Law School Discussion

Find the flaw in this reasoning.

superiorlobe

Find the flaw in this reasoning.
« on: September 21, 2004, 10:57:09 AM »
Here is a line of reasoning.  See if you can find a flaw.

(1)     Jane goes to the party without Paul          (given)
(2)     if ~(Paul goes to the party) then (Jane goes to the party)          (equivalent to (1))
(3)     if Paul doesn't go to the party then Jane goes to the party.          (equivalent to (2))
(4)     (3) is a statement of the form: ~A --> B          (readily apparent)
(5)     Paul goes to the party.          (given)
(6)     (4) is a statement of the form: A          (from (3), (4) & (5))
(7)     Jane goes to the party.          (given -- is compatible with (3) & (5))
(8 )    (7) is a statement of the form: B          (from (3), (4), (5), (6), & (7))

note: the statement  ~A --> B  is compatible with both A and B occuring.

(9)     Jane and Paul both go to the party.          (from (5) & (7))
(10)    Jane goes to the party with Paul.          (from (9))


OKAY:

Statement 10 says: Jane goes to the party with Paul.
Statement 1  says: Jane goes to the party without Paul.

This is a contradiction.  Where is the mistake in the reasoning?


jacy85

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Re: Find the flaw in this reasoning.
« Reply #1 on: September 21, 2004, 11:01:10 AM »
I think your flaw is in #2, actually.

Jane goes to teh party without Paul.

J -> not P

So #2 is a mistaken reversal, since you effectively make it "not P -> J"

Which makes #3 wrong.

Your correct reversal is:  P -> Not J.   (if Paul goes, Jane does not go)