I would recommend "Mindfulness in Plain English" by Henepola Gunaratana. It is indescribably common for Westerners to imperfectly rehash/rediscover the basic philosophy of Buddhism. There's a tiny bit of spiritualism in the book, but it's 95% sheer psychology/philosophy that will teach you how to perceive the heart of what, without the raw self-observation that is boiled down to its essence in vipassana meditation, is just more noise. To put it another way, people like Greene re-describe intellectually something that can only be truly understood experientially. Striking at Greene's idea of the "false self" is just taking out a hydra head.