In my defense, that's a written-at-five-in-the-morning tone, not a condescending tone. I'm not sure what I was trying to write with the "I imagine the author h

In my defense, that's a written-at-five-in-the-morning tone, not a condescending tone. I'm not sure what I was trying to write with the "I imagine the author himself fails (1)" bit, as I am sure Bauer is far beyond me on the subject, as I admitted in my comment. Apologies to Bauer and to all for coming off wrong. Writing 'cavalier attitude to truth' was a poor choice of words, but let me explain what I meant. I agree that intuitionistic math is logically more rigorous, and it sets a higher bar for what can be considered true. But because it rejects the validity of tools like proof by contradiction and the law of the excluded middle—tools that classical mathematicians use to disprove many concepts—intuitionistic math contains a much wider universe of possible mathematical objects. It sets a lower bar for what should be considered untrue. So when you use mathematical objects that only potentially exist—that is, objects whose existence you can neither prove nor disprove—it seems to most classical mathematicians as more than a bit dishonest, because they work only with objects that must exist. (I brought up Nelson's axiomatic approach to infinitesimals because it is analogous in this regard.) Thus Russell's likening postulates to theft. Intutionists get to play with toys that other mathematicians don't because the former are, in a sense, more broad-minded about what toys are (could be) out there. That's all I meant by 'cavalier attitude to truth'. Like I said, I admire this approach, and have tried to pick up some axiomatic approaches myself when they're helpful, but I still do think that Russell's bit of pith is quite apt.