> I will go to the movies. If I do not go to the movies, then it must have rained.

Re: Formal Logic Help - diagramming unless

Posted: Thu Jan 14, 2010 8:52 pm
by JJDancer
studylaw7 wrote:
Camron wrote:
JJDancer wrote:The part after UNLESS becomes the necessary part and you negate the sufficient.
I thought that is how it was ^^

So,
Movies => -Rain
Rain => -Movies
Hmm, you said the same thing as me but I don't think your diagram is right (sufficient -> necessary) since you negated the necessary and not the sufficient. An example could be to get a good mark in class (sufficient), you need to study (necessary). GM -> S But studying does not guarantee a good mark (i.e. S-> GM is not a correct inference), it is just a requirement to get a good mark.


Anyone please correct me if I am wrong.

you're right. rain is the only cause for not going to the movies, therefore under any other circumstance I will still go to the movies...if it does not rain -> I will go to the movies. If I do not go to the movies, then it must have rained.
Got it! Thanks all :)

Re: Formal Logic Help - diagramming unless

Posted: Wed Jan 27, 2010 2:57 pm
by theZeigs
Sorry to revisit this, but I need to brush up on my necessary/sufficient and logical diagramming. I just spent like 20 minutes thinking this through, if you happen to read this, could you please correct me and or tell me if I'm right? PM or post is fine ;)

I WILL GO TO THE MOVIES UNLESS IT RAINS.

Rephrased: Unless it rains, I will go to the movies.
Rephrased: If no rain, I will go to the movies.

-R --> M
therefore -M --> R

No rain is a sufficient condition for going to the movies. i.e. it's ALL/EVERYTHING that is required to go to the movies. OK, I understand this, but...

When I first drew this, I said, like the person above:

M --> -R
therefore R --> -M

If I go to the movies, it has not rained.
If it rained, I did not go to the movies.

Now, is this incorrect because it's POSSIBLE that one goes to the movies even if it rains? i.e. I will go to the movies unless it rains. But I may still go to the movies if it rains...I'm not sure yet. Therefore, me having gone to the movies is not sufficient to prove that is hasn't rained, but it is necessary for me to go to the movies if there is no rain.

So all logical diagrams (if --> then) have the [EDIT] sufficient condition on the left side and the [EDIT] necessary on the right. e.g. if I get an A on all assignments, then I will get an A in the class. But, if I got an A in the class, I don't necessarily have to get an A on all assignments. Therefore, getting an A in the class is necessary if all assignments were A's, but not sufficient to show that all assignments were A's.

Likewise, If I got an A in the class, I had to have turned in my midterm. But if I turned in my midterm, I don't necessarily get an A. Therefore, it is necessary for me to turn in my midterm if I got an A, but not sufficient to turn in a midterm to get an A.

Thus, sufficient conditions ensure a necessary condition, and a necessary condition must have occurred for the sufficient but is not enough. A sufficient condition ensures the occurrence of a necessary condition, but a necessary condition doesn't ensure the occurrence of the sufficient.

Thus, I WILL GO TO THE MOVIES UNLESS IT RAINS doesn't mean "if it rains, I won't go" it means "I will go if no rain, if it rains, who knows." And any thing that is "unless" is the sufficient, negated i.e. -R --> M and -M --> R because I am going to the movies under any circumstance except rain, so if I didn't go, it must have rained.

Man I'm glad I worked through this.

[EDIT] Another way to remember this: "Unless" is neccessary, the rest is negated and becomes sufficient, which is simply the contrapositive of what I've written above. But it rolls off the tongue:
"Unless is necc, rest is negated."

also see (my post in) this thread: http://www.top-law-schools.com/forums/v ... 6&t=105534

Re: Formal Logic Help - diagramming unless

Posted: Wed Jan 27, 2010 4:45 pm
by TLS1776
Now, is this incorrect because it's POSSIBLE that one goes to the movies even if it rains?
Yes. It's wrong because it incorrectly represents what the original statement says. With the original statement you could have M and R at the same time but cannot have ~M and ~R at the same time, while with the second (incorrect) interpretation you can have ~M and ~R at the same time but cannot have M and R at the same time.
I will go to the movies unless it rains. But I may still go to the movies if it rains...I'm not sure yet.
This is what gave me a lot of trouble when I was first learning to interpret "unless" statements on the LSAT. In everyday speech we frequently use "unless" to mean "if not and only if not" (e.g. "Either I'll go to the movies or it will rain, but not both"), but according to the LSAT it only means "if not". That's why you can have seemingly counter-intuitive results like the one you mentioned.
So all logical diagrams (if --> then) have the necessary condition on the left side and the sufficient on the right.
Other way around: suf is on the left, nec is on the right. But the rest of what you said after that was correct.

Re: Formal Logic Help - diagramming unless

Posted: Wed Jan 27, 2010 5:10 pm
by theZeigs
TLS1776 wrote:Other way around: suf is on the left, nec is on the right. But the rest of what you said after that was correct.
Ah yes, a mistype or something.

Thanks for the post, +1.

Re: Formal Logic Help - diagramming unless

Posted: Wed Jan 27, 2010 6:02 pm
by melinda.corbin
JJDancer wrote:I WILL GO TO THE MOVIES UNLESS IT RAINS

How to diagram this and its contrapositive?

Thanks
Your question makes sense. One thing I realized after reading Powerscore Logic Games that if you follow the diagramming rules as described in this book, things become more complicated so the best approach is "hybrid one" where you use your own creativity and some easy rules in the book. This mix approach is known as Hybrid approach.
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