Help with "The Only"

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• 2 Likes

  Adam Hawks Alum Member

  February 2018 990 karma

  The only is a sufficient indicator.

  The Only kids that have red hair are the ginger kids.

  RH -----> Ginger

  Or to use your sample argument : The only kids who have brown eyes have messy hair.

  BE ------> Messy Hair
• 2 Likes

  Seeking Perfection Alum Member

  February 2018 4423 karma

  @amandajwashington said:
  Hi everyone,

  I am on Lesson 17 of 59 in the Intro to Logic (under the Starter course). I am still not fully understanding how "the only" works. For example,

  1. The only kids with messy hair are the kids with brown eyes.
     Translation: If you are a kid with messy hair, then you have brown eyes.
     Why would it be incorrect to say, "If you are a kid with brown eyes, then you have messy hair"?
     Is it because "the only" modifies kids with messy hair (meaning that ONLY kids with messy hair have brown eyes)?

  I am also not understanding the Y's "calling back" to the Xs.

  Also, why is it that in the sentence "Kids with brown eyes are the only kids with messy hair." X is tied to "the only kids"? In other words, why isn't it in the same position that it was before?

  Why does X refer back to Y in this case?

  Why is it that if you have messy hair, then you have brown eyes (and not the other way around)??? I really don't understand.

  I would appreciate your help (in layman's terms ha ha).

  -Amanda

  The only kids with messy hair are the kids with brown eyes.

  As you noted the correct translation is "If you are a kid with messy hair, then you have brown eyes."

  Messy hair --> Brown Eyes
  ¬Brown Eyes --> ¬ Messy Hair

  The reason for this is a little hard to describe since it is sort of just what it means, but I'll try. Let's say there was a kid with blue eyes.

  According to the first sentence could his hair be messy?
  No, only kids with brown eyes can have messy hair according to our sentence. One way to show this is that changing the sentence to "Only kids with brown eyes have messy hair." does not change the meaning.

  Now what if someone has brown eyes? Does there hair have to be messy?

  The answer is no. A kid with brown eyes can have messy hair according to the statement, but does not have to.
• amandajwashington Member

  February 2018 46 karma

  Thank you all for the help! I understand a bit better now.
• mcglz_64 Alum Member

  February 2018 891 karma

  Basically it's because you can't reverse the Sufficient and Necessary conditions. EVER. Unless you contrapose.
  [The only kids with messy hair are the kids with brown eyes.
  Translation: If you are a kid with messy hair, then you have brown eyes. (that's right)]

  IF (KWMH) ------> BrwnEy

  So Kids With Messy Hair is sufficient and Brown Eyes are necessary, right? Right.

  If you have brown eyes, you have messy hair? No. You can have brown eyes and have neat hair. BUT if you have messy hair you necessarily have brown eyes. It may be confusing since obviously in real life, this is hard to imagine. But in Lawgic, it is just not NECESSARILY true that having brown eyes means you have messy hair. It is however, NECESSARILY true that messy hair means you have brown eyes.

  [Why would it be incorrect to say, "If you are a kid with brown eyes, then you have messy hair"?]

  Think of it this way. If you are eating an apple, then you are eating a fruit.

  If (sufficient) APPLE ----> (necessary) FRUIT. If you are eating an apple, you are necessarily eating a fruit. There's just no getting around the fact that eating an apple means you are eating a fruit.

  Now look at what it does when you reverse the sufficient and necessary, without contraposing:

  If you are eating FRUIT, then you are eating an APPLE. Now, is that true? Absolutely not. If someone says you are eating a fruit, that means you could be eating a banana or a strawberry or etc. That is why sufficient and necessary statements cannot accurately be reversed. The statement would just be invalid.
• akistotle Member ⭐ 🍌🍌

  February 2018 edited February 2018 9377 karma

  https://7sage.com/lesson/clarification-for-the-only/

  I don't want to get lost in the "deep, dark, logical cave" (quote by J.Y.), so my explanation might not be right, so I want to tag @"J.Y. Ping" here.....

  I want to use the "Jedi" and "Force" example here because the "messy hair" and "brown eyes" example is confusing.

  　　1) The only living things in the Jedi order are the Force users.
  　　Jedi → Force

  Here "only" is an adjective that modifies "living things." It means there are no other living things in the Jedi order except for those. And what about those living things? They are all Force users.

  　　2) Only the force users can be the Jedi.
  　　Jedi → Force

  Here it means that only those who can use Force can be in the Jedi order. Who can be in the Jedi? Only the force users. (In order to be a Jedi, you have to be able to use Force.)

  I know it's still confusing. So I recommend that you just remember/follow the Group 1 translation. Questions like PT34.2.10 requires us to know "the only" translation.
• 1 Like

  RGBeetobe Alum Member

  February 2018 142 karma

  @amandajwashington I find that the best approach for me for this type of question is to negate it. It takes a bit longer but it ensures that I understand exactly what's being said, since when I'm speed reading a question I might miss nuances such as "THE only" vs. "only".

  So, building on @akistotle 's example, I would approach those two sentences like this :

  1) The only living things in the Jedi order are the Force users.

  If you're NOT a Force user, you CAN'T be a living thing in the Jedi order (LTJO).
  (/Force --> /LTJO)

  Positive: If you ARE a living thing in the Jedi order, then you MUST be a Force user.
  ( LTJO--> Force )

  2) Only the force users can be the Jedi.
  　
  If you're NOT a Force user, you CAN'T be the Jedi.
  (/Force--> /Jedi)

  Positive: If you ARE a Jedi, you MUST be a Force user.
  (Jedi--> Force)

  Like I said, this isn't the most efficient way to approach only/the only questions, but I find that negating these questions clarifies the logic.
• amandajwashington Member

  February 2018 46 karma

  Thank you everyone! These explanations are so helpful.