FOM: Con(ZF)/its platonistic content/intensional problems.
Stephen G Simpson
simpson at math.psu.edu
Thu Aug 27 09:52:02 EDT 1998
To: Robert Tragesser
Thanks for your recent contributions. You are certainly giving
phenomenology a great build-up. If phenomenology is the science of
exact understanding, then maybe I should reconsider my decision not to
read Heidegger, Husserl, ....
> Where Prov.subF.[p] means that p is derivable in the formal
> presentation F,
>
> [RP] If Prov.subF.[p], then p
>
> where F is understood to range over (what Weyl called) the "indeterminate=
> manifold" of formal presentations of set theory ("set theory" understood
> Platonistically as a self-standing being partially capturable by formal
> presentations F).
If I understand you rightly, F is any formal system of set theory,
e.g. F = ZF, and RP(F) is what is sometimes called in the literature a
"soundness principle" or "reflection principle" for F. Maybe that's
why you chose the acronym RP. In any case, RP(F) contains Con(F) as a
special case, taking p to be an absurdity. And clearly RP(F) includes
F itself, and a whole lot more. A typical result is that TM |- RP(ZF)
where TM is Tarski/Morse set/class theory.
Is your point that RP(F) embodies a profounder understanding of F than
Con(F) does?
-- Steve
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