Help with Necessary assumptions

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• 2 Likes

  Alex Alum Member ⭐

  November 2017 23929 karma

  @"Harber.colby" said:
  I took the test in Sept. and I have been able to narrow down the parts of the test that I struggled on. I struggled on the necessary assumptions and the sufficient assumptions on both the practice and real test. I have gone through all of the videos and looked through multiple articles to try to figure out exactly what I am doing wrong and I can't figure it out. It is like when I follow along with JY, I understand perfectly, but when I am doing the questions myself, I never figure it out like he does. Can anyone offer any hints, or articles online that might clear up the situation for me? I would really appreciate it.

  When you go to do an assumption question, where do you typically get confused?

  Are you able to find the conclusion and support?
  Are you able to identify the gap in the reasoning (why the support doesn't substantiate the conclusion)
  Do you have a solid understanding of validity, sufficiency and necessity?
• 1 Like

  BinghamtonDave Alum Member ⭐ 🍌🍌

  November 2017 8716 karma

  Where I would start is by asking in your understanding, what is our job on necessary assumption questions? I believe the way in which you answer that question could reveal where your hang ups might be.
• 1 Like

  thisissparta Alum Member

  November 2017 1363 karma

  You're going to receive generic responses based on your post. Some specificity might help. Talk us through your thinking in some of the difficult questions you've faced, and we'd be able to help you better.

  Feel free to shoot me a PM with the questions.
• 1 Like

  acsimon Alum Member

  November 2017 1269 karma

  Say you are given some premises p1,...,pn and a conclusion c. Assume that the argument is valid, so that the truth of all the premises guarantees the truth of the conclusion. Now say that take away a unspecified number (1 or more) premises from p1,...,pn and present you with an argument schema which is just like the first argument but with the taken premises missing. I present the schema as a knock down argument (i.e., as sound and not just valid, since you're not asked to question the truth of premises in LR but just treat them as true). Well, obviously it's not--important premises are missing (for those that would be pedantic and say that's not right given monotoncity considerations--these are not relevant for thinking about LR arguments).

  Which premises?--the premises I took away. So say I took three away--pi,pm, and ph--all members of the original premise set p1,...,pn. I ask you for a necessary assumption of the argument presented as not including those. What is one?--well, any of the pi,pm,ph premises I took away from the initially valid argument. (This is a simplification, but a harmless one in the present context). They are each necessary to restore the argument to its valid form.

  What's sufficient? Well, the conjunction of all three premises together would be sufficient to restore the argument to a valid form. Their addition "suffices" to yield that result.

  Now for one of the complications ignored above. Take an argument which contains the premises p1,..., pn and the conclusion c. Assume also that the argument, in its current form, is invalid. Now say that the addition of different sets of new premises to p1,...,pn the argument would result in a new argument which would be valid (sound too).

  Say that there are only two such sets of additions:

  (1) r,s,t,w
  (2) r,q,w,v

  Now given that (1) and (2) constitute the only additions to p1,...,pn that would render an argument to conclusion c valid, which are the necessary assumptions?--r and w. Why? Because every expansion of p1,...,pn that yields a valid argument to c includes them.

  So, what is a sufficient assumption? Well, the conjunction of every statement in (1) or alternatively the conjunction of every statement in (2). But neither of these conjunctions is itself necessary, remember, because of the existence of the other alternative which, by hypothesis, suffices to make the original argument valid.

  How does this play out in practice? Consider the following Toy argument.

  P1. It was either the butler, the colonel, or the professor. (Exclusive "or")

  P2. It was done in kitchen.

  P3. It was done with a knife.

  C. It was the professor

  What would a necessary premise be? Clue (no pun): consider a statement such that if it were true, the conclusion would have to be false. Example1: if it was done with a knife, it was the colonel. This has to be false. Negate it and you have a necessary assumption of the argument: it's not the case that if it was done with a knife, it was the colonel.

  Example 2: The professor couldn't have done it with the knife. This has to be false given the argument (remember, you want to put it in a form where the (consistent) premises guarantee the conclusion) so negate it and you get a necessary assumption: the professor could have done it with the knife.

  What about sufficient assumptions? This is any statement whose addition to the premises would suffice to guarantee the truth of the conclusion (remember, the premises are always assumed to be true in LR).

  Example 1: Neither the colonel nor the butler could have done it in the kitchen.

  Example 2: if it was done with the knife, it was the professor.

  The addition of either of these would suffice to render the argument valid. Importantly though, notice that neither of them is, itself, a necessary assumption of the argument. You could easily treat each as false and still add a statement which would guarantee the truth of the conclusion.

  Let's do it. Say both of the statements is false. Add these further (unremarkable) statements to the premises:

  --It wasn't the colonel.

  --It wasn't the butler.

  Boom. The argument would go through again. The point is that sufficent assumptions needn't be true for the argument to be a good on, but it is that if they were true, the argument would surely be a good one.

  Anyways, I hope this helps in some way. Cheers--A.c.S
• 1 Like

  acsimon Alum Member

  November 2017 1269 karma

  Actually, there is an error here. If the indicative conditional is treated as material implication then one has to change one of the statements above to: if it was done with the knife, then it was certainly done by the professor.