On Thursday, September 19, 2013 10:55:15 AM UTC-4, Bruno Marchal wrote:
> On 18 Sep 2013, at 22:11, Craig Weinberg wrote: 
> > 
> > 
> > On Wednesday, September 18, 2013 8:26:35 AM UTC-4, Bruno Marchal   
> > wrote: 
> > 
> > <snip> 
> > 
> > Beyond the ambiguities, comp put the physical universe in the gap,   
> > when the gap is modeled by the logic "*" minus the logic not-"*". 
> > 
> > Why just the physical universe though? Don't you think comp needs to   
> > put itself in the gap too? 
> Here I model the gap by the difference between true and provable,   
> versus true and not provable. 

That's not the gap I'm talking about though (I didn't know that was even a 
gab that was being discussed anywhere, tbh.). The Explanatory Gap, 
philosophically, is about what is experienced directly and what is 
experienced as present independently of our direct experience. Direct 
experiences include those which seem true, experiences which seem provable, 
and experiences which seem unrelated to either proof or truth but are 
merely aesthetic, euphoric, qualitative, phenomena as sources of 
appreciation. Where does fiction fit into your gap?

> It amazes me at first that physics seems to appear only in the gap,   
> but then it is coherent with the idea that is is a first person plural   
> emergence, and that is confirmed by Everett QM. If we look at the same   
> particles we do get entangled and share the foregoing history. That's   
> why Everett saves computationalism from solipsism. 
I don't know that we are looking at the right thing in QM. Instead of 
particles, or waves which physically exist, we should focus on what gives 
physics the ability to cohere as 'particles' or 'waves' in the first place 
- what would make laws of nature manifest as 'forms', when they don't seem 
to do that in a pure computation (i.e. The Mandelbrot Set requires a 
graphic plot to visualize, it doesn't create graphics out of its arithmetic 

> > 
> > 
> > I mean G* minus G, etc. In fact physics (should) appear in Z* minus   
> > Z, X* minus X. 
> > 
> > G* and G don't show up in a Google search. I've never really   
> > understood what you mean by that, but you're welcome to explain if   
> > you have time. 
> I have done this many times on this list,

I know, sorry about that. It hasn't sunk in yet for me.

but I will explain it again   
> on FOAR soon, or later. But I can say to words. G is the modal logic   
> of Gödel's beweisbar (provability by PM, or PA, I mean Principia   
> Mathematica, pr Peano Arithmetic, or any Löbian machine). 
> In fact G correspond to the provability proposition that the machine   
> can prove about herself, and G* corresponds to the true, but not   
> provable by the machine, propositions. 

Ohh, ok. This is the two poles of your version of the Gap (which is not 
explanatory at all, but merely provable). G for a human might be, that they 
are in a hotel, but G* might be that they cannot prove which hotel they are 
in from inside of the room, but they know that the hotel is in Geneva. Or 
something like that.

We're not really talking about the same things then. To me modal logic is 
only relevant to something which relates to logic, and that rules out the 
entire universe of aesthetically experienced physics. In my view modal 
logic has no way to access any kind of experience, it assumes it from the 
start. It assumes a condition of 'provable' or 'true' as independent of 
experience rather than qualities which are abstracted from aesthetic 
comparisons. If I count five fingers, each one becomes an identical digit. 
If I count five leaves, it is the same digit of five. If I have just a 
digit of five however, it does not lead to an imagination of leaves or 
fingers unless I have experienced those prior to counting.

For example, take the (self) consistency proposition ~B f (I don't   
> prove the false). This is a typically true proposition (trivially for   
> the correct machines) but not provable by the machine. So you have G*   
> proves ~B f, but G does not prove it. 

Does ~B f need to be proved, or is it just a given that something is 
conditionally 'truish', where truish = ~B f, true in the sense of it hasn't 
been disproved? It's not clear to me why ~B f needs G* to prove it.

On the contrary, the sentence ~Bf -> ~B(~B f), which is the modal   
> translation of the second incompleteness theorem, (which says if I am   
> consistent then I cannot prove that I am consistent) *is* a theorem of   
> G, meaning that Löbian machine can prove their own incompleteness. 

But can it prove that the proof of incompleteness isn't part of its 
completeness on another level? How does it know if it can prove anything? 
Why do we attribute an expectation of proof?

> > 
> > 
> > Like I said, beyond ambiguities, what you say fits very often comp,   
> > except when you argue *from* what you say, that comp has to be   
> > false, of course. 
> > 
> > Hehe, I can do what comp can't :) 
> Comp is not a person, and not-comp makes the life of my sun-in-law   
> miserable ... ;) 

His life can't be miserable, because we can just peg some register in him 
to be happy no matter what. He doesn't need a steak, because he's got steak 
equivalent data tables to eat.


> Bruno 
> http://iridia.ulb.ac.be/~marchal/ 

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