The opening paragraphs are deceptive in at least two ways.
The first is that it looks like “in classical logic, from a false belief, anything follows,” which is wrong. it’s inconsistency, not falsehood, that can derive anything. One can believe the moon is made of cheese without deriving any conclusion, so long as one does not also believe that the moon is made of something other than cheese.
The second is the if → then format. While true in a sense, it’s deceptive by making it look like a single inferential step, when in fact it takes multiple steps to derive the principle of explosion. The Wikipedia article on the principle of explosion has multiple syllogisms, and the shortest is six steps. Gödel, Escher, Bach derives the principle of explosion in no less than 24 steps! It is not an obvious or immediate deduction.
I downvoted for that and because I didn’t like the rest of the post.
I thought the rewrite made it clear that issues with → and explosion were separate issues (though both different for relevance logics versus classical logic)
The opening paragraphs are deceptive in at least two ways.
The first is that it looks like “in classical logic, from a false belief, anything follows,” which is wrong. it’s inconsistency, not falsehood, that can derive anything. One can believe the moon is made of cheese without deriving any conclusion, so long as one does not also believe that the moon is made of something other than cheese.
The second is the if → then format. While true in a sense, it’s deceptive by making it look like a single inferential step, when in fact it takes multiple steps to derive the principle of explosion. The Wikipedia article on the principle of explosion has multiple syllogisms, and the shortest is six steps. Gödel, Escher, Bach derives the principle of explosion in no less than 24 steps! It is not an obvious or immediate deduction.
I downvoted for that and because I didn’t like the rest of the post.
I thought the rewrite made it clear that issues with → and explosion were separate issues (though both different for relevance logics versus classical logic)