Comments Elsewhere

Incidentally, for an interesting compare and contrast, see Lewis Carroll’s article A Logical Paradox, from the July 1894 issue of Mind, in which Carroll presents a puzzle with a different kind of nested conditional (“If C is true, then: if A is true, B is not true”). Russell and everybody thereafter thought that this puzzle was trivially solved if you based your theory of conditionals on material implication. Of course, Carroll couldn’t be blamed for not seeing this, since there wasn’t any widespread notion of material implication in English logic until a few years after he died; but (the idea goes) you could just chuck the puzzle out once you got rid of primitive vagueness about logical conditionals.

But, given that material implication causes its own problems with seemingly plausible nested conditionals, as seen here, this may just go to show that it’s a bit harder to dismiss puzzles as relics of antiquated logical notation (made obsolete by the march of technical progress) than some philosophers in the last century were inclined to think. And that Carroll’s questions about implication remain interesting (and open) after all these years. (For more, see my extended post on the puzzle.)