Examples 7.5
Conditional Proof
So, here’s not another rule, but a
method
for obtaining conclusions in a proof sequence.
It works, in theory, like the following: imagine that you have a conclusion to derive that’s
a conditional (say, A
⊃
E).
What this conclusion says is that, if we assume A is true,
then we can get E.
So, what we’ll do is just assume A is true.
Then, if we can derive E
(by itself, I mean), we will be allowed to conclude that A
⊃
E (is true).
In other words,
by appealing to this method, you will ensure that your resulting conditional is true
(because you’ve shown that if the antecedent is true, then the conclusion must be true, too
—this avoids the only way of making the overall conditional false). This may seem a bit
like cheating, but it’s totally legal in terms of derivations.
So, if you see that the
conclusion asked for is a conditional (the main operator is a horseshoe), then you might at
least consider using this method (generally, if it’s not the only possible way to derive a
certain conditional, it will at least be WAY shorter than using the other 18 rules).
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 Spring '08
 Barrett
 Logic, Conclusion, The Conclusion, 2005 albums, Assumption of Mary

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