should we be dividing arrogance into two components—over-confidence and dismissive behaviour?
Of course we should! Using the same label for two different things is a frequent source of confusion.
I would even add a third component, a “my time is precious” aspect. If there is only one professor of quantum mechanics and thousand youtube-educated quantum magic worshipers, then even if the professor is very humble and if the professor believes these people are nice and good at heart, having a long and detailed discussion with each one of them would be technically impossible, so the professor must optimize for making the debate short, or even avoiding the whole debate.
Okay, in some sense this is also “dismissive”, but there is a difference between dismissing people like “go away, you are low status”, and dismissing them like “sorry, but there is only one me, and thousands of yous, I can’t really give each of you as much time as you would like to get”.
Of course we should! Using the same label for two different things is a frequent source of confusion.
I would even add a third component, a “my time is precious” aspect. If there is only one professor of quantum mechanics and thousand youtube-educated quantum magic worshipers, then even if the professor is very humble and if the professor believes these people are nice and good at heart, having a long and detailed discussion with each one of them would be technically impossible, so the professor must optimize for making the debate short, or even avoiding the whole debate.
Okay, in some sense this is also “dismissive”, but there is a difference between dismissing people like “go away, you are low status”, and dismissing them like “sorry, but there is only one me, and thousands of yous, I can’t really give each of you as much time as you would like to get”.