Parsons’s Mathematical Thought: Secs. 40-45, Intuitive arithmetic and its limits

Here, as promised, are some comments on Chapter 7 of Parsons’s book. They are quite lengthy, and since in writing them I found myself going back to revise/improve some of my discussions of earlier sections, I’m just posting a single composite version of all my comments on the first seven chapters. I’m afraid that is already over 20K words and 36 single-spaced pages (start at p.31 for the substantially new stuff). So I am sounding off at some length: but it seems to me that the topics tackled in Mathematical Thought are so very central as to be well worth extended discussion.

I’ve still two more chapters to go: next up is a fifty page chapter on induction, which I think can be discussed fairly independently from what’s gone before. So I’ll revert to section-by-section blogging here.

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