On Monday, January 6, 2014 3:27:49 AM UTC-6, Bruno Marchal wrote:
> Hi Gabriel, 
> On 06 Jan 2014, at 02:48, Gabriel Bodeen wrote: 
> > Hi Bruno (& all), 
> > I was trying to read through your paper "The Origin of Physical Laws   
> > and Sensations", which I saw linked to in a conversation earlier.  I   
> > started to get lost about page 13 of the PDF, 
> Waw! Good. No problem with the UDA? 

Heh, well I can't promise I understood fully and correctly, but that 
qualitative section seemed to pass muster in my head.  When it gets down to 
the math, there's less room for me to be fooling myself.

> What is it that you don't understand page 13? You might need to study   
> a good book in logic, like Mendelson,  or Boolos and Jeffrey (+   
> Burgess in late editions). 

What is "DU accessibility"? 

Thanks for the suggested list of books!

> The books above can help, but you can also copy and past the first   
> paragraph that you don't understand, and I can explain more online,   
> although you might need to make more solid your basic knowledge in   
> mathematical logic. 

Going from knowledge to belief makes things much more subtle and 
interesting.  Indeed the paradox above, for example, will occur only if the 
visitor (which the habitant is addressing) believes all his beliefs are 
true. In the case where indeed all his beliefs are true, the reasoning 
above will show that the reasoner can neither believe, nor know for the 
matter, the very fact that all his beliefs are true. So if all the 
propositions Bp -> p are true about you, they cannot all be believed by 
you. Instead of a paradox, we get an incompleteness result. And you don’t 
need really to go on the KK Island; it is enough some habitant asserts 
‘‘Mister X or Misses X will never believe I am knight.’’ That sentence will 
be true, although unbelievable by X, independently of the fact X met such 
sentence. Imagine a native saying ‘‘the Belgians will never believe I am a 
knight,’’ then any Belgian believing in its own accuracy, i.e. believing in 
all the propositions Bp -> p, will be inaccurate, even if the Belgian 
didn’t know anything about the KK Island. Giving that the use of 
‘‘believe’’ instead of ‘‘know’’ evacuates the paradox, such an island could 
well exist and the assertion of their inhabitants could have consequences 
on our ability or inability to believe some truth! This is a very weird 
situation.  To reassure ourselves we can still hope such an island does not 

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