Examples 7.2
More Rules of Replacement!
Constructive Dilemma
(CD)
(P
⊃
Q) · (R
⊃
S)
P v R
Q v S
Here’s a short English equivalent, though, admittedly, we don’t use it much:
If it rains then the game is cancelled, and if I miss the game then I’ll be unhappy.
Either it rains or I miss the game.
Therefore, either the game is cancelled or I’ll be unhappy.
We can view this rule as a double modus ponens.
If the first line is true, and if it’s true
that we have P or R, too, then we’re going to have either Q or S necessarily.
To think of
it in terms of truth value, just imagine that one of the disjuncts of the second premise
HAS to be true.
If that’s the case (and it is), then one of the antecedents in the first
premise has to be true, too.
And, since both conjuncts up there have to be true, if one of
the antecedents is true, then the corresponding consequent will be true, too (or else the
conditional is false—and then so is the whole conjunction).
Thus, if the second premise
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 Spring '08
 Barrett
 Conclusion, The Conclusion, The Rules, 2005 albums, Rule of inference, conjunct

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