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Quick Question Regarding the Necessary-Sufficient Flaw

Edmond.DantesEdmond.Dantes Alum Member
in General 154 karma
Hello! I have a very basic question. This is a bit long, but I appreciate anyone who would provide some thoughts on this.

Q: If an argument commits the necessary, but not sufficient flaw, does it also commit the sufficient, but not necessary flaw?

This question came about after I read two examples in the Trainer:

Example 1: "Everyone who boards the plane has to show his or her ticket to the attendant. Since Tom has shown his ticket, he will be allowed to board the plane."

B -> S
S
------
B

The trainer understood this to be a necessary, but not sufficient flaw (S is necessary, but not sufficient for B). But couldn't you also say that B is sufficient, but not necessary for S?

Example 2: "Every time you drink, you end up feeling sick the next day. You say you are sick today. You must have gone drinking yesterday."

D -> S
S
---
D

The training understood this to be a sufficient, but not necessary flaw (D is sufficient, but not necessary for S). But similarly, couldn't you say that S is necessary, but not sufficient for D?

When I first read this, I was very confused by the fact that two identical argument structures have two "different flaws," which is why I wonder if the two flaws are the same.

I then read this for a bit and now think that the two flaws are different. The two arguments seem to have different emphasis. What makes the first example a "necessary, but not sufficient" is the keywords "he will be allowed to board," which is different from "he must board." I think, if you were to make this change, the first example would be more intuitively a sufficient, but not necessary flaw.

"Everyone who boards the plane has to show his or her ticket to the attendant. Since Tom has shown his ticket, he must have boarded the plane."

What do you think? Since this is so foundational, I appreciate any comments about this. Thanks!

Comments

  • DumbHollywoodActorDumbHollywoodActor Alum Inactive ⭐
    7468 karma
    The big category is sufficiency-necessity confusion. Logically it’s all the same.
    A-->B
    B
    _____
    A

    is the same as

    /B-->/A
    B
    -----------------
    A

    A-->B
    /A
    -------------
    /B

    is the same as
    /B-->/A
    /A
    --------------
    /B

    But you’re right, there is a distinction in English. Remember, everything is relational. Here’s the relevant lesson: https://7sage.com/lesson/relationships-are-relational/

  • Edmond.DantesEdmond.Dantes Alum Member
    154 karma
    Thanks for the inputs! That settles it then. I was afraid that one LSAT question would have in answer choices:

    A) Confuse a necessary condition for a sufficient condition
    B) Confuse a sufficient condition for a necessary condition

  • DumbHollywoodActorDumbHollywoodActor Alum Inactive ⭐
    7468 karma
    It won’t be like that per se. However, there might be answers that LOOK like that but, upon closer inspection, are messing with the relation of the necessary/sufficiency condition.
  • runiggyrunruniggyrun Alum Inactive Sage Inactive ⭐
    2481 karma
    @DumbHollywoodActor is spot on. If you mistake a Necessary for an Sufficient, you automatically mistake the Sufficient for a Necessary, because you've illegally reversed the argument.
    On the LSAT they will be a bit more specific, so even if one answer says "mistakes a necessary condition for a sufficient condition" and the other will be "mistakes a sufficient condition for a necessary" they will specify further, so as long as you know which is which in the original argument you should be able to pick the correct answer
    So, for the plane one they could say:
    A. mistakes the fact that having a boarding pass is a necessary condition to boarding to it being sufficient (correct).
    B. mistakes the fact that having a boarding pass is a sufficient condition to it being necessary (incorrect - having a boarding pass is necessary, not sufficient).
    You are thinking critically of these issues and understanding the concepts, so you're going to do great.
  • Edmond.DantesEdmond.Dantes Alum Member
    154 karma
    Many thanks! This is a great example to illustrate the point.
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