[FOM] Scott's not entirely ingored attempt

A.P. Hazen a.hazen at philosophy.unimelb.edu.au
Fri Jul 4 00:09:12 EDT 2003

Another writer influenced by Scott was James Van Aken, whose
   "Axioms for the set-theoretic hierarchy," JSL 51 (1986),
	pp. 992-1004
presents a variation on Scott's theme, with some discussion of
their intuitive motivation.  Van Aken dubs the relation of later
to early stages "presupposition"; my own feeling is that his paper
represents something of a high-water mark for the metaphysical
view of the iterative hierarchy-- a fe years later, George Boolos
   "Iteration Again," Philosophical Topics 17 (1989), pp. 5-21;
	repr. in Boolos's "Logic, Logic, and Logic"
reminded philosophers of the role of "limitation of size," suggesting
that this was independent of the iterative conception.

Scott's magical way of obtaining induction-on-membership (rank
induction) from assumptions that don't SEEM to include it has
influenced other people as well.  Cf. the article by Geoffrey Hellman
in Sher & Tieszen, eds., "Intuition and Logic."

> Dana Scott's largely-ignored attempt (Proc Symp Pure Math Vol 13 1974),
> to found ZF(C) on the more fundamental idea of "stages" of constructing
> things.


Allen Hazen
Philosophy Department
University of Melbourne

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