Chapter 6 - Logical nihilism

Summary

The idea that there may be more than one correct logic has recently attracted considerable interest. The most notorious bone of contention in the discussion of logical correctness is the law of excluded middle. The connections between sequent calculus, constructive proof transformation, structural completeness, and lem are fixtures from logical knowledge store, but they cannot seriously be thought of as a network of consequences in some allegedly correct logic. The author indicates logic's modern contours, highlighting the fact that the deepest observations logic has to offer come with no ties to preconceptions about its essence. The richness of logic comes into view only when we stop looking for such an essence and focus instead on the accumulation of applications and conceptual changes that have made current logical investigations possible. The study of logic might be the best practical antidote to the view of it that we have inherited.