Direct deduction has the merit of being simple to understand. Unfortunately, as we have seen, the proofs can easily become unwieldy. The deduction theorem helps. It assures us that, if we have a proof of a conclusion form premises, there is a proof of the corresponding implication. However, that assurance is not itself a proof. Natural deduction cures this deficiency through the use of conditional proofs.
We begin this lesson with a discussion of conditional proofs. We then show how they are combined in the popular Fitch proof system. We discuss soundness and completeness of the system. And we finish by providing some tips for finding proofs using the Fitch system.
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