Luke 11:20

“But if I by the finger of God cast out demons, then is the Kingly Rule of God come upon you.”

On the other hand they should consider the fact that if He cast out evil spirits by the finger of God, then it proved that the Kingly Rule of God was present in Him. That it had come on them unexpectedly. This is not arguing that the fact that evil spirits were cast out proved that the Kingly Rule of God had come. Their ‘sons' did similar things and no one suggested that that meant that the Kingly Rule of God had come. All that did was prove that they and He were of God.

What He is saying here is that it is because  He, as God's Anointed One, was doing it by the finger of God that it proved that the Kingly Rule of God had come. For the admission that He did cast out demons by the power of God when combined with His claims (which His success against demons would confirm) would establish His claims. They could not agree that He cast out demons by the power of God and at the same time deny His claims to be the Son of man, for His success against demons would be evidence that God was pleased with Him and acknowledged His claims. That would then be sufficient proof that the Kingly Rule of God had come.

The phrase ‘finger of God' is an Old Testament phrase denoting God's direct action free from any occult methods. The Egyptian magicians used it when they at last had to recognise that Moses was not using conjuring tricks or demonic magic, but that God Himself was acting directly (Exodus 8:19). They recognised that now God had put His seal on things. It was also used of the writing of ‘the ten words on the tablet which were ‘written by the finger of God' (Exodus 31:18; Deuteronomy 9:10). The finger of God was the guarantee that the words were His words. Thus here it is a seal of Who and What Jesus is. Matthew translates it as ‘if I by the Spirit of God' (Matthew 12:28), which is saying the same thing, for the phrase ‘Spirit of God' always indicates direct action.

As the chiasmus demonstrates, these words are central to the whole passage. Luke's central point here is that the Kingly Rule of God has come with power in Jesus as He does battle with the forces of evil. This will then be further emphasised in order to demonstrate that Jesus is the ‘Stronger than he'.