How do you know I’m mad?

‘But I don’t want to go among mad people,’ 
Alice remarked.
‘Oh, you can’t help that,’ said the Cat: ‘we’re all mad here. I’m mad. You’re mad.’ 
‘How do you know I’m mad?’ said Alice.

‘You must be,’ said the Cat, ‘or you wouldn’t have come here.’ 
Alice didn’t think that proved it at all; however, she went on ‘And how do you know that you’re mad?’
‘To begin with,’ said the Cat, ‘a dog’s not mad. You grant that?’
‘I suppose so,’ said Alice.
‘Well, then,’ the Cat went on, ‘you see, a dog growls when it’s angry, and wags its tail when it’s pleased. Now I growl when I’m pleased, and wag my tail when I’m angry. Therefore I’m mad.’ 
‘I call it purring, not growling,’ said Alice. ‘Call it what you like,’ said the Cat.