(For other posts in this series, see here.)
Theologians often try to claim that they can arrive at eternal truths about god by using pure logic. In some sense, they are forced to make this claim because they have no evidence on their side but it is worthwhile to examine if it is possible to arrive at any truth purely logically. If so, we can see if that method can be co-opted to science, thus bypassing the need for evidence.
In mathematics, there is one way to prove that something is true using just logic alone and this is the method known as reductio ad absurdum or reduction to absurdity. The way it works is like this. Suppose you think that some proposition is true and want to prove it. You start by assuming that the negation of that proposition is true, and then show that this leads to a logical contradiction or a result that is manifestly false. This would convincingly prove that the starting assumption (the negation of the proposition under consideration) was false and hence that the original proposition was true.
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