I don't think we can imagine a world without causation. We can imagine one where certain individual aspects appear to happen in a non-causal manner. We can even redefine the understanding of a world down to a point where only these types of event are incorporated. But then, I think, these turn out to be simply artefacts constructed from parts of our own world. Nevertheless, I'm not particularly precious about this. It was a scene-setter - not an argument in its own right. I wanted to get across the idea that causation is a pervasive way of understanding the world, even more so than the understanding that comes with logic or mathematics.
I didn't spell out what I meant very clearly. I disagree that the similarity between the necessity of causation and the force of valid logic are the same, because we are, maybe, using varieties of logical language. Neither am I saying that there is a feeling of truth, or a fit based on some match with experience. That latter point was the empiricist view in a nutshell; Hume coming up with the idea that the constant perception of events we call "causes" prior to the events we call "effects", leads to the impression of a supposed relationship which we imbue with necessity.
What I am saying, is that causation is a principal of our comprehension of the world. I'm with Kant here: it isn't something we derive from experience, it's something a priori which makes our experience possible at all. This is what is in common with logic and mathematics. I think it's necessary to bear in mind that the world is a rather rich and complex place with many aspects that we may only come to experience at different points in our lives. The objection might be raised that it is perfectly possible to go through life with no mathematical concepts at all and yet have a full and useful experience of the world. This may be true, but it's also true that it is when you have understood the rules of mathematics that the mathematical world is available to you. Mathematics makes our experience of the mathematical world possible. Logic makes our experience of the logical world possible. To follow up on your Wittgenstein type of question about artistic/musical etc. propositions: yes, there is a similarity.