Hi Bruno Marchal  

I think in computationalism you only have to be able
to say that the result is arithmetically or algebraically
true. Arithmetic truth is what you seek.

However, I still have yet to know if  a particular
computation seems true to your 1p. That would be
1p truth. Does the arithmetic truth pass the 1p test ?


Roger Clough, rclo...@verizon.net 
11/3/2012  
"Forever is a long time, especially near the end." -Woody Allen 


----- Receiving the following content -----  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-11-02, 13:23:36 
Subject: Re: Numbers in the Platonic Realm 




On 01 Nov 2012, at 22:50, Stephen P. King wrote: 


On 11/1/2012 12:04 PM, Bruno Marchal wrote: 



On 01 Nov 2012, at 01:18, Stephen P. King wrote: 


On 10/31/2012 12:45 PM, Bruno Marchal wrote: 

 can stop reading as you need to assume the numbers (or anything Turing 
equivalent) to get them.  

Dear Bruno, 

    So it is OK to assume that which I seek to explain? 





You can't explain the numbers without assuming the numbers. This has been 
foreseen by Dedekind, and vert well justified by many theorem in mathematical 
logic. Below the number, you are lead to version of ultrafinitism, which is 
senseless in the comp theory. 

 Dear Bruno, 

    I disagree with ultrafinitists, they seem to be the mathematical equivalent 
of "flat-earthers'.  










*and* having some particular set of values and meanings.  


I just assume 


x + 0 = x   
x + s(y) = s(x + y)  


 x *0 = 0 
 x*s(y) = x*y + x   


And hope you understand. 



    I can understand these symbols because there is at least a way to 
physically implement them.  


Those notion have nothing to do with "physical implementation".  


    So your thinking about them is not a physical act? 



Too much ambiguous. Even staying in comp I can answer "yes" and "no". 
Yes, because my human thinking is locally supported by physical events. 
No, because the whole couple mind/physical events is supported by platonic 
arithmetical truth. 








Implementation and physical will be explained from them. A natural thing as 
they are much more complex than the laws above. 

    Numbers are meaningless in the absence of a means to define them. Theories 
do not free-float. 



Truth is free floating, and theories lived through truth, they are truth 
floating, even when false. 










In the absence of some common media, even if it is generated by sheaves of 
computations, there simply is no way to understand anything.  


Why ? 

    Because there is not way to know of them otherwise.  


Our knowing as nothing to do with truth. If an asteroid would have destroy 
Earth before the Oresme bishop dicovered that the harmonic series diverge, she 
would have still diverge, despite no humans would know it. 






Unless you can communicate with me, I have no way of knowing anything about 
your ideas. Similarly if there is no physical implementation of a mathematical 
statement, there is no meaning to claims to "truth" of such statements. 



To claim, no. To be true is independent of the claim of the apes. 










You must accept non-well foundedness for your result to work, but you seem 
fixated against that. 



1004. 

    Pfft. Nice custom made quip. 



You are often escaping answers by inappropriate mathematical precision, which 
meaning contradicts your mathematical super-relativism. It is really 
1004+contradiction. 






     








A statement, such as 2 = 1+1 or two equals one plus one, are said truthfully to 
have the same meaning because there are multiple and separable entities that 
can have the agreement on the truth value. In the absence of the ability to 
judge a statement independently of any particular entity capable of 
"understanding" the statement, there is no meaning to the concept that the 
statement is true or false. To insist that a statement has a meaning and is 
true (or false) in an ontological condition where no entities capable of 
judging the meaning, begs the question of meaningfulness! 
   You are taking for granted some things that your arguments disallow. 





Do you agree that during the five seconds just after the Big Bang (assuming 
that theory) there might not have been any possible observers. But then the Big 
Bang has no more sense. 

    No, I don't. Why? Because that concept of "the five seconds just after the 
Big Bang" is an assumption of a special case or pleading. I might as well 
postulate the existence of Raindow Dash to act as the entity to whom the Truth 
of mathematical statements have absolute meaning. To be frank, I thing that the 
Big Bang theory, as usually explained is a steaming pile of rubbish, as it asks 
us to believe that the totality of all that exists sprang into being from 
Nothing.  


I actually agree, by accident, on this. But this is not relevant for my point. 

    It is very relevant to mine. 


Imagine that we can show that some solution to GR equantion have universe so 
poor that life cannot exist in there, would you say that such universe cannot 
exist? 

    If there does not exist a means to "show the solution" there is no 
solution. 



Mathematical solipsism.  












I believe that the totality of what exists is eternal, having no beginning and 
no end.  


I am OK with that. It is close to Platonism. But with comp we can restrict this 
to the arithmetical truth (a highly non computable structure, but still 
conceivable by universal numbers, relatively). 

    Well, can we work with that agreement? 



Come on, you say that you can escape the consequence of comp, you have to find 
the flaw, or to be more cautious in your judgment. 
There is no one statement I made on this list which I have not published 
before, and there have been a lot of peer-review (especially that many 
philosophers hate that work, but they try to defend the philosophy curriculum 
against a possible invasion of science: that is usual and normal). 










What we infer from our observations of Hubble expansion is just an effect that 
follows, ultimately, from our finiteness.  



Including time and space. So we do agree again.  


    Good! 








I think Brent is right, and Quentin. You confuse 1+1=2 with human expression 
for pointing on that proposition. You obviously needs human to understand those 
" "1+1=2" ", but the content of "1+1=2" has simply no relation at all with the 
human, or with a physical universe. 

    No, none of you have yet to be able to understand my counter-argument. It 
is not complicated. We cannot assume to have something when the means for its 
existence is not allowed. My claim is that meaningfulness supervenes on the 
possibility of interaction of *many* entities and is independent of any *one* 
(or some lesser finite subset) of that Many. 



But arithmetical truth is full of entities, even full of galaxies themselves 
full of self-aware being. That is a fact. But with comp (and UDA), those 
entities are saved from zombieness. 

    Yes, and bundles of arithmetic statements generate many individual 
observers that in turn "interact" (which I model via a combination of cyclic 
gossiping on graphs and bisimulations) with each other to define a common 
physical world which in turn acts to "implement" the arithmetic. It is a loop, 
an eternal cyclical process that never exactly repeats. It is in this infinite 
loop that I see your UD. 



It is not a loop. It is more like a recurring abyss, like the Mandelbrot set. 














I asked you some time ago if you agree with the use of the excluded middle in 
arithmetic. It asserts that for any arithmetical proposition P, even highly non 
computably verifiable, you can accept as new arithmetical truth the proposition 
asserting that P v ~P. Which intuitive meaning that the proposition is 
unambiguously either true, or false, despite you have no idea if it is P or ~P 
which is the true one. To accept this means that you accept that such truth are 
independent of the means to prove or verify them. 

    We must us the principle to excluded middle [PEM] to reason, but this does 
not make the principle something external and independent of us.  


1) the intuitionist can reason without them.  


    Yes, but their reasonings are severely limited. 



You are the one saying that truth is limited to the means of knowing!!! 








2) the PEM is a way to assert formally platonism, and I use it only in 
arithmetic. And it means that the truth is independent of our reasons. 

    Truth is independent of any particular reasoning, but it is NOT independent 
of the reasoning of all entities.  



Ambiguous. trivially true with comp as the reasoning of all entities belongs to 
the (tiny part of) arithmetical reality. 











This is a red herring, Bruno. It is not addressing my claim at all.  


Then you have to try to state it more clearly. 

    I am trying. ;-) 




You seem to be stuck on the idea that only one entity can have or not have some 
property or power and cannot reason about the possibility that *many* may be 
required to solve some problems. A plurality is not a multiplicity...  



This is too vague. 

    OK, I will try again. 


I don't see that one one entity can have or not have some property or power, 
nor why I can't reason on the possibility that ?*many* might be required (on 
the contrary, there are many notion of many playing in comp and the emergence 
of physics. No clue what you mean here. 

    Are you familiar with Jaakko Hintikka's ideas? I am using his concept of 
game theoretic semantics to derive truth valuations. 



I read this. yes. I don't see relevant at all. 
I do appreciate his linking of intention and intension, but it is a bit trivial 
in the comp theory. 




Bruno 






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

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