Hi Anna,

Le 14-déc.-08, à 03:30, A. Wolf a écrit :

> One of the reasons I rarely post to this list is that many people here
> seem trapped in an eternal series of meaningless essentialistic
> debates.

I have already commented this, and I realize I have, more or less 
consciously, associated this critics, or this kind of critics, with the 
"well known" (by logical philosophers) critics of modal logic done by 
Quine or Ruth Barcan Marcus. It concerns the problem of first order 
modal logic, where you quantify simultaneously on variables (like in 
first order logic) and implicitly on worlds, like in Kripke semantics 
of the modal logic.
I guess now, you were using "essentialism" in a more general (and 
vague) sense.
Have you follow this debate? Quine said that modal logic has been 
conceived in sin, and Boolos has already understood that Gödel's 
incompleteness theorems have "redeemed" modal logic by providing a 
transparent purely mathematical (even arithmetical) interpretation of 
the self-reference modal logics (G and G*).
So I can argue informally that there is no essentialism in the UDA 
reasoning, but I can argue also that there is no Quine-Barcus sort of 
more technical essentialism in the arithmetical translation of the UDA.

To be 100% correct, I have to add that another form of essentialism 
appears with some Lobian Machines, when they have too much rich 
"intended interpretation domain". For example, although the (sound and 
complete) propositional self-reference logics of ZF (Zermelo-Fraenkel 
set theory) are still G and G*, there is no clear sense how to extend 
this in the first order modal logic. And this is the reason why I don't 
really trust the set theoretical form of Lobian Machine.

For those who remind the definition of the arithmetical hypostases, the 
'second God" (the intelligible) of Peano Arithmetic is already far 
bigger than its "first God" (indeed it is Pi_1 *in* the first God 
(Truth)). But with the Lobian Machine ZF, the second God could already 
be so big that it would be inconsistent. Set theory is much too big by 
itself. I guess "sound humans" are probably between PA and ZF, with 
respect to their ideal Lobian features. Personally I am not sure we are 
really much more than the PA machine.

OK, sorry for those remark addressed to those who are inclined in the 
Technics. But the whole point of both UDA and AUDA is too makes it 
possible the progressive scientific attitude on question concerning 
self, consciousness and things like that.

Now, if you have an argument that the notion of consciousness is 
necessarily an essentialist notion, I would be glad to hear it, if only 
to have the opportunity to provide supplementary motivation to the use 
of the Gödel-Löb modal logics, which here redeemed the very notion of 
consciousness itself.

We can come back on this if and when we arrive at the AUDA, and the 
arithmetical interpretation of Plotinus hypostases in the current 
(re)-explanation of UDA and AUDA (the KIM threads).


Bruno Marchal


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