This is embarrassingly like Mrs May bringing back her Brexit deal for the n-th time, slightly changed …
But here we go again. This is a slightly revised version of the draft chapters on propositional natural deduction for the second edition of IFL2. (Exercises to be added, which will fill some remaining gaps, like noting the equivalence of DN and Classical Reductio, given the other rules, or dealing with biconditionals.)
To repeat what I have said before, one advantage about basing an intro logic book on trees (as in IFL1) is that people don’t get very exercised about how a tree system should be developed. By contrast, people get decidedly heated about the best form of natural deduction to adopt. But there’s no pleasing everyone!
What I propose is a standard enough Fitch-style system — more standard indeed than in the previous version. I have backtracked from two (connected) deviations in an earlier version, persuaded by the reactions of some — not least David Makinson — that deviating from the straight and narrow path was unwise. I had been minded, in particular, to treat the absurdity sign in natural deduction more in the spirit of an exclamation mark rather than as a wff in its own right (compare the sign used to close off branches in a Smullyan-style tree proof). I still think there are good reasons for doing this — see for example Neil Tennant’s discussion in this paper. However, there are reasons on the other side, and — on further reflection — I do think that there are trumping pedagogic reasons for sticking to a standard presentation in a first-level text book.
So, I hope that these chapters are now in a stable state, at least in terms of approach and detailed shape. But all comments (other than variants on “you have written the wrong book!”), all corrections, and even at this late stage all suggestions for improvement will of course still be very gratefully received, as always.