FOM: Con(ZF)/its platonistic content/intensional problems.

Stephen G Simpson simpson at
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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