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A while ago I read in a book (or a paper?) that a very well-known mathematician (Saunders Maclane?) in his lectures used to mock the classical set-theoretical definition of natural numbers:

0 = {}, 1 = {{}}, 2 = {{}, {{}}}, ...

Who was that mathematician?

(Added after reading comments of Asaf Karagila):

Asaf, thank you for the references, but my question is not about von Neumann definition of ordinals, but (let me repeat again): Who was the famous mathematician, who in his lectures used to critisize the classical set-theoretical definition of natural numbers? Maybe, Saunders Maclane? And what is a reference on this critique?

Victor M
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    That's the von Neumann definition of ordinals, and finite ordinals correspond to the natural numbers. Besides that this appeared more than several times on this website, and you could do well to try and search before posting. – Asaf Karagila Oct 07 '13 at 23:44
  • Here are some threads that you can easily find on this site: http://math.stackexchange.com/q/226090/622, http://math.stackexchange.com/q/53155/622, http://math.stackexchange.com/q/14828/622, http://math.stackexchange.com/q/68659/622 and many many many more. – Asaf Karagila Oct 07 '13 at 23:48
  • Another thread of interest: http://math.stackexchange.com/q/85672/622 – Asaf Karagila Oct 07 '13 at 23:54
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    There are several papers involving MacLane's views and those of some well known set theorists in the book Set Theory of the Continuum (1992). I don't remember how many are by MacLane, but I believe there is more than one paper by him in this collection. For example, Mathias has a paper titled What is Mac Lane Missing? and MacLane has a paper titled Is Mathias an ontologist? I don't know if this is what you're remembering, but I think it's worth a look. – Dave L. Renfro Oct 08 '13 at 16:21
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    @AsafKaragila My apologies. I should have looked at the edit history. I have deleted my comment. – bof Oct 08 '13 at 20:10
  • @bof: No harm, no foul. – Asaf Karagila Oct 08 '13 at 23:47
  • Also posted, in revised form, to MO: http://mathoverflow.net/questions/144332/genetical-and-axiomatic-definitions-of-numbers – Gerry Myerson Oct 09 '13 at 02:47
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    Asaf commenting on something before fully reading the question? Wow I’m so surprised! – Prince M Mar 03 '21 at 18:37

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