FOM: Comment on Parson/Davis

Moshe' Machover moshe.machover at
Sat Mar 14 07:47:36 EST 1998

Parsons says:

>I applaud most of what Martin says in his posting. I hope he'll write up
>the talk so that those of us who won't be at the meeting can read it.

Hear, hear!

>There's one statement I would quarrel with, that Zermelo's axiomatization
>of set theory was "based on" cumulative types. There's no hint in his 1908
>paper or others of that time that that was the way he understood his

I agree. My guess is that Zermelo (like Cantor) thought in terms of
limitation of size.

The strongest argument against the view that in 1908 he had in mind the
cumulative hierarchy is the absence of any postulate ensuring
well-foundedness--Parsons alludes to this in his mention of
Mirimanoff--which is surely the hallmark of the cumulative hierarchy.

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