B meant "This rock is heavier than this pencil." So, "B or ~B" means "Either this rock is heavier than this pencil, or this rock is not heavier than this pencil." Surely that is something that I can say truthfully regardless of where the pencil's weight lies. So I don't understand why you say that we can't say "B or ~B" if the pencil's weight lies in a certain range.

My idea was that the rock weighs 1.5 plus/minus sigma. If the pencil then weighs 1.5 plus/minus sigma, then you can't compare their weights with absolute certainty. The difference in their weights is a statistical proposition; the presence of the sigma factor means that the pencil must weigh less than (1.5 minus sigma) or more than (1.5 plus sigma) for B or ~B to hold. But anyways, I might concede your point as I didn't really intend this to be so technical.

I didn't say that the consequent can imply anything "by logical explosion". On the contrary, since the consequent is a tautology, it only implies TRUE things. Given any tautology T and false proposition P, the implication T => P is false.

Sorry, "logical explosion" is just a synonym for "ex falso quodiblet", which you originally mentioned. You originally pointed out that the consequent can imply anything because of ex falso quodiblet, when A is not true. That wasn't my intention, so I added the A true qualifier.

More generally, I don't understand the principle by which you seem to say that A => ~~A is "too simple", while other tautologies are not. Or are you now saying that all tautologies are too simple, and that you want to focus attention on certain non-tautologies, like "if A AND C, then B" ?

It initially seemed too simple for me, but maybe you are right. My original thinking was that "A => ~~A" seems to mean merely that a statement makes sense, whereas other propositions seem to have more meaning outside of that context. Also, the class of tautologies between different propositions seems to generalize the class of tautologies with a single proposition.

... It doesn't seem right to think of this "obviousness" as having anything to do with the territory. It seems entirely a property of how well we can work with our map.

I hadn't really thought about this, and I'm not sure how important it is to the argument, although it is an interesting point. Maybe we should come back to this if you think this is a key point. For the moment I am going to move to the other reply...