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You have to check Feferman OST [Paradox Hunting] (Was: CET is also needed)

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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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