Incorrect. — Michael

You should have read beyond the first few sentences of that post.

I think it depends on what "logical" is supposed to mean.

I would maybe think of these issues as somewhat analagous to software bugs. Video games are a good example. Some classic games that are very well received are also very buggy. You can break them, either making them trivial or else just causing crashes or all sorts of bizarre behavior.

The game still serves its purpose. It does what we want. We just know, "don't do that or you will break it." And if "that" is not something we're likely to do by accident, it really isn't a huge problem. Yet we still might want to patch the bug, but this can also be done in ways that are straightforward and "make sense," or in ways that just seem like ad hoc papering over, just like you can do good body work on a car and restore it, or just pull out the Bondo and patch it.

But when it comes to "correct reasoning," we are talking about something essential to human flourishing, freedom, and even the rise and fall of civilization. So probably want to get to the bottom of any bugs.

Explosion seems like a bug. Suppose we think common paradoxes of self-reference involve situations where statements are really both true and false. Yet even if this is so, we will likely think that this does not constitute a good reason to think that everything is both true and false.

We just know, "don't do that or you will break it." — Count Timothy von Icarus

Yep, and this goes to @Srap Tasmaner's notion of "degenerate cases" (of, say, the material conditional). If one does not see logic as teleological, then there can be no degenerate or non-degenerate cases.

Note too that formal logic is supposed to involve no rules that require interpretation. But once we introduce "degenerate cases," we have introduced a rule or norm of logic that requires interpretation. This is why formalists dislike the notion of degenerate cases.

Srap Tasmaner's notion of "degenerate cases" — Leontiskos

For the record, it's not my notion, it's what mathematicians call them. A triangle with interior angles of 180/0/0 would be a degenerate triangle. It allows you to say that any three points in a plane determine a triangle instead of saying that any three non-colinear points do. Mathematicians are generally pleased when they don't have to make special rules to cover edge cases.

- :up:

A triangle with interior angles of 180/0/0 would be a degenerate triangle. It allows you to say that any three points in a plane determine a triangle instead of saying that any three non-colinear points do. Mathematicians are generally pleased when they don't have to make special rules to cover edge cases. — Srap Tasmaner

Hmmm . . . so the common triangle is a non-degenerate triangle. I doubt I ever used the expression, "degenerate". But I see it's popular on Wikipedia.

However, I've always liked the expression "indifferent fixed point". Rather than "neutral fixed point".

Who would have thought the ridiculous expression A -> -A would go for one K posts?

In the logic you are using can we use modus ponens as an inference rule?

I do not see why not.

Don't know. There are all sorts of logics out there.