Bruno Marchal wrote:
> 
> 
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Brent Meeker-2 wrote:
>>>>>
>>>>>> The easy way is to assume inconsistent descriptions are merely an
>>>>>> arbitrary
>>>>>> combination of symbols that fail to describe something in
>>>>>> particular and
>>>>>> thus have only the "content" that every utterance has by virtue of
>>>>>> being
>>>>>> uttered: There exists ... (something).
>>>>>>
>>>>>
>>>>> But we need utterances that *don't* entail existence.
>>>>
>>>> If we find something that doesn't entail existence, it still entails
>>>> existence because every utterance is proof that existence IS.
>>>> We need only utterances that entail relative non-existence or that
>>>> don't
>>>> entail existence in a particular way in a particular context.
>>>
>>> You need some non relative absolute base to define relative  
>>> existence.
>> The absolute base is the undeniable reality of there being experience.
> 
> But this one is not communicable. It does play a role in comp, though. 
But we can say "there is an undeniable reality of there being experience".
Isn't this communicating that there is the undeniable reality of there being
experience?
We merely communicate something that everbody already fundamentally knows.
Though some like to deny what they already know.


Bruno Marchal wrote:
> 
> But it is not enough. usually people agree with the axiom of Peano  
> Arithmetic, or the initial part of some set theory.
But Peano Arithmetics is not a non relative absolute base. It is relative to
the meaning we give it and to the existence of some reality. 1+1=2 can have
infinite meanings, that all are relative to our interpretation ("If I lay
another apple into the bowl with one apple in it there are two apples" is
one of them) and there being meaning in the first place. 



Bruno Marchal wrote:
> 
>>
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Brent Meeker-2 wrote:
>>>>>
>>>>> So we can say
>>>>> things like, "Sherlock Holmes lived at 10 Baker Street" are true,
>>>>> even
>>>>> though Sherlock Holmes never existed.
>>>> Whether Sherlock Holmes existed is not a trivial question. He didn't
>>>> exist
>>>> like me and you, but he did exist as an idea.
>>>
>>>
>>> Even if you met *a* Sherlock Holmes in Platonia, you have no cirteria
>>> to say it is the usual fictive person created by Conan Doyle,  
>>> because,
>>> in Platonia, he is not created by Conan Doyle, ...
>> In Platonia he is not created by Conan Doyle, which makes sense,  
>> given the
>> possible that other people use the same fictional character, so he is
>> essentially discovered, not created.
>>
>> But I don't know what you want to imply with that.
> 
> Just that fictionism, the idea that numbers are fiction of the same  
> type as fictive personage from novels does not make sense, except to  
> confuse matter.
Well I didn't want to imply that. Fictionage personage usually refer to some
relative manifestation of an idea, while numbers are a more general and
abstract notion.
And if they are fiction, they are very prevalent fiction (not just among
people but among nature), which makes them basically non-fiction.


Bruno Marchal wrote:
> 
>>
>>
>> Bruno Marchal wrote:
>>>
>>>>
>>>>
>>>> Brent Meeker-2 wrote:
>>>>>
>>>>>> So they don't add anything to platonia because they merely assert
>>>>>> the
>>>>>> existence of existence, which leaves platonia as described by
>>>>>> consistent
>>>>>> theories.
>>>>>>
>>>>>> I think the paradox is a linguistic paradox and it poses really no
>>>>>> problem.
>>>>>> Ultimately all descriptions refer to an existing object, but some
>>>>>> are too
>>>>>> broad or "explosive" or vague to be of any (formal) use.
>>>>>>
>>>>>> I may describe a system that is equal to standard arithmetics but
>>>>>> also
>>>>>> has
>>>>>> 1=2 as an axiom. This makes it useless practically (or so I
>>>>>> guess...) but
>>>>>> it
>>>>>> may still be interpreted in a way that it makes sense. 1=2 may
>>>>>> mean that
>>>>>> there is 1 object that is 2 two objects, so it simply asserts the
>>>>>> existence
>>>>>> of the one number "two". 3=7 may mean that there are 3 objects
>>>>>> that are 7
>>>>>> objects which might be interpreted as aserting the existence of  
>>>>>> (for
>>>>>> example) 7*1, 7*2 and 7*3.
>>>>>>
>>>>>
>>>>> The problem is not that there is no possible true interpretation of
>>>>> 1=2;
>>>>> the problem is that in standard logic a falsity allows you to prove
>>>>> anything.
>>>> Yes, so we can prove anything. This simply begs the question what  
>>>> the
>>>> anything is. All sentences we derive from the inconsistency would
>>>> mean the
>>>> same (even though we don't know what exactly it is).
>>>> We could just write "1=1" instead and we would have expressed the
>>>> same, but
>>>> in a way that is easier to make sense of.
>>>>
>>>> This is not problematic, it only makes the proofs in the inconsisten
>>>> system
>>>> worthless (at least in a formal context were we assume classical
>>>> logic).
>>>
>>> And it would make Platonia worthless. The "real", genuine, Platonia  
>>> is
>>> already close to be worthless due to the consistency of inconsistency
>>> for machine. This already put quite a mess in Platonia. By allowing
>>> complete contradiction, you make it a trivial object.
>> Why? When we contradict ourselves we may simply interpret this as a
>> expression of the trivial truth of existence. This doesn't change  
>> Plantonia
>> at all, because it exists either way.
> 
> The whole point of Gödel's theorem is that M proves 0=1 is different  
> from M proves provable('0=1'). The first implies the second, but the  
> second does not implies the first. The difference between G and G*  
> comes from this fact.
If we know that something can be proven, how is it different from taking it
to be proven? The only difference I could see could be that "M proves
provable('0=1')" means "provable in another system".


Bruno Marchal wrote:
> 
>>
>> And why is inconsistency allowed for machine, but disallowed for other
>> objects?
> 
> Because if a machine proves "0=1", she will be in trouble, but if God  
> or Platonia proves "0=1", then we are *all* in trouble.
I thought we already established that 0=1 can have a clear meaning
(equivalent to statements of the form  0*A+B=1*C+D in standard arithmetics),
and so it poses no problem.

My suggestion is that every statement has such an interpretation. Circles
with edges makes sense if we allow hyperreal numbers as numbers of edges and
lenght of edges, triangles with four sides may mean such a geometric object:
http://commons.wikimedia.org/wiki/File:Triangle-square-area-dev.png and that
God is omnipotent may mean anything.
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