Article View: sci.logic
Article #59Re: Impredicativity - was: Russell's Paradox.
From: Keith Ramsay
Date: Tue, 03 Nov 1992 23:06
Date: Tue, 03 Nov 1992 23:06
27 lines
1573 bytes
1573 bytes
In article <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU>
pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes:
>The iterative hierarchy is consistent with Z but not with ZF.
Oh really?
>Replacement (F) says in effect that any construction you can iterate
>yields a set.
*Very* loose rendering. The process must, at the very least, be
iterated only over a set, not over a proper class such as all ordinals
(and the ranks of the iterative hierarchy are *all* the ordinals).
>Hence if the universe is an iterative hierarchy it is a
>set.
This process is one which could not conceivably be finished as a
physical task, even in principle, so its result is not a set.
>Anyone brought up on the iterative hierarchy was told a lie.
I don't agree.
Keith Ramsay "While this sort of holistic pragmatism is
ramsay@unixg.ubc.ca attractive, it too has serious difficulties. (So
does *every* view; that is why the philosophy of
mathematics is so fascinating.)"
Technical Details
Message-ID:
<1d70krINN1bg@iskut.ucs.ubc.ca>Path:
arc1-ca.pugleaf.net!sparky!uunet!gumby!destroyer!cs.ubc.ca!unixg.ubc.ca!ramsayReferences:
<1992Nov2.040843.4524@CSD-NewsHost.Stanford.EDU> <1992Nov2.205433.21208@tamsun.tamu.edu> <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU>Show Full Headers
Complete Article Headers
Path: arc1-ca.pugleaf.net!sparky!uunet!gumby!destroyer!cs.ubc.ca!unixg.ubc.ca!ramsay From: ramsay@unixg.ubc.ca (Keith Ramsay) Newsgroups: sci.logic Subject: Re: Impredicativity - was: Russell's Paradox. Date: 3 Nov 1992 23:06:03 GMT Organization: University of British Columbia, Vancouver, B.C., Canada Lines: 27 Message-ID: <1d70krINN1bg@iskut.ucs.ubc.ca> References: <1992Nov2.040843.4524@CSD-NewsHost.Stanford.EDU> <1992Nov2.205433.21208@tamsun.tamu.edu> <1992Nov3.041515.27732@CSD-NewsHost.Stanford.EDU> NNTP-Posting-Host: unixg.ubc.ca