Why Can't We Infer "B most A" from "A Most B"? What Assumptions are Made in Doing So?

Comments

• paniz.gh91 Free Trial Member

  February 2017 82 karma

  I usually come up with examples in my mind to make these statements more tangible. So let's say most dogs are black, does that mean that most black things are dogs? No it doesn't. If you diagram these two statements with circles you should be able to see the difference as well. A " might be a small circle that most of it is in "B". But "B" is much bigger than A and only shares a small part with "A". I hope this explanation helps.
• 2 Likes

  DumbHollywoodActor Alum Inactive ⭐

  February 2017 edited February 2017 7468 karma

  A (Most)--> B means over 50% of As must also have B. But what is not addressed is how many Bs must have As. I like the list method to see this understanding. Let's say there are 5 As in the entire universe. By saying A (Most)--> B, we're saying that at least 3 As have a B. But what's not certain is the exact number of Bs in the world. Now, if there are only 4 Bs in the whole world, then you could also infer B (Most)--> A, represented here:

  A
  A
  AB
  AB
  AB
  B

  But it's also possible that there's 14 Bs in the universe. If that were the case, we most certainly CAN NOT infer that B(Most)--> A from A (Most)--> B, represented here:

  A
  A
  AB
  AB
  AB
  B
  B
  B
  B
  B
  B
  B
  B
  B
  B
  B

  Therefore, given all this, and because the number of Bs is unknown, we cannot infer B(Most)--> A solely from A (Most)--> B. You'd be assuming that you know the number of Bs, which you don't.

  Hope this helps
• 3 Likes

  BinghamtonDave Alum Member ⭐ 🍌🍌

  February 2017 edited February 2017 8716 karma

  The relationships don't go backward once we have established they go forward. They can, but it is not a proper inference. I have included the following relationships that I believe hold up in really life in order to make this concept a bit more clear. The latter concept might be a much larger set than the former in each example.

  What we are told: Most NBA players are tall
  What does not follow given the information: That most tall people in the world are NBA players. So there are say 10 million tall people in the world, there are some 300 or so NBA players. The relationship simply doesn't go from tall-----Most----->NBA player.

  What we are told: Most cats are carnivores
  What does not follow given the information: That most things in the world that are carnivores are cats. There are many many more carnivores in the world than there are cats. The set of carnivores is much larger than the set of cats.

  What we are told: Most Americans are Christians
  What does not follow given the information:That most Christians in the world are American.
  The Christians in America do not constitute most of the world's Christians.

  I hope these examples help intuitively
  David
• 1 Like

  Sami Yearly + Live Member Sage ⭐ 7Sage Tutor

  February 2017 10806 karma

  @"Keane Xavier" said:
  Hello, all!

  why can't we infer "B most A" from the statement "A most B"? Perhaps what I'm struggling most to grasp is this: what does one assume in making this erroneous inference?

  >

  Hey, so sometimes to understand the logical idea its necessary to see it in an example:

  So lets say we have a fruit basket. And we are told: Most apples in the basket are red.
  Can you now tell me if most of the red fruit are apples?
  No, because we only have information about apples in the basket, we don't actually have information about the red fruits in the basket.

  Similarly: A most B.
  The sentence above is saying most of A is shared with B. So we have information about the group "A". But we don't have any information about B, except it shares something with A. If the size of group "B" is 10 times the size of group A, then it only shares "some" things with A. But if the size of "B" as as large as "A" or even less than "A", then it could be that it shares most of the things with A or even all. We just don't have information about group "B". As the sentence above only gives us information about "A".

  I hope this helped.
• 2 Likes

  Keane Xavier Alum Member

  February 2017 171 karma

  Thank you, @"paniz.gh91", @DumbHollywoodActor, @BinghamtonDave, and @Sami for your responses. Each provided me with a different perspective from which to think about the issue. You've steered me back on track. I hadn't been thinking about this properly. But I've spent far too long thinking about this today, so it's time for a break! Thank you all for your time!