Reply #59: True Always Implies True

[gagarux]

You have S3 and S4 below exactly backwards, mgr. Trot out the old truth table. Your premise actually states that being cloudy is a necessary condition for rain. A truth value of False can only be obtained if it is cloudy but does not rain (S3). May be because your example was based on a false premise, it confused you (it doesn't always rain when it is cloudy!).

Gary


>S3.)It is cloudy, but there is no rain. Does this condition refute the statement? No it does not, all it does is suggest that other conditions related to being cloudy may be necessary for the statement to be true, it could be that there are no condensation nuclei or the precipitation is coming down as virga. In this case, we conclude only that the condition cloudy is necessary for explaining rain, but not sufficient.

>S4.) It is not cloudy, but there is rain. This refutes the statement.