Start doubting ourselves some more and we'll get a panic attack - our breathing will be disrupted, the pulse will become very fast, we will want to run off the stage, and we will freeze without being able to play anything - especially from memory.
It turns out self-doubts are perfectly natural, even essential. Whoever doesn't have them is either a fool or has simply too little experience.
But when you play, something else is much more important - it doesn't matter what kind of thoughts come to your head, you have to force yourself with all you've got to stick to just one thing - the current measure you are playing. Not to what has just sounded a few seconds ago, not to what will come on the next page, but now.
If you do that, then trusting yourself becomes irrelevant.