Acts 9:22

‘But Saul increased the more in strength, and confounded the Jews who dwelt at Damascus, proving that this is the Christ.'

Meanwhile the more he preached, and the more he studied, the more he increased in effectiveness, and the more he was able to confound the Jews in Damascus by proving that Jesus was the Messiah.

But it is more than likely that after a short period of such preaching and debating he recognised his need to understand more deeply what he was speaking about. He had his whole theology to sort out again. He realised his need for a period of reflection so that he might sort out his what he should teach, and prepare himself for dealing with their questions by a careful consideration of the Old Testament text which he probably knew by heart. He had to build on his testimony, and the few Scriptures that he had at hand, which he could not just go on repeating for ever. This would explain why he took a short break to study in Arabia. It was the visit of unknown duration described in Galatians 1:17. Note his words there. He did not go to Jerusalem to see the Apostles, he went to Arabia. He wanted to consult with God. And there in the deserted wilderness, possibly of ‘Mount Sinai in Arabia' (Galatians 4:25), he thought through his whole doctrine in the light of the Scriptures which now had such new meaning for him. It was possibly then that he came to realise that the true Jerusalem is above and is not a place of binding Law but of glorious freedom (Galatians 4:26), that the true descendants of Abraham and Sarah are the children of promise (Galatians 4:28), that with freedom Christ has made us free, so that we might stand fast and not be entangled again in the bondage from which we have been freed (Galatians 5:1), that those who seek to be justified by the Law have fallen away from the whole concept of grace (Galatians 5:4). Three years later he would go to Jerusalem in order to discuss it all with Peter, but that was later. Now he had to sort things out between himself and God. And once he had done so he returned to Damascus.

It was probably partly as a result of this visit that he ‘increased the more in strength', having now clarified his thinking. Galatians assumes a time away from Damascus, followed by a return there resulting in further ministry, with the whole covering in all ‘three years' (eighteen month upwards). But there is absolutely no reason why Luke should have mentioned the visit to Arabia. We have already seen how he abbreviates his narrative in order to concentrate on what he wishes to emphasise, and he is concerned with the spreading of the word. He is not writing a life of Paul but a description of the outreach of the Good News with regard to which description the visit to Arabia was irrelevant. So Paul's conversion here is described as a part of the ongoing work of spreading the word followed by the initial ministry of three years that resulted from it, which was so effective that he had to flee. What Luke was interested in here was the ministry in Damascus which continued the expansion of the word of God (Acts 9:31).