I found a reference to the book at Amazon - Mind Tools : The Five Levels of Mathematical Reality by Rudy Rucker.

I haven't read it and it's pretty far down on my list - don't think I'll ever get to it. But the idea is really fascinating. We use words all the time and we don't even stop to question (most of us) what they mean. We assume that we understand what a word means to us, and often that everyone understands the same thing by it. Reality, truth, facts (Tarski defined Truth as "correspondence to the facts" but it's not really obvious to me that any sufficiently large number of people wouldn't disagree with what a fact is - where sufficiently large means greater than 1). A few years ago I read Popper's Objective Knowledge. (Great book - written by a philosopher who speaks in words I can almost understand.) In it, he posits three realities - physical reality, individual psychology, and "objective knowledge" or knowledge that has survived a lot of criticism. I've only read it twice and I need to read it at least twice more for it to sink in. My faulty perception of what I've read so far is that he accepts the existence of truth, but believes our knowledge of it is imperfect. That is, knowledge is not truth. (Almost obvious when it's said that bluntly.)


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