There are quotes in chapter 4, which I think present cartoon versions of teachings:
Leaving out the next sentence in the book:“Mindfulness is the quality of mind that notices what is present, without
judgment, without interference.”
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And presumably much that is in the rest of the book...It is like a mirror that clearly reflects what comes before it. Munindraji summed up this quality with one simple expression: knowing things as they are."
However, Bhante G observes later in the chapter:“Mindfulness is mirror-thought. It reflects only what is presently happening
and in exactly the way it is happening. There are no biases...
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This is difficult for me to reconcile with Thanissaro Bhikkhu statement that these other teachers are claiming that:(a) Mindfulness reminds you of what you are supposed to be doing . In meditation, you put your attention on one item. When your mind wanders from this focus, it is Mindfulness that reminds you that your mind is wandering and what you are supposed to be doing. It is Mindfulness that brings your mind back to the object of meditation.
There are certainly some differences between the interpretations of Ven Thanissaro, Bhante G, and Joseph Goldstein. However, when their instructions are taken as a totality the differences seem to me to be often a case of where exactly they choose to classify things amongst right thought, effort, mindfulness, concentration, wisdom, etc.... the Buddha, in defining the faculty of mindfulness in SN 48:10,
didn’t actually define it as memory; he defined it as the mental state that allows
memory to happen. In other words, attention lies in the background of the
definition without actually being mentioned in it.
I've found Ven Thanissaro's expositions of Dhamma very useful and thoughtful. But I'm afraid I find the critiques rather shallow, so I generally ignore them. I much prefer the approach of teachers who simply say: "This is how I see it ..." and leave the listeners to do comparisons or ask questions for clarification.