You are talking about 'dialectical statements' statements that contain an apparent contradiction. They are not true and false at the same time, they are only c

You are talking about 'dialectical statements' statements that contain an apparent contradiction. They are not true and false at the same time, they are only commonly understood to be a contradiction, and the point of the koan or statement is to push the practitioner to is to see through the apparent contradictions. Koans and Zen stories are a training aid, but are not a substitute for common sense. Usually the contradiction occurs because the opposing statements come from different levels of analysis (the conventional: "I am going to 7/11 to get a drink.) the ultimate (I am just an unfolding process dependent on conditions that changes from one second to another, so in a way there is no I that goes to 7/11 ...). The thing is, even though 'ultimate' sounds more awesome, buddhists say "I" all the time. Just the same way that engineers use classical mechanics every day for certain classes of problems, because there's no need to bring in disappearing cats and quantum weirdness for that level of analysis. To every level of suffering, there are appropriate tools, but for some reason in the west, we often prefer to discuss complex subtle metaphysical statements we don't really understand¹, than to just go clean up the mess in the kitchen, which is a more pressing issue. The only reason I'm even engaging in this kind of talk is to discourage others from approaching buddhism that way. 1: Because they are meant to be experienced, not thought about. Full disclosure, I only know what I don't know, and I don't fully understand them either.