‘The incongruity theory was described rather badly by Immanuel Kant in 1790 when he said that laughter ‘is an affectation arising from the sudden transformation of strained expectation into nothing’. His grouchy compatriot Schopenhauer later elaborated on this, defining humour as ‘the incongruity between a concept and the real object to which it was to relate’. And what hilarious gag did Arthur Schopenhauer put forward to support his theory? ‘… for example, the amusing look of the angle formed by the meeting of the tangent and the curve of the circle’. Yes, Frankfurt positively rocked with laughter in the 1840s – the golden age of German comedy.
“Sincerity is everything. If you can fake that, you’ve got it made.”
– George Burns
The set-up of a joke creates a scenario with an assumed conclusion; the punchline provides quite a different conclusion, which subverts your previously held assumptions about the joke scenario. […] For example:
How do you make a dog drink?
Put him in a blender.
[…] It’s not just the words that make the joke work. The best jokes use language with skill and economy to conjure up mental pictures which are hilarious by virtue of their incongruity, shock value, or just sheer silliness. Here’s a lovely one:
Two monkeys are having a bath. One of them turns to the other and says, ‘Oo oo ah ah!’ The other replies, ‘Well, put the cold tap on, then.’
It’s clear that even the shortest one-liner can be prodded and poked and analysed until an inch of its life […].’
– Carr J., Greeves L. 2006. The Naked Jape – Uncovering The Hidden World Of Jokes London, Great Britain: Penguin Books (2007) p. 92-93
Knowledge Guild 
Incongruity also plays a role in magic, as in the famous Pepper’s Ghost.