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The second rule listed here is not necessarily true. While the truth of R is dependent on the truth of Q, truth of Q is not dependent on the truth of R. Try this: "If Mike Huckabee is elected President, his wife will be First Lady. Mrs. Huckabee is not first lady, therefore Mike was not elected President." However, there are (logically, anyways) ways in which Mike could be President without Mrs. Huckabee being First Lady - they could get divorced, the position of First Lady could be abolished, what have you. Is therea logician arouns who could clear this up? [[User:Walt|Walt]] 23:42, 23 November 2007 (EST)
The second rule listed here is not necessarily true. While the truth of R is dependent on the truth of Q, truth of Q is not dependent on the truth of R. Try this: "If Mike Huckabee is elected President, his wife will be First Lady. Mrs. Huckabee is not first lady, therefore Mike was not elected President." However, there are (logically, anyways) ways in which Mike could be President without Mrs. Huckabee being First Lady - they could get divorced, the position of First Lady could be abolished, what have you. Is therea logician arouns who could clear this up? [[User:Walt|Walt]] 23:42, 23 November 2007 (EST)
:It seems that someone raised the point I wish to raise a long time ago. The second rule is not deduction, it is induction, since produces a conclusion that goes beyond the available evidence.
If Q is true, then R is true. If we say "Q is true" then we can deduce that R is also true.
But, if we say "R is true" then it does not logically follow that Q is true, nor is is the case if in both instances we swap true with not true. Indeed, if R is true then it is possible that Q is also true, but we cannot conclude that it definitely is. As such, I have deleted the second rule. [[User:DWiggins|DWiggins]] 21:36, 29 October 2009 (EDT)