XPost: sci.logic, sci.math   
   From: janburse@fastmail.fm   
      
   Hi,   
      
   You are still hunting Paradoxes, is   
   this still a noble occupation?   
   You have to check Feferman OST etc..   
      
   The statement is only, that for A,   
   formula, there exists t_A a term,   
   such that:   
      
   t_A(x) = tt <=> A(x)   
      
   Gödel used the same, t_A is nothing   
   else than a Gödelization of A. Only   
   in Gödel numbers were used, and Gödel   
      
   usually written as {A}. And already   
   Gödel showed before Curry all kind of   
   fixpoint paradoxes. But Feferman does   
      
   not allow arbitrary A, and a modern   
   branch of Feferman OST would be Reverse   
   mathematics having a bunch of allowed   
      
   or disallowed forms of A. What Feferman   
   OST shows if he makes small large cardinals   
   plausible, he shows of course also   
      
   that the thingy is not inconsistent, i.e.   
   has no Paradox under certain circumstances.   
      
   Have Fun!   
      
   Bye   
      
   BTW: OST is related to Gödels constructive   
   universe L, and papers such as these are   
   full of V = L assumptions:   
      
   https://home.inf.unibe.ch/gerhard.jaeger/16-relativizing_OST.pdf   
      
   But I don't know how substantial the stuff   
   there is. I only use the fact that t is a term,   
   and then terms in my Prolog system Dogelog Player   
      
   correspond to compiled code. So t_A is basically   
   not anymore the original formula A, as already in   
   OST, but its not so much viewed as a Gödelization   
      
   out of the blue, more as a code for some Prolog machine.   
      
   Ross Finlayson schrieb:   
   > It may remind one of the Curry correspondence.   
   >   
   > Of course, in mathematics, that then gets into   
   > compactness and fixed-point theorem(s) and   
   > definition(s) of the direct product of integers.   
   >   
   > I.e., in mathematics, "equality" begets infinitary reasoning.   
   >   
   > Some years ago, there was a thread on sci.logic   
   > about Curry correspondence, I wrote on it, so,   
   > there's probably something meaningful to it.   
   >   
   > In, "the logic", say.   
   >   
   > https://sci.logic.narkive.com/36tgd6NK/curry-s-paradox-in-propositional-logic   
   >   
   >   
   >   
      
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