Hi Bruno Marchal  

Is sigma_6 truth truth with only a 6 sigma possibility of error ? 

Roger Clough, rclo...@verizon.net 
11/5/2012  
"Forever is a long time, especially near the end." -Woody Allen 


----- Receiving the following content -----  
From: Bruno Marchal  
Receiver: everything-list  
Time: 2012-11-04, 08:56:01 
Subject: Re: The two types of truth 


On 03 Nov 2012, at 12:45, Roger Clough wrote: 

> Hi Bruno Marchal and Stephen, 
> 
> http://www.angelfire.com/md2/timewarp/leibniz.html 
> 
> "Leibniz declares that there are two kinds of truth: 
> truths of reason [which are non-contradictory, are always either 
> true or false], 

We can only hope that they are non contradictory. 
And although true or false, they are aslo known or unknown, believed  
of not believed, disbelieved or not disbelieved, etc. 




> and truths of fact [which are not always either true or false]. 

Why? They are contextual, but you can study the relation fact/context  
in the higher structure level. 


> 
> Truths of reason are a priori, while truths of fact are a posteriori. 
> Truths of reason are necessary, permanent truths. Truths of fact are  
> contingent, empirical truths. 
> Both kinds of truth must have a sufficient reason. Truths of reason  
> have their 
> sufficient reason in being opposed to the contradictoriness and  
> logical inconsistency 
> of propositions which deny them. Truths of fact have their  
> sufficient reason in 
> being more perfect than propositions which deny them." 

Unfortunately, this is acceptable below Sigma_1 truth, but doubtable  
above, so even in the lower complexity part of arithmetic, things are  
not that simple. 

Bruno 




> 
> 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: 2012-11-03, 07:13:24 
> Subject: Re: Numbers in the Platonic Realm 
> 
> 
> On 02 Nov 2012, at 23:12, Stephen P. King wrote: 
> 
>> On 11/2/2012 1:23 PM, Bruno Marchal wrote: 
>>>>>> 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. 
>> Dear Bruno, 
>> 
>> Where is the evidence of the existence of a Platonic realm? 
> 
> It is part of the assumption. We postulate arithmetic. I try to avoid 
> the use of "platonic" there, as I used the term in Plato sense. In 
> that sense Platonia = the greek No?, and it is derived from 
> arithmetic and comp. 
> 
> All you need is the belief that 43 is prime independently of "43 is 
> prime". 
> 
> 
> 
>> The mere self-consistency of an idea is proof of existence 
> 
> Already in arithmetic we have the consistence of the existence of a 
> prrof of the false, this certainly does not mean that there exist a 
> proof of the false. So self-consistency is doubtfully identifiable 
> with truth, and still less with existence. 
> 
> 
> 
>> but the idea must be understood by a multiplicity of entities with 
>> the capacity to distinguish truth from falsehood to have any 
>> coherence as an idea! 
> 
> Not at all. 43 is prime might be true, even in absence of universe and 
> observer. 
> 
> 
> 
>> We cannot just assume that the mere existence of some undefined acts 
>> to determine the properties of the undefined. Truth and falsity are 
>> possible properties, they are not ontological aspects of existence. 
> 
> Truth is no more a property than existence. It makes no sense. 
> 
> Bruno 
> 
> 
> http://iridia.ulb.ac.be/~marchal/ 
> 
> 
> 
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http://iridia.ulb.ac.be/~marchal/ 



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