> On 8 Mar 2019, at 15:49, John Clark <johnkcl...@gmail.com> wrote:
> 
> On Fri, Mar 8, 2019 at 5:05 AM Bruno Marchal <marc...@ulb.ac.be 
> <mailto:marc...@ulb.ac.be>> wrote:
> 
> >> Assuming you're just using 2 symbols (like 0 and 1) there are (16001)^8000 
> >>  different 8000 state Turing Machines. And that is a very large number but 
> >> a finite one. And one of those machines makes the largest number of FINITE 
> >> operations before halting. And that number of operations is BB(8000).  
> >> Even theoretically, much less practically,  you can never compute that 
> >> number but I have given a unique description of it, no other 8000 state 
> >> Turing Machine has that propertie.
>  
> > Yes, sure BB(8000) is a precise well defined finite number. But it is no 
> > what logician and philosopher call a “name”, where the number should be 
> > computable in principle. My point is just a vocabulary point,
> 
> I agree it's just a question of vocabulary but to avoid confusion if logician 
> and philosophers want to use commonly used words then their technical meaning 
> should have some relationship to their common meaning. Parents can give a 
> precise definition to their child (he's the only kid in the crib) so they can 
> "name" him even though they can't calculate him.
>  
> > and a way to remind a nice problem which I have used to illustrate some 
> > less known application of Cantor’s diagonal.
> 
> It always seemed to me that if Cantor had taken just one more small step he 
> could have proven the existence of non computable numbers more than 40 years 
> before Turing did.


Similarly, if you read Plotinus’ Ennead “On the Number”, you can see that 
Plotinus was foreseeing the Difficulty that Cantor was confronted with the 
notion of set, notably by trying to get a number of the numbers, which was a 
natural idea for a platonician, but one of those ideas which leads to 
conceptual difficulties, and theological one too, as Cantor saw by having an 
heavy correspondence with the catholic clergy. 
I think that if we would not have been obliged, by violence and terror, to 
separate science and theology, and to not have mixed it with the State(s), the 
whole “Church-Turing-Gödel” revolution could have appeared 500 hundred years 
before. I take the discovery of the Universal Machine, made by Babbage, Post, 
Church Turing is the biggest discovery made by the humans ever. It changes 
literally everything including the conception we can have on everything.

Bruno






> 
>  John K Clark
> 
> 
>  
> 
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