Jeff Pelletier was on my PhD committee, so I'm naturally curious to see what he wrote here. As it turns out, I spent quite a bit of time on natural deduction and was fairly good at it (it made a lot more sense than semantics, which I always thought of as a bit of a sleight of hand). Natural deduction is basically a rules-based linear form of reasoning, which makes for easy conversion into prose, and is characterized by 'sub-proofs', which allow you to consider (and draw conclusions from) hypotheticals. This article follows the development of natural deduction through predicate and modal logics, and ends, as I suppose it must, with Michael Dummett, one of the more engaging but densely complex philosophers I've read. Here's Dummett in a nutshell: "intuitionism as applied to logic urges meaning to be given by rules of how to use the connectives. Classical logic, on the other hand, assumes that there is a pre-given notion of reference and designation."
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