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negation/logical opposites

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pocketaces:
hello everyone,

i have a question from powerscore's section on statement negations (its from the end of the assumption chapter in the LR bible). how do you negate sentences like this --

Unless the stock market rebounds, the economy will not recover this year.

i'd think to put this in conditional form, so that it becomes

economy recovers this year ---> stock market rebounds

and then make it so that the necessary condition doesn't necessarily happen:

economy recovers this year ---> stock market does not rebound

However, the answer apparently is "the economy will recover this year even if the stock market does not rebound."

Where does the "even if" come from? Is "even if" the same thing as "only if?" I don't remember seeing "even if" in PS's list of necessary condition indicators; also, it doesn't seem to make sense.

Thanks.

bass:
Hmm.. I think that I should think about this before posting, since it's troublingly difficult.  At any rate, here's my thought.

You are right to translate this as saying that the stock market rebound in the necessary condition for economic recovery.

To my mind, the negation would be that the rebound is NOT a necessary condition for economic recovery.  That is to say that economic recovery is possible with or without the rebound.

For this reason, I think the bible is wrong (as books can be).  It is not that "the economy will recover this year even if the stock market does not rebound."  I believe that it is instead that the economy CAN recover regardless of whether the stock market rebounds.

Two notes here: the "regardless of whether" is equivalent to "even  if," just clearer for me.  The first part is what's different.  The negation does not mean a recovery is assured, just possible without the necessary precondition of the original statement.

Herein lies the rub.  A conditional is a statement of a neccesary requirement.  Negating a conditional means denying the necessity of a presumed necessary condition.

Ex.

In order to go to law school, it is neccesary that one take the LSAT.  (LS -> LSAT)

Negated:

The LSAT is not a necessary condition for law school

OR

One can go to law school regardless of whether she has taken the LSAT ("even if she hasn't").

bass:
I should say that my analysis is in part based on truth tables.  The one thing that makes a conditional A->B false is if B is false while A is true.  For example, if I said, "All cats smell like gouda," the only way to prove me wrong is to find a cat (A) that did not smell like gouda (~B).  So the negation of a conditional is a negation of the necessity of a condition.

LizPendens™:
No, the book is correct

Don't forget you have to remember to negate BOTH the sufficient and the necessary part of the statements along with transposing 'unless' to 'even if'. Which means if you have a negative statement(s), it becomes positive. Are you confused yet?

page 270-271, #9 - for those that want to play along.

"Unless the stock market rebounds, the economy will not recover this year."

Negate Sufficient:         The economy WILL recover this year...
Change UNLESS to EVEN IF:     ...even if...
Negate Necessary:          ...the stock market DOES NOT rebound

Finished Negation:
"The economy WILL recover this year EVEN IF the stock market DOES NOT rebound."


Oh and bass, kudos to you for the brainwork, but you are way overthinking it. Formulate simple rules (they are buried in the text and examples) and apply as needed.   


redemption:
Is the LSAT really this complicated? Isn't it easier just to bubble in the correct answer?

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