Sufficient & Necessary Diagramming--How do you diagram this?

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LSAT_Padawan
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Sufficient & Necessary Diagramming--How do you diagram this?

Postby LSAT_Padawan » Mon Mar 22, 2010 11:44 pm

Since no one who was promoted during the past year failed to attend the awards banquet, evidently none of the office managers attended the banquet this year since they were all denied promotion.

Can someone please show me how to diagram this? Thanks!

dakatz
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Re: Sufficient & Necessary Diagramming--How do you diagram this?

Postby dakatz » Mon Mar 22, 2010 11:50 pm

LSAT_Padawan wrote:Since no one who was promoted during the past year failed to attend the awards banquet, evidently none of the office managers attended the banquet this year since they were all denied promotion.

Can someone please show me how to diagram this? Thanks!


This isn't logically correct, but I'm guessing the error is meant to be there.

We know that "no one who was promoted during the past year failed to attend the awards banquet". Said another way, if they were promoted, they attended the banquet.

Promoted ----> Attended Banquet

The second sentence says that, because they were not promoted, the office managers did not attend the banquet.

Not Promoted ----> Not Banquet

The error here is that you can't just negate the sufficient and necessary conditions and come out with a logical deduction. The lack of a specific sufficient condition does not mean that the necessary condition will not occur. In simple terms, sure we know that if you got promoted, you went to the party, but that doesn't tell us anything about the people who didn't get promoted. They might or might not be at the party. All we know is a fact about those who DID get promoted.

waxecstatic
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Re: Sufficient & Necessary Diagramming--How do you diagram this?

Postby waxecstatic » Tue Mar 23, 2010 11:19 am

LSAT_Padawan wrote:Since no one who was promoted during the past year failed to attend the awards banquet, evidently none of the office managers attended the banquet this year since they were all denied promotion.

Can someone please show me how to diagram this? Thanks!


No need to diagram really. It means everyone who was promoted during the past year attended the banquet due to the double negatives (which makes it an extremely poorly written sentence but that's another story). The second part of the sentence is logically incorrect. While everyone who was promoted attended, it is still possible people who were not promoted could have been at the banquet. HTH

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blhblahblah
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Re: Sufficient & Necessary Diagramming--How do you diagram this?

Postby blhblahblah » Tue Mar 23, 2010 1:27 pm

Since no one who was promoted during the past year failed to attend the awards banquet, evidently none of the office managers attended the banquet this year since they were all denied promotion.


P1: P->AAB

C1: :. OM->~AAB

P2: OM->~P

Flawed reasoning because it mistakes a sufficient for a necessary. The fact that office managers have not been promoted does not necessitate their being absent from the banquet party.

To justify the conclusion, add the premise AAB->P (making both AAB and P sufficient AND necessary for each other). That is, all those who got promoted attended the banquet party AND all those who attended the banquet party were promtoed.

With this additional promise in hand, the second premise in the stimulus would allow to the conclusion to be properly drawn.




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