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It is entirely possible to believe in fate and recognize the existence of coincidence at the same time.
Everything that happens to us is a coincidence in the sense that it all coincided with something else within incomprehensibly complex chains of cause and effect. Nothing is so disparate to be unlinked from reason.
But this is not to be mistaken with the belief in fate, for fate doesn’t merely ask why individual events occur in the first place; it asks why the chain of effect was designed to cascade in the way that it does.