wow this is a nice concept

$(P \ \& \sim P) \supset Q$

For those who favour inconsistency, anything follows.

The "argument" for banning inconsistencies is what in logic is known as argumentum ad consequentiam (appeal to consequences). Note it's a fallacy

What's the consequence that's, well, unacceptable?

Ex falso [sequitur] quodlibet (Principle of Explosion)

1. P & ~P (inconsistency means contradiction implied)
2. P (1 Simp)
3. P v Q (2 Add) [note: Q is any proposition)
4. ~P (1 Simp)
Ergo,
5. Q (3, 4 DS)

As you might've noticed, I could've used ~Q from 3 to 5, the conclusion then becomes ~Q.

In other words, allowing inconsistencies implies a contradiction and from a contradiction anything follows.

What does one mean by "anything follows"? Well, it means contradictions result.

What bothers me is the circularity in the logic here. Allow me to explicate.

Q1. What's wrong with inconsistencies?
A1. They lead to contradictions.

Q2. What's wrong with contradictions?
A2. Ex falso [sequitur] quodlibet i.e. anything follows.

Q3. What do you mean "anything follows"?
A3. They lead to contradictions.


The problem with contradictions is they lead to (more) contradictions! Basically, contradictions are unacceptable because contradictions are unacceptable (circulus in probando)

The problem with murders is they lead to (more) murders! Yes, but why are murders a problem? In other words, why are contradictions a problem?

Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned. — Avicenna

Now that's more like it.