How often is a "most" statement wrong in a Necessary Assumption Q?

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• BinghamtonDave Alum Member ⭐ 🍌🍌

  December 2016 edited December 2016 8716 karma

  A few remarks: The negation of "most" is tricky. Check out the quiz in the CC titled "Negation 3 w/ Answers" Question 1 is instructive. It isn't in my understanding correct to say that the negation of "most" is "some." The negation of most in a sentence would be something akin to "it is not the case that..." and then we have a relationship.
  
  So if I tell you that Most cats like yarn, the negation would be (for the purposes of simplification) It is not the case that most cats like yarn. How I translate this in my mind is that the statement "most cats like yarn" tells us that 51% of cats like yarn. The negation to that would be to push that 51% to 49.9%. There are several members of our community here that have backgrounds in logic far more extensive than mine that would probably take issue with the simplification of my use of logic there, but it has served me well.
  
  So now the core issue here. There are really no silver bullets on this exam. I have not found in my studies for this exam an ability to eliminate a necessary assumption answer choice on the basis of the word most. Remember our task on necessary assumption questions: find what needs to be true for the argument to stand. This task is why negating a true necessary assumption is such an effective tool for confirmation, because if we apply that negated form of our answer choice to the argument as if it were true, our argument falls apart.
  
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  Alex Alum Member ⭐

  December 2016 23929 karma

  @BinghamtonDave said:
  So now the core issue here. There are really no silver bullets on this exam.
  

  Very, very true. Best bet is to return to the lessons on most/some/other quantifiers and re-do the quizzes daily until they are second nature! Re doing these lessons and memorizing them has been how I've been spending a lot of my time - it truly pays dividends!
• Stevie C Alum Member

  December 2016 edited December 2016 645 karma

  I think a "most" statement can be necessary. For example, if an argument requires the assumption that "all A are B", then doesn't it also require "most A are B" and "some A are B"?
  
  if it's not the case that most A are B, then it cannot be the case that all A are B
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  Q.E.D Alum Member

  December 2016 556 karma

  Binghamton's comments x2 with some minor niceties.
  
  The negation of 'most', e.g. in
  
  (1) ~(most A are
  
  would amount to
  
  (2) most A are not B
  
  That means >50% of As are not-Bs. By the same token, the Bs among the As must be <50%, as in the example due to @BinghamtonDave.
  
  Maybe no As are Bs, though. Assuming 49% of As are Bs will have the same logical valence in most situations, just remember you aren't guaranteed a 'some' leftover from a negated 'most'.
  
  For example, be careful not to proceed from (2) to
  
  (3) some As are Bs
  
  - as if to say "oh, only some and not most of them are Bs." It won't matter in most cases, but I would set that trap for you if I worked for LSAC.
  
  To demonstrate, suppose the stim said "It's not true that most dogs are terrier-dachshund hybrids." If you go on to conclude 49% of dogs are such hybrids, you might be tempted by an answer choice saying "Only some dogs are T-D hybrids."